Iowa Electronic Markets and TradeSports
We can obtain an approximate sense of the accuracy of probability estimate prediction markets by eyeballing them. Let us consider the most venerable collection of prediction markets, the Iowa Electronic Markets, created by professors at the business school at the Figure 1.1 illustrates the prices at which contracts last traded in the market at the end of each trading day.16 It is clear that the prices of the Bush and the Kerry shares are virtual (though not perfect) mirror images of each other. This alone is not enough to validate the results, of course, but if the Bush and the Kerry shares appeared to move inconsistently, that might furnish an argument that prediction market predictions appear irrational or random. The price lines also appear rational when compared against actual events in the election campaign. Although they cover only four months of the election cycle, the price lines appear at least roughly to correspond to the candidates’ chances of victory as indicated by the polls. Figure 1.2 shows Bush’s polling share (excluding undecided or third-party voters) for all major national polls.17 The race appeared to be quite close until Bush began to take a lead at about the beginning of September, possibly in part as a result of aggressive advertising by a group called Swift Boat Veterans for Truth that questioned Kerry’s record in the Vietnam War, though this lead dwindled through mid-October. The spikes in figure 1.1 are greater than the spikes in figure 1.2 because a small difference in poll numbers can result in a large difference in probabilities. Had Bush been leading Kerry 60 percent to 40 percent in the polls, after all, his victory would have been virtually certain on Election Day. Electoral trends are somewhat easier to deduce with the prediction market forecasts of figure 1.1 than with the polls of figure 1.2, because trends are accentuated and because there is less noise from anomalous polling results. A better assessment of overall predictive accuracy can be obtained by comparing predictions with results across a range of markets. Figure 1.3 reports results from twenty-five winner-take-all markets sponsored by the Iowa Electronic Markets. Wolfers and Zitzewitz collected data about the last trade each day for each tradable contract in each of these markets, producing a total of more than twenty-three thousand observations.18 For each one-percentage-point market price interval, they then counted the proportion of times the event being predicted in fact occurred. For example, if prediction markets are accurate, then one would expect contracts priced at about fifty cents to result in payoffs about 50 percent of the time and contracts priced at about eighty cents to result in payoffs about 80 percent of the time. The data appear to reflect this expectation. Higher contract prices appear to bear an approximately linear relationship to probabilities. For comparison purposes, figure 1.3 includes a forty-five-degree line that would represent perfect prediction accuracy. Figure 1.3 does show a variety of anomalies. But this is because in a sample of only twenty-five elections, a few unexpected election outcomes or dramatic shifts mid-election can affect a relatively large number of data points. Figure 1.4 thus shifts from the Iowa Electronic Markets to TradeSports, a for-profit exchange that includes trading on a wide variety of events, including athletic and political contests. For example, for a particular baseball game, TradeSports might include contracts concerning whether a particular team will win, whether the total score will exceed a particular number, and whether a particular team will win by at least a specified number of points. It thus serves as a market alternative to more traditional forms of sports betting. Figure 1.4 reflects 145,388 trades on a total of 1,508 contracts determined by the outcome of Major League Baseball games that TradeSports decided to feature in 2005. With this larger sample, the data appear to reflect more consistently the forty-five-degree line that one would expect if prices can be interpreted as probabilities.19 Two significant caveats are worth making. First, we cannot guarantee that the regularities observed in this case will be perfectly replicated in other markets. In an analysis of 384,655 trades on National Football League games over the course three seasons, Richard Borghesi found some small but systematic anomalies.20 Borghesi found that on average, prices decreased from early values by approximately 3.42 ticks (34.2¢ on a $10 contract), indicating that bettors generally are overly optimistic about the probability that the contract will pay off, that is, that the named team will win. By combining TradeSports data with play-by-play football data, Borghesi shows that the market tends to underreact to information. In the minute following a touchdown, the market continues the rise caused by the touchdown itself, and, indeed, the trend continues for another nine minutes, with additional average increases in price for a touchdown for the named team of 0.14 ticks. Although these findings are statistically significant, they imply only small deviations from accurate probability estimates, so prices still can be said at least roughly to reflect probabilities. One possible explanation for the poor performance of these markets relative