Modelling and simulation for one-day cricket
Tim B. SWARTZ1 *, Paramjit S. GILL2 and Saman MUTHUKUMARANA1 of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 2 Mathematics, Statistics and Physics Unit, University of British Columbia Okanagan, Kelowna, British Columbia, Canada V1V 1V7 Key words and phrases: Bayesian latent variable model; cricket; Markov chain methods; Monte Carlo simulation; sports statistics; WinBUGS. MSC 2000: Primary 62P99; secondary 62F15. Abstract: This article is concerned with the simulation of one-day cricket matches. Given that only a ﬁnite number of outcomes can occur on each ball that is bowled, a discrete generator on a ﬁnite set is developed where the outcome probabilities are estimated from historical data involving one-day international cricket matches. The probabilities depend on the batsman, the bowler, the number of wickets lost, the number of balls bowled and the innings. The proposed simulator appears to do a reasonable job at producing realistic results. The simulator allows investigators to address complex questions involving one-day cricket matches. The Canadian Journal of Statistics 37: 143–160; 2009 © 2009 Statistical Society of Canada Resume: Cet article porte sur la simulation de matchs de cricket d’une seule journ´ e. Etant donn´ qu’il y a e ´ e ´ ´ un nombre ﬁni d’´ v´ nements possibles a chaque lancer de balle, un g´ n´ rateur discret. Sur un ensemble ﬁni e e e e ` est d´ velopp´ o` les probabilit´ s de chacun des ev´ nements sont estim´ es a partir de donn´ es historiques e e u e e ` e ´ e provenant de matchs de cricket international d’une seule journ´ e. Les probabilit´ s d´ pendent du batteur, du e e e lanceur, du nombre de guichets perdus, du nombre de balles lanc´ es et des manches. Le simulateur propos´ e e semble faire un travail raisonnable en produisant des r´ sultats r´ alistes. Il permet aux chercheurs d’´ tudier e e e des questions complexes concernant les matchs de cricket d’une seule journ´ e. La revue canadienne de e statistique 37: 143–160; 2009 © 2009 Société statistique du Canada 1 Department
1. INTRODUCTION Simulation is a practical and powerful tool that has been used in a wide range of disciplines to investigate complex systems. When a simulation model is available, it is typically straightforward to address questions concerning the occurrence of various phenomena. One simply carries out repeated simulations and observes the frequency with which the phenomena occur. In one-day international (ODI) cricket, there are an endless number of questions that are not amenable to experimentation or direct analysis but could be easily addressed via simulation. For example, on average, would England beneﬁt from increasing the number of runs scored by changing the batting order of their third and sixth batsmen? As another example, what percentage of time would India be expected to score more than 350 runs versus Australia in the ﬁrst innings? To provide reliable answers to questions such as these, a good simulator for one-day cricket matches is required. Surprisingly, the development of simulators for one-day cricket is a topic that has not been vigorously pursued by academics. In the pre-computer days, Elderton (1945) and Wood (1945) ﬁt the geometric distribution to individual runs scored based on results from test cricket. Kimber & Hansford (1993) argue against the geometric distribution and obtain * Author to whom correspondence may be addressed. E-mail: firstname.lastname@example.org © 2009 Statistical Society of Canada / Société statistique du Canada
SWARTZ, GILL AND MUTHUKUMARANA
Vol. 37, No. 2
probabilities for selected ranges of individual scores in test cricket using product-limit estimators. More recently, Dyte (1998) simulates batting outcomes between a speciﬁed test batsman and bowler...