What would you want to have done...

[Light]

Originally Posted by TrifectaMike

Is that third dimension a light phase?

Its the holy grail of racing that no handicapping philosophy nor software has attained or probably ever will. The negative probability of this game is very strong due to this 3d reality vs. our 2d paper handicapping. And yes you will need at least something like a "phaser" to overcome the lack of an entire dimension.

One thing comes to mind in this area is beginners luck. I had it when I started and it is a phenomena that might encroach on this sorely needed 3rd dimension. Beginners do not think at all like seasoned handicappers. They don't have all the rules in place and are not as analytical,yet many have tremendous "luck" when they first start out and even embarass their hosts who try to explain the game from 30 years of "experience" .What's happening is these "lucky" newbies are thinking outside the box and don't even realize it. Of course it doesn't last,but during that "innocent" phase it can be uncanny. Now program that part and I'll buy it.

[Fastracehorse]

[QUOTE=TrifectaMike]

Originally Posted by Fastracehorse

Whatever works for you.

Mike (Dr Beav)

,,,,,whatever works.

fffastt

[Fastracehorse]

[QUOTE=Jeff P]

Originally Posted by Fastracehorse

I'd argue that the ability to make intelligent play or pass decisions has far more effect on the player's long term expectation than the selection process itself. In the right hands, a good oddsline can assist in that.

Suppose for the sake of argument you are a good handicapper with a proven track record. Through your own good "handicapping" you select a horse. Let's also say that you feel pretty strongly about your selection and like its chances in today's race.

You look up at the tote board and you see that the public doesn't agree with you. Some other horse that you don't like is the favorite. Your selection is 4-1.

Do you bet? (Most likely yes... no oddsline required.)

What if the same horse in the same race is 2-5? Do you still make the bet? Or do you sit on your hands?

What if someone sitting next to you offers 6-1 on your horse? Do you bet then?

Or what if you looked at the exotics and saw a way to get 8-1 on your selection?

To my way of thinking, price is everything because it drives value - which I'd argue is more important than the selection process or picking winners.


-jp

.

.........that I do a rudimentary oddsline naturally through the handicapping process. For eg., I generally know what the public will like; and I know if I horse I like will be a $. It's impossible to avoid. My point was that it is not neccessary to consciously formulate fair value for horses that are not going to run anyways - it's too time consuming.

The final tote is what it is.

Interesting point you make: value trumps the selection process.

I love longshots but I have faith in the selection process. I do think it is important to play lower % creative angles; that are good $'s - to try and get some of that value.

fffastt

[Fastracehorse]

Originally Posted by Light

Its the holy grail of racing that no handicapping philosophy nor software has attained or probably ever will. The negative probability of this game is very strong due to this 3d reality vs. our 2d paper handicapping. And yes you will need at least something like a "phaser" to overcome the lack of an entire dimension.

One thing comes to mind in this area is beginners luck. I had it when I started and it is a phenomena that might encroach on this sorely needed 3rd dimension. Beginners do not think at all like seasoned handicappers. They don't have all the rules in place and are not as analytical,yet many have tremendous "luck" when they first start out and even embarass their hosts who try to explain the game from 30 years of "experience" .What's happening is these "lucky" newbies are thinking outside the box and don't even realize it. Of course it doesn't last,but during that "innocent" phase it can be uncanny. Now program that part and I'll buy it.

......I would enjoy the read.

fffastt

[TrifectaMike]

Originally Posted by GameTheory

Like others here, I am having trouble following what you are getting at here, although I think I am somewhat familiar with the concepts, but not with the terms you are using since I am not formally trained in these things. (I had to look up "degenerate distribution" just now to find out that it meant "an oddsline with a single 1.0 and the rest 0.0".) I need dumbed-down explanations with worked-through examples that I can follow along, which is why my own posts on such subjects are usually so long-winded. Plus I think you are holding back the good parts, eh?

Am I holding back the good parts? Absolutely!

The purpose of using the term degenerate distribution was purposeful. If you have an interest in this subject, you would think of the Probability mass function as a Dirac Delta function, and the Cumulative distribution function as a translated Heaviside step function.

Let's assume our intent is to simplify the choice of the prospective winners in a horse race.

One way to accomplish this task is to stretch the distances between the higher probability horses and the lower probability horses. Transforming probabilities toward the direction of preferred probabilities is to change from an arithmetic scale to a geometric scale.

Another way to accomplish the same task is instead of transformation, a probability distribution (degenerate distribution(s)) is directly introduced.

Mike (Dr Beav)

[GameTheory]

Originally Posted by TrifectaMike

Am I holding back the good parts? Absolutely!

