Bayesian survival analysis of batsmen in Test cricket

Oliver George Stevenson; Brendon J. Brewer

doi:10.1515/jqas-2016-0090

Article

Bayesian survival analysis of batsmen in Test cricket

Oliver George Stevenson and Brendon J. Brewer

Published/Copyright: March 17, 2017

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Journal of Quantitative Analysis in Sports Volume 13 Issue 1

Abstract

Cricketing knowledge tells us batting is more difficult early in a player’s innings but becomes easier as a player familiarizes themselves with the conditions. In this paper, we develop a Bayesian survival analysis method to predict the Test Match batting abilities for international cricketers. The model is applied in two stages, firstly to individual players, allowing us to quantify players’ initial and equilibrium batting abilities, and the rate of transition between the two. This is followed by implementing the model using a hierarchical structure, providing us with more general inference concerning a selected group of opening batsmen from New Zealand. The results indicate most players begin their innings playing with between only a quarter and half of their potential batting ability. Using the hierarchical structure we are able to make predictions for the batting abilities of the next opening batsman to debut for New Zealand. Additionally, we compare and identify players who excel in the role of opening the batting, which has practical implications in terms of batting order and team selection policy.

Keywords: Bayesian survival analysis; cricket; hierarchical modelling

Acknowledgement

It is a pleasure to thank Berian James (Square), Mathew Varidel (Sydney), Ewan Cameron (Oxford), Ben Stevenson (St Andrews), Matt Francis (Ambiata) and Thomas Lumley (Auckland) for their helpful discussions. We would also like to thank the reviewers and journal editors for their useful comments and suggestions.

Appendix A New Zealand opening batsmen

Table 3

Test career records for New Zealand opening batsmen who debuted since 1990.

Player	Matches	Innings	Not-outs	Runs	High-score	Average	Strike rate	100s	50s
D. White	2	4	0	31	18	7.75	33.33	0	0
B. Hartland	9	18	0	303	52	16.83	31.33	0	1
R. Latham	4	7	0	219	119	31.28	48.99	1	0
B. Pocock	15	29	0	665	85	22.93	29.80	0	6
B. Young	35	68	4	2034	267*	31.78	38.95	2	12
C. Spearman	19	37	2	922	112	26.34	41.68	1	3
M. Horne	35	65	2	1788	157	28.38	40.78	4	5
M. Bell	18	32	2	729	107	24.30	37.81	2	3
G. Stead	5	8	0	278	78	34.75	41.43	0	2
M. Richardson	38	65	3	2776	145	44.77	37.66	4	19
L. Vincent	23	40	1	1332	224	34.15	47.11	3	9
M. Papps	8	16	1	246	86	16.40	35.34	0	2
C. Cumming	11	19	2	441	74	25.94	34.86	0	1
J. Marshall	7	11	0	218	52	19.81	39.06	0	1
P. Fulton	23	39	1	967	136	25.44	39.27	2	5
J. How	19	35	1	772	92	22.70	50.45	0	4
A. Redmond	8	16	1	325	83	21.66	39.01	0	2
T. McIntosh	17	33	2	854	136	27.54	36.20	2	4
R. Nicol	2	4	0	28	19	7.00	26.66	0	0

Players are listed in order of debut, oldest to most recent.

Table 4

Posterior summaries for all New Zealand opening batsmen since 1990, including our estimate for the next opener to debut for New Zealand (listed as “NZ opener”).

