Bayesian Probability of Bullshit

[TrifectaMike]

This may provide a teachable moment...

Let's say that we have a poster that has made 12 new post, since a particular starting period and 2 were deemed to be "Bullshit". Let's try and answer this question:

How likely it is that this poster that posted 2 bullshit and 10 non bullshit posts is a 50% bullshit poster.

Classical statistics would say formulate a null hypothesis that the poster is a 50% bullshitter, and determine the probability that a poster would post 2 bullshit to 10 non-bullshit post by chance.

The null hypothesis would most likely be rejected since the probability would be around 2%.

However, you determined nothing about the likelihood that the poster actually is a 50% bullshitter, only the likelihood that he/she would post 2 bullshit and 10 non-bullshit posts if they were in fact a 50% bullshitter.

To determine

the likelihood that the poster actually is a 50% bullshitter

we can instead use a Bayesian approach.

If there is interest, I'll go step-by-step on how to use a Bayesian approach to arrive at the answer.

Mike (Dr. Beav)

[thaskalos]

You say that 2 of his 12 posts were "deemed to be bullshit"...

Did you mean to say "proven to be bullshit"?

[TrifectaMike]

You say that 2 of his 12 posts were "deemed to be bullshit"...

Did you mean to say "proven to be bullshit"?

Thask, Thask, give it up... deemed, proven, assumed, considered,...you choose.


Mike (Dr Beav)

[Greyfox]

I'm experiencing "deja moo" ...a feeling I've heard this bull before. :lol:

[thaskalos]

Thask, Thask, give it up... deemed, proven, assumed, considered,...you choose.


Mike (Dr Beav)
I was being sincere Mike...and I don't relish arguments.

My only point was that a post may seem to be bullshit...but it can actually be true.

[TrifectaMike]

I'm experiencing "deja moo" ...a feeling I've heard this bull before. :lol:

Answer: A possible answer 22%

Happy now?

Mike (Dr Beav)

[Robert Goren]

My God, It has started already. I knew this thread was headed for trouble already. Go ahead and try to explain Bayes since that what you want to do anyway. Danger Will Robertson! It is very hard to explain. I took a class in college about it. It was the only thing covered in the class. There times a week for a semester and still some of the kids didn't get it. Try not to screw it up too bad.

[PhantomOnTour]

What's the Bayesian Probability that you guys will just agree to disagree and...let...it...go?
Without any formulae and/or algorythmic-logarythmic factorial numerical (insert StarTrek lingo) i say it's 0%.
And that's as scientific and mathematical as it gets.

[thaskalos]

I am very interested in the demonstration that is about to take place...and I promise that I will not interfere in the least.

[Tom]

Someone PM me when something relevant is posted. I can't waste another week om life like the last teaching thread.

Post #1 really is a good hook for a serious discussion. Like the sign in the Men's room - Do Not Eat the Big White Mint.

[TrifectaMike]

Someone PM me when something relevant is posted. I can't waste another week om life like the last teaching thread.

Post #1 really is a good hook for a serious discussion. Like the sign in the Men's room - Do Not Eat the Big White Mint.

No PM needed. No interest. No teaching moment. I've learned my lesson.

Mike (Dr Beav)

[TrifectaMike]

My God, It has started already. I knew this thread was headed for trouble already. Go ahead and try to explain Bayes since that what you want to do anyway. Danger Will Robertson! It is very hard to explain. I took a class in college about it. It was the only thing covered in the class. There times a week for a semester and still some of the kids didn't get it. Try not to screw it up too bad.

You are right. It is a difficult subject to grasp even in it's simplest use.

Mike (Dr Beav)

[Cratos]

This may provide a teachable moment...

Let's say that we have a poster that has made 12 new post, since a particular starting period and 2 were deemed to be "Bullshit". Let's try and answer this question:

How likely it is that this poster that posted 2 bullshit and 10 non bullshit posts is a 50% bullshit poster.

Classical statistics would say formulate a null hypothesis that the poster is a 50% bullshitter, and determine the probability that a poster would post 2 bullshit to 10 non-bullshit post by chance.

The null hypothesis would most likely be rejected since the probability would be around 2%.

However, you determined nothing about the likelihood that the poster actually is a 50% bullshitter, only the likelihood that he/she would post 2 bullshit and 10 non-bullshit posts if they were in fact a 50% bullshitter.

To determine

the likelihood that the poster actually is a 50% bullshitter

we can instead use a Bayesian approach.

If there is interest, I'll go step-by-step on how to use a Bayesian approach to arrive at the answer.

Mike (Dr. Beav)

Mike, I would encourage you to complete your example because I believe many of us will learn something that might change our thinking when we consider submitting a BS post in the future.

[CBedo]

I hope you do continue with the explanation. I know I could learn something.

[TrifectaMike]

Let's us start with a few definitions. They are not required to solve the problem, but they will at least set up what Bayes is about. When possible I'll take liberty with exact definitions in order to make it simpler to understand.

Classical Probability: Simple probability... coining tossing, choosing cards from a deck, selecting balls from urns and the like.

Frequentist Probability: Only applies to repeated (under identical conditions) events. The limiting value of the relative frequency with which an event A appears in the repetitions.

Bayesian Probability: Imagine betting with someone about the truth of a proposition, and ask yourself what are the odds in favor of the proposition I would need to receive or give in order that I judge the bet to be fair.

All forms of uncertainty are quantifiable with Bayesian probability.

Bayes Theorem

P(A|D) = P(A)P(D|A)/P(D)

P(A|D) reads the probability of A given D
P(A) reads the probability of A
P(D|A) reads the probability of D given A
P(D) reads the probability of D

The formula seems simple enough, but what heck does it mean?

Some of you may have used Bayes Theorem in a college course and basically worked with point probabilities...P(A) =.25, P(D) = .60, etc.

In our example, we will work with distributions instead of point probabilities.

Let me describe in words:

A is an unknown quantity and D will stand for some data relevant to my uncertainty about A.

P(unknown|data) = P(unknown)P(data|unknown)/Normalized constant

Bayes Theorem also has a sequential nature of a learning process. You'll have some describe the theorem as such:

posterior = constant * prior * likelihood

There is also a Bayes Theorem in odds form:

posterior odds = prior odds * Bayes Factor

In our bullshit problem we want to find the probability of A given D, [P(A|D)], which is to say that we want to find the probability that a bullshitter drawn from a prior population distribution is actually a 50% (or better) bullshitter given that we have observed 2 bullshit answers and 10 non bullshit answers. To do this, we need to find the probabilities P(D|A),
P(A), and P(D).

Mike (Dr Beav)

[TrifectaMike]

One of the more difficult aspects of Bayes probability is in our ability to define a prior probability distribution.

In our example, it'll be rather easy to define a prior.

We have to make an assumption about the population that the bullshitter is drawn from. Let's assume bullshitters on PA follow a normal distribution with a mean of 50% and standard deviation of 5.0 %. (I have chosen this mean to make the math simpler-no reflection on PA posters)

This is our prior distribution, Normal with a mean of .50 and a standard deviation of .05.

Mike (Dr Beav)

[Robert Fischer]

going to read this over when i get a chance
interesting topic Trifecta Mike :ThmbUp:
interested in learning your bayesian example.

[Robert Goren]

Did everybody get that? :confused: :D

[Jeff P]

Did everybody get that? :confused: :D

I did.

Or did I?

What's the probability that when I say "I did" I'm bullshitting?


-jp

.

[TrifectaMike]

P(A) is the simplest. This is the probability of a random poster drawn
from our prior distribution is at least a 50% bullshitter. This is just .50, because the population is centered around .50. So, P(A)=.5.

P(D) will require more work. This is the probability that we observe
a random bullshitter drawn from our prior distribution to post 2 bullshit and 10 non bullshit.

For any one bullshitter with a known (p), the probability of posting 2 bullshit and 10 non-bullshit is

( 12! / (2! * 10!) ) * p^2 * (1-p)^10

Now is where the calculus comes into the picture.

P(D) = INTEGRAL(f(p) * ( ( 12! / (2! * 10!) ) * p^2 * (1-p)^10 ) dp)

f(p) is our prior normal distribution pdf, which is:

f(p) = e^((-((p-u)^2))/(2*VAR))/(sqrt(2*Pi*VAR)) ;
u=.5, VAR=.05^2=.0025, Pi =3.1415....
and we integrate from 0 to 1.

P(D) = .02

Don't get confused here. Don't worry about the math. Recall that

P(unknown|data) = P(unknown)P(data|unknown)/Normalized constant

P(D) is our Normalized constant.

Mike (Dr Beav)

[Robert Goren]

A better example might be the principle of restricted choice in contract bridge or the Monty Hall problem. You can google either of them. I was already a pretty good bridge player and knew about restricted choice when I took my class on Bayes 40 years ago. I was one up on most of the class. Very few people believe it until you actually get a deck of cards and show them. Nobody believes the Monty Hall answer until you show them with pictures either.

[benzer]

Seems like reaching a bit to deep for no reasonable return. What is the point in this?

[TrifectaMike]

A better example might be the principle of restricted choice in contract bridge or the Monty Hall problem. You can google either of them. I was already a pretty good bridge player and knew about restricted choice when I took my class on Bayes 40 years ago. I was one up on most of the class. Very few people believe it until you actually get a deck of cards and show them. Nobody believes the Monty Hall answer until you show them with pictures either.

They are both trivial.

Mike (Dr Beav)

[TrifectaMike]

Seems like reaching a bit to deep for no reasonable return. What is the point in this?

To see how far I can continue this exercise without making an error.

Mike (Dr Beav)

[benzer]

To see how far I can continue this exercise without making an error.

Mike (Dr Beav)
LOL :)

[TrifectaMike]

We have computed P(A) = .50 and P(D) = .02 recall that

P(A|D) = P(A)P(D|A)/P(D)

Finally, we have to compute P(D|A). This is the probability of
observing 2 bullshit and 10 non-bullshit, given that we are drawing a random poster from the prior distribution that fulfills condition A, which is that the poster is at least a 50% bullshitter. This is done in a similar fashion to finding P(D) except we are only considering values of p>.5.

We calculate the same definite integral as before, but from
.5 to 1 instead of from 0 to 1. This gives a value of .0045. which is normalized by .5.
So, P(D|A) = .009

Voila, we are done.

P(A) = .50
P(D) = .02
P(D|A) = .009

P(A|D) =.009*.5/.02 = .22

the likelihood that the poster actually is a 50% bullshitter is 22%

Neat ha and not too painful. However, this too is a very trivial example, but at least gives one some idea of Bayesian probability.

It may not be obvious, but we actually have the entire distribution of P(A|D).

Mike (Dr Beav)

[benzer]

We have computed P(A) = .50 and P(D) = .02 recall that

P(A|D) = P(A)P(D|A)/P(D)

Finally, we have to compute P(D|A). This is the probability of
observing 2 bullshit and 10 non-bullshit, given that we are drawing a random poster from the prior distribution that fulfills condition A, which is that the poster is at least a 50% bullshitter. This is done in a similar fashion to finding P(D) except we are only considering values of p>.5.

We calculate the same definite integral as before, but from
.5 to 1 instead of from 0 to 1. This gives a value of .0045. which is normalized by .5.
So, P(D|A) = .009

Voila, we are done.

P(A) = .50
P(D) = .02
P(D|A) = .009

P(A|D) =.009*.5/.02 = .22

the likelihood that the poster actually is a 50% bullshitter is 22%

Neat ha and not too painful. However, this too is a very trivial example, but at least gives one some idea of Bayesian probability.

It may not be obvious, but we actually have the entire distribution of P(A|D).

Mike (Dr Beav)
Good,
Now relate that into how that helps people wagering the horse races. I'm not trying to down play your posts. Just wondering and bullshitting with you.

[TrifectaMike]

Good,
Now relate that into how that helps people wagering the horse races. I'm not trying to down play your posts. Just wondering and bullshitting with you.

A reasonable question.

Let's change some of the variable definitions.

Instead of a poster, posting 2 bullshit and 10 non-bullshit...
A horse with 2 wins and 10 losses.....

Mike (Dr Beav)

[benzer]

A reasonable question.

Let's change some of the variable definitions.

Instead of a poster, posting 2 bullshit and 10 non-bullshit...
A horse with 2 wins and 10 losses.....

Mike (Dr Beav)
Mike,
That reply does not answer the question. We can change some of the variable definitions all day long. Never mind, I hear what you are saying in the last post. :)

[TrifectaMike]

Mike,
That reply does not answer the question. We can change some of the variable definitions all day long.

You REALLY didn't get that. I'm sorry. I have nothing further to say.

Mike (Dr Beav)

[Robert Goren]

Just about what I expected. A bunch of Math formulas that few people have seen before and no real explaination what they mean. If someone hasn't taken a calculus class in the last year they probably got lost. When people see something like f(x), their eyes glaze over. But I will give for you get an "A" for at least trying.

[Tom]

Just about what I expected. A bunch of Math formulas that few people have seen before and no real explaination what they mean. If someone hasn't taken a calculus class in the last year they probably got lost. When people see something like f(x), their eyes glaze over. But I will give for you get an "A" for at least trying.

Maye even an f(A)! :D

Just a suggestion, instead of starting with the math, start with an explanation of what you are going to end up with. I have always been better able to follow along things that I know where they were going. The detail of the trip were never as important the first time. Tell me where we are going, then put me there, and I will be interested in delving into the details once I have a clue what they are doing.

[Native Texan III]

One simple example to perhaps make it easier to understand where it could be going:

Imagine that some people are lost in a forest and the rescuers are searching for them methodically. They could split the forest area into 3 parts A, B and C.

Before they start, the probability the folks are in A, B or C is 1/3 (3 x 1.3 = 1) - the prior probability

They do a thorough search of A and no one is found. Given that new information, the probability of folks being in B or C has risen to 0.5 (2 x 0.5 = 1) - the posterior probability given the new information.

If no one is found in B then new posterior probability of them being in area C is 1.0 (but in real life there is a possibility they could have walked into area A by now - so it is less than 1.0, which is the real problem with assuming any probability distributions).


For racing, say with a 10 horse race the prior probability of each horse is 0.1 (10 x 0.1 =1) if nothing else is known. But what about the stuff we do already know - some horses won last race or ran top Beyer, so we can uses Mikes' formulae to use that new data to increase the (prior) probabilities of horses having that data to posterior probabilities and so on - similar to forest search example. That is the practical example that folks may wish to see explained.

Bayes was an English Methodist preacher so shame on him.

[JustRalph]

I did.

Or did I?

What's the probability that when I say "I did" I'm bullshitting?


-jp

.

Now that's funny........ best post in the thread. You do have a sense of humor...........who'd a thunk it..........?

[Cratos]

You REALLY didn't get that. I'm sorry. I have nothing further to say.

Mike (Dr Beav)

Mike, thanks for trying

[Cratos]

One simple example to perhaps make it easier to understand where it could be going:

Imagine that some people are lost in a forest and the rescuers are searching for them methodically. They could split the forest area into 3 parts A, B and C.

Before they start, the probability the folks are in A, B or C is 1/3 (3 x 1.3 = 1) - the prior probability

They do a thorough search of A and no one is found. Given that new information, the probability of folks being in B or C has risen to 0.5 (2 x 0.5 = 1) - the posterior probability given the new information.

If no one is found in B then new posterior probability of them being in area C is 1.0 (but in real life there is a possibility they could have walked into area A by now - so it is less than 1.0, which is the real problem with assuming any probability distributions).


For racing, say with a 10 horse race the prior probability of each horse is 0.1 (10 x 0.1 =1) if nothing else is known. But what about the stuff we do already know - some horses won last race or ran top Beyer, so we can uses Mikes' formulae to use that new data to increase the (prior) probabilities of horses having that data to posterior probabilities and so on - similar to forest search example. That is the practical example that folks may wish to see explained.

