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A SECOND LOOK AT DUCKWORTH-LEWIS IN TWENTY20 CRICKET A SECOND LOOK AT DUCKWORTH-LEWIS IN TWENTY20 CRICKET Harsha Perera Department of Statistics and Actuarial Science Simon Fraser University Joint SFU-UBC Student Seminar in Statistics Fall 2011

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CONTENTS CONTENTS Introduction Motivation Cricket : The Game Duckworth – Lewis Resource Table A New Resource Table for Twenty20 Remarks

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INTRODUCTION

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International Cricket Council (ICC) countries : AustraliaBangladeshEngland IndiaNew ZealandPakistan South AfricaSri LankaWest Indies Zimbabwe Three formats of cricket : Test Cricket One-Day Cricket (50 overs) Twenty20 or T20 Cricket (20 overs)

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MOTIVATION

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Twenty20 cricket differs from One-Day cricket. Duckworth-Lewis Resource Table designed for One-Day cricket matches but applied to Twenty20 matches.

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CRICKET: THE GAME

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DUCKWORTH-LEWIS RESOURCE TABLE

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First developed by two British academics, Frank Duckworth and Tony Lewis in 1998. Updated in 2004. Improvement over the run rate method.

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Scaled Duckworth- Lewis (DL) Resource Table for Twenty20 cricket Scaled Duckworth- Lewis (DL) Resource Table for Twenty20 cricket

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Team A scores 150/8 for 20 overs. Rain interrupts the game and the match is reduced to 12 overs for Team B. Team B target is: According to the D-L method : [( 150 * 0. 664)] +1 = 100.6 ~ 100 According to Run Rate method : [ (150/20) * 12 ] + 1 = 91

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Two resources at disposal of scoring side : Number of overs left Wickets left. Mathematical relation between overs left and wickets left is : where average total score in u overs in an unlimited overs match where w wickets are lost. asymptotic average total score from the last (10 – w) wickets in unlimited overs. exponential decay constant. for w = 0, 1,..., 9.

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Is it the best curve to fit? Why a formula of unlimited overs was used for a limited overs game? The last two columns have some identical entries. Is it plausible ?

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A NEW RESOURCE TABLE FOR T20

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Data Collection First innings data from 388 T20 matches were collected from www.cricinfo.com for the period February 17, 2005 to May 28, 2011.www.cricinfo.com Included 146 ICC T20 matches and 242 IPL matches over four seasons.

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The likelihood of the first innings data is: Key modelling assumptions are:

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The full conditional distributions are: Subject to the constraints; for and

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where is the number of matches that pass through, and The sum is taken over all matches that passes through.

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The New Resource Table (NRT) for Twenty20

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Heat map of the absolute differences between DL and NRT

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COMPARISON 1 COMPARISON 1 Match 1: England vs West Indies, 15 th June 2009. England made 161/6 in 20 overs. Rain interrupted the game and WI innings was reduced to 9 overs. D-L : 80 runs (achieved in 8.2 overs) NRT : 85 runs

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COMPARISON 2 COMPARISON 2 Match 2: England vs West Indies, 03 rd May 2010. England scored 191/5 in 20 overs. Rain interrupted the game and WI innings was reduced to 6 overs. D-L : 60 runs (achieved in 5.5 overs) NRT : 72 runs

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REMARKS

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The resource table suggests a difference in scoring patterns between Twenty20 and One-Day cricket. Our intention is not to supplant the Duckworth- Lewis table but to highlight its shortcomings.

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THANK YOU

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Abbreviated version of the Duckworth- Lewis (DL) Resource Table (Standard Edition for One-Day cricket)

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