Player	μ₁	68% C.I.	μ₂	68% C.I.	L	68% C.I.
D. White	6.3− 3.3+ 5.6	[3.0, 11.9]	16.7− 7.0+ 13.9	[9.7, 30.6]	2.7− 2.1+ 4.9	[0.6, 7.6]
B. Hartland	6.9− 2.9+ 4.6	[4.0, 11.5]	20.7− 4.6+ 6.6	[16.1, 27.3]	1.9− 1.4+ 3.3	[0.5, 5.2]
R. Latham	10.5− 5.8+ 9.9	[4.7, 24.4]	35.9− 10.6+ 17.5	[25.3, 53.4]	4.1− 3.2+ 7.6	[0.9, 11.7]
B. Pocock	8.4− 3.3+ 5.5	[5.1, 13.9]	26.4− 4.7+ 6.4	[21.7, 32.8]	1.9− 1.4+ 3.4	[0.5, 5.3]
B. Young	15.0− 4.9+ 5.9	[10.1 , 20.1]	36.0− 4.8+ 6.4	[31.2, 42.4]	4.4− 3.0+ 6.3	[1.4, 10.7]
C. Spearman	13.1− 4.8+ 6.2	[8.3, 19.3]	28.8− 4.8+ 5.9	[24.0, 34.7]	2.0− 1.5+ 3.4	[0.5, 5.4]
M. Horne	14.3− 4.3+ 5.4	[10.0, 19.7]	32.3− 4.5+ 5.7	[27.8, 38.0]	4.4− 2.7+ 5.1	[1.7, 9.5]
M. Bell	4.9− 1.8+ 3.0	[3.1, 7.9]	32.7− 6.7+ 10.1	[26.0, 42.8]	3.2− 2.5+ 5.4	[0.7, 8.6]
G. Stead	18.0− 8.6+ 11.5	[9.4, 29.5]	35.8− 9.8+ 14.9	[26.0, 50.7]	3.1− 2.4+ 6.7	[0.7, 9.8]
M. Richardson	30.7− 8.8+ 8.5	[21.9, 39.2]	46.1− 5.6+ 6.8	[40.5, 52.9]	3.6− 2.8+ 6.9	[0.8, 10.5]
L. Vincent	13.5− 5.2+ 7.0	[8.3, 20.5]	40.6− 7.4+ 10.1	[33.2, 50.7]	6.0− 4.5+ 7.7	[1.5, 13.7]
M. Papps	4.4− 1.9+ 3.3	[2.5, 7.7]	23.6− 6.2+ 11.0	[17.4, 34.6]	3.0− 2.2+ 5.1	[0.8, 8.1]
C. Cumming	14.2− 5.7+ 7.0	[8.5, 21.2]	29.3− 6.5+ 9.3	[22.8, 38.6]	3.3− 2.5+ 5.9	[0.8, 9.2]
J. Marshall	7.3− 3.7+ 5.9	[3.6, 13.2]	24.0− 6.3+ 9.8	[17.7, 33.8]	2.1− 1.6+ 3.7	[0.5, 5.8]
P. Fulton	11.5− 4.0+ 5.0	[7.5, 16.5]	31.1− 5.9+ 8.4	[25.2, 39.5]	5.4− 3.4+ 6.7	[2.0, 12.1]
J. How	10.1− 3.9+ 5.6	[6.2, 15.7]	25.0− 4.1+ 5.3	[20.9, 30.3]	1.2− 0.9+ 2.7	[0.3 3.9]
A. Redmond	10.5− 4.2+ 5.7	[6.3, 16.2]	28.2− 7.3+ 11.9	[20.9, 40.1]	5.2− 3.4+ 6.9	[1.8, 12.1]
T. McIntosh	8.0− 3.0+ 4.5	[5.0, 12.5]	40.0− 9.2+ 13.8	[30.8, 53.8]	9.2− 5.3+ 8.0	[3.9, 17.2]
R. Nicol	5.9− 3.0+ 5.4	[2.9, 11.3]	16.5− 7.0+ 13.7	[9.5, 30.2]	3.0− 2.2+ 5.0	[0.8, 8.0]
NZ opener	9.6− 5.7+ 11.7	[4.0, 21.3]	27.7− 11.9+ 21.0	[15.8, 48.7]	3.1− 2.4+ 6.0	[0.8, 9.1]

Players are ordered by Test debut date (older to recent).

References

Agresti, A. and M. Kateri. 2011. Categorical Data Analysis. Berlin: Springer.10.1007/978-3-642-04898-2_161Search in Google Scholar

Allison, P. D. 1982. “Discrete-time Methods for the Analysis of Event Histories.” Sociological Methodology 13:61–98.10.2307/270718Search in Google Scholar

Bracewell, P. J. and K. Ruggiero. 2009. “A Parametric Control Chart for Monitoring Individual Batting Performances in Cricket.” Journal of Quantitative Analysis in Sports 5:1–9.10.2202/1559-0410.1160Search in Google Scholar

Brewer, B. J. 2008. “Getting your Eye in: A Bayesian Analysis of Early Dismissals in Cricket.” ArXiv preprint:0801.4408v2.Search in Google Scholar