Bayes was an English Methodist preacher so shame on him.

A good example and thanks for posting it.

[WPL]

One of the more difficult aspects of Bayes probability is in our ability to define a prior probability distribution.

Mike (Dr Beav)

To do so is artful more than scientific, IMhO. If one would stumble upon that prior prob distribution one would not be so eager to share the knowledge. I like the point, and take it to heart.

Good and provocative posts, T. Mike.

B.

[benzer]

You REALLY didn't get that. I'm sorry. I have nothing further to say.

Mike (Dr Beav)
That is slick how you pick a part of someones reply to post about. Here is my original reply:

That reply does not answer the question. We can change some of the variable definitions all day long. Never mind, I hear what you are saying in the last post.

Brain farts: A part of everyday life.

[TrifectaMike]

That is slick how you pick a part of someones reply to post about. Here is my original reply:

That reply does not answer the question. We can change some of the variable definitions all day long. Never mind, I hear what you are saying in the last post. This sentence wasn't in your post when I responded. It appears that I responded to your post moments before you made your edit.

Brain farts: A part of everyday life.

Mike (Dr Beav)

[raybo]

It's hard to teach someone something when they don't have the educational prerequisites to understand the technical portions. Cratos and Native Texan appear to be the only ones with the required prerequisites.

Are you unable to come down to the rest of us, regarding educational level?
I have a brother-in-law who is an EE and I am lost immediately, when discussing anything remotely related to technical subjects. He just cannot come down to my level.

[Tom]

http://www.amazon.com/Probability-Dummies-Deborah-Rumsey-Johnson/dp/0471751413

Very good book for those who have not yet used probability distributions very much.

[KidCapper]

I think I just stepped in a pile of Bayesian. Damn dog !!!

[TrifectaMike]

If there is enough interest, I'll show you how to use Bayesian probability and Bayesian Learners. I'll use race times, speed ratings and variants from a reliable source. Our goal will be to purchase the best ratings for a two week period at several tracks, and NEVER have to purchase them again.

We'll use Bayesian probability and Bayesian Learners to generate ratings going forward at NO COST.

If enough people are interested, I'll demonstrate how it can be done.

Let me know.

Mike (Dr Beav)

[Robert Goren]

I don't know anything about Bayesian Learners, so I will check my cynicism at the door. Good luck with your endeavors.

[riskman]

http://www.amazon.com/Probability-Dummies-Deborah-Rumsey-Johnson/dp/0471751413

Very good book for those who have not yet used probability distributions very much.

Actually, I went to this link, and found this comment among others reviewing the book-- and reviewers reviewing reviewers :) .

"Dick Mitchell once wrote, the goal of handicapping horses is not to pick winners, it's to make a profit. North American horse racing odds are determined by how much is bet on each horse - the parimutuel system - not the house like a casino. By making more accurate estimations of the probabilities of horses winning a race than the public, you find opportunities where the public's odds vary from your hopefully more accurate odds and you bet on those situations where the expectation is in your favor (the public underestimates a horse's chance of winning and thus pays higher odds than it deserves). You're placing your bets on the horses with the highest positive expectation, not the highest chance of winning (Mitchell's point, which took me a long time to grasp). If every bet you make carries a positive edge, you can't help but make a profit. Of course, you should have determined that your odds are more accurate than the public's through statistical hypothesis testing before risking any money. But if your odds estimation is statistically significant to the 99th percentile, you have tested your wagering methodology via monte carlo simulation, etc. and you're only betting when you have a positive edge, you're doing anything but gambling as the edge is in your favor. Many players will say "Every winner is an overlay (positive expectation bet)" or "I'd rather have the right horse at the wrong odds than vice versa" but they're not seeing the mathematical truth of the long-run expectation. The saying "You can beat a race, but you can't beat the races" is the exact opposite of the truth. You can't guarantee an outcome of any single race, but you can beat the races by having a positive expectation and wagering reasonable amounts to achieve the mathematical long-run and your mathematical expectation."

Any comments?

[Overlay]

Actually, I went to this link, and found this comment among others reviewing the book-- and reviewers reviewing reviewers :) .

"Dick Mitchell once wrote, the goal of handicapping horses is not to pick winners, it's to make a profit. North American horse racing odds are determined by how much is bet on each horse - the parimutuel system - not the house like a casino. By making more accurate estimations of the probabilities of horses winning a race than the public, you find opportunities where the public's odds vary from your hopefully more accurate odds and you bet on those situations where the expectation is in your favor (the public underestimates a horse's chance of winning and thus pays higher odds than it deserves). You're placing your bets on the horses with the highest positive expectation, not the highest chance of winning (Mitchell's point, which took me a long time to grasp). If every bet you make carries a positive edge, you can't help but make a profit. Of course, you should have determined that your odds are more accurate than the public's through statistical hypothesis testing before risking any money. But if your odds estimation is statistically significant to the 99th percentile, you have tested your wagering methodology via monte carlo simulation, etc. and you're only betting when you have a positive edge, you're doing anything but gambling as the edge is in your favor. Many players will say "Every winner is an overlay (positive expectation bet)" or "I'd rather have the right horse at the wrong odds than vice versa" but they're not seeing the mathematical truth of the long-run expectation. The saying "You can beat a race, but you can't beat the races" is the exact opposite of the truth. You can't guarantee an outcome of any single race, but you can beat the races by having a positive expectation and wagering reasonable amounts to achieve the mathematical long-run and your mathematical expectation."

Any comments?
Every word 100% true, as far as I'm concerned, including your difficulty (shared, I think, by many other people who bet the races) in grasping the concept that the goal is to base wagers on expected monetary outcome rather than on winning probability.

[raybo]

Actually, I went to this link, and found this comment among others reviewing the book-- and reviewers reviewing reviewers :) .

"Dick Mitchell once wrote, the goal of handicapping horses is not to pick winners, it's to make a profit. North American horse racing odds are determined by how much is bet on each horse - the parimutuel system - not the house like a casino. By making more accurate estimations of the probabilities of horses winning a race than the public, you find opportunities where the public's odds vary from your hopefully more accurate odds and you bet on those situations where the expectation is in your favor (the public underestimates a horse's chance of winning and thus pays higher odds than it deserves). You're placing your bets on the horses with the highest positive expectation, not the highest chance of winning (Mitchell's point, which took me a long time to grasp). If every bet you make carries a positive edge, you can't help but make a profit. Of course, you should have determined that your odds are more accurate than the public's through statistical hypothesis testing before risking any money. But if your odds estimation is statistically significant to the 99th percentile, you have tested your wagering methodology via monte carlo simulation, etc. and you're only betting when you have a positive edge, you're doing anything but gambling as the edge is in your favor. Many players will say "Every winner is an overlay (positive expectation bet)" or "I'd rather have the right horse at the wrong odds than vice versa" but they're not seeing the mathematical truth of the long-run expectation. The saying "You can beat a race, but you can't beat the races" is the exact opposite of the truth. You can't guarantee an outcome of any single race, but you can beat the races by having a positive expectation and wagering reasonable amounts to achieve the mathematical long-run and your mathematical expectation."

Any comments?

I agree whole-heartedly, the "sticking point is "your odds are more accurate than the public's". What factor, or, factors are you using from which to base your odds? Are they accurate? Will they carry forward? Are they truly independent of each other? Etc..

Much research and analysis must be done first, before calculating probabilities/odds.

Then you must keep your data updated continuously, verifying that they are still better than the public's, and at which tracks and in what types of races, etc..

Most players don't even track their wagers, hit rate, ROI, etc., so they're supposed to do all these things first? Fat chance.

[thaskalos]

Actually, I went to this link, and found this comment among others reviewing the book-- and reviewers reviewing reviewers :) .

"Dick Mitchell once wrote, the goal of handicapping horses is not to pick winners, it's to make a profit. North American horse racing odds are determined by how much is bet on each horse - the parimutuel system - not the house like a casino. By making more accurate estimations of the probabilities of horses winning a race than the public, you find opportunities where the public's odds vary from your hopefully more accurate odds and you bet on those situations where the expectation is in your favor (the public underestimates a horse's chance of winning and thus pays higher odds than it deserves). You're placing your bets on the horses with the highest positive expectation, not the highest chance of winning (Mitchell's point, which took me a long time to grasp). If every bet you make carries a positive edge, you can't help but make a profit. Of course, you should have determined that your odds are more accurate than the public's through statistical hypothesis testing before risking any money. But if your odds estimation is statistically significant to the 99th percentile, you have tested your wagering methodology via monte carlo simulation, etc. and you're only betting when you have a positive edge, you're doing anything but gambling as the edge is in your favor. Many players will say "Every winner is an overlay (positive expectation bet)" or "I'd rather have the right horse at the wrong odds than vice versa" but they're not seeing the mathematical truth of the long-run expectation. The saying "You can beat a race, but you can't beat the races" is the exact opposite of the truth. You can't guarantee an outcome of any single race, but you can beat the races by having a positive expectation and wagering reasonable amounts to achieve the mathematical long-run and your mathematical expectation."

Any comments?
Yes, I have a comment...

I am well acquainted with the quote highlighted above, having seen it in practically every "responsible" handicapping book published in the last 20 years. What I seldom see, however, is a practical way of putting this theory into practice.

Consider this:

A serious horseplayer determines that his "key" win wagers succeed 30% of the time, and, at that rate, he can expect to encounter streaks of 15 - 20 consecutive losers from time to time; so he ponders the size of bankroll needed to protect him against this game's violent swings.

He decides that a bankroll of 100 betting units would give him the long term confidence he needs, in order to play this game without the fear of going broke...and now he is set to go.

Or is he?

As long as our player sticks to betting his top choices at "acceptable" odds, his sizable bankroll may indeed keep him "in business" during the losing streaks that are bound to show up in the course of regular play. But what happens if this player starts wagering on his 2nd, 3rd, and 4th choices as well...because he deems that these choices are grossly overlaid, and they present a "better" bet than what his top choice might be.

Instead of wagering on his TOP horse, which he "knows" figures to win 30% of the time...he now is betting on the 2nd, 3rd, or even 4th-best horse in the race -- and his losing streaks are sure to get much LONGER. So long, in fact, that his 100 bet bankroll no longer provides a big enough "cushion" to allow him to survive the turbulence of long-term play.

And yet, handicapping authors continue to pursuade players to shop for VALUE instead of concentrating on their top choices...without giving those players adequate information on how to make the process work.

Years ago, I encountered another piece of advice given by Dick Mitchell...which almost ruined my gambling career.

He argued that, since a 2-1 race favorite represented 33% of the win pool, we didn't need to fret over which horse to play in those races where the 2-1 favorite figured to lose. A play on ANY other horse in the race, he reasoned, would lead to long term profits...because the odds were on our side.

To my considerable surprise I discovered that, while these false favorites continued to lose, my profits were nowhere to be found.

Having said all this, let me also add that I too look for value in the race...and I often bet on my 2nd and 3rd choices to win. But I do it while knowing full well what the bankroll requirements are for such a style of play.

I would wager that the average "bargain hunting" horseplayer doesn't...

[riskman]

Years ago, I encountered another piece of advice given by Dick Mitchell...which almost ruined my gambling career.

He argued that, since a 2-1 race favorite represented 33% of the win pool, we didn't need to fret over which horse to play in those races where the 2-1 favorite figured to lose. A play on ANY other horse in the race, he reasoned, would lead to long term profits...because the odds were on our side.

To my considerable surprise I discovered that, while these false favorites continued to lose, my profits were nowhere to be found.

In the past ,we have all been burned by taking others advice whether they be a handicapping author, system seller, or various so called successful bettors we run across at the track,OTB, Internet etc.
I did not particularly pick out Mitchell, he just happened to be the one referred to in the quote at the link Tom had in his post.
I have read some of Mitchell's works and found many of them helpful and still today, remember a lot of what he had to say.This I remember,"Never Risk any of your money until you have tested your strategy on paper or with small insignificant wagers until you can statistically validate it." I guess that applies to his own work as well.

[WPL]

If there is enough interest, I'll show you how to use Bayesian probability and Bayesian Learners. I'll use race times, speed ratings and variants from a reliable source. Our goal will be to purchase the best ratings for a two week period at several tracks, and NEVER have to purchase them again.

We'll use Bayesian probability and Bayesian Learners to generate ratings going forward at NO COST.

If enough people are interested, I'll demonstrate how it can be done.

Let me know.

Mike (Dr Beav)

Count me amongst the interested.

B.

[CBedo]

Count me in!

[HUSKER55]

I will be there

[TrifectaMike]

It's hard to teach someone something when they don't have the educational prerequisites to understand the technical portions. Cratos and Native Texan appear to be the only ones with the required prerequisites.

Are you unable to come down to the rest of us, regarding educational level?
I have a brother-in-law who is an EE and I am lost immediately, when discussing anything remotely related to technical subjects. He just cannot come down to my level.

Raybo,

Of all the posts in this thread, I've read yours several times. I agree. It is a difficult situation when the necessary prerequisites aren't in place. However, I don't believe it is a question of not being unable to "come down". It is a question of "doing" or implementation. One can "come down" all day, but eventually one must "do". And it is the "doing" that introduces road blocks.

Let me provide an example.

You and I are in phone contact. You have yourself planted in a gas station looking at a sign which says 10 miles to NYC, and you ask me:

What is the probability that I am 10 miles from NYC? Without hesitation I reply zero. Your first reaction would be that I am joking. I make a feeble attempt to explain why. You don't get it. I try removing another layer of logic or math, and try to explain again. At this "new" level of discussion, I encounter more difficulties. So, I try removing more layers, again and again ...only to realize that I have removed so many layers that the original question is so far removed that it is no longer relevant.

Also keep in mind that lack of prerequisites occur at all levels to all people. As another example, I see references to Taleb's The Black Swan here on PA, as well as in many other circles. What I find fascinating is that so many use The Black Swan to explain away their inability to understand or their failures.... it's the Black Swan effect.

The entire basis of the Black Swan is that rare events can not be estimated from observation since they are rare. The Black Swan is really an advertisement for Bayesian Probability.

Well, I appreciate what you are saying. However, I don't have a good answer.

Mike (Dr Beav)

[Tom]

A good teacher sends the lesson in a formt that can be understood by the student. I had a professor for Probability and Statistics that was able to make most everyone usderstnad what he was teaching, while the one I had the following semester was an absolute waste of time. Look at the way in which the Dummies books are written as compared to a test book.

It is not a case of coming down so much as a case of being able to communicate. Try expaling what a CPK is to a factory worker. Some books are zero help, while other make it clear as all getout.

[raybo]

Mike,

IMO, the problem with what you want to teach us, is not that we don't understand the problem area, but rather, we can't "implement" the technical portions. Giving us non-racing examples doesn't really explain things that are needed to be understood, prior to incorporating them into the math. And then, we have to understand the math, regarding the formulas. For someone who got only as far as high school or college algebra, the formulas you posted might be unusable. Show us how to write the formulas in basic algebraic form and maybe we can reproduce them, either on paper or in an Excel spreadsheet.

Perhaps if you used a common racing example and used basic math, we would all be able to do something about implementation.

Of course, we still have to have a grading system, of some sort, that can be used to calculate a valid odds for each horse in a race (which is superior to what the public odds are), which is of primary importance, before we even begin to calculate odds.

