Dark Horses, Long Shots, and Kentucky Derby Betting
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.
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.
So how do you find attractive Derby dark horses? It won't be among the 13 horses that have received serious Derby attention since the beginning of the year. These are Alpha, Creative Cause, Dullahan, El Padrino, Ever So Lucky, Gemologist, Hansen, I’ll Have Another, Liaison, Rousing Sermon, Sabercat, Take Charge Indy, and Union Rags. Five other horses, Daddy Nose Best, Howe Great, Optimizer, Prospective, and Went the Day Well, came on the scene later, but are known quantities now. Not all of these horses will actually be in the Derby (the runners are announced on Wednesday, May 2), but if they are, their prospects will be well-known. The only way I know to make money betting these horses is to be an expert handicapper or have inside information.
There will be at least two Derby runners not on the list above. This year for the first time there is an intriguing new category for dark horse bettors. The Derby will list four “also eligible” horses that will be offered the chance to run if any of the 20 starters drop out. Owners of many good horses will not accept these slots due to the trouble and expense of preparing for a Derby run without knowing if their horse will be invited, and also due to the disadvantage of having the highest post position. If one or more of these horses run, especially if the decision is made late, they're likely to be the darkest dark horses in recent Derby memory.
What do you look for in a dark horse? The most important thing is shortening odds, especially in the last few minutes before post time. It also helps to know a little bit about handicapping. The traditional science relies on seven criteria:
1. Is the horse trying to win? I'm not talking about fixed races here (although that does happen), but about trainers putting horses in races for experience without preparing or pushing them hard to win. Owners sometimes like to lengthen the odds on their horses by letting them run easy in a few races before the owner places a large bet and makes an all-out effort to win. One of the pleasant things about Derby betting is that a Derby victory is so valuable that everyone is trying to win, so this is not a factor.
2. Speed. Surprisingly to most people, how fast a horse can run is not the most important factor in racing, but it does matter. There are elaborate systems, the most popular is one devised by Andrew Beyer, for estimating a horse's speed from previous races. If a horse is at long odds because it doesn't have speed, it's a poor dark horse choice. The circumstances that allow a slow horse to win the Derby are essentially random, and their probability is reasonably well-known. You won't find great value here.
3. Pace. There are horses with early speed that like a low post position so they can spring into an early lead, hug the rail (and thereby have the shortest path to the finish line), and hold off all competitors. Other horses are closers who let other horses burn themselves out fighting for the early lead, and then they gallop past everyone on the outside in the stretch. There are permutations and variations of these styles. Depending on the mix of horses in a race, one style or another can have an advantage. Pace is also influenced by weather, track condition, and length (the Derby at one and one-quarter miles, is a relatively long race). If a horse is a long shot in part because it is deemed to have the wrong style, it can be a good dark horse choice. It takes a lot of attention to determine style, and races do not always go the way the experts expect.
4. Class. This refers to the caliber of the competition in a horse's previous races. Horses moving up in class are suspect, and often start with long odds relative to their ratings on other handicapping factors (horses moving down in class are tricky, but there aren't any of these in the Derby because there is no higher class). Derby favorites are generally the horses that have won the important two-year-old and pre-Derby three-year-old races, running against horses of Derby quality. The long shots consist of the losers from these races, along with horses that have never run against top competition. It is the second group that provides the best dark horses for bettors.
6. Breeding. With young and relatively untested horses in the Derby, handicappers give a lot of weight to the horse's ancestry. How many Derby winners is it descended from and is its history similar to any of them? For a good dark horse choice, the worse the breeding, the better. You don't want a horse that's just like a previous winner, but slower. You want a horse that's running is unpredictable.
7. Trainer and jockey. Trainers and jockeys play important roles in determining the winner of races. On top of that, the best trainers get the best horses and hire the best jockeys to ride them. This one is trickier than the others. On one hand, you like a new trainer or jockey, because people know less about how good they are. But you won't find many of these in the Derby, and they may be running more to make a name for themselves than because they have much chance of winning. But if a top trainer brings a long shot to Louisville, or a top jockey agrees to ride a long shot, they probably know something you don't.
A longshot paying better than 20-1 has won 14 of the 137 Derbys, about 10% of the time, with an average payout of 34-1. If you bet all long shots, that's a terrible record. There are about seven 20-1 or worse horses running in an average year, so you have to bet on 70 horses for each 34-1 payout. That's a -50% return. On the other hand, if you could identify each year the long shot that is going to win, assuming a long shot does win, you would only have to bet on 10 horses for each payout, a positive 250% return.
In recent times, the picture is better. Six of the last 17 Derbys have been won by long shots, namely in 1995 (Thunder Gulch at 24.50-1), 1999 (Charismatic at 31.30-1), 2002 (War Emblem at 20.50-1), 2005 (Giacomo at 50.30-1), 2009 (Mine That Bird at 50.60-1), and 2010 (Super Saver at 20.90-1). Over that stretch, it was actually slightly profitable to bet all long shots, but it was probably an anomaly. Still, it shows that you don't have to be ashamed of looking for dark horses. You'll probably lose, but you have a fighting chance of making a bet with positive expected value, unlike the people who bet on the favorites, who are more likely to win but less likely to have made positive expected value bets. And if you carry the lesson over to life, to look for the dark horses that are good bets and not worry about failures or other people's opinions, you can be the biggest winner of all.