Brewer, B. J. and T. M. Elliott. 2014. “Hierarchical Reverberation mapping.” Monthly Notices of the Royal Astronomical Society: Letters 439:L31–L35.10.1093/mnrasl/slt174Search in Google Scholar

Cai, T., R. J. Hyndman, and M. Wand. 2002. “Mixed Model-based Hazard Estimation.” Journal of Computational and Graphical Statistics 11:784–798.10.1198/106186002862Search in Google Scholar

Clarke, S. R. 1988. “Dynamic Programming in One-day Cricket-optimal Scoring Rates.” Journal of the Operational Research Society 39:331–337.10.1057/9781137534675_5Search in Google Scholar

Clarke, S. R. and J. M. Norman. 1999. “To Run or Not?: Some Dynamic Programming Models in Cricket.” Journal of the Operational Research Society 50:536–545.10.1057/palgrave.jors.2600705Search in Google Scholar

Clarke, S. R. and J. M. Norman. 2003. “Dynamic Programming in Cricket: Choosing a Night Watchman.” Journal of the Operational Research Society 54:838–845.10.1057/palgrave.jors.2601527Search in Google Scholar

Damodaran, U. 2006. “Stochastic Dominance and Analysis of ODI Batting Performance: The Indian Cricket Team, 1989–2005.” Journal of Sports Science and Medicine 5:503–508.Search in Google Scholar

Davis, J., H. Perera, and T. B. Swartz. 2015. “A Simulator for Twenty20 Cricket.” Australian and New Zealand Journal of Statistics 57:55–71.10.1111/anzs.12109Search in Google Scholar

Elderton, W. and G. H. Wood. 1945. “Cricket Scores and Geometrical progression.” Journal of the Royal Statistical Society 108:12–40.10.2307/2981193Search in Google Scholar

Foreman-Mackey, D. 2016. “corner.py: Scatterplot Matrices in Python.” JOSS 1. http://dx.doi.org/10.21105/joss.00024.10.21105/joss.00024Search in Google Scholar

Ganesh, T. V. 2016. cricketr: Analyze Cricketers Based on ESPN Cricinfo Statsguru. http://CRAN.R-project.org/package=cricketr, r package version 0.0.12.Search in Google Scholar

Hastings, W. K. 1970. “Monte Carlo Sampling Methods Using Markov Chains and Their Applications.” Biometrika 57:97–109.10.1093/biomet/57.1.97Search in Google Scholar

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) 153:443–455.10.2307/2983068Search in Google Scholar

Koulis, T., S. Muthukumarana, and C. D. Briercliffe. 2014. “A Bayesian Stochastic Model for Batting Performance Evaluation in One-day Cricket.” Journal of Quantitative Analysis in Sports 10:1–13.10.1515/jqas-2013-0057Search in Google Scholar

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.Search in Google Scholar

Lemmer, H. H. 2011. “The Single Match Approach to Strike Rate Adjustments in Batting Performance Measures in Cricket.” Journal of Sports Science and Medicine 10:630.Search in Google Scholar

McCullagh, P. 1980. “Regression Models for Ordinal Data.” Journal of the Royal Statistical Society. Series B (Methodological) 42:109–142.10.1111/j.2517-6161.1980.tb01109.xSearch in Google Scholar

Norman, J. M. and S. R. Clarke. 2010. “Optimal Batting Orders in Cricket.” Journal of the Operational Research Society 61:980–986.10.1057/jors.2009.54Search in Google Scholar

Preston, I. and J. Thomas. 2000. “Batting Strategy in Limited Overs Cricket.” Journal of the Royal Statistical Society: Series D (The Statistician) 49:95–106.10.1111/1467-9884.00223Search in Google Scholar

Skilling, J. 2006. “Nested Sampling for General Bayesian Computation.” Bayesian Analysis 1:833–859.10.1214/06-BA127Search in Google Scholar

Swartz, T. B., P. S. Gill, D. Beaudoin, and B. M. de Silva. 2006. “Optimal Batting Orders in One-day Cricket.” Computers and Operations Research 33:1939–1950.10.1016/j.cor.2004.09.031Search in Google Scholar

Published Online: 2017-3-17

Published in Print: 2017-3-1

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/jqas-2016-0090

Keywords for this article

Bayesian survival analysis; cricket; hierarchical modelling