[CBedo]

What I find fascinating is that so many use The Black Swan to explain away their inability to understand or their failures.... it's the Black Swan effect.Interestingly, this is par of what Taleb talks about in Fooled By Randomness

[CBedo]

Mike,

IMO, the problem with what you want to teach us, is not that we don't understand the problem area, but rather, we can't "implement" the technical portions. Giving us non-racing examples doesn't really explain things that are needed to be understood, prior to incorporating them into the math. And then, we have to understand the math, regarding the formulas. For someone who got only as far as high school or college algebra, the formulas you posted might be unusable. Show us how to write the formulas in basic algebraic form and maybe we can reproduce them, either on paper or in an Excel spreadsheet.\I have thought about both of Raybo's posts and Mike's response, and I think it is somewhat difficult to "get at both sides" of the issue. I think you can come down to somewhat practically explain the "process" without the technical, but without the technical, it's unimplementable (I doubt that's a real word, but I'm using it), but with the technical explanation, some don't understand, or want the "give me an example" way to use it. I think the problem with this approach is that people want a cookie cutter approach to using it and don't fully understand it, so they either don't use it, or misuse it since they don't have a full understanding (Mike's previous mention of confidence intervals comes to mind).

For me, I need a little of both. Practical examples always drive things home, but I have to comprehend or make the effort to learn enough of the technical so I can not just use the approach as the author does, but understand it enough to use my imagination in when it might be a good tool to to use in other situations.

[Robert Goren]

My first stats teacher hated people who just used formulas. If he asked on a question a test and you just wrote down a formula and then used to it come up with the answer you got zero points for your answer. At least he warned several times us before the first hour exam. Mike, with all due respect, if you had given the kind of answer you posted here, you might have gotten 5 out of a possible 30 if he was feeling generous. You had know to the idea behind the formulas to pass his course. I don't think anyone got the idea behind of the math from what you posted.

[bob60566]

If there is enough interest, I'll show you how to use Bayesian probability and Bayesian Learners. I'll use race times, speed ratings and variants from a reliable source. Our goal will be to purchase the best ratings for a two week period at several tracks, and NEVER have to purchase them again.

We'll use Bayesian probability and Bayesian Learners to generate ratings going forward at NO COST.

If enough people are interested, I'll demonstrate how it can be done.

Let me know.

Mike (Dr Beav)
Give the guy chance on the above statement he made and if we learn something new great at no cost great
Mac:) :)

[raybo]

My first stats teacher hated people who just used formulas. If he asked on a question a test and you just wrote down a formula and then used to it come up with the answer you got zero points for your answer. At least he warned several times us before the first hour exam. Mike, with all due respect, if you had given the kind of answer you posted here, you might have gotten 5 out of a possible 30 if he was feeling generous. You had know to the idea behind the formulas to pass his course. I don't think anyone got the idea behind of the math from what you posted.








Yeah, brings back bad memories of the first hour test I took in Physics 101. The instructor was a graduate student and looked like he hadn't brushed his hair in a month, and he was constantly running his hands through it and rubbing his head. You know the type, typical absent minded professor type.

Well, prior to that test he was doing some math on the board. I was up in the top of a 300 person lecture theater and couldn't see what he was doing on the board, someone in the front asked him what it was he was scrawling on the board. He replied, "It's just calculus". The student then said, "But this is a "non-calc course". The instructor simply replied, "Well, it's easier this way".

Needless to say, the average score on the test was 46, I think i got a 58, and one girl up front, who had taken a high school calculus course, and was a whiz anyway, blew the curve with a 98.

Yeah, technical aspects of almost anything, if one doesn't have a good knowledge of the math discipline involved, is almost a waste of time to try to learn.

However, if Mike is able and willing to "dummy down" a little, I'm very interested in his continuing with the instruction.

[TrifectaMike]

My first stats teacher hated people who just used formulas. If he asked on a question a test and you just wrote down a formula and then used to it come up with the answer you got zero points for your answer. At least he warned several times us before the first hour exam. Mike, with all due respect, if you had given the kind of answer you posted here, you might have gotten 5 out of a possible 30 if he was feeling generous. You had know to the idea behind the formulas to pass his course. I don't think anyone got the idea behind of the math from what you posted.

Mr. Goren,

Do you really believe writing Bayes Theorem is a solution to any problem, because one can simply plug some numbers into it. I don't think so. You gotta be kidding.

I'd like to give your stats teacher a test. I'm sure I can figure out how to get him a big fat zero.

Mike (Dr Beav)

[Robert Goren]

Yeah, brings back bad memories of the first hour test I took in Physics 101. The instructor was a graduate student and looked like he hadn't brushed his hair in a month, and he was constantly running his hands through it and rubbing his head. You know the type, typical absent minded professor type.

Well, prior to that test he was doing some math on the board. I was up in the top of a 300 person lecture theater and couldn't see what he was doing on the board, someone in the front asked him what it was he was scrawling on the board. He replied, "It's just calculus". The student then said, "But this is a "non-calc course". The instructor simply replied, "Well, it's easier this way".

Needless to say, the average score on the test was 46, I think i got a 58, and one girl up front, who had taken a high school calculus course, and was a whiz anyway, blew the curve with a 98.

Yeah, technical aspects of almost anything, if one doesn't have a good knowledge of the math discipline involved, is almost a waste of time to try to learn.

However, if Mike is able and willing to "dummy down" a little, I'm very interested in his continuing with the instruction.My CALC II class had a 38 average on the first hour exam and a 27 on the second. I never took CALC III because I knew even though I got a "B", I did not have a clue. It was also about the same time I became a "legal" drinker which had a huge influence on my life at the time. But I digress from the matter at hand.

[TrifectaMike]

I realized that there is NO way I will try and describe how to use Bayesian probability and Bayesian Learners. The complexity is too great for an easy explanation, and simple implementation.

Mike (Dr Beav)

[Robert Goren]

Mr. Goren,

Do you really believe writing Bayes Theorem is a solution to any problem, because one can simply plug some numbers into it. I don't think so. You gotta be kidding.

I'd like to give your stats teacher a test. I'm sure I can figure out how to get him a big fat zero.

Mike (Dr Beav)I don't know, but in teaching it might be a good idea to at least explain the thought behind.I have seen some crazy things passed off as good statistical methods and people here eating it up. Perhaps the crazy one was that the pay outs from a system was a distribution was normal. 40% of the distribution was exactly one number, the minimum number, zero. Somebody had just looked at some formulas and did not realize that treating it as normal was going get crazy results.

[TrifectaMike]

I don't know, but in teaching it might be a good idea to at least explain the thought behind.I have seen some crazy things passed off as good statistical methods and people here eating it up. Perhaps the crazy one was that the pay outs from a system was a distribution was normal. 40% of the distribution was exactly one number, the minimum number, zero. Somebody had just looked at some formulas and did not realize that treating it as normal was going get crazy results.

At a minimum get this part correct, I have not performed a statistical analysis.

Ok, you tell me what the distribution of 100 payouts is? Think hard my friend, before you answer.

Since you are an expert, can you describe in words how you would solve the following?

A horse has started a new campaign with a record of 2 wins and 10 losses. What is the probability that this particular horse is a 50% or greater winner?

I'll wait. It should be simple.

Mike (Dr Beav)

[raybo]

At a minimum get this part correct, I have not performed a statistical analysis.

Ok, you tell me what the distribution of 100 payouts is? Think hard my friend, before you answer.

Since you are an expert, can you describe in words how you would solve the following?

A horse has started a new campaign with a record of 2 wins and 10 losses. What is the probability that this particular horse is a 50% or greater winner?

I'll wait. It should be simple.

Mike (Dr Beav)

LOL, I got the first part, he's won 16.67% (2/12 or 1/6) of his races, and he has lost 83.33% (10/12 or 5/6). Now I have absolutely no idea of where to go from here.

See how dumb I am? But, since we don't know the age of the horse and we don't know if, or how much, the horse is likely to improve, and we don't know how many races he will run in his racing career, or, if his trainer will be changed, at some time in the future, to a better or lesser one, etc., etc., there appears to not be enough data to even guess at the "probable" answer.

The point I'm trying to make with this "tongue in cheek" post is that I'm/we're dumb, when it comes to probabilities and their calculations, and you're smart, so teach us dummies in a way that our uneducated mind can grasp the concept and the terms needed to plug into the formula(s). Oh, and type the formula(s) so we all know how to do the math, without having to go back to college and take an intermediate/advanced math class, I'm 62 and have no desire to make a fool of myself in front of a bunch of high school grads.

[Tom]

Forget the reason why it can't be done and just do it.
Ignore all questions and comments until you have completed the project.
This is exactly what happened in the other thread.....focus on the material and not the audience.

Everyone else, get up to speed here.....



http://www.google.com/url?sa=t&source=web&cd=3&ved=0CCgQFjAC&url=http%3A%2F%2Fwww.fil.ion.ucl.ac.uk%2F~jchumb%2 Fpowerpoint%2520presentations%2FBayes%2520for%2520 Beginners.ppt&rct=j&q=bayes%20for%20dummies&ei=TJgCTsXBCcPLgQf3r_jJDQ&usg=AFQjCNERgIAqk1dtU6czT09PJjEyIWGqQA&cad=rja

[Robert Goren]

At a minimum get this part correct, I have not performed a statistical analysis.

Ok, you tell me what the distribution of 100 payouts is? Think hard my friend, before you answer.

Since you are an expert, can you describe in words how you would solve the following?

A horse has started a new campaign with a record of 2 wins and 10 losses. What is the probability that this particular horse is a 50% or greater winner?

I'll wait. It should be simple.

Mike (Dr Beav)You can not determine it without knowing what the distribution is of % winners. In the real world I can guarantee it is not a normal distribution.

[Robert Goren]

At a minimum get this part correct, I have not performed a statistical analysis.

Ok, you tell me what the distribution of 100 payouts is? Think hard my friend, before you answer.



Mike (Dr Beav)I have no idea other than it will not fit the bell curve of a normal distribution. There are several skewed curves that can be dealt with in advance mathematics but I do not know how nor am I even sure that it would fit any of them. Not everything fits a normal curve as much as we would like it to. The least squared method of producing a SD is useless is a number in distributions that are not normal.

[Robert Goren]

One thing else, You do not need a normal distrubution to use Bayes, In fact most uses of Bayes do not use a normal distrubution of estimated %.

[raybo]

Forget the reason why it can't be done and just do it.
Ignore all questions and comments until you have completed the project.
This is exactly what happened in the other thread.....focus on the material and not the audience.

Everyone else, get up to speed here.....



http://www.google.com/url?sa=t&source=web&cd=3&ved=0CCgQFjAC&url=http%3A%2F%2Fwww.fil.ion.ucl.ac.uk%2F~jchumb%2 Fpowerpoint%2520presentations%2FBayes%2520for%2520 Beginners.ppt&rct=j&q=bayes%20for%20dummies&ei=TJgCTsXBCcPLgQf3r_jJDQ&usg=AFQjCNERgIAqk1dtU6czT09PJjEyIWGqQA&cad=rja

Ok, I downloaded your PPT show and got to slide 7 before getting totally lost.

Nothing on that slide makes sense to me. That's what I'm talking about. If that presentation is for probabilities beginners, then I'm somehow, way below beginners level.

I give up, you guys with previous related education have fun, too bad, I would have liked to be able to follow along.

[TrifectaMike]

You can not determine it without knowing what the distribution is of % winners. In the real world I can guarantee it is not a normal distribution.

You can't determine, but you can guarantee. Sounds logical to me. Duh!

I have no idea other than it will not fit the bell curve of a normal distribution. There are several skewed curves that can be dealt with in advance mathematics but I do not know how nor am I even sure that it would fit any of them. Not everything fits a normal curve as much as we would like it to.I don't recall anyone saying everything fits a normal distribution The least squared method of producing a SD is useless is a number in distributions that are not normal.<- What does this mean and what is the relevancy to this discussion?

You don't know. You're not sure. Not everything fits a normal curve. <-Is this a Chinese menu.

Mike (Dr Beav)

[Robert Goren]

True probability is logic. Statistic is manipulating numbers to get estimates. which may or may not be estimates of probabilities. People tend forget that they are estimates.

[Robert Goren]

You can't determine, but you can guarantee. Sounds logical to me. Duh!



You don't know. You're not sure. Not everything fits a normal curve. <-Is this a Chinese menu.

Mike (Dr Beav) Yes, just like life.

[TrifectaMike]

One thing else, You do not need a normal distrubution to use Bayes. Now you are making stuff up. Who said this? In fact most uses of Bayes do not use a normal distrubution of estimated % I don't understand what this means. Bayes doesn't define any distribution. Someone using Bayes defines a prior.



Robert,

I'm sure you mean well, but I don't think this is your area of expertise.

Mike (Dr Beav)

[TrifectaMike]

I have no idea other than it will not fit the bell curve of a normal distribution. There are several skewed curves that can be dealt with in advance mathematics but I do not know how nor am I even sure that it would fit any of them. Not everything fits a normal curve as much as we would like it to. The least squared method of producing a SD is useless is a number in distributions that are not normal.

Let me help you. Maybe I can manipulate the data so it can fit a normal. Tell how badly skewed is the data? I'm sure you know. Can you tell me some of these skewed curves? So, are you saying that payouts can't be modeled? I highly doubt this statement.

Mike (Dr Beav)

[TrifectaMike]

How about this part...any ideas?

Since you are an expert, can you describe in words how you would solve the following?

A horse has started a new campaign with a record of 2 wins and 10 losses. What is the probability that this particular horse is a 50% or greater winner?

Mike (Dr Beav)

[TrifectaMike]

Forget the reason why it can't be done and just do it.
Ignore all questions and comments until you have completed the project.
This is exactly what happened in the other thread.....focus on the material and not the audience.

Everyone else, get up to speed here.....



http://www.google.com/url?sa=t&source=web&cd=3&ved=0CCgQFjAC&url=http%3A%2F%2Fwww.fil.ion.ucl.ac.uk%2F~jchumb%2 Fpowerpoint%2520presentations%2FBayes%2520for%2520 Beginners.ppt&rct=j&q=bayes%20for%20dummies&ei=TJgCTsXBCcPLgQf3r_jJDQ&usg=AFQjCNERgIAqk1dtU6czT09PJjEyIWGqQA&cad=rja (http://www.google.com/url?sa=t&source=web&cd=3&ved=0CCgQFjAC&url=http%3A%2F%2Fwww.fil.ion.ucl.ac.uk%2F%7Ejchumb %2Fpowerpoint%2520presentations%2FBayes%2520for%25 20Beginners.ppt&rct=j&q=bayes%20for%20dummies&ei=TJgCTsXBCcPLgQf3r_jJDQ&usg=AFQjCNERgIAqk1dtU6czT09PJjEyIWGqQA&cad=rja)

Tom, the exercise is complete. I've used the term Bayesian often. So, my intent was to show how Bayesian probability gives answers where classical/frequentist probability can't.

I don't expect anyone to become a Bayesian.

Mike (Dr Beav)

[thaskalos]

How about this part...any ideas?

Since you are an expert, can you describe in words how you would solve the following?

A horse has started a new campaign with a record of 2 wins and 10 losses. What is the probability that this particular horse is a 50% or greater winner?

Mike (Dr Beav)
Mike...is this really a question that the handicapper should concern himself with?

Does a 2 and 10 race record really say anything about a horse's ability...and does this record really reveal what the horse figures to do in the future?

Doesn't the horse's level of competition change as its racing career goes on...and shouldn't we get a close look at those wins and losses before we can determine the real consistency of this horse?

[TrifectaMike]

Mike...is this really a question that the handicapper should concern himself with?

Does a 2 and 10 race record really say anything about a horse's ability...and does this record really reveal what the horse figures to do in the future?

Doesn't the horse's level of competition change as its racing career goes on...and shouldn't we get a close look at those wins and losses before we can determine the real consistency of this horse?

You are reading too much into this. It is only an example.

Mike (Dr Beav)

[sjk]

I suspect you will tell us the answer is 22%.

Can you name any horse in the last 20 years who started his career 2 for 10 and at the end of his carreer had won 50% of his starts?

[HUSKER55]

Thanks for your efforts mike. I appreciate your effort and time. However, I got lost. You are past me by a bundle. Thanks again.

[TrifectaMike]

I suspect you will tell us the answer is 22%.

