Race structure analysis

[whodoyoulike]

Originally Posted by cashmachine

I am not sure what do you mean by "charts". Try to click "PRE-RACE" on the black stripe (command menu) on the top of the page, there they have some info like trainer-jockey etc. stats.

Do they have race charts similar to the ones which recap how a race was run by each horse in the race for the PP you provided in the link?

Something similar to this link.


http://www.brisnet.com/cgi-bin/insta...e=inc&print=on

[cashmachine]

Originally Posted by whodoyoulike

Do they have race charts similar to the ones which recap how a race was run by each horse in the race for the PP you provided in the link?

Something similar to this link.


http://www.brisnet.com/cgi-bin/insta...e=inc&print=on

It looks like you want sectional time and position, like:
http://www.hkjc.com/english/racing/d...Raceno=8&All=0.
For the race card I gave link above this information is not available yet, because it is a FUTURE race.

[cashmachine]

In general, for the past races info available for free on the HK Jockey Club website: http://racing.hkjc.com/racing/Info/M.../20140525/st/1
They have info for all races going years back, you just need to change date, track and race number in the url to get whatever you want.

[Robert Fischer]

You have (at least) two major dynamics going on in your different "race structures".

Distribution of the pool money.
and
Distribution of the quality of the contenders.

Originally Posted by cashmachine

I noticed that my program much more successful in one particular type of race: when there are exactly 3 or 4 approximately equal horses and the rest of horses is much weaker (field size is 12-14 horses). My program either doesn't bet or loses badly when there are only 1 or 2 strong horses and rest is much weaker; it is also not successful when there are more than 4 strong horses.

One (perhaps oversimplified) hypothesis to this phenomena would be that in fields which your program identified either relatively few or many contenders, the former race structure selections were too "chalky", while the latter indicated a lack of sufficient information with which to separate contenders.

Another very important factor would be the actual "race structure" as opposed to your program. The public odds could give an indication. If the public odds varied wildly from your program's contender selection (and it wasn't producing overlays), then it could simply be a function of your program's contenders best matching the "set" of public contenders within race structures of 3-4 contenders.

Originally Posted by cashmachine

I am thinking about separate analysis for every type of race but currently cannot yet give precise definition of "race structure" so I can't program it. I am curious whether somebody is also thinking along these lines? How exactly would you define race structure? Did anybody do any research on this topic? Any ideas would be much appreciated.

Interesting stuff so far.

[cashmachine]

Originally Posted by Robert Fischer

You have (at least) two major dynamics going on in your different "race structures".

Distribution of the pool money.
and
Distribution of the quality of the contenders.

How about estimating the quality of the contenders by the current odds? Of course odds are not perfect but in average they are very close to the real win probability. I don't think it is practical to separate these two things, otherwise we will not have means to estimate "quality of the contenders".

[Magister Ludi]

Originally Posted by cashmachine

I am thinking about separate analysis for every type of race but currently cannot yet give precise definition of "race structure" so I can't program it. I am curious whether somebody is also thinking along these lines? How exactly would you define race structure? Did anybody do any research on this topic? Any ideas would be much appreciated.

I believe that your "race structure" may be defined by a statistical classification of races according to the subjective probability distribution of each horse's winning chances and a comparison of the mathematical expectation with previous data. This is known as race entropy.

[Robert Fischer]

Originally Posted by cashmachine

How about estimating the quality of the contenders by the current odds?

Using the current odds is a good way to do it.

[Robert Fischer]

Originally Posted by Magister Ludi

I believe that your "race structure" may be defined by a statistical classification of races according to the subjective probability distribution of each horse's winning chances and a comparison of the mathematical expectation with previous data. This is known as race entropy.

Would this be similar to making pars for Race Structure types?

I'm interested in more about your idea of looking at it as a measure of entropy.

[Magister Ludi]

Originally Posted by Robert Fischer

Would this be similar to making pars for Race Structure types? No.

I'm interested in more about your idea of looking at it as a measure of entropy.

Entropy is disorder in a closed system. It measures the competitiveness of a race. A maximum entropy race would be a race where all of the horses have the same probability of winning. A minimum entropy race would be a uniform distribution of probabilities over the interval 0 to 1.

