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Dark Horses, Long Shots, and Kentucky Derby Betting

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On the first Saturday in May, 20 three-year-old thoroughbreds run for the roses. If you want to make a buck on it, you must come to the dark side.

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The Kentucky Derby (CHDN) caps a month-long series of festivals in Louisville, a beautiful and hospitable city that mixes Southern graciousness with frontier ambition. Everyone says you cannot actually see the Derby, the grandstand and clubhouse are too far away and the infield is too crowded. Everyone is wrong. There are excellent vantages in both places. Yes, there are enormous crowds and a lot of drinking, so you need plenty of patience and cheerfulness to maneuver, but it's easy to have a wonderful time attending the race. Of course, it's even easier and cheaper to watch the Derby on television. Just don't put sugar in whiskey, however much people tell you it's traditional. Neat bourbon at room temperature with soda on the side is a far better choice.

Either way, the race is more fun if you have a little money at stake. People have studied horse-race betting for centuries, but the first serious academic attention came from Richard Griffith in 1949. Griffith was a pioneer in mathematical psychology and a lifelong Kentucky resident. His main finding was that betting on short-odds horses (that is, horses relatively likely to win the race, and therefore offering relatively low payouts like 2-1 or 3-1) was less unprofitable than betting on long shots (horses unlikely to win and therefore offering payouts like 20-1 or 50-1).

For example, if you had bet $2 on every favorite horse going back to the first Kentucky Derby in 1875, you would have $260 in winnings to show for your $274 in bets, a loss of about 5%. That is typical of betting on short-odds horses in general. There are some data and definitional problems with determining how much you would get from betting on all the long shots, but it's likely you would have lost something like 50% of the amount you bet. The reason that both bets are unprofitable is that the track takes out a fraction of all the money wagered. If you place your bet at something other than track odds, the bookie or Internet site taking the bet will extract some form of "vigorish" to cover expenses and make a profit. Therefore, betting on a randomly-selected horse will lose money in the long run.

Sixty-three years of academic research on horse racing has strengthened Griffith's observation. The "favorite-long-shot bias," as it has come to be called, is among the best-established real-world behavioral regularities about risk-taking. If you ask a non-gambling academic advice about betting on horses, the second most common answer you will get is "bet the favorite" (the most common answer is "don't bet").

This is the wrong interpretation of Griffith's finding for several reasons. The most important reason is that you're not trying to minimize your expected losses by betting the favorite with a -5% expectation; you're trying to find a bet with a positive expected value. The favorites are known quantities whose prospects are studied closely by many experts. Favorites seldom go off at odds that make them attractive.

Among the long shots, however, there may be "dark horses." A literal dark horse is one that's parentage is unknown. You won't find any of these in the Derby -- now officially titled the Derby presented by Yum Brands (YUM) -- since it's restricted to thoroughbreds, horses whose precise ancestry can be traced back for many generations. A figurative dark horse is one that is not well-known, a horse that's going off at long odds not because people know of reasons it probably won't win but because no one knows of any reason it might win. Although the average long shot bet will cost you 50% of the amount you wager, it's much easier to find an attractive dark horse bet among the long shots than it is to find a short-odds horse sufficiently underpriced to be a worthwhile bet.

Consider, for example a short-odds horse going off at 2-1 odds versus a long shot at 29-1. The first horse would have to win 1 time in 3, or 20 times in 60 to be a break-even bet. But since favorites are generally overpriced by 5%, the horse will probably have about 19 chances in 60 of winning. The 29-1 horse must win 1 time in 30 to break even, that's 2 times in 60. Since long shots generally cost 50% of the amount bet, its true probability of winning might be 1 in 60.

Now suppose you discover some private information that the horse's chance of winning is 1 in 20 (or 3 in 60) -- better than other people expect. That gives the first horse 22 chances in 60 of winning, and a bet on it has a positive expected return of 10%. The same information would give the second horse 4 in 60 chances of winning, and an expected return of 100% on investment.

Now the question is whether it's easier to find a favorite or a long shot that's chances of winning are underestimated by 1 in 20? In the first place, it doesn't have to be easier to find the long shot, it only has to be less than 10 times as hard, since you get 10 times the return if you succeed. Then consider that there are more long shots than short-odds horses, and that they're less well studied.

On the other hand, you might argue that the market assigning a 19/60 chance to a horse with 22/60 chance of winning is only a 15% error, while assigning 1/60 to a 4/60 horse is a 75% error and therefore less likely. For mathematical reasons I won't go into, this isn't the right calculation. In fact, it's natural to expect the absolute error in the favorite to be about 3.6 times as large as the absolute error in the long shot. In that case, the horse with a market estimate of 19/60 chance of winning is roughly as likely to have 30/60 chance of winning as the horse with a market estimate of 1/60 having 4/60. That still means we have a 50% expected profit from the favorite versus 100% from the long shot.

But this is not an argument to be settled by theory. The way to learn if it's possible to find attractive dark horses is to try to do it. This is one problem I have with the economic literature on the subject -- thousands of papers published, very few bets placed. It reminds me of Francis Bacon's famous story of the learned experts arguing for days over how many teeth a horse has, and when a humble stable boy suggests opening a horse's mouth and counting, the experts beat him and brand him a fool. There are many wealthy horse bettors with long-term records of success; studying their bets seems to me more productive than analyzing statistics about average bets.

There are two major problems with the average-bet data. The first is that it doesn't take into account the total amount wagered. We know that horses that go off at 29-1 odds win about 1 time in 60. That means if you bet $2 on each horse, you will get back only $1 per race on average. But what if races with attractive dark horses have more betting action, so that more is bet on the winners than the losers?

The second problem is the odds that a horse goes off at are not known to bettors at the time they place their bets. In typical pari-mutual betting (a system in which payouts are set by the amount bet on each horse rather than by a bookie), about half the money is placed within the three minutes before post time, and half long before that. Another strong empirical regularity is that the late money is the smart money.

Suppose that $50 is placed early, $5 on horse A and $5 on horse B (both are 9-1 horses, neither short-odds nor long shots). Then $50 comes in late, with $10 going to horse A and nothing to horse B. A horse that's odds shorten in late betting (like horse A) is more often a good bet than a horse that's odds lengthen (like horse B). Now horse A is a 5.7-1 short-odds horse and B is a 19-1 long shot. The economist notes that horse A is a better bet than horse B, which is true, but because A's odds shortened at the end, not because A is a short-odds horse. Betting on horses that are long shots in the morning line is a better strategy than betting on horses that go off at long odds (and the second strategy is impossible to implement, so of course it is the one economists prefer to study), because you benefit from picking some dark horses whose odds shorten late, and you avoid some overpriced short-odds horses whose odds lengthen late.

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