Can you name any horse in the last 20 years who started his career 2 for 10 and at the end of his carreer had won 50% of his starts?

No, I would not tell you it is 22%. Some very bad assumptions on your part.

You assumed that I would use the same prior as the Bullshit prior (state of knowledge or belief) in the example. A newly defined prior tells me how to update beliefs based upon current data.

Not even a nice try.

Mike (Dr Beav)

[Tom]

If there is enough interest, I'll show you how to use Bayesian probability and Bayesian Learners. I'll use race times, speed ratings and variants from a reliable source. Our goal will be to purchase the best ratings for a two week period at several tracks, and NEVER have to purchase them again.

We'll use Bayesian probability and Bayesian Learners to generate ratings going forward at NO COST.

If enough people are interested, I'll demonstrate how it can be done.

Let me know.

This is what I was just referring to....this has been completed already?

[sjk]

You did not answer my question.

Tell me what you think the correct percent is based on your analysis and perhaps we can make a bet as to whether the actual data bears you out.

I am a betting man. Are you? (Note the punctuation; this is a question to be answered)

BTW. I have at least as many PhDs in mathematics as you have and a long record of success in betting races. Please stop talking down to me and the others.

SJK

[raybo]

This is what I was just referring to....this has been completed already?

Yeah, I wish he'd just go ahead and finish what he started, for once, and then when he's done maybe someone who is willing and able, can explain it to those of us who need a more elementary understanding of all the disciplines involved. Last time I checked, 1+1 still equaled 2.

Seems like we've been down this road before, with similar results.

[TrifectaMike]

You did not answer my question.

Tell me what you think the correct percent is based on your analysis and perhaps we can make a bet as to whether the actual data bears you out.

I am a betting man. Are you? (Note the punctuation; this is a question to be answered)

BTW. I have at least as many PhDs in mathematics as you have and a long record of success in betting races. Please stop talking down to me and the others.

SJK

I only have one PhD. Since you have so many, you tell us all the answer.

Sir, it was you who was talking down. For a person with SO MANY PhD's your question was not very well thought out. It was minor league. You should have anticipated my response.

Mike (DR Beav)

P.S. I'm glad to hear you have a long record of success. I'm certain you are proud of your record.

[Grits]

No, this hasn't been a teachable moment as you've not taught anything. You've made poor use of your time and that of others. Instead, you're determined to insult members of this board. (In this thread it begins with your 3rd post and continues throughout.) Why should anyone desire to learn from one whose skill in communicating with others is so poor, so unfortunate? This is the way you use your education, Dr.Beav? What a waste.

You may want to go out the door, and return when you can respect these gentlemen because at this point you're reading like the proverbial rat in a coffee can whose still running in circles looking for a corner to **** in. No one else is.

Good luck moving foreward.

This may provide a teachable moment...

Let's say that we have a poster that has made 12 new post, since a particular starting period and 2 were deemed to be "Bullshit". Let's try and answer this question:

How likely it is that this poster that posted 2 bullshit and 10 non bullshit posts is a 50% bullshit poster.

[TrifectaMike]

No, this hasn't been a teachable moment as you've not taught anything. You've made poor use of your time and that of others. Instead, you're determined to insult members of this board. (In this thread it begins with your 3rd post and continues throughout.) Why should anyone desire to learn from one whose skill in communicating with others is so poor, so unfortunate? This is the way you use your education, Dr.Beav? What a waste.

You may want to go out the door, and return when you can respect these gentlemen because at this point you're reading like the proverbial rat in a coffee can whose still running in circles looking for a corner to **** in. No one else is.

Good luck moving foreward.

[/b]

Thank you.

Mike (Dr Beav)

[Grits]

Thank you.

Mike (Dr Beav)

You're very welcome. Be well!! ;-)

[Robert Goren]

Let me help you. Maybe I can manipulate the data so it can fit a normal. Tell how badly skewed is the data? I'm sure you know. Can you tell me some of these skewed curves? So, are you saying that payouts can't be modeled? I highly doubt this statement.

Mike (Dr Beav) I took my last math class 40 years ago and have no desire to revisit it. I have tried to keep an interest in stats, math logic and strategy over the years. The way I would handle the payouts is to separate them into random groups. The means of those groups should form a normal distribution. The real question is how big to make those groups. That is an answer I don't have readily available although I am sure if you wanted to find it you could with some effort. I am also not sure how useful information would. Somewhere there is probably a curve that fits does fit the data of individual payout and there is probably a way to estimate levels in it. I just am not interested in finding it. I know one thing it is not the bell shaped normal curve.
I do think that Bayes could be used on your par time/speed rating quest if you careful in the way you manipulate the data. I wish you the best in your quest.

[Tom]

I should have stopped at Post #10.

[sjk]

I only have one PhD. Since you have so many, you tell us all the answer.

Sir, it was you who was talking down. For a person with SO MANY PhD's your question was not very well thought out. It was minor league. You should have anticipated my response.

Mike (DR Beav)

P.S. I'm glad to hear you have a long record of success. I'm certain you are proud of your record.

I have one as well which in my book qualifies as at least as many as yours.

I was hoping for direct answers to some of my questions and perhaps the opportunity to win some of your money.

You are right. I should have anticipated your response.

[Robert Goren]

In the early 70s, I took a SPSS class. I wanted run run a multiple regression on the finish of a horse race compared to things printed in DRF. I got a formula which produce a small profit for many years until training method changed in late 80s and early 90s. The class was designed for PHD candidates who wanted prove something out their research to use in their thesis. I remember my teacher warning them over and over again being careful about trying to using methods that did fit their data. Ah, the wonderful days of punch cards. Every building on campus had a punch card machine hidden away someplace. Now we can do things on our home PCs that we didn't dare to dream about back.

[Robert Goren]

I should have stopped at Post #10.Let that be a lesson to you.;)

[TrifectaMike]

I have one as well which in my book qualifies as at least as many as yours.

I was hoping for direct answers to some of my questions and perhaps the opportunity to win some of your money.

You are right. I should have anticipated your response.

This a direct answer.

1. Assume a prior.

Make an assumption about the population that the horse is drawn from. You can seek a prior on theoretical considerations or simply pick a "subjective" prior distribution that best represents your knowledge about the set of uncertain parameters for the problem.

2. Follow the steps as outlined in the "bullshit" example.

3. Arrive at an answer.

You don't need me to answer your question nor do you need to bet. The betting shit is just a smoke screen. If you really want the answer, do it yourself.

Mike (Dr Beav)

[maddog42]

One of the more difficult aspects of Bayes probability is in our ability to define a prior probability distribution.

In our example, it'll be rather easy to define a prior.

We have to make an assumption about the population that the bullshitter is drawn from. Let's assume bullshitters on PA follow a normal distribution with a mean of 50% and standard deviation of 5.0 %. (I have chosen this mean to make the math simpler-no reflection on PA posters)

This is our prior distribution, Normal with a mean of .50 and a standard deviation of .05.

Mike (Dr Beav)
First of all, no reflection on mathematicians, but the standard of deviation of bullshit is damn near 100% with this bunch. From 0% to 99.9%.

[TrifectaMike]

I realize that my prior in the "Bullshit" example requires a revisit. The prior distribution I assumed is no longer valid. Due to length and content of this thread, we have to assume a revised prior.

The "Bullshit" posts due to this thread have increased ( I, too, am included in the new prior). I no longer have confidence in the 50% mean of posts are bullshit.

Mike (Dr Beav)

[Elliott Sidewater]

Not that I have any realistic hope of stopping this titanic display of ill-will, but maybe this will put things in perspective:

Monty Python's -The Argument Sketch

A man walks into an office.

Man: (Michael Palin) Ah. I'd like to have an argument, please.

Receptionist: Certainly sir. Have you been here before?

Man: No, this is my first time.

Receptionist: I see. Well, do you want to have the full argument, or were you thinking of taking a course?

Man: Well, what would be the cost?

Receptionist: Well, It's one pound for a five minute argument, but only eight pounds for a course of ten.

Man: Well, I think it's probably best if I start with the one and then see how it goes from there, okay?

Receptionist: Fine. I'll see who's free at the moment.

(Pause)

Receptionist: Mr. DeBakey's free, but he's a little bit conciliatory. Ahh yes, Try Mr. Barnard; room 12.

Man: Thank you. (Walks down the hall. Opens door.)

Angry man: WHADDAYOU WANT?

Man: Well, Well, I was told outside that...

Angry man: DON'T GIVE ME THAT, YOU SNOTTY-FACED HEAP OF PARROT DROPPINGS! (http://www.montypython.net/sounds/sketches/snotty.wav)

Man: What?

A: SHUT YOUR FESTERING GOB, YOU TIT! YOUR TYPE MAKES ME PUKE! YOU VACUOUS TOFFEE-NOSED MALODOROUS PERVERT!!! (http://www.montypython.net/sounds/sketches/abuse.wav)

M: Yes, but I came here for an argument!!

A: OH! Oh! I'm sorry! This is abuse!

M: Oh! Oh I see!

A: Aha! No, you want room 12A, next door.

M: Oh...Sorry...

A: Not at all!

A: (under his breath) stupid git.

(The man goes into room 12A. Another man is sitting behind a desk.)

Man: Is this the right room for an argument? (http://www.montypython.net/sounds/sketches/argument.wav)

Other Man:(John Cleese) I've told you once.

Man: No you haven't!

Other Man: Yes I have.

M: When?

O: Just now.

M: No you didn't!

O: Yes I did!

M: You didn't!

O: I did!

M: You didn't!

O: I'm telling you, I did!

M: You did not!

O: Oh I'm sorry, is this a five minute argument, or the full half hour? (http://www.montypython.net/sounds/sketches/5minute.wav)

M: Ah! (taking out his wallet and paying) Just the five minutes.

O: Just the five minutes. Thank you.

O: Anyway, I did.

M: You most certainly did not!

O: Now let's get one thing quite clear: I most definitely told you!

M: Oh no you didn't!

O: Oh yes I did!

M: Oh no you didn't!

O: Oh yes I did!

M: Oh no you didn't!

O: Oh yes I did!

M: Oh no you didn't!

O: Oh yes I did!

M: Oh no you didn't!

O: Oh yes I did!

M: Oh no you didn't!

O: Oh yes I did!

M: No you DIDN'T!

O: Oh yes I did!

M: No you DIDN'T!

O: Oh yes I did!

M: No you DIDN'T!

O: Oh yes I did!

M: Oh look, this isn't an argument!

(pause)

O: Yes it is!

M: No it isn't!

(pause)

M: It's just contradiction!

O: No it isn't!

M: It IS!

O: It is NOT!

M: You just contradicted me!

O: No I didn't!

M: You DID!

O: No no no!

M: You did just then!

O: Nonsense!

M: (exasperated) Oh, this is futile!!

(pause)

O: No it isn't!

M: Yes it is!

(pause)

M: I came here for a good argument!

O: AH, no you didn't, you came here for an argument! (http://www.montypython.net/sounds/sketches/futile.wav)

M: An argument isn't just contradiction.

O: Well! it CAN be!

M: No it can't!

M: An argument is a connected series of statements intended to establish a proposition.

O: No it isn't!

M: Yes it is! 'tisn't just contradiction.

O: Look, if I *argue* with you, I must take up a contrary position!

M: Yes but it isn't just saying 'no it isn't'.

O: Yes it is!

M: No it isn't! (http://www.montypython.net/sounds/sketches/contrary.wav)

O: Yes it is!

M: No it isn't!

O: Yes it is!

M: No it ISN'T! Argument is an intellectual process. Contradiction is just the automatic gainsaying of anything the other person says. (http://www.montypython.net/sounds/sketches/gainsay.wav)

O: It is NOT!

M: It is!

O: Not at all!

M: It is!

(The Arguer hits a bell on his desk and stops.)

O: Thank you, that's it.

M: (stunned) What?

O: That's it. Good morning.

M: But I was just getting interested!

O: I'm sorry, the five minutes is up.

M: That was never five minutes just now!!

O: I'm afraid it was.

M: (leading on) No it wasn't.....

O: I'm sorry, I'm not allowed to argue any more.

M: WHAT??

O: If you want me to go on arguing, you'll have to pay for another five minutes.

M: But that was never five minutes just now!
Oh Come on!
Oh this is...
This is ridiculous!


O: I told you... I told you, I'm not allowed to argue unless you PAY!

M: Oh all right. (takes out his wallet and pays again.) There you are.

O: Thank you.

M: (clears throat) Well...

O: Well WHAT?

M: That was never five minutes just now.

O: I told you, I'm not allowed to argue unless you've paid!

M: Well I just paid!

O: No you didn't!

M: I DID!!!

O: YOU didn't!

M: I DID!!!

O: YOU didn't!

M: I DID!!!

O: YOU didn't!

M: I DID!!!

O: YOU didn't!

M: I don't want to argue about it!

O: Well I'm very sorry but you didn't pay!

M: Ah hah! Well if I didn't pay, why are you arguing??? Ah HAAAAAAHHH! Gotcha!

O: No you haven't!

M: Yes I have! If you're arguing, I must have paid.

O: Not necessarily. I *could* be arguing in my spare time.

M: I've had enough of this!

O: No you haven't.

M: Oh shut up! (Man leaves the office)

[Robert Goren]

First of all, no reflection on mathematicians, but the standard of deviation of bullshit is damn near 100% with this bunch. From 0% to 99.9%.The voice of truth emerges from the floor of the feed lot.

[Robert Goren]

I think we can safely eliminate the subset of 0% bullshitters from consideration here.

[TrifectaMike]

I think we can safely eliminate the subset of 0% bullshitters from consideration here.

Now, that is something we can agree on.

Mike (Dr Beav)

[raybo]

The thread starter post, although I should have known better from previous experience, got my attention. But, nothing has materialized, that is actually usable in horse handicapping (this is the "General Handicapping Discussion" forum by the way). Therefore, I think this thread belongs in a different forum.

You pick the name, but you can't include the words horse, handicapping, or bullshit in it. You can, however, include the words, complete, waste, of, time. But, these words must appear inclusive of one another, and, in the posted order of finish.

[HUSKER55]

I WAS HOPING..........BUT ALAS :(

[TrifectaMike]

The thread starter post, although I should have known better from previous experience, got my attention. But, nothing has materialized, that is actually understood or usable by me in horse handicapping (this is the "General Handicapping Discussion" forum by the way). Therefore, I think I shouldn't read it this thread belongs in a different forum.

You pick the name, but you can't include the words horse, handicapping, or bullshit in it. You can, however, include the words, complete, waste, of, time unless you have an open mind to new ideas. But, these words must appear inclusive of one another, and, in the posted order of finish.

Am I to assume that you speak for everyone on PA?

Mike (Dr Beav)

[Tom]

At least two.

[raybo]

Am I to assume that you speak for everyone on PA?

Mike (Dr Beav)

As I said previously, there appears to be only 2 that understand the math you posted.

I didn't purvey that I don't "have an open mind", I purveyed that unless you somehow become a better teacher, the vast majority of readers here won't have a clue, not because they are dumb, but because they don't have the math background you apparently do, and because you have not shown the capability, or the willingness, to express yourself in such a way that the non-advanced math people can follow along.

Why do you think that most of your posts result in exactly what is happening in this thread?

Now, who doesn't "have an open mind"?

[thaskalos]

As I said previously, there appears to be only 2 that understand the math you posted.

I didn't purvey that I don't "have an open mind", I purveyed that unless you somehow become a better teacher, the vast majority of readers here won't have a clue, not because they are dumb, but because they don't have the math background you apparently do, and because you have not shown the capability, or the willingness, to express yourself in such a way that the non-advanced math people can follow along.

Why do you think that most of your posts result in exactly what is happening in this thread?

Now, who doesn't "have an open mind"?
I don't expect TrifectaMike to waste his time teaching me the "Bayesian Probability Theory"...but would it be too much to ask to have him explain how it applies to the art/science of handicapping horse races?