The purpose of using the term degenerate distribution was purposeful. If you have an interest in this subject, you would think of the Probability mass function as a Dirac Delta function, and the Cumulative distribution function as a translated Heaviside step function.

Let's assume our intent is to simplify the choice of the prospective winners in a horse race.

One way to accomplish this task is to stretch the distances between the higher probability horses and the lower probability horses. Transforming probabilities toward the direction of preferred probabilities is to change from an arithmetic scale to a geometric scale.

Another way to accomplish the same task is instead of transformation, a probability distribution (degenerate distribution(s)) is directly introduced.

I do have an interest in the subject, but it is just over my head. I have no idea what you are saying. I understand the goal -- spreading the probabilities. Introducing a degenerate distribution? What does that mean, i.e. how do you do that? No clue.

[gm10]

Originally Posted by TrifectaMike

Am I holding back the good parts? Absolutely!

The purpose of using the term degenerate distribution was purposeful. If you have an interest in this subject, you would think of the Probability mass function as a Dirac Delta function, and the Cumulative distribution function as a translated Heaviside step function.

Let's assume our intent is to simplify the choice of the prospective winners in a horse race.

One way to accomplish this task is to stretch the distances between the higher probability horses and the lower probability horses. Transforming probabilities toward the direction of preferred probabilities is to change from an arithmetic scale to a geometric scale.

Another way to accomplish the same task is instead of transformation, a probability distribution (degenerate distribution(s)) is directly introduced.

Mike (Dr Beav)

Mike, are you adding the degenerate RV

a) because your base probabilities are not very good and you want to improve them?

or

b) regardless of how good the base probabilities are, you are trying to make a intentionally inaccurate 'odds-line' whose only purpose it is to make money?

In either case, can you show us, without revealing your good parts, what the effect is of inserting this Dirac guy into your system? It sounds like it's working for you.

[yak merchant]

I definitely can't keep up with all this, one minute something seems to make sense, the next I'm not sure if I'm doing significance calcs correctly. I have a sneaking suspicion it will end up with a discussion on Laplace and/or Z transforms and like always I'll have no clue. Nevertheless maybe I'll learn something, so I appreciate those taking the time to post.

[TrifectaMike]

Originally Posted by gm10

Mike, are you adding the degenerate RV

a) because your base probabilities are not very good and you want to improve them?

or

b) regardless of how good the base probabilities are, you are trying to make a intentionally inaccurate 'odds-line' whose only purpose it is to make money?

In either case, can you show us, without revealing your good parts, what the effect is of inserting this Dirac guy into your system? It sounds like it's working for you.

b) is close to truth.

Without getting too technical or complex, and still maintain some distance to what I'm actually doing, let me attempt to describe some simple ideas.

Let's assume I have an extremely well calibrated oddsline (unbiased). Now, this oddsline will look good theoretically according to all the statistical tests. However, will it differ sufficiently from the tote odds derived probabilities to make it long term profitable? Maybe or maybe not.

We spoke of calibration (what old-timers called reliability) in this thread. We spoke of averaging being at the heart of most techniques.

Let me speak of averaging in a different sense. Let's assume we have a great oddsline and has fidelity with the tote-odds. Not very helpful as a decision tool, but a good tool nonetheless. The objective probability is most likely in the neighborhood of the probability line. It could be below or above the probability value for each horse.

Okay, I hope so far.

Now, let me introduce (this for explanation only, but you'll get the idea) some subjectivity (Bayesian stuff on a single race basis), so that it can some how bound the objective probability from below and above. So, we have have this well calibrated oddsline, which we believe is within a distance X of the objective probability, and we have some subjectivity, which we believe contains bounds on the objective probabilities. So, if we can strategically introduce a single race subjective distribution (s) to "merge" with the oddsline, it will appear to be less calibrated, but sharper.

However, appearance isn't always reality. It only appears less claibrated according to the objective function we defined in determining the probability curve for the oddsline.

Let me try a very simple example (this might help, I hope).

Let's take two handicappers. Each produces an oddsline according their methodology (one can be a logistic regression, the other based on a scoring system) and both are well calibrated according to a scoring rule.Suppose we know the objective probability of Horse A to be .3. Handicapper 1 says it is .4, and Handicapper 2 says it is .2. A simple average would be closer to the truth, because the REAL value is bounded by their estimates.

If both handicappers are both below or above, then averaging will drive us further from the objective probability. So, it would be better to accept one of the probabilities over the other (so we have choice over averaging in this case.

If you can understand what I said, it can be helpful, otherwise it'll make absolutely no sense to you.