One way to quantify race entropy is as follows:

Sum{1/[O(i)+1]^2}/N

where O(i) = odds of the ith horse
N = number of entries

The smaller the value, the more competitive is the race. Dr. Beav was kind enough to share this formula on this forum. My entropy model incorporates numerous factors with the same end as Dr. Beav's formula.

[Robert Fischer]

Originally Posted by Magister Ludi

Entropy is disorder in a closed system. It measures the competitiveness of a race. A maximum entropy race would be a race where all of the horses have the same probability of winning. A minimum entropy race would be a uniform distribution of probabilities over the interval 0 to 1.

One way to quantify race entropy is as follows:
Sum{1/[O(i)+1]^2}/N

where O(i) = odds of the ith horse
N = number of entries

The smaller the value, the more competitive is the race. Dr. Beav was kind enough to share this formula on this forum. My entropy model incorporates numerous factors with the same end as Dr. Beav's formula.

Very cool.

This makes me want to calculate some races to see what they look like per the formula.

Also interesting that you are using additional factors.

[cashmachine]

Originally Posted by Magister Ludi

A maximum entropy race would be a race where all of the horses have the same probability of winning. A minimum entropy race would be a uniform distribution of probabilities over the interval 0 to 1.

That's wrong. Maximum of your formula will be achieved when all the horses (except 1) have large odds and one horse has very small odds - in other words when there is one extremely strong favorite and the rest is equally weak. Maximum entropy will be when all of the horses have the same probability of winning.

[Hoofless_Wonder]

Cashmachine - thanks for the link to those nice PPs. Looks like they have a 14 day trial, and accept Paypal. Only a bit more than a month of racing left in Hong Kong before the summer break, but I'm looking forward to trying these out.

As for the observation on races with 3-4 stronger contenders producing max profits, that sounds like a typical race at Sha Tin. The races there are very formful, and at least half the field can be downgraded due to being off form, bad post, or racing against a bias.

When the remaining contenders are sorted out, it makes sense that there would be more inefficiencies with the larger number that can win. When there are only one or two contenders, the odds reflect it, and there's not much left to shoot for in the win pool - so then the exotics come into play.

It sounds like you have a sophisticated program that can take advantage of this angle - very nice.....

[Robert Fischer]

Originally Posted by cashmachine

That's wrong. Maximum of your formula will be achieved when all the horses (except 1) have large odds and one horse has very small odds - in other words when there is one extremely strong favorite and the rest is equally weak. Maximum entropy will be when all of the horses have the same probability of winning.

I believe ML's statement should be correct.

If all the horses have the same odds (or were all handicapped to have the same probability estimate), - that should be the maximum entropy. Closely matched rivals, high potential for disorder.

If there was a heavy (true)favorite, then that should be the minimum entropy.


Is the formula finding different results?

[Sapio]

Originally Posted by Robert Fischer

I believe ML's statement should be correct.

If all the horses have the same odds (or were all handicapped to have the same probability estimate), - that should be the maximum entropy. Closely matched rivals, high potential for disorder.

If there was a heavy (true)favorite, then that should be the minimum entropy.


Is the formula finding different results?

Hi Robert

You, Magister and Cash are all correct. The confusion is that I believe Magister meant to say, "A minimum entropy race would be a non-uniform distribution of probabilities over the interval 0 to 1.". More likely a highly skewed beta distribution.

Thomas Sapio

[cashmachine]

Originally Posted by Robert Fischer

I believe ML's statement should be correct.

If all the horses have the same odds (or were all handicapped to have the same probability estimate), - that should be the maximum entropy.

Let's do the math together. Assume 5 horses, no track take.

Case 1. Extremely strong favorite: $99996 bet on horse 1, $1 bet on the other 4 horses. Odds will be 0.0 for horse 1, and 99999 for each of other horses. Substitute into formula: (1/(0.0 + 1)^2 + 4*1/(100000)^2)/5 = (1 + 4 * 0)/5 = 0.2

Case 2. Equal odds: 20000 bet on each horse. Odds will be 4 for every horse. Substitute into formula: (5/(4+1)^2)/5 = 1/25 = 0.04

As you can see, formula produced much bigger result for the case 1 (extremely strong favorite). In other words, formula gives maximum when there is absolute structure, and formula gives minimum when it is complete chaos. In other words, his formula is NOT entropy, it is mirror opposite to entropy: entropy is maximum when it is complete chaos.