He started by inferring that a horse's 2 and 10 race record might somehow be used to predict something about the horse's future performance...but, when pressed, he indicated that this was only an "example"...

What is it that we are supposed to learn in this thread?

[Tom]

What is it that we are supposed to learn in this thread?

Not to get involved in any more like it?:D

[TrifectaMike]

I don't expect TrifectaMike to waste his time teaching me the "Bayesian Probability Theory"...but would it be too much to ask to have him explain how it applies to the art/science of handicapping horse races?

He started by inferring that a horse's 2 and 10 race record might somehow be used to predict something about the horse's future performance...but, when pressed, he indicated that this was only an "example"...

What is it that we are supposed to learn in this thread?

If one can't understand the Bullshit example, why would they understand a horse raceing example?

Everyone wants an answer to a specific horse racing example. It is understandable. So, I did say change the variables and and considered it as 2 and 10 race record. That is simple enough. Then the question becomes one of actually computing a realistic situation with real data. The process is still the same with artificial data with one exception. For me to give you a "real" answer to your question, I would would have to disclose the prior distribution that would make the answer viable in ones handicapping. That I am not willing to share. However, it doesn't mean the example is meaningless. The process is the same.

For example, if I were giving an example on regression analysis is it necessary for me to supply you with my coefficients for a real world problem for you to understand the process.

Mike (Dr Beav)

[TrifectaMike]

Not to get involved in any more like it?:D

Not to worry Mr. Tom there will not be any new threads started by me like the last.

Mike (Dr Beav)

[sjk]

The number of horses that have begun their careers 2 for 10 and then ended up with 50% wins is very nearly zero.

[TrifectaMike]

The number of horses that have begun their careers 2 for 10 and then ended up with 50% wins is very nearly zero.

May I ask in which area of study you received a doctorate in?

You do know, you have available to you, the entire posterior distribution. So, you also should have the answer to ending up with ...1%,,,,10%,,,,20%,,,30%,,,,etc.

Mike (Dr Beav)

[sjk]

Mathematics; UC Berkeley

[thaskalos]

If one can't understand the Bullshit example, why would they understand a horse raceing example?

Everyone wants an answer to a specific horse racing example. It is understandable. So, I did say change the variables and and considered it as 2 and 10 race record. That is simple enough. Then the question becomes one of actually computing a realistic situation with real data. The process is still the same with artificial data with one exception. For me to give you a "real" answer to your question, I would would have to disclose the prior distribution that would make the answer viable in ones handicapping. That I am not willing to share. However, it doesn't mean the example is meaningless. The process is the same.

For example, if I were giving an example on regression analysis is it necessary for me to supply you with my coefficients for a real world problem for you to understand the process.

Mike (Dr Beav)
We don't want you to divulge any of your secrets Mike...just tell us this:

You started off by saying that you would be able to determine the likelihood that a poster is a 50% bullshitter, just by the fact that he had made 2 bullshit posts out of 12.

Then you said that the poster in your example could be replaced by a horse that has won 2 races out of 12...

Is this meant to imply that you can determine the likelihood of a horse winning 50% of its starts...JUST by the fact that this horse started off with a 2 and 10 record?

[TrifectaMike]

We don't want you to divulge any of your secrets Mike...just tell us this:

You started off by saying that you would be able to determine the likelihood that a poster is a 50% bullshitter, just by the fact that he had made 2 bullshit posts out of 12.

Then you said that the poster in your example could be replaced by a horse that has won 2 races out of 12...

Is this meant to imply that you can determine the likelihood of a horse winning 50% of its starts...JUST by the fact that this horse started off with a 2 and 10 record?

Yes. I believe sjk has already performed the calculation with a prior that he assumed.

Mike Dr Beav

[thaskalos]

Yes. I believe sjk has already performed the calculation with a prior that he assumed.

Mike Dr Beav
I don't think that sjk performed any calculation...

I think he just REPEATED the "22%" which YOU provided as an answer to your initial example.

[sjk]

I have not done any calculations; I merely looked for examples of horses that fit the criteria. There are so few that I would think the probability is indistiguishable from zero.

[TrifectaMike]

As I said previously, there appears to be only 2 that understand the math you posted.

I didn't purvey that I don't "have an open mind", I purveyed that unless you somehow become a better teacher, the vast majority of readers here won't have a clue, not because they are dumb, but because they don't have the math background you apparently do, and because you have not shown the capability, or the willingness, to express yourself in such a way that the non-advanced math people can follow along.

Why do you think that most of your posts result in exactly what is happening in this thread?

Now, who doesn't "have an open mind"?

My last post on this subject. I looked at the slides that Tom linked to. In my opinion the slides present the material in its most basic form. If there is difficulty in understanding the information on those slides, I can't be of much help.

Mike (Dr Beav)

[Native Texan III]

Anyone still wanting to read up further how Bayes is applied to sports including racing might take a look at Tony Drapkin's book "Punters Revenge". Subject is very clearly explained. It was written in the 90's for UK racing but the subject methods are universal.

http://www.amazon.co.uk/Punters-Revenge-Chapman-Hall-computing/dp/0412277700/ref=ntt_at_ep_dpt_1/280-4775747-0748125

Or free download "chapters" at:
http://sports.groups.yahoo.com/group/hoof-ratings/files/


Horse racing and betting...
...have been closely associated for over two centuries. The HOOF race ratings service publishes accurate, innovative, and informative race ratings to guide your betting, with the emphasis placed firmly on finding good value. We have been on the Internet since the 1995-96 NH season, initially as a free service, and latterly by subscription. The success of the race ratings and the integrity of the service means that we have stood our ground with a small but loyal nucleus of satisfied users.

The software which generates the ratings uses Bayes' theorem to offer an effective and mathematically principled calculation of every horse's chance in a given race. Embedded in the program are around 2500 Bayesian likelihood ratios, derived from independent factors in a sample consisting of over 20,000 races and a quarter of a million individual runs.

The principles behind the program were established tweny years ago by Tony Drapkin and Richard Forsyth in their influential book 'The Punter's Revenge'. The book is now outdated in some areas, but the statistical principles outlined in the chapters on horse racing and football betting remain valid. An online version of the book is now available free at the HOOF ratings forum (http://sports.groups.yahoo.com/group/hoof-ratings/).



http://www.hoof.demon.co.uk/hfintro.html





http://www.hoof.demon.co.uk/line.colorbar.gif

[raybo]

If one can't understand the Bullshit example, why would they understand a horse raceing example?

Everyone wants an answer to a specific horse racing example. It is understandable. So, I did say change the variables and and considered it as 2 and 10 race record. That is simple enough. Then the question becomes one of actually computing a realistic situation with real data. The process is still the same with artificial data with one exception. For me to give you a "real" answer to your question, I would would have to disclose the prior distribution that would make the answer viable in ones handicapping. That I am not willing to share. However, it doesn't mean the example is meaningless. The process is the same.

For example, if I were giving an example on regression analysis is it necessary for me to supply you with my coefficients for a real world problem for you to understand the process.

Mike (Dr Beav)

So, are you saying that you could, if you wanted, explain the math so we could all understand it, but you won't because you would have to divulge the "Holy Grail" that has made you millions in horse racing? Well, we certainly wouldn't want you to tell us the "answer" to what all of us have been trying to find all these years.

But, then if you could, but you won't, then why did you start the thread and why did you infer you were going to teach? There has been no teaching in this thread yet.

My God man. You sound exactly like the database guys, "It took me years to do this, so I'm not going to tell you anything that will actually help you do it yourself".

If I took that approach, AllData and AllDatabase wouldn't exist. If Doug took that approach, "HandiFast" would never have existed.

Just what is your real purpose, in this thread, anyway?

[Greyfox]

So, are you saying that you could, if you wanted, explain the math so we could all understand it, but you won't because you would have to divulge the "Holy Grail" that has made you millions in horse racing?.....
Just what is your real purpose, in this thread, anyway?

:ThmbUp: I agree, raybo.

Back in Post #4 of this thread I commented:

I'm experiencing "deja moo" ...a feeling I've heard this bull before. :lol:

[benzer]

There have been no answers to questions from the start of this thread. A lot of loop to loop but no real meat.

[TrifectaMike]

So, are you saying that you could, if you wanted, explain the math so we could all understand it, but you won't because you would have to divulge the "Holy Grail" that has made you millions in horse racing? Well, we certainly wouldn't want you to tell us the "answer" to what all of us have been trying to find all these years

Since I've done such a poor job, why not ask any member on PA (there are some very smart guys on this forum) to explain the example I have demonstrated. Let him/her use math that anyone can understand.

GT, the explain-er of record (who does a fine job) may be able to succeed where I have failed. Or possibly skj most definitely should be able to take the math to a level that is understandable by anyone with a minimal background.

I'll ignore the rest of your post and chalk it up to frustration.

Mike (Dr Beav)

[On Spec]

Is Trifecta Mike a screen name that PA uses to increase hits to the site?;)

[TrifectaMike]

Is Trifecta Mike a screen name that PA uses to increase hits to the site?;)

Nope, but I will say that there are a number of people who read these post from outside PA that understand what I've demonstrated. I am aware of the audience within and outside PA.

Mike (Dr Beav)

[thaskalos]

Nope, but I will say that there are a number of people who read these post from outside PA that understand what I've demonstrated. I am aware of the audience within and outside PA.

Mike (Dr Beav)
Correct!

In fact, if MY calculations are correct :)...the OUTSIDE audience outnumbers the PA members by at least a 6 to 1 ratio...

[TrifectaMike]

Just about what I expected. A bunch of Math formulas that few people have seen before and no real explaination what they mean. If someone hasn't taken a calculus class in the last year they probably got lost. When people see something like f(x), their eyes glaze over. But I will give for you get an "A" for at least trying.

Mr. Goren,

Surly with your full one term college course that discussed nothing but Bayes Theorem qualifies you to give a simple basic math explanation of the example (try to keep it simple...a bit of addition, multiplication, and some really basic algebra). Especially since your instructor based his grades on explanations and not on formulation.

You could be a great help. Why not try?

Mike (Dr Beav)

[TrifectaMike]

I took my last math class 40 years ago and have no desire to revisit it. I have tried to keep an interest in stats, math logic and strategy over the years. The way I would handle the payouts is to separate them into random groups. The means of those groups should form a normal distribution. The real question is how big to make those groups. That is an answer I don't have readily available although I am sure if you wanted to find it you could with some effort. I am also not sure how useful information would. Somewhere there is probably a curve that fits does fit the data of individual payout and there is probably a way to estimate levels in it. I just am not interested in finding it. I know one thing it is not the bell shaped normal curve.
I do think that Bayes could be used on your par time/speed rating quest if you careful in the way you manipulate the data. I wish you the best in your quest. Can you expand on this. It could be helpful to all of us. You obviously get it.

Mike (Dr Beav)

[TrifectaMike]

I suspect you will tell us the answer is 22%.

Can you name any horse in the last 20 years who started his career 2 for 10 and at the end of his carreer had won 50% of his starts?

This is not the sort of comment I would expect with someone with a Ph.D in mathematics from UC at Berkeley to make.

I would expect someone with your credentials would have understood my first post.

Your posts really confuse me. Why not explain what I am doing wrong or right. Maybe give us additional insights.

Mike (Dr Beav)

[thaskalos]

Many years ago I had the privilege of attending a seminar, in which, the great physicist Richard Feynman explained his work in Quantum Mechanics to an enthralled audience.

When he was finished, a member of the audience raised his hand and preceded to compliment Mr. Feynman for making such a difficult subject so easy to understand.

Feynman waved away the compliments and stated that..."until a person is capable of clearly explaining a complicated subject to a layman...he hasn't really mastered that subject himself..."

[TrifectaMike]

A better example might be the principle of restricted choice in contract bridge or the Monty Hall problem. You can google either of them. I was already a pretty good bridge player and knew about restricted choice when I took my class on Bayes 40 years ago. I was one up on most of the class. Very few people believe it until you actually get a deck of cards and show them. Nobody believes the Monty Hall answer until you show them with pictures either.

Do you really believe that any of these examples would help one understand how to solve the problem that was solved in this thread? If so, why not be helpful and explain how.

Mike (Dr Beav)

[TrifectaMike]

A good teacher sends the lesson in a formt that can be understood by the student. I had a professor for Probability and Statistics that was able to make most everyone usderstnad what he was teaching, while the one I had the following semester was an absolute waste of time. Look at the way in which the Dummies books are written as compared to a test book.

It is not a case of coming down so much as a case of being able to communicate. Try expaling what a CPK is to a factory worker. Some books are zero help, while other make it clear as all getout.

Tom,

You are an odd one in this thread. You made some comments that are "cute", but at least you provided some links to material that could be helpful.

Mike (Dr Beav)

[TrifectaMike]

Many years ago I had the privilege of attending a seminar, in which, the great physicist Richard Feynman explained his work in Quantum Mechanics to an enthralled audience.

When he was finished, a member of the audience raised his hand and preceded to compliment Mr. Feynman for making such a difficult subject so easy to understand.

Feynman waved away the compliments and stated that..."until a person is capable of clearly explaining a complicated subject to a layman...he hasn't really mastered that subject himself..."

I wonder how many in the audience would have felt the same way, if he worked out a problem in Quantum Mechanics...apples and oranges

Mike (Dr Beav)

[TrifectaMike]

Feynman waved away the compliments and stated that..."until a person is capable of clearly explaining a complicated subject to a layman...he hasn't really mastered that subject himself..."

Yes, we've all heard this statement. I suugest if you are ever in need of a brain surgeon, you have him explain the procedure to a layman, and if the layman doesn't comprehend it, I suggest you disqualify him/her.

Mike (Dr Beav)

[raybo]

Many years ago I had the privilege of attending a seminar, in which, the great physicist Richard Feynman explained his work in Quantum Mechanics to an enthralled audience.

When he was finished, a member of the audience raised his hand and preceded to compliment Mr. Feynman for making such a difficult subject so easy to understand.

Feynman waved away the compliments and stated that..."until a person is capable of clearly explaining a complicated subject to a layman...he hasn't really mastered that subject himself..."

That about says it. You're either a teacher or you're not. You may have mastered the subject matter, but if you can't talk about it with people who have little or no knowledge of the subject, in such a way that they can understand what you're saying to them, then the only use your mastery has is to yourself and other knowledgeable people, of the subject matter.

Posting something of this complexity, and with such a knowledge specific subject, on a forum like this one, will almost surely be of no use to a very high percentage of it's members, unless you are a very good teacher and communicator.

[thaskalos]

Yes, we've all heard this statement. I suugest if you are ever in need of a brain surgeon, you have him explain the procedure to a layman, and if the layman doesn't comprehend it, I suggest you disqualify him/her.

Mike (Dr Beav)
This isn't brain surgery Mike...and what you are doing now is not showing you in very good light.

You have provided very little instruction in this thread...and yet, you now have proceeded to "grade" our posts one by one.

[TrifectaMike]

This isn't brain surgery Mike...and what you are doing now is not showing you in very good light.

You have provided very little instruction in this thread...and yet, you now have proceeded to "grade" our posts one by one.

You can handle a little bit of push back. If I had responded in kind, it could get rather nasty.

Mike (Dr Beav)

[thaskalos]

You can handle a little bit of push back. If I had responded in kind, it could get rather nasty.

Mike (Dr Beav)
Nastiness is not my style...:)

[TrifectaMike]

As I said previously, there appears to be only 2 that understand the math you posted.

I didn't purvey that I don't "have an open mind", I purveyed that unless you somehow become a better teacher, the vast majority of readers here won't have a clue, not because they are dumb, but because they don't have the math background you apparently do, and because you have not shown the capability, or the willingness, to express yourself in such a way that the non-advanced math people can follow along.

Why do you think that most of your posts result in exactly what is happening in this thread?

