A Bayesian stochastic model for batting performance evaluation in one-day cricket

Theodoro Koulis 1 , Saman Muthukumarana 1 ,  and Creagh Dyson Briercliffe 1
  • 1 Department of Statistics, University of Manitoba, Winnipeg Manitoba, Canada
Theodoro Koulis, Saman Muthukumarana and Creagh Dyson Briercliffe

Abstract

We consider the modeling of individual batting performance in one-day international (ODI) cricket by using a batsman-specific hidden Markov model (HMM). The batsman-specific number of hidden states allows us to account for the heterogeneous dynamics found in batting performance. Parallel sampling is used to choose the optimal number of hidden states. Using the batsman-specific HMM, we then introduce measures of performance to assess individual players via reliability analysis. By classifying states as either up or down, we compute the availability, reliability, failure rate and mean time to failure for each batsman. By choosing an appropriate classification of states, an overall prediction of batting performance of a batsman can be made. The classification of states can also be modified according to the type of game under consideration. One advantage of this batsman-specific HMM is that it does not require the consideration of unforeseen factors. This is important since cricket has gone through several rule changes in recent years that have further induced unforeseen dynamic factors to the game. We showcase the approach using data from 20 different batsmen having different underlying dynamics and representing different countries.

  • Akaike, H. 1973. “Information Theory and an Extension of The Maximum Likelihood Principle.” in 2nd International Symposium on Information Theory, 267–281.

  • Albert, J. 2002. “Hitting with Runners in Scoring Position.” Chance 15:8–16.

    • Crossref
  • Bailey, M. and S. Clarke. 2004. “Market Inefficiencies in Player Head to Head Betting on The 2003 Cricket World Cup.” pp. 185–202 in Economics, Management and Optimization in Sport, edited by S. Butenko, J. Gil-Lafuente, and P. Pardalos. Heidelberg: Springer-Verlag.

    • Crossref
  • Bailey, M. and S. Clarke. 2006. “Predicting the Match Outcome in One Day International Cricket Matches, While The Match is in Progress.” Journal of Science and Sports Medicine 5:480–487.

  • Barbu, V. and N. Limnios. 2008. “Semi-Markov Chains and Hidden Semi-Markov Models Toward Applications: Their Use in Reliability and DNA Analysis, Lecture Notes in Statistics-Springer, Springer Science + Business Media.

  • Beaudoin, D. 2003. The Best Batsmen and Bowlers in One-Day Cricket. Master’s thesis, Simon Fraser University, Department of Statistics and Actuarial Science.

  • Brewer, B. J. 2008. “Getting Your Eye in: A Bayesian Analysis of Early Dismissals in Cricket,” pre-print, arXiv:0801.4408v2 [stat.AP].

  • Carlin, B. P. and S. Chib. 1995. “Bayesian Model Choice via Markov Chain Monte Carlo Methods.” Journal of the Royal Statistical Society. Series B (Methodological) 57:473–484.

    • Crossref
  • Congdon, P. 2006. “Bayesian Model Choice Based on Monte Carlo Estimates of Posterior Model Probabilities.” Computational Statistics & Data Analysis 50:346–357.

    • Crossref
  • Daniyal, M., T. Nawaz, I. Mubeen, and M. Aleem. 2012. “Analysis of Batting Performance in Cricket Using Individual and Moving Range (mr) Control Charts.” International Journal of Sports Science and Engineering 6:195–202.

  • de Campos, C. P. and A. Benavoli. 2011. “Inference with Multinomial Data: Why to Weaken the Prior Strength,” pp. 2107–2112 in Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence..

  • de Silva, B. and T. B. Swartz. 1997. “Winning the Coin Toss and The Home Team Advantage in One-Day International Cricket Matches.” New Zealand Statistician 32:16–22.

  • Frühwirth-Schnatter, S. 2010. Finite Mixture and Markov Switching Models. Springer Series in Statistics, Springer.

  • Green, P. J. 1995. “Reversible Jump Markov chain Monte Carlo Computation and Bayesian Model Determination.” Biometrika 82:711–732.

    • Crossref
  • Hintze, J. L. and R. D. Nelson. 1998. “Violin plots: A Box plot-Density Trace Synergism.” The American Statistician 52:181–184.

  • Jensen, S. T., B. B. McShane, and A. J. Wyner. 2009. “Hierarchical Bayesian Modeling of Hitting Performance in Baseball.” Bayesian Analysis 4:631–652.

