Pari-Mutuel Wagering
The probability estimate prediction market represents an improvement over what might have been the best earlier approach for aggregating bets on a particular outcome: pari-mutuel wagering, commonly used in horse racing. In pari-mutuel wagering, a bettor can place money on any possible outcome. For example, in a horse race, a bettor could place $1 on a particular horse that the bettor predicts will win the race. All bets are pooled, and after the race sponsor takes a percentage commission, the remaining money is distributed to the individuals who bet on the correct outcome. For example, suppose that $10,000 was bet in all, but only $500 was bet on the winning horse. If the commission rate is 10 percent, then $9,000 remains to be distributed among the individuals who collectively paid $500, so $18 is paid out for every $1 invested, producing a profit of $17.25 Pari-mutuel wagering provides incentives similar to those provided by the probability estimate prediction market. In the latter, one can profit by buying low or selling high–that is, by identifying tradable contracts that are mispriced. In pari-mutuel wagering, one may profit by betting on an outcome that too few people have bet on. For example, if a horse player expects that there is a 10 percent chance that a horse will win but less than 10 percent of the money in the pool has been placed on that horse, then the horse player might have an incentive to bet on the horse, depending on whether the difference is sufficiently large to outweigh the expected commission. If pari-mutuel wagering works sufficiently well, less money will be gambled on long shots than on favorites. Given any particular commission, it is straightforward to convert odds into probability estimates; they are two different ways of expressing the same information. Economic studies have shown that pari-mutuel wagering, indeed, is relatively efficient.26 That is, just as probability estimate prediction markets provide numbers that, experience suggests, truly can be interpreted as probability estimates, so will odds tend to correspond to the expected probability that any particular horse will win. This is true also for more complicated bets involving relatively large numbers of outcomes, for example, the trifecta. In order to win the trifecta, a bettor must correctly predict the first-, second-, and third-place winners of the race. At least one anomaly, however, is apparent, even in bets on a single race. In general, favorites tend to produce better payoffs than long shots, controlling for the fact that more money will be wagered on favorites than on long shots.27 Some evidence suggests that this is the result of some type of human cognitive bias,28 but there is also a relatively simple possible partial explanation.29 Bettors with relatively good information, based on either superior analytical abilities or particular facts known only to a few, often bet at the last minute. Otherwise, other bettors might see heavier-than-expected betting on a particular horse and add their own bets on that horse to the pool, thus reducing the horse’s odds. The horses that remain long shots after such last-minute betting can then be expected to return less per dollar bet than horses that attracted last-minute betting. A related point is that some bettors may be far more sophisticated than others. If a certain percentage of people bet on horses based on caprice or on flawed methodologies, more sophisticated bettors will have incentives to bet against them. The activity of the more sophisticated bettors should move the odds closer to true probability representations. Because of commissions, however, sophisticated bettors will not have an incentive to bet enough to compensate entirely for the actions of unsophisticated bettors. There is an additional incentive to place pari-mutuel bets at the last minute: information can change, so one might as well make a final decision at the last possible moment. A particularly important type of information is the amount that other bettors will place on a particular outcome, so even if one is confident that one’s probability assessment will not change before the start of a race, it may make sense to wait to determine which outcomes are relatively good bargains. This incentive to place bets at the last minute, however, suggests a significant weakness of pari-mutuel betting relative to prediction markets. Traders in a prediction market will generally have an incentive to trade on information at the earliest possible time, before the market has fully priced the information. As a result, probabilities in a prediction market should come close to reflecting all available information at any time. Moreover, the ability to buy and sell in a prediction market allows someone to profit on information without waiting for the conclusion of an event that might depend on many subsequent pieces of information as well. Someone who acquires information early can buy tradable contracts and then sell them once the information becomes generally known. With pari-mutuel betting, by contrast, some available information will not be priced efficiently until later, and bettors must wait for the event to conclude in order to profit on sound bets. We will see that one could design a pari-mutuel betting scheme that, like a probability estimate prediction market, produces incentives for information aggregation over time (see Chapter 3). There is relatively little incentive, however, for race tracks to adopt such a scheme, because it does not matter to race tracks whether the odds at any given time are as accurate as they can be. The media, however, generally have an interest in reporting the best available information, even for topics such as horse racing. It is interesting that prediction markets for horse racing also exist (for example, on TradeSports), and so the information from such markets might well be valuable to bettors. I do not know of any study comparing early betting on TradeSports to early odds, but it seems possible that TradeSports might be a slightly more accurate predictor well before a race. Of course, because the total amount bet on such prediction markets is relatively small, bettors with private information still might choose not to reveal their information by participating in the prediction market, and so the final odds at the track might still better reflect the outcomes of the race than those offered by TradeSports. At the least, newspapers that publish odds and betting lines for sporting events might consider publishing prediction market forecasts, especially when significant trading has occurred sufficiently in advance of the event to make the late edition. Newspapers sometimes claim that they publish odds for entertainment purposes. However dubious this claim, a sports fan might derive some value from obtaining predictions of upcoming events. Of course, prediction markets may suffer from a chicken-and-egg problem; newspapers will not publish prediction market results when readers do not understand what they mean or think them relevant, and readers will not learn when newspapers will not publish. Someday, though, it is quite possible that prediction market predictions will earn a place in the morning sports pages beside the scores and the standings. Sports pages might also include prediction market trading on past events. TradeSports allows betting not only before but also during athletic contests; pari-mutuel wagering, by contrast, cannot occur during the event. In a graph representing prediction market trading, the price lines show the progress of a game. Consider, for example, figure 1.5, which reports the TradeSports prices from a basketball game in which the favorite initially fell behind and then staged a comeback, winning in overtime. In contrast, a game in which the favorite performs about as expected can be visualized as more or less a straight line rising slightly to the maximum payoff (which, in TradeSports, is ten dollars rather than one dollar per contract). The more ups and downs the line has, the more exciting the game. In the game represented in figure 1.5, the excitement began only shortly before the two-hour mark. It may be a long time before readers of the sports pages do what readers of the business pages often do: look at a price graph for a snapshot of the day’s news. But such graphical representation can leave the media to focus on what the graph cannot convey: the individual plays and performances that make sports more interesting to watch than stock tickers.
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April 12th, 2010 at 3:11 pm
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May 13th, 2010 at 3:57 am
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