Now, who doesn't "have an open mind"?

My understanding is that there are over 20,000 viewers of PA. Where in the thread starter post does it state that this thread was started for only Mr. Raybo, Mr. Goren, or Mr Thaskalos or for that matter any individual. Since when do you speak for the entire community.

Mike (Dr Beav)

[Saratoga_Mike]

My understanding is that there are over 20,000 viewers of PA. Where in the thread starter post does it state that this thread was started for only Mr. Raybo, Mr. Goren, or Mr Thaskalos or for that matter any individual. Since when do you speak for the entire community.

Mike (Dr Beav)

Have you ever considered you do a lousy job of explaining things? Seriously, has that ever crossed your mind for one second, "Dr" Beav?

[TrifectaMike]

Have you ever considered you do a lousy job of explaining things? Seriously, has that ever crossed your mind for one second, "Dr" Beav?

Be a bit more specific, if you want me to take that comment seriously.

Mike (Dr Beav)

[Saratoga_Mike]

Be a bit more specific, if you want me to take that comment seriously.

Mike (Dr Beav)

I'll take that as a no (not surprised). Your first few posts on this subject were interesting, but you never went anywhere with them.

[raybo]

My understanding is that there are over 20,000 viewers of PA. Where in the thread starter post does it state that this thread was started for only Mr. Raybo, Mr. Goren, or Mr Thaskalos or for that matter any individual. Since when do you speak for the entire community.

Mike (Dr Beav)

I don't speak for the entire community, and I'm sure that PA would admonish me, righteously, if I attempted to do so. The 3 members you mention are not the only ones in this thread who have expressed confusion and lack of understanding regarding your instruction on this subject, and the same expressions of confusion and lack of understanding exists, rampantly, in many of your other postings.

You tend to retaliate negatively, when someone asks a question or doesn't understand you, instead of making a sincere attempt to reword or explain, in layman's terms, the posting in question.

It's obvious to most of us that you are intelligent, and have good advanced math/probability/statistical knowledge. But, you don't seem to be able to respond to doubt, question, or challenge in a rational manner, but rather prefer to insult or dismiss.

Most of the members here are also intelligent, but don't have the advanced training, in particular disciplines, that you have. Does that mean that those members are not to be included and respected in your threads or postings? Do you assume that only members having the needed advanced educational training will try to learn and participate in these discussions?

[TrifectaMike]

I'll take that as a no (not surprised). Your first few posts on this subject were interesting, but you never went anywhere with them.

Post 15,16,20,26 addressed and solved the problem I defined in Post 1. Everything else was noise. I suggest you re-read.

Mike (Dr Beav)

[TrifectaMike]

I don't speak for the entire community, and I'm sure that PA would admonish me, righteously, if I attempted to do so. The 3 members you mention are not the only ones in this thread who have expressed confusion and lack of understanding regarding your instruction on this subject, and the same expressions of confusion and lack of understanding exists, rampantly, in many of your other postings.

You tend to retaliate negatively, when someone asks a question or doesn't understand you, instead of making a sincere attempt to reword or explain, in layman's terms, the posting in question.

It's obvious to most of us that you are intelligent, and have good advanced math/probability/statistical knowledge. But, you don't seem to be able to respond to doubt, question, or challenge in a rational manner, but rather prefer to insult or dismiss.

Most of the members here are also intelligent, but don't have the advanced training, in particular disciplines, that you have. Does that mean that those members are not to be included and respected in your threads or postings? Do you assume that only members having the needed advanced educational training will try to learn and participate in these discussions?

I suggest you re-read the thread. And you tell me at what point the insults started.

Mike (Dr Beav)

[Robert Goren]

I might add that some of us have tried applying the principles you mentioned over the years. We have made some of the same mistakes you have. I know I have no animosity toward you, but I am trying to correct some mistakes you made. I wish you all the luck in your endeavors.

[TrifectaMike]

I might add that some of us have tried applying the principles you mentioned over the years. We have made some of the same mistakes you have. I know I have no animosity toward you, but I am trying to correct some mistakes you made. I wish you all the luck in your endeavors.

I gotta go now, but I would appreciate if you could show me some of the mistakes I've made.

Mike (Dr Beav()

[Cratos]

Post 15,16,20,26 addressed and solved the problem I defined in Post 1. Everything else was noise. I suggest you re-read.

Mike (Dr Beav)
Mike, your explanations in posts 15,16,20 & 26 worked just fine for me

[chickenhead]

2 for 12 horse, 50% lifetime.

To get a ballpark of what that answer would be (the actual answer and the math is not something I'm interested in but the concept in its crudest form is)...change PA to something like .01. And you get an answer of something like .4% likelihood a horse that has 2 wins and 10 losses will end his career a 50% winner.

The prior distribution used in the bullshitter example is that it's normal for us to be 50% bullshitters based on our population. It's not normal for horses to be 50% winners, I'm using 1% of horses end up as 50% winners as a WAG...but that is the concept behind it, I believe.

In reality, a horse that is 2-12 needs at least 20 career races to end up 10-20. The more races a horse has, the more rare a 50% winner will be. So you also need to factor in what are the odds that horses with 20+ races end up as 50% winners, that is the actual distribution you'd want to use. Which is probably an order of magnitude lower than my WAG.

So lets say .04%. A horse that starts 2-12 has about, somewhere in the ballpark of, a .04% chance of ending their career a 50% winner.

[Saratoga_Mike]

Mike, your explanations in posts 15,16,20 & 26 worked just fine for me

...which proves my point. thanks.

[Robert Goren]

I gotta go now, but I would appreciate if you could show me some of the mistakes I've made.

Mike (Dr Beav() The best mistake you have made is that you try to apply statistical methods meant for normal distributions that are not normal. But that aside the other problem you have is throwing out math formulas with out explaining what they mean. Most people have trouble understanding reverse Polish logic, let alone integrals. Some of the stuff you have thrown out there confuses anyone who has not taken a college calc in the last year. Combined that with Bayes which most people have really hard time with anyway, you are going to run to trouble. The idea of Bayes and SR/par times is probably workable. It is not something I would want to do because of the time and the amount of work involved. Besides I have another horse racing project going now. I do not want live breathe horse racing stats all day long.

[raybo]

...which proves my point. thanks.

Mine too, Cratos was 1 of the 2, knowledgeable in the required disciplines, that I referred to earlier.

[Robert Fischer]

... nearing 100% certainty!!!!!!!!! :D

actually this is an interesting thread.

[TrifectaMike]

The best mistake you have made is that you try to apply statistical methods meant for normal distributions that are not normal. But that aside the other problem you have is throwing out math formulas with out explaining what they mean. Most people have trouble understanding reverse Polish logic, let alone integrals. Some of the stuff you have thrown out there confuses anyone who has not taken a college calc in the last year. Combined that with Bayes which most people have really hard time with anyway, you are going to run to trouble. The idea of Bayes and SR/par times is probably workable. It is not something I would want to do because of the time and the amount of work involved. Besides I have another horse racing project going now. I do not want live breathe horse racing stats all day long.

Firstly, what statistical method are you referring to?

Secondly, what is this peculiar hangup do you have with normal distributions?

Thirdly, not I or anyone else has asked you to work on any project...Bayesian or whatever!

Lastly, I am not responsible for your inability to understand a concept.

Mike (Dr Beav)

[TrifectaMike]

Do you realize how ridiculous some of you sound in your posts?

I can't count, so do use counting. I can't understand, so don't use algebra.

I don't understand probability, so don't use probability.

I can't follow the logic, so don't use logic.

I failed calculus, so don't use calculus.

I don't understand distributions, so don't use distributions.

I don't understand Binomial distributions, so do not use a Binomial distributions.

Bayesian stuff is hard, so don't even try explaining it.

I don't understand any of this, so you are a terrible teacher.

Did you ever consider the fact that you might be a terrible student that doesn't belong in the class!!

Mike (Dr Beav)

P.S. No one, not I, asked you to participate in this thread, if you didn't feel like you had the necessary background. You could have simply ignored it. There are other threads. You are not a captured audience. You could have simply clicked on another thread, instead of making fools of yourself.

[TrifectaMike]

The best mistake you have made is that you try to apply statistical methods meant for normal distributions that are not normal.
long.

I'm sorry, but I've had enough of your bullshit. What the hell are you talking about? What planet are you from? What statistical method not meant for normal distributions. You have ZERO, and I repeat ZERO understanding of Bayes theory! Your post make absolutely NO sense.

I've tried being nice, but you leave me no choice. Your statement borders on stupidity!!!

Mike (Dr Beav)

[PaceAdvantage]

Do you realize how ridiculous some of you sound in your posts?

I can't count, so do use counting. I can't understand, so don't use algebra.

I don't understand probability, so don't use probability.

I can't follow the logic, so don't use logic.

I failed calculus, so don't use calculus.

I don't understand distributions, so don't use distributions.

I don't understand Binomial distributions, so do not use a Binomial distributions.

Bayesian stuff is hard, so don't even try explaining it.

I don't understand any of this, so you are a terrible teacher.

Did you ever consider the fact that you might be a terrible student that doesn't belong in the class!!

Mike (Dr Beav)

P.S. No one, not I, asked you to participate in this thread, if you didn't feel like you had the necessary background. You could have simply ignored it. There are other threads. You are not a captured audience. You could have simply clicked on another thread, instead of making fools of yourself.Not a pretty way to end this thread.

And I must say, you have a habit of blowing up like this when the masses don't fall in line behind you...

[johnhannibalsmith]

...

Did you ever consider the fact that you might be a terrible student that doesn't belong in the class!!

... You are not a captured audience. ...

This was actually my first and only consideration, but I enjoy threads where people get snarly with one another, so I am captive. :jump:

[thaskalos]

I'm sorry, but I've had enough of your bullshit. What the hell are you talking about? What planet are you from? What statistical method not meant for normal distributions. You have ZERO, and I repeat ZERO understanding of Bayes theory! Your post make absolutely NO sense.

I've tried being nice, but you leave me no choice. Your statement borders on stupidity!!!

Mike (Dr Beav)
No offense, but if we decide that we need help with our math in the future...we will enlist the help of Dr. Sjk...

He seems alot more even-tempered...

[raybo]

QUOTE=TrifectaMike Do you realize how ridiculous some of you sound in your posts?

I can't count, so do use counting. I can't understand, so don't use algebra.

The problem is that you didn't use "counting" or "algebra" you used calculus.

I don't understand probability, so don't use probability.

I thought your purpose for starting the thread was to teach us about probability, using Bayesian.

I can't follow the logic, so don't use logic.

It wasn't the logic we had trouble following, it was the math.

I failed calculus, so don't use calculus.

Most of us have never taken calculus, that was the "math" we were having trouble following

I don't understand distributions, so don't use distributions.

Most of us have never taken statistics and therefore don't know what a "distribution" is, you seem to think that statistics is a basic discipline.

I don't understand Binomial distributions, so do not use a Binomial distributions.

If most of us have never taken statistics and don't know what a distribution is, then why would we know what a "binomial distribution" is?

Bayesian stuff is hard, so don't even try explaining it.

Bayesian may be hard, probably is, but when we can't understand your calculus, what chance have we to understand your Bayesian?

I don't understand any of this, so you are a terrible teacher.

When the vast majority of the posters in this thread express confusion with your examples and "teaching", are they all at fault, or is it more likely that the "teacher" is at fault?

Did you ever consider the fact that you might be a terrible student that doesn't belong in the class!!

I can't speak for the rest of the people, regarding what kind of student they are, however,I can speak for myself. I was a straight A student throughout my schooling, graduated in my class' top 10%, am a "National Honor Society" member, was in Honors English all 4 years of High School, and made top grades in Algebra, Algebra II, Plane Geometry, Solid Geometry, Trigonometry, and Analytical Geometry, all taken in Junior High and High School, and had no trouble with College Algebra at UT Austin. I doubt I would have accomplished all these things if I were a "terrible student".

Mike (Dr Beav)

P.S. No one, not I, asked you to participate in this thread, if you didn't feel like you had the necessary background. You could have simply ignored it. There are other threads. You are not a captured audience. You could have simply clicked on another thread, instead of making fools of yourself.

There is only one person in this thread who made a fool of themselves, and it wasn't any of the people who expressed confusion and lack of understanding regarding your posts. And it certainly wasn't either of the 2 or 3 people who had prior knowledge of the subject matter. Who did I leave out? /QUOTE

[TrifectaMike]

QUOTE=TrifectaMike Do you realize how ridiculous some of you sound in your posts?

I can't count, so do use counting. I can't understand, so don't use algebra.

The problem is that you didn't use "counting" or "algebra" you used calculus.

I don't understand probability, so don't use probability.

I thought your purpose for starting the thread was to teach us about probability, using Bayesian.

I can't follow the logic, so don't use logic.

It wasn't the logic we had trouble following, it was the math.

I failed calculus, so don't use calculus.

Most of us have never taken calculus, that was the "math" we were having trouble following

I don't understand distributions, so don't use distributions.

Most of us have never taken statistics and therefore don't know what a "distribution" is, you seem to think that statistics is a basic discipline.

I don't understand Binomial distributions, so do not use a Binomial distributions.

If most of us have never taken statistics and don't know what a distribution is, then why would we know what a "binomial distribution" is?

Bayesian stuff is hard, so don't even try explaining it.

Bayesian may be hard, probably is, but when we can't understand your calculus, what chance have we to understand your Bayesian?

I don't understand any of this, so you are a terrible teacher.

When the vast majority of the posters in this thread express confusion with your examples and "teaching", are they all at fault, or is it more likely that the "teacher" is at fault?

Did you ever consider the fact that you might be a terrible student that doesn't belong in the class!!

I can't speak for the rest of the people, regarding what kind of student they are, however,I can speak for myself. I was a straight A student throughout my schooling, graduated in my class' top 10%, am a "National Honor Society" member, was in Honors English all 4 years of High School, and made top grades in Algebra, Algebra II, Plane Geometry, Solid Geometry, Trigonometry, and Analytical Geometry, all taken in Junior High and High School, and had no trouble with College Algebra at UT Austin. I doubt I would have accomplished all these things if I were a "terrible student".

Mike (Dr Beav)

P.S. No one, not I, asked you to participate in this thread, if you didn't feel like you had the necessary background. You could have simply ignored it. There are other threads. You are not a captured audience. You could have simply clicked on another thread, instead of making fools of yourself.

There is only one person in this thread who made a fool of themselves, and it wasn't any of the people who expressed confusion and lack of understanding regarding your posts. And it certainly wasn't either of the 2 or 3 people who had prior knowledge of the subject matter. Who did I leave out? /QUOTE

As I said, you were in the wrong class.

Mike (Dr Beav)

[Greyfox]

In fairness to you Dr beav or Trifecta Mike one would have to assume that you knew the answer to the question that you posed. Certainly it was not to see how far you could go without making a mistake.
(Obviously you know your math, but so what?) Was that your intent? We would have accepted you at your word. But what was the motivation for the thread? You could show us how to calculate an orbit around the moon, ..bully on you. But can you apply to something relevant here. Connect the dots for us, if you can. For example, can you give us a logical probable winner at any track tomorrow using your Bayesian material??

So why this example?
Why this question?
How does it apply to horse racing? Or what can I learn from it? (In plain language.)
Give us a concrete example for Sunday (tomorrow) at any track of your choice.

[GameTheory]

If the students to be taught already know the subject, then teaching is not necessary. Of course the students don't know the subject at the beginning -- that's where the teaching and the learning come in.

[raybo]

As I said, you were in the wrong class.

Mike (Dr Beav)

Nah, I just had a host/presenter rather than a teacher. One that had such a high opinion of himself, and such a biased opinion of his own intelligence and ability to instruct, that he continually assumed that 90+% of the participants were stupid, because they were unable to follow his instruction.

