Operational Research Applied to Sports

Transcription

1 Operational Research Applied to Sports

2 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 (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

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

4 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 First published 2015 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number , 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 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 ISBN (ebook) DOI / 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.

5 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

6 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

7 List of Figures and Tables Figures 1.1 The various distances in long jump Flow chart for simulation of optimal aiming line Simulation results of E(D) (for 3000 series of three jumps) as a function of Z a Approximate values of Za The observed and fitted distributions of the length of jumps The observed and fitted distributions of the take-offs around the aimed at line Possible perceptual games for Hooligan Fans Authorities perceived Intervention game (with Potentially Troublesome crowd type) Intervention hypergame Authorities view, preparatory and intervention phases linked Fans view of overall system Format and dimensions of the dartboard A sector showing the target points Expected score along a vertical line through the centre of the board (σ = 0.5) Branch-and-bound tree at a hypothetical stage in the processing Solution algorithm Comparisons for first half-hour Low-cost comparisons Average number of runs from overs remaining with wickets lost Setting Team 2 s target score when Team 1 s innings is interrupted 136 vii

8 viii List of Figures and Tables 10.1 Gain for home team Al from fouling scenario Gain for away team A2 from fouling scenario Gain for Manchester United from fouling scenario Gain for Watford from fouling scenario Gain for home team Al from fouling scenario Gain for away team A2 from fouling scenario Gain for Manchester United from fouling scenario Gain for Watford from fouling scenario Gain for away team A2 from being fouled scenario Probabilities of winning when playing through, f 1 (q), and when setting, f 2 (q), at in women s singles games for different values of q 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 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 Actual scoring pattern for an illustrative game under the new rules Evolving probabilities of my winning an illustrative game under the new rules Illustration of heuristical and exact beam search Optimal strategy in first to 30 game, with one challenge left 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 Joint frequency distribution of x and y* 29

9 List of Figures and Tables ix 3.1 The highest expected gains for five selected values of s Definitions of the five classes Rules for determining a player s class Optimal strategies for each class Optimal strategies for classes A and B, s = Dismissal probabilities Optimal run rate and expected score in remainder of innings under optimal policy Probability of scoring a further s runs with 300 balls to go Comparisons between the three methods Norms and percentage factors for the PARAB and WC96 methods Percentage of innings resources remaining (an extract from the table) Calculations of the revised target score in hypothetical 50 over examples Calculations of the revised target score in actual matches Sydney 2000 results Sensitivity of q* 0 (%) to parameters α and β for Sydney Evolution of q* 0 (%) in the last five Olympics ( no medals won, + not participated) Efficiency of organising countries Technical and scale efficiencies for Sydney 2000 (ordered by scale efficiency) Optimal setting decision thresholds under the old rules, where q is the probability that the team with the option wins any particular rally Comparisons of scoring rules for the 2006 Commonwealth Games Single RRT for n = Mirrored double RRT for n = 6 202

10 x List of Figures and Tables 12.3 Running times optimal solutions Running times first solution Quality first solution Coefficients of the terms of the functional equation Statistics on challenges during Wimbledon