Apparently the idea explored in my prior post, which I thought was a novel one, is not so new. Mark Cramer long ago had asserted a critical corollary in handicapping; that the wager value of handicapping data is inversely proportional to its degree of use. Information that allows a handicapper to duplicate the public's laudable 33% win rate will also duplicate the public's 9% flat bet loss on favorites. How did I learn of Mark Cramer? I learned of Cramer from James Quinn's masterpiece, The Best of Thoroughbred Handicapping. This is by far the best book for those new to Handicapping as it provides a survey of the literature. That notwithstanding, however, Chapter 14 of said book is one of the worst I have read. After advocating for Optimal Betting via the Kelly Criterion in Chapter 2, Quinn seems to indicate that longer odds should have higher bets. While there is a more devastating reason that this is absolutely false, even the criterion he advocates teaches the exact opposite. Assuming a flat bet ROI of 10%, the percent of capital wagered via the Kelly Criterion is, for example, 10% on a 1:1 shot while it is 0.5% on a 20:1 shot.
Unfortunately for bettors, the Kelley Criterion is not usually the limiting factor for determining bet size, at least not for bettors with any appreciable bankroll. The tricky thing about pari-mutuel betting is that it allows the greedy gambler to destroy the overlay he meant to exploit. Placing a large bet on a long shot will significantly alter the odds.
The math is somewhat complicated and it is out of scope for me to present it here. The profit function is the bet size times the expectation value. The expectation value is the probability of winning times the odds being offered. The odds being offered are a function of the total wager pool, the wager pool on the horse in question, and the house cut. Two of these are a function of the bet size. Only by setting the derivative of the profit function to zero can the maxima of the profit function be determined.
Keep in mind too, that this can be done with the best of intentions but that the odds are still subject to change after you place your wager. It is also the case that the expectation values that feed into the Kelly Criterion optimal bet size are also a function of wager size. These two functions (profit function and optimum bet) can be plotted against bet size. There are generally four possibilities. There is no profitable bet, the Kelly Criterion dictates, the Profit Function Dictates, or the two functions intersect. In the event where a profitable bet is possible, I advocate 50 - 100% of the lesser of the three (the Kelly Optimum, the Intersection, or the Profit Function Maximum).
From what I have read in the handicapping literature, this is my new contribution (I think, I haven't stumbled across it yet). Note that the profit function derivative method can also be applied to Dr. Z's system for place and show betting on favorites.
This Material is Copyright (c) 2010 by EquineActuary.Com and Jim Sullivan
Tuesday, February 9, 2010
Thursday, January 21, 2010
Handicapping Horses is NOT About Picking Winners
There is a lot of literature available on handicapping horses. The focus, invariably, is on determining which horse is most likely to win a given race. However, as Robert Rowe points out, the favorite only wins about 33% of the time. The fact that the favorite usually loses teaches us something, however. The outcome of a horse race is probabilistic, not deterministic. The handicapper's job is to know the probability for each horse to win. With the probabilities in hand and the odds on the tote board, the handicapper can identify positive expectation bets.
Granted, players that bet on the favorites fare less poorly than the public at large (losing only 11% of each dollar wagered as opposed to 17% - 20%), however they are still losing. And although the favorite wins more often than any other horse, the favorite still loses 2 out of every 3 races. So while focusing on likely winners seems likely to be a good starting point, it is not enough. With the proliferation of sophisticated handicapping tools, the favorite's winning percentages have increased from 31% to 33% (i.e. the public has been right more often) but this hasn't changed the expectation value of betting on favorites because the odds on the favorites have been less favorable.
Each race has between 5 - 12 betting opportunities. Each opportunity will, on average, have a negative expectation between 17% and 20%. However there is variability in the expectation value. With a reasonable standard deviation, which past experience has demonstrated to exist, it is likely that within each race there are 0 - 2 positive expectation bets. A positive expectation bet is one where the probability of a horse's winning times the payback (including initial wager) is greater than or equal to the initial wager.
A good handicapper may also find may additional positive expectation wagers in the exactas, trifectas, and other exotic wagers. The key is to know the probability of each possible final outcome. Then the math is the same. Probability times payout must be greater than the layout. If a handicapper is correct in their assessment of the probabilities and makes only positive expectation wagers they will win in the long run. Andrew Beyer, a proponent but not a slave of speed handicapping, tells an excellent story of how he laid down several thousand dollars in double triple combinations to win 1/10 of a 1.3 million dollar prize. This was not done by luck, but by knowing which horses had decent probabilities of showing and then betting every possible combination of those horses.
This all sounds great in theory, but does it work? We weren't sure how we'd do going into our first season as NFL oddsmakers ( bestofblog.net ) but we finished at 62% against the spread (93 wins verses 57 losses). We're in the process of developing our system of determining the probabilities of each horse winning. We'll see how it goes and we'll keep you posted. Unlike the NFL, however, when we couldn't move the line and were therefore able to post our picks days before game-time, we're unlikely to do that here. Again, we'll see. Our season (Emerald Downs) doesn't begin until April.
Granted, players that bet on the favorites fare less poorly than the public at large (losing only 11% of each dollar wagered as opposed to 17% - 20%), however they are still losing. And although the favorite wins more often than any other horse, the favorite still loses 2 out of every 3 races. So while focusing on likely winners seems likely to be a good starting point, it is not enough. With the proliferation of sophisticated handicapping tools, the favorite's winning percentages have increased from 31% to 33% (i.e. the public has been right more often) but this hasn't changed the expectation value of betting on favorites because the odds on the favorites have been less favorable.
Each race has between 5 - 12 betting opportunities. Each opportunity will, on average, have a negative expectation between 17% and 20%. However there is variability in the expectation value. With a reasonable standard deviation, which past experience has demonstrated to exist, it is likely that within each race there are 0 - 2 positive expectation bets. A positive expectation bet is one where the probability of a horse's winning times the payback (including initial wager) is greater than or equal to the initial wager.
A good handicapper may also find may additional positive expectation wagers in the exactas, trifectas, and other exotic wagers. The key is to know the probability of each possible final outcome. Then the math is the same. Probability times payout must be greater than the layout. If a handicapper is correct in their assessment of the probabilities and makes only positive expectation wagers they will win in the long run. Andrew Beyer, a proponent but not a slave of speed handicapping, tells an excellent story of how he laid down several thousand dollars in double triple combinations to win 1/10 of a 1.3 million dollar prize. This was not done by luck, but by knowing which horses had decent probabilities of showing and then betting every possible combination of those horses.
This all sounds great in theory, but does it work? We weren't sure how we'd do going into our first season as NFL oddsmakers ( bestofblog.net ) but we finished at 62% against the spread (93 wins verses 57 losses). We're in the process of developing our system of determining the probabilities of each horse winning. We'll see how it goes and we'll keep you posted. Unlike the NFL, however, when we couldn't move the line and were therefore able to post our picks days before game-time, we're unlikely to do that here. Again, we'll see. Our season (Emerald Downs) doesn't begin until April.
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