Now what's the probability of 90% of the participants in a class, assuming a prior knowledge of the intellect of those participants, as experienced by his reading and discussing other subjects, with those same members, in the past, as being 100% stupid?

You may use calculus in your calculations, if you like.

[TrifectaMike]

In fairness to you Dr beav or Trifecta Mike one would have to assume that you knew the answer to the question that you posed. Certainly it was not to see how far you could go without making a mistake.
(Obviously you know your math, but so what?) Was that your intent? We would have accepted you at your word. But what was the motivation for the thread? You could show us how to calculate an orbit around the moon, ..bully on you. But can you apply to something relevant here. Connect the dots for us, if you can. For example, can you give us a logical probable winner at any track tomorrow using your Bayesian material??

So why this example?
Why this question?
How does it apply to horse racing? Or what can I learn from it? (In plain language.)
Give us a concrete example for Sunday (tomorrow) at any track of your choice.

Fair enough questions.

Let me start with the third question.

Let's assume we have a distribution of winning speed rating gaps, and I have a particular interest in Horse A. I would like to know the probability distribution of Horse A winning in the race given he has a speed gap of x.

This example is a take off on me calling someones comments in a post bullshit.

Mike (Dr Beav)

[HUSKER55]

AND NOW YOU KNOW WHY I DRINK :lol:

GIVE IT A REST GUYS!

[Tom]

There are two parts to teaching - the teacher and the student.
No one would be foolish enough to assume that all teachers are capable, now would they.

What is the probability of that? :rolleyes:

[Greyfox]

Fair enough questions.

Let me start with the third question.

Let's assume we have a distribution of winning speed rating gaps, and I have a particular interest in Horse A. I would like to know the probability distribution of Horse A winning in the race given he has a speed gap of x.

This example is a take off on me calling someones comments in a post bullshit.

Mike (Dr Beav)

I know what a speed rating is, but....

What is a speed rating gap???

[TrifectaMike]

I know what a speed rating is, but....

What is a speed rating gap???

Take a set of speed ratings in a race. (70,72,67,81,79), order them (81,79,72,70,67) and use the min or max value as a reference and compute a speed rating gap vector for the race, (0,-2,-9,-11,-14) or (0,3,5,12,14).

Mike (Dr Beav)

[thaskalos]

Take a set of speed ratings in a race. (70,72,67,81,79), order them (81,79,72,70,67) and use the min or max value as a reference and compute a speed rating gap vector for the race, (0,-2,-9,-11,-14) or (0,3,5,12,14).

Mike (Dr Beav)
Should we worry that some of these speed ratings might be nonrepresentative?

Or do we just go ahead and use them all?

I am not trying to start an argument...I really want to take a good look at your point of view.

[TrifectaMike]

Should we worry that some of these speed ratings might be nonrepresentative?

Or do we just go ahead and use them all?

I am not trying to start an argument...I really want to take a good look at your point of view.

The speed rating vector (is a race vector) represents one rating per horse and not a vector rating per horse. It can represent the last race rating, next to last, best of last 3 or last 5. However, it must be consistent with the prior distribution that you have assumed or determined.

Thask, once again this is an example. I am by no means saying you must do this.

Mike (Dr Beav)

[thaskalos]

The speed rating vector (is a race vector) represents one rating per horse and not a vector rating per horse. It can represent the last race rating, next to last, best of last 3 or last 5. However, it must be consistent with the prior distribution that you have assumed or determined.

Thask, once again this is an example. I am by no means saying you must do this.

Mike (Dr Beav)
Oh...sorry,

I thought that the set of speed ratings you listed were all taken from the same horse.

[sjk]

Should we worry that some of these speed ratings might be nonrepresentative?

Or do we just go ahead and use them all?

I am not trying to start an argument...I really want to take a good look at your point of view.


It acutally makes good sense to me to use several speed ratings, say four based on information from each of the most recent four races.

As Mike says the value of the speed rating projection is representative of a distribution whose spread is based both on the inherent variability of racing and race data and also on the acuity of the projection process used.

You can create a line for each horse which is the weighted average of the distributions you constructed from the last four races.

Then you can calculate the probability of each of the horses running 1st to make an odds line. There are reasons why this odds line needs improvement but it is a good starting point.

[raybo]

The speed rating vector (is a race vector) represents one rating per horse and not a vector rating per horse. It can represent the last race rating, next to last, best of last 3 or last 5. However, it must be consistent with the prior distribution that you have assumed or determined.

Thask, once again this is an example. I am by no means saying you must do this.

Mike (Dr Beav)

When you say "speed rating vector", do you mean, in this context, "speed rating gap vector"?

[TrifectaMike]

It acutally makes good sense to me to use several speed ratings, say four based on information from each of the most recent four races.

As Mike says the value of the speed rating projection is representative of a distribution whose spread is based both on the inherent variability of racing and race data and also on the acuity of the projection process used.

You can create a line for each horse which is the weighted average of the distributions you constructed from the last four races.

Then you can calculate the probability of each of the horses running 1st to make an odds line. There are reasons why this odds line needs improvement but it is a good starting point.

Very well said and I agree.

Mike (Dr Beav)

[TrifectaMike]

When you say "speed rating vector", do you mean, in this context, "speed rating gap vector"?

You are correct.

Mike (Dr Beav)

[raybo]

So, here, "gap vector" means, the position and distance, of each speed rating, from a reference point (the minimum/smallest speed rating or the maximum/largest speed rating)?

[TrifectaMike]

So, here, "gap vector" means, the position and distance, of each speed rating, from a reference point (the minimum/smallest speed rating or the maximum/largest speed rating)?

That is true. Unless you were interested in doing something with ordered statistics, I don't believe that position is necessary. In the example described, I am interested in the distance, and the population distribution would follow the same condition.

Mike (Dr Beav)

[raybo]

It acutally makes good sense to me to use several speed ratings, say four based on information from each of the most recent four races.

As Mike says the value of the speed rating projection is representative of a distribution whose spread is based both on the inherent variability of racing and race data and also on the acuity of the projection process used.

You can create a line for each horse which is the weighted average of the distributions you constructed from the last four races.

Then you can calculate the probability of each of the horses running 1st to make an odds line. There are reasons why this odds line needs improvement but it is a good starting point.

Are the 2 highlighted portions of your post related? I mean, is the "information" where the "weighting" is derived?

[raybo]

That is true. Unless you were interested in doing something with ordered statistics, I don't believe that position is necessary. In the example described, I am interested in the distance, and the population distribution would follow the same condition.

Mike (Dr Beav)

So, you're only interested in one direction, from the reference point, high to low, or, low to high?

[TrifectaMike]

Let me expand on what I've I said a bit further. Let's say I recorded (data) of winners as a function of speed rating gap. And I determine a probability density function (pdf). This would serve as my prior distribution, P(A).

We can use this pdf to find the probability of a random horse drawn from our prior distribution that has at least an x gap.

Mike (Dr Beav)

[dav4463]

Is anyone else totally confused by this entire thread? :confused:

[TrifectaMike]

Normally I don't do this, but I'll make an exception.

Here is how I would determine my prior distribution for this particular example. I would fit a Logistic (Sigmoid type ) function to selected data.

Use a function of this type:

p = 1/(1+10^(-A(g-B))

where

p -> probability (percentage of winners)
A,B ->constants to be determined by linear regression
g ->speed gap

The parameter A affects how steeply the function rises as it passes through the mid-point (p=.5), while parameter B determines at which speed gap the midpoint occurs.

This logistic function fit is a cumulative probability function. Once the A and B is determined, we can differentiate this function. The derivative will be our prior pdf, P(g).

Mike (Dr Beav)

[TrifectaMike]

Is anyone else totally confused by this entire thread? :confused:

I am. I'm very confused. I can't believe I'm still posting in this thread.

You are not alone.

Mike (Dr Beav)

[Greyfox]

Sorry, but in my life at the track I've always believed,

BULLSHIT BAFFLES BRAINS.

In Post 163 or somewhere around this endeavour, I asked.

Give us a concrete example for Sunday (tomorrow) at any track of your choice.

Answer: _______________________________


Your credibility might have been enhanced Trifecta Mike with a simple example, from any track of your choice.
That you did not provide that was not particularly surprising.
That you continue this lark is enjoyable. Best luck with your approach to the races. Money for the rest of us winners as far as I can determine so far.:lol:

I remain:

Bull I've experienced before sensation is , deja moo.

Greyfox

[TrifectaMike]

Sorry, but in my life at the track I've always believed,

BULLSHIT BAFFLES BRAINS.

In Post 163 or somewhere around this endeavour, I asked.

Give us a concrete example for Sunday (tomorrow) at any track of your choice.

Answer: _______________________________


Your credibility might have been enhanced Trifecta Mike with a simple example, from any track of your choice.
That you did not provide that was not particularly surprising.
That you continue this lark is enjoyable. Best luck with your approach to the races. Money for the rest of us winners as far as I can determine so far.:lol:

I remain:

Bull I've experienced before sensation is , deja moo.

Greyfox

No problem. Give me an address and I'll ship the money to you.

Mike (Dr Beav)

[TrifectaMike]

Let me see if I can get Greyfox to explode again.

I forgot to add that the Sigmoid function output ranges from 0 to 1. Because the function maps a very large input domain to a small range of outputs, it is also sometimes referred to as the squashing function.

Mike (Dr Beav)

[raybo]

Oops, thought we were finally getting somewhere. Help!!

[Greyfox]

Let me see if I can get Greyfox to explode again.

I forgot to add that the Sigmoid function output ranges from 0 to 1. Because the function maps a very large input domain to a small range of outputs, it is also sometimes referred to as the squashing function.

Mike (Dr Beav)

So what?
I didn't explode in the first place.
You continue to try to demonstrate that:
"Bullshit baffles brains"

A Sigmoid function doesn't help anyone.
You were asked to show an example for Sunday, at any track you wanted,
and you didn't. Deja Moo.

[Fastracehorse]

Many years ago I had the privilege of attending a seminar, in which, the great physicist Richard Feynman explained his work in Quantum Mechanics to an enthralled audience.

When he was finished, a member of the audience raised his hand and preceded to compliment Mr. Feynman for making such a difficult subject so easy to understand.

Feynman waved away the compliments and stated that..."until a person is capable of clearly explaining a complicated subject to a layman...he hasn't really mastered that subject himself..."

Einstein said the same thing about theory: paraphrase: 'if you can't teach it to a child it probably can't be proven'

it's an important point you make because it is human nature to want to work hard to achieve something, but more importantly, where to focus the effort is the difficult part - same goes for horse racing, much logic defied

fffastt

[CBedo]

Einstein said the same thing about theory: paraphrase: 'if you can't teach it to a child it probably can't be proven'So I guess the quadratic equation can't be proven...

[sjk]

Are the 2 highlighted portions of your post related? I mean, is the "information" where the "weighting" is derived?

Ray,

Those are separate issues.

The "information" is anything that can be gleaned from an individual past race such as speed rating, adjustments due to pace or bias, information about the other horses in that race, etc.

The "weighting" is how you allocate importance to each of the four (in this example) prior races. Using 40%/ 30%/ 20%/ 10% is not a bad way to go. If you were seriously going to use this you would study the data to refine that weighting.

[HUSKER55]

what are constants determined by linear regression?

[TrifectaMike]

what are constants determined by linear regression?

I wouldn't concern myself with that question.

Why not you ask?

Because the FoxyLady (Better known as Deja Moo) has rescued you. I was informed early this morning that he'll show you how to get all the winners with ease and literally take ("steal") away money from other players.

I'm sure we will soon see a thread soon from the FoxyLady explaining how he and soon you too will be raking in the cash.

I know, I'm excited. I can't wait. Cleared my schedule for the day. I hope he'll start sooner than later.

Mike (Dr Beav)

[raybo]

Ray,

Those are separate issues.

The "information" is anything that can be gleaned from an individual past race such as speed rating, adjustments due to pace or bias, information about the other horses in that race, etc.

The "weighting" is how you allocate importance to each of the four (in this example) prior races. Using 40%/ 30%/ 20%/ 10% is not a bad way to go. If you were seriously going to use this you would study the data to refine that weighting.

Understood. Appreciate the clarification.

[HUSKER55]

wow! and just when I was starting to get the idea of what you were trying to accomplish.

All I did was ask a simple question.

Gov Walker is right. Teachers are over paid and over rated.

Don't worry though. USC has a tutor program and sometimes those kids will answer questions like this from grumpy old bastards like me.

But you are 100% right on one point. People like me should not be in a class like yours.

Have a nice day!:)

[thaskalos]

I wouldn't concern myself with that question.

Why not you ask?

Because the FoxyLady (Better known as Deja Moo) has rescued you. I was informed early this morning that he'll show you how to get all the winners with ease and literally take ("steal") away money from other players.

I'm sure we will soon see a thread soon from the FoxyLady explaining how he and soon you too will be raking in the cash.

I know, I'm excited. I can't wait. Cleared my schedule for the day. I hope he'll start sooner than later.

Mike (Dr Beav)
Doubtful...

Greyfox seldom initiates threads. :)

[TrifectaMike]

wow! and just when I was starting to get the idea of what you were trying to accomplish.

All I did was ask a simple question.

Gov Walker is right. Teachers are over paid and over rated.

Don't worry though. USC has a tutor program and sometimes those kids will answer questions like this from grumpy old bastards like me.

But you are 100% right on one point. People like me should not be in a class like yours.

Have a nice day!:)

I apologize to you. My post was not aimed at you. Of course, I'll answer your question.

What are constants determined by linear regression?

The logistic function as defined in the thread has two unknown constants, A and B. In order for the equation to be useful, we'll use actual data (speed gap and winning percentage) to determine A and B. Linear regression is one way of accomplishing it (It can be done in Excel).

Mike (Dr Beav)

[Robert Goren]

I apologize to you. My post was not aimed at you. Of course, I'll answer your question.

What are constants determined by linear regression?

The logistic function as defined in the thread has two unknown constants, A and B. In order for the equation to be useful, we'll use actual data (speed gap and winning percentage) to determine A and B. Linear regression is one way of accomplishing it (It can be done in Excel).

Mike (Dr Beav) That was not only correct, but also understandable. Good job, Mike.

[TrifectaMike]

Doubtful...

Greyfox seldom initiates threads. :)

Is that a good thing or a bad thing?

[Greyfox]

Is that a good thing or a bad thing?

Capper Al started "A Thread about Nothing."
I think that he got the idea from the meaningless drivel that you are floating.

[TrifectaMike]

Let's put Bayesian probability aside for the moment and revisit the Logistic Function.

p = 1/(1+10^(-A(x-B))

where

p -> probability (percentage of winners)
A,B ->constants to be determined by linear regression

Let x represent some performance value ( I prefer gaps, Z-scores).

With the use of some algebra and a log transformation ( if you need to know the steps involved I can show you), we can get the equation into this form:

-log((1-p)/p) = A(d-B)

It may not be obvious, but the equation is exactly the equation for a straight line, y = ax + b

where

y = -log((1-p)/p) and a =A and b = -AB

With the use of the Linear Regression in Excel, you can determine a and b and the determine A and B.

You know have a probability curve that corresponds to the factor of your choice.

Mike (Dr Beav)

P.S. Raybo, I'm certain you can find a use for this in your AllData program

[TrifectaMike]

Capper Al started "A Thread about Nothing."
I think that he got the idea from the meaningless drivel that you are floating.

If 5 members indicate that this material is meaningless drivel. I'll stop posting about this subject.

Mike (Dr Beav)

[Greyfox]

There is no doubt that you know your math.
It seems that your intent in starting the thread was to show us your agility in that domain. Mission accomplished. You are, probably, "the smartest boy in the class" for that subject.

However, what you haven't accomplished to this point is to demonstrate that a knowledge of Bayes, as per the example you've outlined, adds one iota of improvement to anyone's ability pick winners.
While there are many routes up the handicapping mountain to improvement, this isn't the quickest trail nor likely the most profitable one.