to the markets illustrated in figure 1.4 is that the figure includes only “featured games,” which may have higher liquidity and receive more careful attention from traders. Second, that the prices of contracts reflect probabilities does not mean that the prediction market is particularly accurate. If for each of a large number of athletic contests I made a trade at fifty cents on a randomly selected team, then I would win about 50 percent of the time (and lose a great deal of money on a Web site that charges commissions). Although it could be said that my trades reflect accurate probabilities, they reflect guesses or no information at all. Given prices that correspond closely to probability estimates, the higher the proportion of trades on the extremes of a probability distribution, the more confidence a prediction market will inspire. For example, if the predictions implied by prices for a season’s baseball games were almost all below five cents or above ninety-five cents a day before the games, and those prices still turned out to reflect actual probabilities, that would either be truly impressive or reveal an unusually imbalanced level of baseball competition. It is possible to derive formulas that can be used to compare sets of probability predictions (see Chapter 4), but in the absence of a set of predictions from some other source to compare to those used by TradeSports, one cannot say whether these are particularly good or particularly bad. What one can say with confidence is that if there are methodologies that can produce predictions considerably better than those used by TradeSports, the gap should narrow over time. The reason is that someone with a superior methodology has a profit incentive to trade on TradeSports. If the methodology is superior, then it should be profitable. The trading on the methodology might have at least some effect on prices of transactions not involving the party practicing the methodology, if third parties take the trades into account in formulating their own probability assessments. If trades have no effect on prices of transactions by other traders, then the individual with the better methodology will make more and more money over time and presumably will be willing to risk progressively higher amounts in the market. Eventually, then, this trader would be responsible for a high volume of trading. Betting pursuant to a successful methodology will nudge market predictions in the direction suggested by that methodology. This does not mean that at any given time the predictions of TradeSports will be better than what any given person could produce. Because of commission charges and the costs of risk, one will only have an incentive to place bets when one’s methodology allows for a considerable improvement in the market price. It will not be worth paying a commission of four cents per tradable contract to improve a prediction by less than four cents per tradable contract. But given current commission levels, a risk-averse participant will generally trade on information when the bet will improve the probability by 0.8 percentage points or more.21 This suggests that, at least if trading on a prediction market actually occurs at regular intervals, the prices at which the trades occur should be close to the best that can be produced by any other known method, on average and in the long run. Sometimes, someone might be hesitant to trade because of uncertainty about whether the market price already incorporates insights from the methodology, but at least those with the best information will trade when they have reason to believe that market prices appear markedly wrong. The strongest theoretical defense of prediction markets it that traders can profit from information suggesting that the market price is wrong, yet at any given time they have not done so. Current trading prices in prediction markets in which considerable trading occurs provide roughly accurate estimates of the probability that a designated event will occur. One caveat is that at any given time, some traders might be able to beat the market with careful analysis. But there may be no uncontroversial way of identifying the people who are most likely to do so, and a prediction market allows these market-beaters to push the market price in the right direction up to the limits of their risk tolerance. Another caveat is that prediction markets are superior only to known methodologies, and it is possible that other predictive institutions might produce better results. But prediction markets provide at least a modest financial incentive for individuals to identify better methodologies and apply them.22 It is interesting that prediction markets have proved successful even in the absence of a financial incentive. Some prediction markets use “play money” or virtual currencies rather than real cash, in part because of regulatory obstacles to real-money markets. And yet many of those play-money markets have been shown to have considerable success. For example, four economists compared the accuracy of NewsFutures, which uses play money, with TradeSports in predicting the outcome of National Football League games in 2003 and found that neither performed better than the other.23 Similarly, the Hollywood Stock Exchange, a play-money market that predicts the box office returns of various 
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