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Originally Posted by blackthroatedwind
Another is that favorites are overbet in place pools for the most part and as they finish first or second around 50% of the time they will artificially deflate place payoffs on the other horse.
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Originally Posted by Dunbar
That's an interesting idea, but I'd like to see some data. It should be very easy to substantiate that. If it's true, then place bets placed on favorites should lose at more than the track take. (I can't think of any other definition of "overbet" that would apply here.)
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I'm re-thinking the highlighted part of what I wrote. It turns out to NOT be easy to substantiate it.
For a 15% track takeout, the average return for a $2 place bet should be 1.70. When btwind says that favorites are overbet in the place pool, I think that means that $2 bet on all favorites must return an average of less than 1.70.
Let's say we look at 500 favorites and take the average payout of a $2 place bet on each one, including using $0 payout for the losers. If our average comes out to be $1.64, which would suggest that place bets on favs lose at 18%, is that difference from $1.70 statistically meaningful? I don't think so. I estimate the standard error of the mean* on those 500 bets would be 0.14. That's more than twice as large the 0.06 difference between $1.70 and $1.64. That, in turn, means there there is a very good chance that the "real value" for place bets on favs is $1.70, even though our 500-bet average is $1.64. In other words, the difference of 0.06 would be statistically meaningless.
To get the standard error down to 0.03, you'd need to look at the place payoff of 10,000 favorites!
I'm putting the details and math in a footnote, so that if I'm making a blunder, someone can point it out.
--Dunbar
* If we looked at 500 $2 place bets on favorites, about half of them will return $0, and the rest will return $2.10 up to $7 or more. But about 2/3 of the payoffs would lie in the range of $0 to $5. So we can estimate the standard deviation (of place payouts on favorites) at about $3.
When you take an average of something, you can estimate the uncertainty in that value with "the standard error of the mean". You get the standard error by dividing the standard deviation by the square root of the number of values in your average. For 500 place bets, the square root of 500 is 22. So, the standard error on the mean would be $3.00/22 = 0.14.
If you are trying to demonstrate that 2 numbers are different, you'd like them to differ by AT LEAST one standard error, preferably two standard errors. In the case of distinguishing a 15% takeout from a 20% takeout, the difference in average values (0.06) is much less than even one standard error after 500 bets.
If we looked at 10,000 favs, then square root of 10,000 is 100. The standard error becomes $3/100 = 0.03. Now, an observed difference of 0.06 would be meaningful. (because it would be 2 standard errors.)