Abstract
There is much interest in studying the hot hand behavior of individuals and teams in sports. We collect success/failure data for each of the hitters in a particular baseball season, focusing on the spacings or number of at-bats between consecutive successes. Consistent and streaky models are defined on the basis of the underlying geometric probabilities and a Bayes factor statistic is developed to compare the two models. By looking at the ensemble of test statistics over all players, we see if the patterns of streakiness differ from what one would predict from a consistent hitting model. An interesting observation from this study is the pattern of streakiness depends on how one defines a success in a plate appearance.
References
Albert, J. 2008. “Streaky Hitting in Baseball.” Quantitative Analysis of Sports 4:1.10.2202/1559-0410.1085Search in Google Scholar
Albert, J. 2005. “A Batting Average: Does it Represent Ability or Luck?.” STATS 44:Fall-Winter issue 3–6.Search in Google Scholar
Albert, J. 2006. “Pitching Statistics, Talent and Luck, and the Best Strike-out Seasons of All-Time.” Journal of Quantitative Analysis of Sports 2.Search in Google Scholar
Albright, S. 1993. “A Statistical Analysis of Hitting Streaks in Baseball.” Journal of the American Statistical Association 88:1175–1183.10.1080/01621459.1993.10476395Search in Google Scholar
Bar-Eli, M., S. Avugos, and M. Raab. 2006. “Twenty Years of Hot Hand Research: Review and Critique.” Psychology of Sport and Exercise 7:525–553.10.1016/j.psychsport.2006.03.001Search in Google Scholar
Dorsey-Palmateer, R. and G. Smith. 2004. “Bowlers Hot Hands.” The American Statistician 38–45.10.1198/0003130042809Search in Google Scholar
Efron, B. and C. Morris. 1975. “Data Analysis Using Steins Estima- tor.” Journal of the American Statistical Association 70:311–319.10.1080/01621459.1975.10479864Search in Google Scholar
Gilovich T., R. Vallone, and A. Tversky. 1985. “The Hot Hand in Basket-ball: on the Misperception of Random Sequences.” Cognitive Psychology 17:295–314.10.1016/0010-0285(85)90010-6Search in Google Scholar
Good, I. J. 1967. “A Bayesian significance test for multinomial distributions.” Journal of Royal Statistical Society B 399–431.10.1111/j.2517-6161.1967.tb00705.xSearch in Google Scholar
Jeffreys, W. 1961. Theory of Probability, Oxford Press.Search in Google Scholar
Kass, R. and A. Raftery. 1995. “Bayes Factors.” Journal of the American Statistical Association 90:773–795.10.1080/01621459.1995.10476572Search in Google Scholar
Kass, R. and S. Vaidyanathan. 1992. “Approximate Bayes Factors and Orthogonal Parameters, with Application to Testing Equality of Two Binomial Proportions.” Journal of the Royal Statistical Society, Series B: 129–144.Search in Google Scholar
Klaassen, F. and J. Magnus. 2001. “Are Points in Tennis Independent and Identically Distributed? Evidence from a Dynamic Binary Panel Data Model.” Journal of the American Statistical Association 96:500–509.10.1198/016214501753168217Search in Google Scholar
Makri, F., A. Phillippou, and Z. Psillakis. 2007. “Shortest and Longest Length of Success Runs in Binary Sequences.” Journal of Statistical Planning and Inference 137(7): 2226–2239.10.1016/j.jspi.2006.07.007Search in Google Scholar
Muselli, M. 1996. “Simple Expressions for Success Run Distributions in Bernoulli trials.” Statistics and Probability Letters 31:121–128.10.1016/S0167-7152(96)00022-3Search in Google Scholar
Raftery, A. 1996. “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalised Linear Models.” Biometrika 129–144.10.1093/biomet/83.2.251Search in Google Scholar
Reifman, A. 2012. Hot Hand: The Statistics Behind Sports’ Greatest Streaks, Potamac Books.Search in Google Scholar
Sevcan, D. and S. Eryilmaz. 2010. “Success Runs in a Sequence of Exchangeable Binary Trials.” Statistical Papers 51(4):959–973.10.1007/s00362-008-0191-7Search in Google Scholar
Tversky, A. and T. Gilovich. 1989. “The Cold Facts about the Hot Hand in Basketball.” Chance 2:16–21.10.1080/09332480.1989.11882320Search in Google Scholar
Wardrop, R. L. 1995. “Simpsons Paradox and the Hot Hand in Basketball.” American Statistician 49:2428.10.2307/2684806Search in Google Scholar
Yang, T. Y. 2004. “Bayesian binary segmentation procedure for detecting streakiness in sports.” Journal of the Royal Statistical Society, Series A 167:627–637.10.1111/j.1467-985X.2004.00484.xSearch in Google Scholar
Zhang, Y., E. Bradlow, and D. Small. 2012. “New measures of clumpiness for incidence data.” Working Paper, Wharton School, University of Pennsylvania.Search in Google Scholar
©2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Masthead
- Analysis of the NCAA Men’s Final Four TV audience
- Are the official world golf rankings biased?a
- The effect of batting during the evening in cricket
- Looking at spacings to assess streakiness
- Around the goal: examining the effect of the first goal on the second goal in soccer using survival analysis methods
- A proposed general rating system for which the Colley Matrix Rating System is a special case
- Ranking rankings: an empirical comparison of the predictive power of sports ranking methods
- Bicycle tours: modeling the perceived exertion of a daily path