STATISTICAL MODELLING IN LIMITED OVERS INTERNATIONAL CRICKET Muhammad ASIF Ph.D. Thesis 2013 i STATISTICAL MODELLING IN LIMITED OVERS INTERNATIONAL CRICKET Muhammad ASIF Centre for Sports Business, Salford Business School, University of Salford Manchester, Salford, United Kingdom. Submitted in Partial Fulfilment of the Requirements of the Degree of Doctor of Philosophy, July 2013 ii CONTENTS LIST OF FIGURES..………………………………………………………………….iv LIST OF TABLES..………………………………………...………………………...vii DECLARATION……….…..………………………………..…………………….….ix AKNOWLEDGMENT……..…………………………………...…………………….x ABSTRACT……………………………………………………..…………………….xi CHAPTER 1 Introduction .......................................................................................... 1 1.1 Aims and Objectives ......................................................................................... 1 1.2 History of the Limited Overs International (LOI) cricket ................................. 2 1.3 The Game of cricket .......................................................................................... 2 1.4 Thesis structure and contribution ...................................................................... 5 CHAPTER 2 The Problem of Interruption in Limited Overs Cricket ................... 7 2.1 Introduction ....................................................................................................... 7 2.2 Brief overview of some simple methods ........................................................... 8 2.2.1 Run rate method ....................................................................................... 8 2.2.2 Highest Scoring Overs (HSO) method ..................................................... 9 2.2.3 Equivalent Point (EP) method ................................................................ 10 2.2.4 PARAB method ..................................................................................... 10 2.3 Brief overview of the advanced methods ........................................................ 11 2.3.1 The Duckworth-Lewis (D/L) method .................................................... 11 2.3.2 The Jayadevan ( VJD) method ............................................................... 12 2.3.3 The Probability Preservation method ..................................................... 13 2.4 Summary ......................................................................................................... 14 CHAPTER 3 The Duckworth-Lewis (D/L) Method ............................................... 15 3.1 Introduction ..................................................................................................... 15 3.2 The Duckworth-Lewis Model ......................................................................... 16 3.3 Cricket data for the D/L modelling ................................................................. 17 3.4 Runs scoring pattern (ODI and T20I) .............................................................. 18 3.5 Estimation of the Duckworth-Lewis method (Professional Edition) .............. 19 3.5.1 Estimation of Z0, b and F(w) .................................................................. 19 3.5.2 Estimating λ and n(w) ............................................................................ 20 iii 3.6 The D/L model fit result .................................................................................. 20 3.7 Summary ......................................................................................................... 21 CHAPTER 4 The Duckworth-Lewis Method Compared to Alternatives ............ 23 4.1 Introduction ..................................................................................................... 23 4.2 The standard desirable properties of a method to revise targets ..................... 24 4.3 Jayadevan‟s (VJD) method ............................................................................. 25 4.3.1 First and Third desirable properties for the VJD system ....................... 26 4.3.2 Second and Fourth desirable properties for the VJD system ................. 28 4.4 Bhattacharya‟s version of the D/L method for T20I ....................................... 30 4.5 Stern‟s adjusted D/L method ........................................................................... 31 4.6 Iso-Probability (IP) method ............................................................................. 33 4.7 Summary ......................................................................................................... 34 CHAPTER 5 A Modified Duckworth-Lewis Method ............................................. 36 5.1 Introduction ..................................................................................................... 36 5.2 Issues in Duckworth-Lewis method ................................................................ 36 5.3 A new model for the D/L method ................................................................... 39 5.3.1 Model for the F(w) ................................................................................. 39 5.3.2 Model for the Z(u, w) ............................................................................. 40 5.3.3 Goodness of fit ....................................................................................... 43 Model adjustment for high scoring matches .......................................... 45 5.3.5 Testing the model adjustment ................................................................ 46 5.4 Modified D/L model and future research work ............................................... 48 5.5 Summary ......................................................................................................... 49 CHAPTER 6 In-Play Forecasting in Cricket and Generalized Linear Models ... 51 6.1 Introduction ..................................................................................................... 51 6.2 Bailey/Clarke and Akhtar/Scarf approach for in-play forecasts ..................... 52 6.3 Generalized Linear Model (GLM) ................................................................. 54 6.4 Model diagnostic measures ............................................................................. 56 6.4.1 Test the significance of association ........................................................ 56 6.4.2 The strength of association ..................................................................... 56 6.4.3 Model selection ...................................................................................... 57 6.5 Summary ......................................................................................................... 60 iv CHAPTER 7 In-play Forecasting of win probability in One-Day International Cricket: A Dynamic Logistic Regression Model ..................................................... 61 7.1 Introduction ..................................................................................................... 61 7.2 Data and covariates ......................................................................................... 62 7.2.1 Pre-match covariates .............................................................................. 62 7.2.2 In-play covariates ................................................................................... 65 7.2.3 Organizing data for modelling ............................................................... 70 7.3 Modelling procedure for the DLR models ...................................................... 71 7.3.1 Modelling match outcome ...................................................................... 72 7.3.2 Modelling the coefficients on the covariates: A recursive process ........ 73 7.4 The model fit results ........................................................................................ 76 7.4.1 A model for estimating pre-match win probability ................................ 76 7.4.2 A series of models for estimating in-play win probabilities .................. 77 7.4.3 Assessing forecasting accuracies ........................................................... 81 7.4.4 Smoothing the estimated coefficients: A dynamic logistic regression (DLR) model ....................................................................................................... 84 7.4.5 Strength of association (Nagelkerke's R2) .............................................. 90 7.5 Comparison with betting market ..................................................................... 92 7.6 The DLR models and future research .............................................................. 95 7.7 Summary ......................................................................................................... 95 CHAPTER 8 Summary and Future work ............................................................... 97 8.1 Summary of the thesis ..................................................................................... 97 8.2 Future work ................................................................................................... 100 Appendix I .................................................................................................................. 102 Appendix II ................................................................................................................. 105 References…………………………………………………………………………108 v LIST OF FIGURES Figure 1.1 The images of the ICC's standard pitch (left panel), and a wicket that stake on each of the pitch (right panel) .......................................................................... 4 Figure 1.2 A cricket ground show the players