A different Breeders Cup Topic

[BitPlayer]

Jimbo -

Doesn\'t the binomial distribution require random/independent samples?  13 horses in the same race, all subject to the same factors like pace and traffic that may affect their performance, seems pretty far from random sampling to me.

[bobphilo]

Bit,

Idependent doesn\'t mean the subjects are exposed to the same variables or conditions. It just means that the the result of one case is not dependent on the result of another. In other words the performance of one horse is not necessarily the result of that of the others.

Bob

[bobphilo]

bobphilo Wrote:
-------------------------------------------------------
> Bit,
>
> Idependent doesn\'t mean the subjects are exposed
> to the same variables or conditions. It just means
> that the the result of one case is not dependent
> on the result of another. In other words the
> performance of one horse is not necessarily the
> result of that of the others.
>
Oops, a typo. I meant that independent does NOT mean the subjects are subject to the same variable or conditions.

[BitPlayer]

Bob -

I stand corrected.  What about random?

BitPlayer

[bobphilo]

Bit

Random means that all members of a population are equally likely to be included in the sample, and there is no bias in the selection. That makes the sample more likely to be representaive of the population as a whole. Good job of stating the requirements for a binomial distribution, though.

Bob

[David57]

Now that we\'ve mastered binomial distribution, can any of you mathematicians explain how to apply Six Sigma methodology to the handicapping process? I don\'t know about you guys, but I\'ve been experiencing a hell of a lot more than 3.4 defects per million opportunities.

[BitPlayer]

Bob -

I\'m obviously out of my depth here.  I\'ve had only one course in statistics (and a bad one at that) several years ago.  This board is the only place I\'ve ever heard of Six Sigma.  Rather than continue to ask you what various statistical terms mean (e.g., is selecting horses from a single race a \"biased\" selection?), I\'ll defer to you to answer the question at hand:  Do you think the binomial distribution is a statistically sound method of analyzing the probability that the Rags figures for the BC Distaff are accurate?

BitPlayer

[bobphilo]

LOL, good point David. I think we got involved in these fine points of statistical definitions, to answer the original question of the thread, which was - what is the probability that the the success of the \"super trainers\" on BC day was due to chance or are they up to there old tricks? My take is that while 8 races are only 8 races, no matter how important they are, the results are consistant with the pattern of hundreds of other races with the conclusion that  these guys are up to something less than honerable.

Bob

[jimbo66]

The formula is fine, the question is whether you agree with the 45% figure Jerry is using.  

I am not sure what Jerry is using 45% to represent.  If it is 45% that one of the entrants will run an \"x\", then 45% is just an average based on 1000\'s of horses, not the individual chance of each horse in the race based on her pattern.

If you accept the 45% as a valid variable, then the formula is most definitely 100% usable to express the chances of 12 of the 13 horses running that \"x\".

[David57]

I agree with your conclusion. So, as handicappers, can we use that conclusion to our advantage? That is, rather than quit the game in disgust or just play minor tracks where these guys don\'t show up, can we ascertain any patterns that \"tell\" us when one of the magical move ups is more likely to occur (or not) and bet accordingly? I don\'t begin to have the answer, but maybe some of TG\'s trainer stats, if parsed correctly, would shed some light on this.

[bobphilo]

Bit,

I think we may have 2 different threads going on simultaniuosly. One as to whether the BC results implicate the \"super trainers\". and another with regard to the legitamitcy of the Rags figures for the day. If it makes you feel any better, I find the issue of applying the binomial distribution to these results a bit confusing myself. The good news is that the answer lies in simply applying your common sense knowledge of whether the figures make sense with respect to the horses previous performances. Personally, my first quick look at the Rags figures show some problems there due to mixing unlike populations by refusing to break races loose. I think detailed knowledge of sigma six or the binomial distribution are not neceassarily required here. Combine this with the answer I just gave to David\'s post and that\'s my best guess answer to both questions. Hope this helps.

Bob

[Caradoc]

Jimbo: I’m not sure I completely follow it either, but let’s try looking at it this way.  Assume the parameters in Jerry’s post as of 5:19 today are true: a) that the starters in the BC Distaff this year made 74 starts this year prior to the Distaff, b) on Ragozin’s data, 33 of those 74 efforts were “off” (meaning in this case more than 3 points off their top), and c) 12 of the 33 “off” races were run by Hollywood Story and Island Fashion.

One of the problems is that without having the Ragozin data to analyze, we don’t know precisely how to calculate the probability of an outcome where all the entrants except one run more than three points off their top, a point Jerry has acknowledged.  If you make some reasonable assumptions, the chance of 12 of 13 (excepting Pleasant Home) running more than three points off their top are higher than the earlier posts today suggested, mine included.  Hollywood Story and Island Fashion, who account for 12 of the off races, ran 14 times this year prior to the BC.  For their two other races, I don’t know whether one of them ran two “pairs” or whether both ran a pair.  Assume both ran a pair.  Of the other 11 entrants, as a group they had run 21 “off” races out of 60 this year prior to the BC.  Again, I have no idea how these 21 were distributed among the others, but solely for the purpose of illustrating the point, assume that the 21 “off” races are distributed evenly among the other 11 entrants with one exception.  That exception relates to Stellar Jayne, who had run only twice before the BC this year, so if you assign 2 off races to her, you will completely skew the results.  Assume she ran one off race, and all other entrants ran two off races.  If you do, I calculate the odds of the odds of everyone in the field except Pleasant Home running more than 3 points off their top as 1 in 18,018.

God help anyone who wants to see the calculations.

I don\'t think you can figure out the probability of all the horses \'X\'ing except one by looking at all the \'X\'s within the group vs. all the starts. There are obvious problems like the one already identified where a couple of horses have a lot of Xs and skew the results.

You have to analyze it one horse at a time and get individual probabilities.  

I also think there\'s virtually no way to get at the probabilities of an individual horse \'X\'ing by only looking at its previous figures. You have to look at the reasons for the previous Xs and be aware that under today\'s conditions an X may be more or less likely.  

1. Some of the previous Xs could have been at the wrong distance, on off tracks, on the wrong surface, with a horrible trip etc... meaning that Xing is less likely under suitable conditions.  The opposite is also true.

2. Horses are more likely to X late in the season.

3. Horses are much more likely to X in a race like the Breeder\'s Cup/K Derby etc.. where there are many high quality horses and a large field because many horses never get into their preferred racing position. (# 4 and #5 are an extension of this)

4. A very competitive race development or fast pace could cause most of the horses in a race to run slower than expected (look at the Juvenile Filly race for a clear example). If only 1 or 2 avoided racing close to the action, then they would be the only 2 likely to duplicate their expected figures.

5. Multiple horses in a large field can get checked, run into traffic, etc...

I\'m sure there are plenty of other issues, but off the top of my head these are the most obvious.




   

Another 1st time Dutrow

http://www.drf.com/news/article/70132.html

[miff]

Class,

The insult to everyone\'s intelligence is that ALL the previous trainers of his unbelievable move up performers were incapable of detecting that these horses had problems up front or behind. Only Rick can detect these problems.I believe it.

Mike