How often can a 20-1 shot have a probability of winning 20% of the time ?

[formula_2002]

Correct me if I’m wrong on the math.
How many races must elapse for a 20-1 shot to win 20% of the races and not exceed 1 standard deviation.

With no adjustment for a long to short odds bias, a 20-1 shot in a 15% take-out game has a 4% probability of winning ((1/(20+1) *.85 ) =.04)

To get to an answer, I’ll change the question a bit.
The question becomes:
In sets of 100 races, how often can a probability of 4%, win at a rate of 20% ,and not exceed 1 standard deviation.?

.04 x 100 = a mean of 4

1 standard deviation = sqrt(.04*.94*100) = 1.93, say 2

In 100 races, a probably of 4% could win 6 times (4+2) and not exceed 1 standard deviation.

To win 20 times and not exceed 1 standard deviation, 333 games would have elapsed (20/6 X 100).
But of course you would not play every game, you would knowingly wait for those games where your play has a 20% chance to win.
You will only play 100 of those games.
So 1 in 3.3 games would be playable

To win 20 times and not exceed the mean of 4, 500 games would have elapsed(20/4 x 100).
So your play would be limited to 1 in 5 games.

[ryesteve]

Correct me if I’m wrong on the math.
The problem with the math is that the probability of a 20-1 shot winning isn't governed by a binomial distribution. It's governed by how good of a handicapper you are. The only constraint is that, as a group, these horses win at 4%.

So, let's say you are a handicapping savant, and you're able to identify and eliminate longshots with total confidence that they have a 0% chance of winning. In that case, out of every group of twenty-five 20-1 shots, of which one wins, you've eliminated twenty as definite losers, which leaves you with five, of which one wins... thus your 20% hit rate. You've selected 5 out of 25 horses, so in this case, you would say that 20-1 shots have a 20% probability of winning 20% of the time.

You can construct various other hypotheticals based on the handicapper's skill. Looking at this question as measuring the probability of outliers in a series of random outcomes isn't correct.

[formula_2002]

The problem with the math is that the probability of a 20-1 shot winning isn't governed by a binomial distribution.

Rye, I can point to countless number of papers and books that treat horse racing probability as a binomial distribution.
Most, if not all of the papers I have read in "Efficiency of Racetrack Betting Markets", Fabricand's, "Horse Sense" which I first read back in the early 70's (my friend had a copy of the 1st publication in 1965),
Quirin's book, all point to a binominal distribution in their analysis of the odds.

I'm going to stick with them..

[ryesteve]

And I can point to some old writings that describe the earth as being flat. Feel free to stick with those too.

In fairness, perhaps their particular application of a binomial distribution was appropriate to whatever point they were trying to make, but in this case, it doesn't apply at all. If all race outcomes were governed by a binomial distribution dependent on odds, then winning would be statistically impossible. Which leaves you with trying to decide between a) your premise is incorrect, or b) all the folks who claim to be winners are lying

[formula_2002]

In fairness, perhaps their particular application of a binomial distribution was appropriate to whatever point they were trying to make, but in this case, it doesn't apply at all. If all race outcomes were governed by a binomial distribution dependent on odds, then winning would be statistically impossible. Which leaves you with trying to decide between a) your premise is incorrect, or b) all the folks who claim to be winners are lying

That was my point a few years ago right on this board.
But I didn't say they were lying, I said they could not prove it...
Do you know how many UDM's I have that a produce $$$$ in hundreds of plays only to flop in the next series?? :bang:

[ryesteve]

That was my point a few years ago right on this board.
But I didn't say they were lying, I said they could not prove it...
I'm not sure what you mean by "prove it". Do you mean scanning and uploading their 1040's, or statistically proving that their results aren't merely the result of the good fortune of statistical anamolies? You can't be assuming that so many people are crammed into the tail of a statistical distribution, can you? But the alternative is that you think this place is full of self-aggrandizing liars.

Your UDM analogy isn't valid because those are based on back-fitting data. There's no guarantee that a back-fit model will replicate its results going forward, and they usually don't. This is governed by completely different principles than those that govern the likelihood of a successful player replicating his >actual results< going forward.

[formula_2002]

statistically proving that their results aren't merely the result of the good fortune of statistical anamolies? .

yes

There's no guarantee that a back-fit model will replicate its results going forward, and they usually don't.
I agree, i was just throwing that in as a point of information..

