Operational Research Applied to Sports

Operational Research Applied to Sports

OR Essentials The OR Essentials series presents a unique cross-section of high quality research work fundamental to understanding contemporary issues and research across a range of Operational Research (OR) topics. It brings together some of the best research papers from the highly respected journals of the Operational Research Society, also published by Palgrave Macmillan. OR deals with the use of advanced analytical methods to support better decision making. As a multidisciplinary field, it has strong links to management science, decision science, computer science and has practical applications in areas such as engineering, manufacturing, commerce, healthcare and defence. OR has long-standing historical roots. However, as a modern discipline its origins lie in the years immediately before World War II when mathematical techniques were developed to address urgent defence problems. Now it is commonplace and a key discipline taught in universities across the world, at undergraduate and postgraduate levels. There are several international societies dedicated to the advancement of OR (e.g. the Operational Research Society and INFORMS The Institute for Operations Research and the Management Sciences) and there are many high quality peer-reviewed journals dedicated to the topic. The OR Essentials books are a vital reference tool for students, academics, and industry practitioners, providing easy access to top research papers on cuttingedge topics within the field of OR. Titles include: Simon JE Taylor (editor) AGENT-BASED MODELLING AND SIMULATION Roger A Forder (editor) OR, DEFENCE AND SECURITY Mike Wright (editor) OPERATIONAL RESEARCH APPLIED TO SPORTS OR Essentials series Series Standing Order ISBNs 978 1 137 45360 0 (hardback) (outside North America only) You can receive future titles in this series as they are published by placing a standing order. Please contact your bookseller or, in case of difficulty, write to us at the address below with your name and address, the title of the series and the ISBN quoted above. Customer Services Department, Macmillan Distribution Ltd, Houndmills, Basingstoke, Hampshire RG21 6XS, England

Operational Research Applied to Sports Edited by Mike Wright Lancaster University, UK

Selection, introduction and editorial matter Mike Wright 2015 Individual chapters Operational Research Society 2015 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6 10 Kirby Street, London EC1N 8TS. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their rights to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2015 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS. Palgrave Macmillan in the US is a division of St Martin s Press LLC, 175 Fifth Avenue, New York, NY 10010. Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world. Palgrave and Macmillan are registered trademarks in the United States, the United Kingdom, Europe and other countries. ISBN 978-1-349-56807-9 ISBN 978-1-137-53467-5 (ebook) DOI 10.1057/9781137534675 This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin. A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. Typeset by MPS Limited, Chennai, India.

Contents List of Figures and Tables vii Introduction 1 Mike Wright 1 The Optimal Aiming Line 18 SP Ladany, JW Humes and GP Sphicas 2 Using Hypergames to Model Difficult Social Issues: An Approach to the Case of Soccer Hooliganism 32 PG Bennett, MR Dando and RG Sharp 3 Optimal Strategies for the Game of Darts 54 D Kohler 4 Dynamic Programming in One-Day Cricket Optimal Scoring Rates 77 SR Clarke 5 Scheduling English Cricket Umpires 87 MB Wright 6 Computer Forecasting of Australian Rules Football for a Daily Newspaper 97 SR Clarke 7 Timetabling County Cricket Fixtures Using a Form of Tabu Search 109 M Wright 8 A Fair Method for Resetting the Target in Interrupted One-Day Cricket Matches 128 FC Duckworth and AJ Lewis 9 Measuring the Performance of Nations at The Summer Olympics Using Data Envelopment Analysis 144 S Lozano, G Villa, F Guerrero and P Cortés 10 The Professional Foul in Football: Tactics and Deterrents 165 M Wright and N Hirotsu 11 A Mathematical Analysis of Badminton Scoring Systems 181 DF Percy v

vi Contents 12 A Branch-and-Price Algorithm for Scheduling Sport Leagues 201 D Briskorn and A Drexl 13 Optimal Challenges in Tennis 224 SR Clarke and JM Norman Index 240