(Hint: It doesn't take a rocket scientist to tweak a few variables and develop a linear regression equation that works well without using any complicated formulae at all.)

[TrifectaMike]

There is no doubt that you know your math.
It seems that your intent in starting the thread was to show us your agility in that domain. Mission accomplished. You are, probably, "the smartest boy in the class" for that subject.

However, what you haven't accomplished to this point is to demonstrate that a knowledge of Bayes, as per the example you've outlined, adds one iota of improvement to anyone's ability pick winners.
While there are many routes up the handicapping mountain to improvement, this isn't the quickest trail nor likely the most profitable one.

(Hint: It doesn't take a rocket scientist to tweak a few variables and develop a linear regression equation that works well without using any complicated formulae at all.)

I'll assume that is a vote in affirmative to stop posting.

[TrifectaMike]

There is no doubt that you know your math.
It seems that your intent in starting the thread was to show us your agility in that domain. Mission accomplished. You are, probably, "the smartest boy in the class" for that subject.

However, what you haven't accomplished to this point is to demonstrate that a knowledge of Bayes, as per the example you've outlined, adds one iota of improvement to anyone's ability pick winners.
While there are many routes up the handicapping mountain to improvement, this isn't the quickest trail nor likely the most profitable one.

(Hint: It doesn't take a rocket scientist to tweak a few variables and develop a linear regression equation that works well without using any complicated formulae at all.)

Hint: Ordinary linear regression has one formulation. There isn't one that is simpler for you and more complicated for me. Deja Moo Moo

Moo Moo? I recall my grandmother referring to a type of a dress as a moo moo.

Mike (Dr Beav)

[TrifectaMike]

Capper Al started "A Thread about Nothing."
I think that he got the idea from the meaningless drivel that you are floating.

I'm glad to hear that Capper Al had an idea. And even happier to hear that I might have inspired that idea.

Mike (Dr Beav)

[TrifectaMike]

There is no doubt that you know your math.
It seems that your intent in starting the thread was to show us your agility in that domain. Mission accomplished. You are, probably, "the smartest boy in the class" for that subject.

However, what you haven't accomplished to this point is to demonstrate that a knowledge of Bayes, as per the example you've outlined, adds one iota of improvement to anyone's ability pick winners.
While there are many routes up the handicapping mountain to improvement, this isn't the quickest trail nor likely the most profitable one.

(Hint: It doesn't take a rocket scientist to tweak a few variables and develop a linear regression equation that works well without using any complicated formulae at all.)

And you have accomplished?

[Greyfox]

I'll assume that is a vote in affirmative to stop posting.

Wrong. Post as much and as often as you want.
To this point I've seen nothing that would help me as a handicapper.
Others may well be getting something out of it.
What I have seen though is a poster who for whatever reason needs ego strokes and is trying to get them by demonstrating mathematical facility.
That seems to overshadow whatever pearls of wisdom have been tossed out, imo.

[TrifectaMike]

Wrong. Post as much and as often as you want.
To this point I've seen nothing that would help me as a handicapper.
Others may well be getting something out of it.
What I have seen though is a poster who for whatever reason needs ego strokes and is trying to get them by demonstrating mathematical facility.
That seems to overshadow whatever pearls of wisdom have been tossed out, imo.

If I have the need for some ego stroking, I'd write another paper on Ring Theory. You think too much of yourself!

Mike (Dr Beav)

[Greyfox]

Ring theory??? You publish in a boxing magazine too??:lol:

[pondman]

Interestingly, this is par of what Taleb talks about in Fooled By Randomness

Taleb?

This is better way...observing disorder and how to predict order out of the mess.

Throw out the bell curve and anything else related to samples and sizes. Throw out quantitative processes. And what are you left with?

It's all about class and where the horse is place in a race. Are the connections ready for the home run?

[pondman]

How likely it is that this poster that posted 2 bullshit and 10 non bullshit posts is a 50% bullshit poster.



People may or may not participate in bullshit. To apply bullshit to ALL people would require bullshit or tales to be clustered into categories:

1. Tall
2. Romantic-- those required to seduce a women( or a man)
3. Minor

To apply bullshit to one individual would require a disorder methology, which must include who the individual is bullshitting towards. You'd need to answer why, not "is he going to bullshit again?"

[Cratos]

Mike, I admire your tenacity because you have given many speed figure aficionados an insight to speed figures in your posts of 170, 172, 182, and 184 that they never had or never thought of.

Also if math and statistics was easy to learn or teach many students wouldn’t be avoiding those two subjects when they are in college.

You have done a good job in explaining your thoughts in this thread; keep up the good work

[Ocala Mike]

Ring theory??? You publish in a boxing magazine too??:lol:

I thought he was a plumber discussing bathtubs on Saturday nights in a poor neighborhood. :lol:

[Tom]

Mike, I admire your tenacity because you have given many speed figure aficionados an insight to speed figures in your posts of 170, 172, 182, and 184 that they never had or never thought of.

Also if math and statistics was easy to learn or teach many students wouldn’t be avoiding those two subjects when they are in college.

You have done a good job in explaining your thoughts in this thread; keep up the good work

What makes you think that? I have been using the idea of gaps for a long time. I have spot plays based on them, and I model them. Gaps for more than speed figs.

[dnlgfnk]

"an insight to speed figures"...

Perhaps. And I admire the math. But it is irrelevant to a horse like Achak in Sunday's 7th at Hollywood, whose last two figures were superior to any rival's lifetime best, but were earned by saving ground on most of both turns in his last two efforts. On Sunday, he drew his widest post position in at least his last ten races. Anticipating the ground loss and different, more difficult trip Sunday, and returning to the theme of this thread, I didn't need a mathematician as much as a video replay to acquire the value in playing against Achak.

[TrifectaMike]

Normally I don't do this, but I'll make an exception.

Here is how I would determine my prior distribution for this particular example. I would fit a Logistic (Sigmoid type ) function to selected data.

Use a function of this type:

p = 1/(1+10^(-A(g-B))

where

p -> probability (percentage of winners)
A,B ->constants to be determined by linear regression
g ->speed gap

The parameter A affects how steeply the function rises as it passes through the mid-point (p=.5), while parameter B determines at which speed gap the midpoint occurs.

This logistic function fit is a cumulative probability function. Once the A and B is determined, we can differentiate this function. The derivative will be our prior pdf, P(g).

Let's use just words.

So we have a prior probability density function that can be used to determine the probability of winning for a horse A with a gap greater or equal to g.

(In this case larger gap is better)

Horse A has a speed gap of 2 (Rather straight forward to determine the probability of this horse winning) and I like this horse. However, there is also a horse in the race with a superior speed gap of 4.

I want to determine

the likelihood that Horse A actually is a 4 gap horse.

To arrive at this answer we can use a Bayesian approach.Mike (Dr Beav)

[Greyfox]

"
I didn't need a mathematician as much as a video replay to acquire the value in playing against Achak.

I played against Achak too.
1. Mitchell had tried to sell this horse for $25,000, it won and Mitchell kept him at $25,000 - should have been rising
2. Then Mitchell raised it to $40,000 and it was the only horse in the race with a price tag. I knew there had to be a hole in it somewhere. I think that hole was revealed on Sunday and it took a pisspot full of sucker money.

[WPL]

Thanks for taking the time to post your ideas, T Mike.
I'm glad to read the stat stuff, which is challenging to me.
Learning something new is a good challenge, and personally I do not like to be spoon fed.
Some people may feel differently about that, some others are obviously not challenged by the same numbers and it's not new for them.

My vote is continue the thread as you see fit and I will continue to read and hopefully find a way to apply it in my own manner.

B.

[Cratos]

What makes you think that? I have been using the idea of gaps for a long time. I have spot plays based on them, and I model them. Gaps for more than speed figs.

Why are you so sensitive? I didn't single you out nor did I say "all" of the speed figure users; please read the post again in the context for which it was written and I apologize if I OFFENDED YOU

[TrifectaMike]

End of thread for me. I will not show any calculus or any calculations. As I said I've learned my lesson. Those of you with the necessary background can perform the actual calculations. Those who can not...can't.

Mike (Dr Beav)

P.S. The speed rating gap example is very similar to the bullshitter example. The math is similar without the Bernoulli (see below)

For any one bullshitter with a known (p), the probability of posting 2 bullshit and 10 non-bullshit is

( 12! / (2! * 10!) ) * p^2 * (1-p)^10

[ALL CIRCUITS GO]

long ago I learned

If you can't baffle them with brilliance,

befuddle them with bullsh!t...

and so it goes.

After reading this thread, I can't figure out if I'm baffled or befuddled.

:cool:

[PaceAdvantage]

End of thread for me.WHAT? You got nowhere near your five man requirement...WTF :confused:

[Tom]

Why are you so sensitive? I didn't single you out nor did I say "all" of the speed figure users; please read the post again in the context for which it was written and I apologize if I OFFENDED YOU

Why are YOU so sensitive?
All I did was make a statement. There was no attack in there. No offense was intended or taken. Chill!

[TrifectaMike]

WHAT? You got nowhere near your five man requirement...WTF :confused:

I completed the example. The exercise is over. I'll entertain questions on the examples, but I'm not going to write a book. Unfortunately even if I wanted to continue, the mathematical portion would get more complex.

The two examples I've described were isolated cases, P(A|B)

P(A|B) Probability of A given that event B has occurred.

I can't only imagine the reaction when I explain how to take into account conditioning on multiple events. Unfortunately the math is an integral part of the process.

I believe I can summarize the process for those that might be interested in exploring Bayesian probability further. At minimum they'll know what to expect.

Mike (Dr. Beav)

[TrifectaMike]

The two examples,"bullshitter" and speed gaps were specific and I attempted to explain the reasoning involved and some math.

In this post, I'll generalize the approach.

Let's revisit the Bayes Theorem,

Bayes Theorem

P(A|D) = P(A)P(D|A)/P(D)

P(A|D) reads the probability of A given D
P(A) reads the probability of A
P(D|A) reads the probability of D given A
P(D) reads the probability of D

Let me define P(D|A) in slightly different terms.

If A is true, what is the probability of observing this particular piece of evidence, D?

The answer to this question is what enables us to answer the initial question P(A|D).

In solving real life problems like horse racing, we are not confronted with not just asking and answering a single question. We are confronted with a multitude of questions, P(Dn|A) where n =1,2,3,..,k

So, if we asked 3 questions, we would have P(D1|A), P(D2|A) and P(D3|A). If the questions were independent of each other, we would say:

P(D|A) = P(D1|A)P(D2|A)P(D3|A) where D is now the event that D1,D2, and D3 occur or given.

I'll take questions, but no calculations will be given nor further examples.

Mike (Dr Beav)

[Robert Goren]

For those who understand the formulas, but hate actually doing the math, here is a link to a Bayes calculator that may be useful in some the more simple cases.

http://stattrek.com/Tools/BayesRuleCalculator.aspx

[HUSKER55]

Thank you mike for your efforts but I have come to the conclusion I am not smart enough to master it.

Thank you for your time and effort.

[TrifectaMike]

Mike, I admire your tenacity because you have given many speed figure aficionados an insight to speed figures in your posts of 170, 172, 182, and 184 that they never had or never thought of.

Also if math and statistics was easy to learn or teach many students wouldn’t be avoiding those two subjects when they are in college.

You have done a good job in explaining your thoughts in this thread; keep up the good work

Thank you Cratos, and good luck on your endeavors.

Mike (Dr Beav)

[TrifectaMike]

The two examples,"bullshitter" and speed gaps were specific and I attempted to explain the reasoning involved and some math.

In this post, I'll generalize the approach.

Let's revisit the Bayes Theorem,

Bayes Theorem

P(A|D) = P(A)P(D|A)/P(D)

P(A|D) reads the probability of A given D
P(A) reads the probability of A
P(D|A) reads the probability of D given A
P(D) reads the probability of D

Let me define P(D|A) in slightly different terms.

If A is true, what is the probability of observing this particular piece of evidence, D?

The answer to this question is what enables us to answer the initial question P(A|D).

In solving real life problems like horse racing, we are not confronted with not just asking and answering a single question. We are confronted with a multitude of questions, P(Dn|A) where n =1,2,3,..,k

So, if we asked 3 questions, we would have P(D1|A), P(D2|A) and P(D3|A). If the questions were independent of each other, we would say:

P(D|A) = P(D1|A)P(D2|A)P(D3|A) where D is now the event that D1,D2, and D3 occur or given.

I'll take questions, but no calculations will be given nor further examples.

Mike (Dr Beav)

Now, for some A, we have a number of items of evidence which support A. They are D1,D2,..., Dn.

If all the evidence is available at once, we can calculate P(D|A) as the product of the individual P(Di|A)and then find P(D|A).

However, there are times when the evidence is not available all at once (track, conditions, biases, tote odds, etc). In this case, we can perform the computation in stages, applying the evidence, D1,D2,..., Dn, and its effects as we get the evidence.

Since we are for the most part familiar with loops (in the sense of pseudo code) I'll outline the process.

I'll describe this in terms of prior and posterior distributions. (Recall that the prior is P(A) and posterior is P(A|D) )

Step 1
P(A) is the prior of A.

Step2
For some given evidence Di, we have P(Di|A).

Step 3
Applying Bayes theorem, we compute P(A|Di). This is the posterior of A.

Step 4
Now, we can disregard the evidence contained in Di and replace the prior of A with the a new prior of A, which is now P(A|Di).

Step 5
Select the next piece of evidence, Di to incorporate and GOTO Step 1.

Stop when you have exhausted all the bits of evidence.

Mike (Dr Beav)

[sjk]

Is this Bayes Law?

I have used speed and pace figures and other relavent data to determine that a particular horse has a 20% chance of winning but I have used no information pertaining to when his past races took place.

I know that this horse has not raced in more than 100 days.

Among all horses the win rate is 12.8%. Among horses that have not run in at least 100 days the win rate is 10.3%.

I incorporate the new information as .20 x .103/.128 = .161 so the revised probability is 16.1%.

[TrifectaMike]

Is this Bayes Law?

I have used speed and pace figures and other relavent data to determine that a particular horse has a 20% chance of winning but I have used no information pertaining to when his past races took place.

I know that this horse has not raced in more than 100 days.

Among all horses the win rate is 12.8%. Among horses that have not run in at least 100 days the win rate is 10.3%.

I incorporate the new information as .20 x .103/.128 = .161 so the revised probability is 16.1%.

Let's do it.

P(A|D) = Probability this horse wins its race given he hasn't raced in
100 days.
P(A) = .20 Probability that this horse wins it race.
P(D|A) = .103 The probability it has not raced in 100 days given the
horse wins the race,
P(D) = .128 A random winner drawn from your prior

Your calculation is based on Bayes theorem.

Mike (Dr Beav)

[TrifectaMike]

Originally Posted by sjk
Is this Bayes Law?

I have used speed and pace figures and other relavent data to determine that a particular horse has a 20% chance of winning but I have used no information pertaining to when his past races took place.

I know that this horse has not raced in more than 100 days.

Among all horses the win rate is 12.8%. You might want to rethink this number. I believe you mean to say: The percentage of horses that haven't raced in more than or equal to 100 days Among horses that have not run in at least 100 days the win rate is 10.3%.

I incorporate the new information as .20 x .103/.128 = .161 so the revised probability is 16.1%.


Let's do it.

P(A|D) = Probability this horse wins its race given he hasn't raced in
100 days.
P(A) = .20 Probability that this horse wins it race.
P(D|A) = .103 The probability it has not raced in 100 days given the
horse wins the race,
P(D) = .128 A random winner drawn from your prior

Your calculation is based on Bayes theorem.

Mike (Dr Beav)

[sjk]

No there is a disconnect between the calculation and the application of Bayes Law.

The percentage of horses that have not run in 100 days is more like 5.2%