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root
Posts:
56
Registered:
8/26/09


Horse racing
Posted:
Apr 1, 2013 4:18 PM


A friend of mine enjoys horse racing and is a regular small time bettor. He has roughly broken even over several decades of betting. I do not bet, but I am interested in the processes he uses to determine his bets.
Along those lines I came up with an idea to possibly increase his handicapping success. I asked him, for every race, to divide the horses into three groups, group Y included horses which had a chance of winning the race. Group M were those horses that could, maybe, win. And group N were horses he thought had no chance of winning. Of course, some races were won by horses in groups M and N.
After some time we computed the ratio of horses in group Y which went on the win the race. That ratio is W/Y where Y is the total number of horses ranked Y, and W is the number of those that did win. Some, even most, races have more than one Y candidates. It turns out the ratio of W/Y was 3/8 for my friend.
What I was hoping to achieve is a measure of what odds a Y rated horse should pay before that horse would be bet. It isn't enough to reckon that a horse is the best choice to win, the odds that horse pays must be high enough to overcome the uncertainty.
I have stumbled on to a conceptual error in my thinking. In some ways, W/Y does represent a probability but I am unable to rationalize that interpretation given that some horse must win every race, and that the apriori probabilities for the various horses must add up to 1. Given that most races have more than one Y candidate, their chances of winning are not independently related to W/Y. Clearly W/Y does not represent the probability that a Y candidate will win.
Everything becomes simpler if I interpret W/Y as the chance (probability) that in a given race with at least one Y rated horse, that a(any) Y rated horse will win. Given that interpretation I can say that if there are m Y rated horses in a given race then the probility that one of them will win is, on average, W/Y. Given that, and assuming that all Y rated horses are equivalent, then each Y rated horse has a probability of W/(m*Y) of winning. To be a good bet, then, the Y rated horse must pay better than m*Y/W.
I would appreciate any comments. Thanks.