[Overlay]

With no adjustment for a long to short odds bias, a 20-1 shot in a 15% take-out game has a 4% probability of winning ((1/(20+1) *.85 ) =.04)

Along the lines of the point that ryesteve was making, the above statement would be true if the odds were set based on strict mathematical probabilities, but can you apply that model to odds set by public opinion? Despite the aggregate, long-run accuracy of the public in setting odds, is it valid to assume that each of those 20-1 shots does in fact have a 4% chance of winning?

[ryesteve]

yes

Then I'll go back to "You can't be assuming that so many people are crammed into the tail of a statistical distribution". I don't have the time for a moot mathematical exercise, but imagine the probability of someone showing a profit in a sequence of 1000 bets against a 20% takeout, if those results were governed strictly by random probability. Next, compound that by the probability of encountering a dozen or two such people within a group of a couple hundred. I don't think our screens are wide enough to accomodate all the zeroes that would be to the right of the decimal point, if you attempted to represent that probability. How is that not proof?

[formula_2002]

Along the lines of the point that ryesteve was making, the above statement would be true if the odds were set based on strict mathematical probabilities, but can you apply that model to odds set by public opinion? Despite the aggregate, long-run accuracy of the public in setting odds, is it valid to assume that each of those 20-1 shots does in fact have a 4% chance of winning?

I think that on "any given Sunday" a 20-1 can win,
in a "month of sundays" 20-1 shots can win more than their share, but after 100 sundays the probability of winning 20-1 shots start to conform to the normal curve, even more so after 1000 sundays.
The key to my thinking is, the game conforms to the bell curve.. if you are going to beat it, you have to wind up in the small part of the tail..

I think thats where these papers I mention earlier are leading to.

Meanwhile, i have to go and generate my QUANTUM PICKS, JUST IN CASE I'M WRONG.. ;)

[cj]

The whole flaw in your argument is you give no credence to the possibility that a successful handicapper can differentiate between 20-1 shots. They obviously are not all equal. Some win, some run last, most somewhere in between. THEY ARE NOT ALL THE SAME!

[formula_2002]

The whole flaw in your argument is you give no credence to the possibility that a successful handicapper can differentiate between 20-1 shots. They obviously are not all equal. Some win, some run last, most somewhere in between. THEY ARE NOT ALL THE SAME!

Not true, I gave you guys plenty of credit. The point of this note was, how many races would you have to review and not bet that 20-1 shot.
Depending on the level of risk, it could be 333 or 500 or some other number I may agree to ;)

Remember, I'm bound by the curve, no one else need be (if that is possible).

[classhandicapper]

If your question is how large a sample of 20-1 shots that are winnning 20% of the time is large enough to give you 95% or so confidence that it's not just a run of good luck, I'm sure one of the stat guys can give you an answer.

[formula_2002]

If your question is how large a sample of 20-1 shots that are winnning 20% of the time is large enough to give you 95% or so confidence that it's not just a run of good luck, I'm sure one of the stat guys can give you an answer.

nope. thats not what I'm talking here, but that was a similar subject that I refered to in my post,
http://www.paceadvantage.com/forum/showthread.php?t=29823

[PlanB]

A good heady discussion and I have just a few remarks. RE the PR of 4%
of 20:1 shots, I think that isn't a probability but an expectation.
Also, as with Rye, I don't think the binomial suits perfectly. Is the data
that symmetric? RE distributions, I never heard of anyone specifying what distribution impact values followed, have you? That's why I think all sorts
of crazy accidental relationships were found.

[freeneasy]

and i may have missed the point here but are you identifying a true 20-1 shot that has a 4% chance of winning along with a horse that has a legitimate 20% chance of winning whose board odds are at 20-1?
there is that difference.
if you made a horse 5-1 and another 20-1 and they both go off at 20-1, you should figure your 5-1 to outrun your 20-1 most of the time as well as win more often then your 20-1 figure horse.
a more further and proper validation is needed here
20-1 shots with a 20% chance of winning just cant be counted into the same catagory as the same 20-1 shots that have a 4% chance of winning

[skate]

good one ryes

that 20% means as much as 5 grains of sand in the turf