PERFORMANCE MODELLING IN SPORT Stephen R. Clarke BSc(Hons), DipEd, MA A thesis submitted for the degree of Doctor of Philosophy School of Mathematical Sciences Swinburne University of Technology December 1997 ii Acknowledgments My thanks to the following for their contribution to this thesis. John Norman for first arousing my interest in applications in sport, for his continued encouragement, support and collaboration over many years, and for his advice and assistance on this thesis. Ray Stefani, a most knowledgeable person on sport, for his collaboration on football tipping and home advantage. David Noble, for the interest he has shown over the years in sporting applications, for his collaboration on several projects, for conscientiously reading my drafts and offering his considered and helpful advice, and for being such a considerate supervisor. Many anonymous referees, editors and other colleagues, who with their comments and advice have improved the original papers which form the bulk of this thesis. Swinburne and in particular the School of Mathematical Sciences for providing encouragement for my research and leave to write up this thesis. My mother, Connie Clarke, for providing the initial impetus by often asking when I was going to do a PhD, and who by taking her first parachute jump at age 83 demonstrated it was never too late to achieve an ambition. Finally my wife Kaye, for bearing the brunt of late nights and untidy home offices, for listening to my half formed ideas, correcting my original drafts, helping to proof read this thesis, and assisting me in many other ways. iii Candidates statement This work has not previously been submitted by the candidate for any degree or similar award in a tertiary institution. Except where acknowledged in the text the work is my own. Stephen R. Clarke iv Preface This thesis is submitted under Swinburne University Policy for the Degree of Doctor of Philosophy, Regulation 4.2, Admission to candidature for thesis by publication. This allows for "thesis by publication on the basis of research which has been carried out prior to admission by candidature and which has been published, normally in texts or refereed publications. Only those publications not previously submitted by the applicant for a degree in any tertiary institution may be included in support of the application for candidature and in the Candidates thesis. In such cases the...Candidate must produce a significant body of work on an integrated theme that will comprise the thesis. This thesis would normally include a substantial introduction showing the relevance of the publications to development of the theme, plus a series of publications and any necessary linking commentary. All publications must be appropriately identified and referenced and the contributions of the Candidate to each publication must be clearly specified." From my work in applications in sport over many years, I have selected for this thesis some of the papers relating to performance measurement in football (including Australian rules and English soccer), and cricket. Most of the football work relates to measurement of home advantage and forecasting match results. The football work has the advantage from an operational research viewpoint that it is heavily based on real data, and has also been implemented to the degree that the results have been regularly published in the popular media. The work on performance measurement and tactics in cricket makes up the second part of the thesis and uses the traditional OR technique of dynamic programming. I toyed with the idea of using my work on squash and badminton, which also falls in the general theme, but thought the thesis already long enough. In this thesis each chapter usually comprises one publication. This has meant some repetition, as there is some commonality in literature surveys and game descriptions in various papers. However it has the advantage that each chapter is self contained and may be read in isolation. The content of each publication is as it originally appeared, but with style changes to create uniformity of presentation throughout the thesis. This necessitated some superficial changes. All headings, tables, figures and equations have been renumbered using the chapter number as a prefix. The style of referencing has v been standardised, and the references consolidated in the bibliography at the end of the thesis. In a very few cases notation has been changed and tables and figures given a more descriptive caption. A commentary section which details later developments or further work has been added at the end of some chapters. The following lists the publications used in each chapter, states if they were refereed, and specifies the candidates input to co-authored papers. Chapter I. Written specifically for the thesis. Chapter II. The early part of this chapter is based loosely on Stefani, R. T., & Clarke, S. R. (1991), Australian rules football during the 