List of Figures and Tables Figures 1.1 The various distances in long jump 20 1.2 Flow chart for simulation of optimal aiming line 22 1.3 Simulation results of E(D) (for 3000 series of three jumps) as a function of Z a 23 1.4 Approximate values of Za 0 25 1.5 The observed and fitted distributions of the length of jumps 30 1.6 The observed and fitted distributions of the take-offs around the aimed at line 30 2.1 Possible perceptual games for Hooligan Fans 37 2.2 Authorities perceived Intervention game (with Potentially Troublesome crowd type) 42 2.3 Intervention hypergame 44 2.4 Authorities view, preparatory and intervention phases linked 47 2.5 Fans view of overall system 49 3.1 Format and dimensions of the dartboard 55 3.2 A sector showing the target points 58 3.3 Expected score along a vertical line through the centre of the board (σ = 0.5) 62 3.4 Branch-and-bound tree at a hypothetical stage in the processing 66 7.1 Solution algorithm 119 7.2 Comparisons for first half-hour 124 7.3 Low-cost comparisons 125 8.1 Average number of runs from overs remaining with wickets lost 133 8.2 Setting Team 2 s target score when Team 1 s innings is interrupted 136 vii

viii List of Figures and Tables 10.1 Gain for home team Al from fouling scenario 1 171 10.2 Gain for away team A2 from fouling scenario 1 171 10.3 Gain for Manchester United from fouling scenario 1 172 10.4 Gain for Watford from fouling scenario 1 173 10.5 Gain for home team Al from fouling scenario 2 173 10.6 Gain for away team A2 from fouling scenario 2 174 10.7 Gain for Manchester United from fouling scenario 2 174 10.8 Gain for Watford from fouling scenario 2 175 10.9 Gain for away team A2 from being fouled scenario 1 175 11.1 Probabilities of winning when playing through, f 1 (q), and when setting, f 2 (q), at 10-10 in women s singles games for different values of q 184 11.2 Probabilities of winning a women s singles game for different values of q under the old rules when serving first and under the new rules 190 11.3 Mean numbers of rallies per game for different values of q under the new rules and for women s (W) and men s (M) singles and all doubles (D) events under the old rules 192 11.4 Actual scoring pattern for an illustrative game under the new rules 197 11.5 Evolving probabilities of my winning an illustrative game under the new rules 198 12.1 Illustration of heuristical and exact beam search 213 13.1 Optimal strategy in first to 30 game, with one challenge left 232 13.2 Optimal strategy with one challenge left for the player serving the first game, (player X), for a first to six-game advantage set, each game being first to 4 points 236 Tables 1.1 The sampled values of pairs of x and y in centimetres 28 1.2 Joint frequency distribution of x and y* 29

List of Figures and Tables ix 3.1 The highest expected gains for five selected values of s 61 3.2 Definitions of the five classes 67 3.3 Rules for determining a player s class 67 3.4 Optimal strategies for each class 68 3.5 Optimal strategies for classes A and B, s = 61 107 71 4.1 Dismissal probabilities 81 4.2 Optimal run rate and expected score in remainder of innings under optimal policy 81 4.3 Probability of scoring a further s runs with 300 balls to go 84 7.1 Comparisons between the three methods 124 8.1 Norms and percentage factors for the PARAB and WC96 methods 131 8.2 Percentage of innings resources remaining (an extract from the table) 134 8.3 Calculations of the revised target score in hypothetical 50 over examples 138 8.4 Calculations of the revised target score in actual matches 139 9.1 Sydney 2000 results 151 9.2 Sensitivity of q* 0 (%) to parameters α and β for Sydney 2000 155 9.3 Evolution of q* 0 (%) in the last five Olympics ( no medals won, + not participated) 157 9.4 Efficiency of organising countries 160 9.5 Technical and scale efficiencies for Sydney 2000 (ordered by scale efficiency) 161 11.1 Optimal setting decision thresholds under the old rules, where q is the probability that the team with the option wins any particular rally 189 11.2 Comparisons of scoring rules for the 2006 Commonwealth Games 194 12.1 Single RRT for n = 6 202 12.2 Mirrored double RRT for n = 6 202

x List of Figures and Tables 12.3 Running times optimal solutions 219 12.4 Running times first solution 220 12.5 Quality first solution 221 13.1 Coefficients of the terms of the functional equation 229 13.2 Statistics on challenges during Wimbledon 2009 230