Learning Performance of Prediction Markets with Kelly Bettors

In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called "wisdom of crowds" effect, which roughly says that the average of participants performs much better than the average participant. The market price---an average or at least aggregate of traders' beliefs---offers a better estimate than most any individual trader's opinion. In this paper, we ask a stronger question: how does the market price compare to the best trader's belief, not just the average trader. We measure the market's worst-case log regret, a notion common in machine learning theory. To arrive at a meaningful answer, we need to assume something about how traders behave. We suppose that every trader optimizes according to the Kelly criteria, a strategy that provably maximizes the compound growth of wealth over an (infinite) sequence of market interactions. We show several consequences. First, the market prediction is a wealth-weighted average of the individual participants' beliefs. Second, the market learns at the optimal rate, the market price reacts exactly as if updating according to Bayes' Law, and the market prediction has low worst-case log regret to the best individual participant. We simulate a sequence of markets where an underlying true probability exists, showing that the market converges to the true objective frequency as if updating a Beta distribution, as the theory predicts. If agents adopt a fractional Kelly criteria, a common practical variant, we show that agents behave like full-Kelly agents with beliefs weighted between their own and the market's, and that the market price converges to a time-discounted frequency. Our analysis provides a new justification for fractional Kelly betting, a strategy widely used in practice for ad-hoc reasons. Finally, we propose a method for an agent to learn her own optimal Kelly fraction

To what extent can new web-based technology improve forecasts? Assessing the economic value of information derived from Virtual Globes and its rate of diffusion in a financial market

As the rate of information availability increases, the ability to use web-based technology to improve forecasting becomes increasingly important. We examine Virtual Globe technology and show how the arrival of unprecedented types of web-based information enhances the ability to forecast and can lead to significant, measurable economic benefits. Specifically, we use market prices in a betting market over an eighteen-year period to examine how new elevation data from Virtual Globes (VG) enabled improved forecasting decisions and we explore how this information diffused through the betting market. The results demonstrate how short-lived, profitable opportunities arise from the arrival of novel information, and the speed at which markets adapt over time to account fully for new data

The wisdom of crowds: predicting a weather and climate-related event

types: ArticleArticle published in open-access journal, Judgment and Decision Making, vol. 8(2), pp. 91-105Environmental uncertainty is at the core of much of human activity, ranging from daily decisions by individuals to long-term policy planning by governments. Yet, there is little quantitative evidence on the ability of non-expert individuals or populations to forecast climate-related events. Here we report on data from a 90-year old prediction game on a climate related event in Alaska: the Nenana Ice Classic (NIC). Participants in this contest guess to the nearest minute when the ice covering the Tanana River will break, signaling the start of spring. Previous research indicates a strong correlation between the ice breakup dates and regional weather conditions. We study betting decisions between 1955 and 2009. We find the betting distribution closely predicts the outcome of the contest. We also find a significant correlation between regional temperatures as well as past ice breakups and betting behavior, suggesting that participants incorporate both climate and historical information into their decision-making

When do betting odds best represent the actual outcomes? Predicting NHL results based on moneyline odds movement

The sports betting market has grown quickly over the past the few decades mostly due to the digitalization of the business. The bookmakers have moved online from the physical locations. The market has thus globalized, and the competition has increased, forcing the bookmakers to produce more accurate estimates about the events to keep up with the competition. This study investigates the accuracy of NHL moneyline betting odds, in predicting the actual outcomes of games throughout the time that the betting events are open. The dataset covers three full seasons from 2015 to 2018. The odds are collected at 5 different time points for each game and the differences in the predictive power of time points is analyzed. Then, the odds and their movement is investigated further to see if there are profitable betting strategies to be found based solely on information about odds movement. The tests related to the prediction accuracy of the odds reveal that there are no statistically significant differences between the prediction accuracy for different time points. Aggregate results are rather consistent though in showing that before the day of the game, the estimates implied by the odds aren’t quite as accurate as they are during the game day. The regression tests further indicate that when the implied probability of a selection grows, the objective probability grows at a higher rate, meaning that there’s a Favorite-Longshot Bias in the market. This means that betting on a more likely outcome yields better returns on average. The tests for finding profitable betting strategies further enforce the notion of Favorite-Longshot Bias and subsequently all of the consistently profitable betting strategies, that are found, involve only betting on favorites. The data about the odds movement between time points and splitting the teams to favorites and underdogs reveals that betting on favorite teams who have had their odds rising in a given time point interval, yields a profit for 80% of the intervals. The margins are so small that none of the returns for profitable strategies are significantly larger than zero in a statistical sense but the difference to the average bookmaker margin is more significant. According to the analysis about different staking strategies, for this kind of betting system where no estimate is calculated individually for each game, simple staking strategies of betting a fixed amount or to win fixed amount, yielded the best balance of capital growth and risk. The study concludes that there is little difference in predictive power of NHL moneyline betting odds at different time points throughout the life cycle of betting events. Based on the results it’s clear that the bookmaker margin isn’t allocated evenly between favorites and underdogs and there’s an apparent Favorite-Longshot Bias in the market, which is in contrast with previous research about NHL moneyline odds. The bias logically leads to favorites being the side that offers better returns and betting on favorites with rising odds offers returns that consistently beat the bookmaker margin and are also marginally profitable

Sports betting: a new asset class to bet on

This dissertation has the aim to present a complete overview of the current features and activities related to the sports betting industry and to explain the reasons why it can be considered a new asset class to invest on. The first chapter explains the main features of both fixed-odds and exchange betting market, the second describes the activity of sport trading, while the third presents a deep investigation concerning the market efficiency. Chapter 4 shows the arbitrage opportunities implementable in this market, that come from the efficiency study of the previous chapter. Before the conclusion, a personal study about the value betting arbitrage opportunity is presented, confirming that abnormal returns are achievable

Pari-mutuel betting markets: racetracks and lotteries revisited

This survey discusses the state of the art in research in racetrack and lottery investment markets. Market efficiency and the pricing of various wagers are studied along with new developments since the Thaler & Ziemba (1988) review. The weak form inefficient market pricing approach using stochastic programming optimization models changed racetrack betting from handicapping to a financial market allowing professional syndicates to operate as hedge funds. Topics discussed include arbitrage and risk arbitrage, syndicates, betting exchange rebates, behavioral biases, and fundamental and mispricing information in racetrack and lottery markets. Similar models can be used to successfully trade stock market anomalies. Supplemental Materials are included online

Parimutuel betting markets: racetracks and lotteries revisited

This paper surveys the state of the art in research in racetrack and lottery markets. Market efficiency and the pricing of various wagers is studied along with new developments since the Thaler and Ziemba JEP review. Other sports betting markets are also discussed. The role of syndicates, betting exchange rebates, behavioral biases and fundamental information is discussed

Isoelastic Agents and Wealth Updates in Machine Learning Markets

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012