1980s. ASOR Bulletin, 10(3), 11- 15. The paper evolved from a 50% contribution by Professor Stefani and a 50% contribution from myself. In Chapter II, I have repeated all the analysis on 16 years of data. The latter part of the chapter is from Clarke, S. R. (1997a), Home ground advantage in the Australian Football League, 1980-85, a paper presented at the APORS conference 1997, Melbourne. Chapter III. Clarke, S. R., & Norman, J. M. (1995), Home ground advantage of individual clubs in English soccer. The Statistician, 44, 509-521. Refereed. The conception of this paper resulted from joint collaboration. Professor Norman assisted with the collection of data, which I computerised and analysed. I wrote the first draft of the paper, but Professor Norman assisted with following drafts and provided the necessary local knowledge. The commentary material is based on Clarke, S. R. (1996b), Home advantages in balanced competitions - English soccer 1990-1996. In N. de Mestre (Ed.), Mathematics and Computers in Sport (pp. 111-116). Gold Coast, Qld.: Bond University. Chapter IV. Clarke, S. R. (1993), Computer forecasting of Australian rules football for a daily newspaper. Journal of the Operational Research Society, 44(8), 753-759. Refereed. vi Chapter V. Clarke, S. R. (1992), Computer and human tipping of AFL football - a comparison of 1991 results. In N. de Mestre (Ed.), Mathematics and Computers in Sport (pp. 81-93). Gold Coast, Qld: Bond University. Chapter VI. Stefani, R. T., & Clarke, S. R. (1992), Predictions and home advantage for Australian rules football. Journal of Applied Statistics, 19(2), 251-261. Refereed. This paper resulted from joint discussions over several years on computer tipping and home advantage. I provided the data and my computer methods for the Australian rules analysis, Professor Stefani provided the least squares method as well as the data and results for the other sports. Chapter VII. Clarke, S. R. (1996a), Calculating premiership odds by computer - an analysis of the AFL final eight play-off system. Asia Pacific Journal of Operational Research, 13(1), 89-104. Refereed. The commentary is based on my own work not yet submitted. Chapter VIII. Clarke, S. R., & Norman, J. M. (1998b), When to rush a behind in Australian rules football: a dynamic programming approach. Journal of the Operational Research Society, in press. Refereed. In terms of input this paper is the complement of Chapter III. The conception of the paper resulted from joint collaboration. The development of the model was a joint exercise, but Professor Norman wrote the computer implementation and the first draft of the paper. I assisted with further development of the model and the paper, and provided the necessary local knowledge. Chapter IX. Clarke, S. R. (1997b), Test Statistics. In J. Bennet (Ed.), Statistics in Sport. Edward Arnold (to appear). This is a slightly reduced version of the material to be published in the text. Several figures and tables extracted from published works and required for the text have been omitted here. Chapter X. Clarke, S. R. (1986), Another look at the 1985/86 Sheffield Shield competition cricket results. Sports Coach, 10(3), 16-19. vii Chapter XI. Clarke, S. R. (1988), Dynamic Programming in one day cricket - Optimal scoring rates. Journal of the Operational Research Society, 39(4), 331-337. Refereed. The commentary is based on Johnston, M. I., Clarke, S. R., & Noble, D. H. (1992), An analysis of scoring policies in one day cricket. In N. de Mestre (Ed.), Mathematics and Computers in Sport (pp. 71-80). Gold Coast, Qld: Bond University. I wrote this paper based on joint development of my original idea by all authors. Mr Johnston wrote all the necessary computer programs. Chapter XII. Clarke, S. R., & Norman, J. M. (1998a), Dynamic programming in cricket: Protecting the weaker batsman. Asia Pacific Journal of Operational Research, in press. Refereed. I developed the models and paper with the continued assistance of Professor Norman's help and advice. Chapter XIII. Clarke, S. R., & Norman, J. M. (1997c), To run or not? Some Dynamic Programming models in cricket. In R. L. Jenson & I. R. Johnson (Eds.), Proceedings of the Twenty-Sixth Annual Meeting of the Western Decision Sciences Institute (pp. 744-746). Hawaii: Decision Sciences Institute. The full paper, which appears here, was refereed. The above is a shorter version published in the proceedings as is the practice at this conference. I developed Models 1 and 2 along with the necessary computer programs. Professor Norman developed Model 3 along with the necessary computer programs. I wrote the first draft of the paper. Both authors provided assistance and advice to the other in the development of the models and the paper. Chapter XIV. Johnston, M. I., Clarke, S. R., & Noble, D. H. (1993), Assessing player performance in one-day Cricket using dynamic programming. Asia-Pacific Journal of Operational Research, 10, 45-55. Refereed.