    • Crossref
  • Kass, R. E. and A. E. Raftery. 1995. “Bayes Factors.” Journal of the American Statistical Association 90:773–795.

    • Crossref
  • Kimber, A. C. and A. R. Hansford. 1993. “A Statistical Analysis of Batting in Cricket.” Journal of the Royal Statistical Society. Series A (Statistics in Society) 156:443–455.

    • Crossref
  • Lemmer, H. H. 2004. “A Measure for The Batting Performance of Cricket Players.” South African Journal for Research in Sport, Physical Education and Recreation 26:55–64.

  • Lemmer, H. H. 2007. “The Allocation of Weights in The Calculation of Batting and Bowling Performance Measures.” South African Journal for Research in Sport, Physical Education and Recreation 29:75–85.

  • Lemmer, H. H. 2011. “The Single Match Approach to Strike Rate Adjustments in Batting Performance Measures in Cricket.” Journal of Sports Science & Medicine 10:630–634.

  • Martin, J. 1967. Bayesian Decision Problems and Markov Chains. Publications in Operations Research, Wiley.

  • Rabiner, L. R. 1989. “A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition.” Proceedings of the IEEE 77:257–286.

    • Crossref
  • Raj, B. 2002. “Asymmetry of Business Cycles: The Markov-Switching Approach.” pp. 687–710 in Handbook of Applied Econometrics and Statistical Inference, edited by A. Ullah, A. Wan, and A. Chaturvedi. New York: Marcel Dekker.

  • Roy, D. and R. Gupta. 1992. “Classifications of Discrete Lives.” Microelectronics Reliability 32:1459–1473.

    • Crossref
  • Ryden, T. 2008. “EM versus Markov Chain Monte Carlo for Estimation of Hidden Markov Models: A Computational Perspective.” Bayesian Analysis 3:659–688.

    • Crossref
  • Sadek, A. and N. Limnios. 2002. “Asymptotic Properties for Maximum Likelihood Estimators for Reliability and Failure Rates of Markov Chains.” Communications in Statistics-Theory and Methods 31:1837–1861.

    • Crossref
  • Schwarz, G. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics 6:461–464.

    • Crossref
  • Scott, S. L. 2002. “Bayesian Methods for Hidden Markov Models: Recursive Computing in the 21st Century.” Journal of the American Statistical Association 97:337–351.

    • Crossref
  • Swartz, T. B., P. S. Gill, D. Beaudoin, and B. de Silva. 2006. “Optimal Batting Orders in One-Day Cricket.” Computers and Operations Research 33:1939–1950.

    • Crossref
  • Swartz, T. B., P. S. Gill, and S. Muthukumarana. 2009. “Modelling and Simulation for One-Day Cricket.” Canadian Journal of Statistics 37:143–160.

    • Crossref
  • Tucker, B. C. and M. Anand. 2005. “On the Use of Stationary versus Hidden Markov Models to Detect Simple versus Complex Ecological Dynamics.” Ecological Modelling 185:177–193.

    • Crossref
  • Valero, J. and T. B. Swartz. 2012. “An Investigation of Synergy Between Batsmen in Opening Partnerships.” Sri Lankan Journal of Applied Statistics 13:87–98.

    • Crossref
  • van Staden, P. 2009. “Comparison of Cricketers’ Bowling and Batting Performances using Graphical Displays.” Current Science 96:764–766.

  • van Staden, P., A. Meiring, J. Steyn, and I. Fabris-Rotelli. 2010. “Meaningful Batting Averages in Cricket.” pp. 75–82 in Proceedings of the 52nd Annual Conference of the South African Statistical Association for 2010, edited by P. Debba, F. Lombard, V. Yadavalli, and L. Fatti, Potchefstroom: North-West University.

  • Xie, M., O. Gaudoin, and C. Bracquemond. 2002. “Redefining Failure Rate Function for Discrete Distributions.” International Journal of Reliability, Quality and Safety Engineering 9:275–285.

    • Crossref
  • Zucchini, W. and I. MacDonald. 2009. Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Taylor & Francis.

Purchase article
Get instant unlimited access to the article.
$42.00
Log in
Already have access? Please log in.


or
Log in with your institution

Journal + Issues

JQAS, an official journal of the American Statistical Association, publishes research on the quantitative aspects of professional and collegiate sports. Articles deal with subjects as measurements of player performance, tournament structure, and the frequency and occurrence of records. Additionally, the journal serves as an outlet for professionals in the sports world to raise issues and ask questions that relate to quantitative sports analysis.

Search