Mike (Dr. Beav)

[Cratos]

Originally Posted by GameTheory

I do have an interest in the subject, but it is just over my head. I have no idea what you are saying. I understand the goal -- spreading the probabilities. Introducing a degenerate distribution? What does that mean, i.e. how do you do that? No clue.

If I understand Mike, he means by a degenerate random variable which is called X; X has only a single possible value with probability 1. If this is true Mike, what is X or is that something that cannot be revealed.

[GameTheory]

Originally Posted by Cratos

If I understand Mike, he means by a degenerate random variable which is called X; X has only a single possible value with probability 1. If this is true Mike, what is X or is that something that cannot be revealed.

I'm wondering more at what stage of the process is it "introduced" and what does "introduced" mean exactly?

[gm10]

Originally Posted by Cratos

If I understand Mike, he means by a degenerate random variable which is called X; X has only a single possible value with probability 1. If this is true Mike, what is X or is that something that cannot be revealed.

That is the crux of the matter.
Maybe it's some sort of elimination variable. For example. If the horse has won over the distance, the variable takes value 1, otherwise 0.

[TrifectaMike]

Originally Posted by GameTheory

I'm wondering more at what stage of the process is it "introduced" and what does "introduced" mean exactly?

I kinda left this hanging. I've given it some thought, and I believe I have a way of explaining in understandable terms without giving up too much info.

I'm going to present the statements below without proof or justification, nor will I use a Bayesian framework. In spite of this the information I'll present can be used in a crude fashion...but usable.

When there are n horses in a race, your beliefs about the horses are represented by the probability vector

p = (p1,........,pn)

(where 0<= pi <= 1 for i = 1,......n, and the sum of the p i's = 1)

The question I'll ask is a follows.

If uncle Guido has some "additional" information about a particular horse, i, how do I reassign (or reshape) the probability vector?

Uncle Guido may operate as an angle player and has a terrific angle. Or he might be tuned into some inside information, or he maybe a great handicapper and is totally selection oriented.

As I said without proof or justification, here is how to update the probability vector:

Pnew = (1 - a)p + aei (This doesn't have a name, so let's call it Mike's update)

where ei = (0,.....0, 1 , .......0) is a degenerate distribution assigning all probability mass to the ith horse (Guido' s horse) and

0< a <= 1. a represents the confidence in uncle Guido's horse.

This should help. I won't go any further, but I will answer questions on the above equation.This sets the groundwork for getting expected winners toward 1 and the other horses toward 0.

Mike (Dr Beav)

[pondman]

Originally Posted by TrifectaMike

If you had access to a mathematician, an expert horse player, the finances, the desire, and commitment, what type of horse racing selection process would you like to develop?
Mike (Dr. Beav)

Because I single out horses for win bets, I take the Black Swan (Nassim Taleb) approach to explain why my methods work. I make a profit because I make bets on horses when they are not expected to win by the crowd. And the profit come as the result of a few longer shots, meaning I limit a large number of bets on short priced horses. It's not difficult.

I don't see any way of quantifying this, other than employing some gimmicky math learned in fourth grade. I'd have to add a few circles for boolean routines (if the horse)-- but I think that was covered in 6th grade. I do use trend lines provided by excell, but all of you will point out future profits can't be predicted (I probably would agree.) But it's fun to see if my profits are above or below the trend for the year.

I think pace and speed knowledge is required by people searching for contenders in a pick 4 or 6. But I want the single, which over time will crush the field (at high odds.) And so most of my thinking is based on class and on why a trainer would place a horse in a race. I absolutely ignore beyers numbers or any other figures. And with the exception of horses off a maiden win (I want to know it won) or maidens on grass in S. California, I ignore the past performances entirely.

I'm the expert! I've analyzed racing at a number of tracks and have the belief each is unique, has it own structure, and gems and thorns. Therefore handicapping methods from one track should never be utilized for another.

I'm only going to step to the window when I know a horse belongs and has an advantage at a certain condition. Again that's some unknown quantity defined as class. I don't have a quantitative method of ranking class, other than it ran against better.

My financing is manageable. I'm comfortable in the $100 -300 range. Because I'm betting on California I could bump it up another few hundred, but again this would cause some discomfort when I go on a 7 horse losing streak.

I write this all for only one reason:

You are making it too difficult on yourself. You've probably heard it before, but watch the game until you can pick a winner at a good price.

[TrifectaMike]

Originally Posted by pondman

I write this all for only one reason:

You are making it too difficult on yourself. You've probably heard it before, but watch the game until you can pick a winner at a good price.

One would believe that after 45 years at this I would have have learned that lesson.

Thanks for the advice.

Mike (Dr Beav)