Berkeley STAT 157 - On Probabilistic Excitement of Sports Games

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Journal of Quantitative Analysis inSportsVolume 3, Issue 3 2007 Article 6On Probabilistic Excitement of Sports GamesJan Vecer∗Tomoyuki Ichiba†Mladen Laudanovic‡∗Department of Statistics, Columbia University, [email protected]†Department of Statistics, Columbia University, [email protected]‡Department of Statistics, Columbia University, [email protected]2007 The Berkeley Electronic Press. All rights reserved.On Probabilistic Excitement of Sports Games∗Jan Vecer, Tomoyuki Ichiba, and Mladen LaudanovicAbstractIn this paper we introduce a quantitative measure of the excitement of sports games. Thismeasure can be thought of as the variability of the expectancy of winning as a game progresses.We illustrate the concept of excitement at soccer games for which the theoretical win expectancycan be well approximated from a Poisson model of scoring. We show that in the Poisson model,higher scoring rates lead to increased expected excitement. Given a particular strength of a team,the most exciting games are expected with opponents who are slightly stronger. We apply thistheory to the FIFA World Cup 2006 games, where the winning expectancy was independentlyestimated by betting markets. Thus, it was possible to compute the expected and the realizedexcitement of each given game from the trading data.KEYWORDS: excitement, win expectancy, Markov model of scoring, intensity of scoring∗The authors would like to thank Benjamin Alamar, Mark Broadie, Rachel Schutt and the twoanonymous referees for helpful comments and suggestions which led to the improvement of themanuscript.1 IntroductionIn this paper we propose a novel measure of the excitement of a game that depends on thepredictability of the outcome of the game. Knowing the outcome of a game upfront does notchange the winning expectancy during the game, thus making it less exciting. On the otherhand, if the winner is undetermined up until the last moment with many swings in the scorethroughout the game, this constitutes a highly exciting situation. Thus it makes sense toassociate the excitement of the game with the variability of the win expectancy. The greaterthe variability, the more exciting is the game. In order to distinguish from other possiblemeasures of excitement, we call the variability of win expectancy probabilistic excitement.One can think of other measures of excitement, such as the number of viewers, or mea-sures which depend on the athletic performance of the players. Unfortunately, the numberof viewers does not necessarily reflect the quality or excitement of the game, but rather itis more associated with the importance of the game. The final game of a championshiptypically has the largest number of viewers, but it often does not turn out to be the mostexciting game of the season. Similarly, it is hard to quantify events such as a great shot ora great hit during the game, that are often associated with game excitement.Measuring excitement has potentially important consequences. One can argue that moreexciting games will be able to attract larger audiences, and thus create more commercialopportunities for advertisement or the promotion of the sport itself. Also within the gameitself, some events are more exciting than others, for instance a game-winning point at thelast minute of a match has a larger impact on excitement than a game-winning point thathappens in the beginning of the match. Although it is not possible to say how excitinga game will be beforehand, one can determine the expected excitement before the gamebegins. Usually games with closely matched teams with high scoring intensities (expectednumber of points scored during the game) tend to have higher expected excitement levels.Our approach to quantitatively measure the excitement via variability of the win ex-pectancy described in this paper is novel and it could be applied to all sports played withtwo competing teams. There are already some cases of sports specific attempts to measureexcitement. The problem is that for many sports, it is not entirely clear how to determine thewin expectancy during the course of the game. The evolution of the game can be modeledwith rather simplifying assumptions for only a small number of sports. The simplest andanalytically tractable models assume no memory during the game which suggests the useof Markov models. Sports whose evolution could be approximated well by Markov modelsinclude baseball, tennis, soccer, or hockey.Win expectancy in baseball has been extensively studied and is computed for instancein Tango et. al. [7]. Using data from real games, the website fangraphs.com lists statisticsof the variability of the winning chances, calling it Win Probability Added (WPA). Thisconcept fits our definition of the probabilistic excitement of the game. However, research onbaseball win expectancies uses the rather simplifying assumption that the play is betweentwo teams with equal strengths.Variability of win expectancy has been studied less for other sports, but there are severalpapers which determine the win expectancy itself during the game. For instance, tennis winexpectancy was determined in the paper of Newton et. al. [2]. Win expectancy in soccergames can be calculated from the theoretical Poisson model of scoring which assumes thememoryless property. As we show in this article, the assumption of no memory in the soccergame is reasonable and leads to results consistent with game data. It is also supportedby other works. See for instance Wesson [9]. Hockey is very similar to soccer in terms of1Vecer et al.: On Probabilistic Excitement of Sports GamesPublished by The Berkeley Electronic Press, 2007scoring (each goal counts as one point), and it can be also well approximated by the Poissonmodel as shown in Taylor [8]. Other sports are typically less tractable in terms of winexpectancy analysis, for instance football games have typically strong memory, and thus thecorresponding models of score evolution require more complexity.Win expectancy can be also obtained from betting markets such as Betfair or Trade-sports. It is possible to buy or sell a futures contract on the winning or losing of a particularteam, and the price of this contract can serve as an independent estimate of the win ex-pectancy. In this article we illustrate the concept of probabilistic excitement for soccer.We use data from games in FIFA World Cup Soccer 2006, where we can estimate the winexpectancies both from the


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