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
CONTENTS • Introduction • Motivation • Cricket : The Game • Duckworth – Lewis Resource Table • A New Resource Table for Twenty20 • Remarks
International Cricket Council (ICC) countries : Australia Bangladesh England India New Zealand Pakistan South Africa Sri Lanka West Indies Zimbabwe • Three formats of cricket : • Test Cricket • One-Day Cricket (50 overs) • Twenty20 or T20 Cricket (20 overs)
Twenty20 cricket differs from One-Day cricket. • Duckworth-Lewis Resource Table designed for One-Day cricket matches but applied to Twenty20 matches.
First developed by two British academics, Frank Duckworth and Tony Lewis in 1998. • Updated in 2004. • Improvement over the run rate method.
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
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.
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 ?
Data Collection • First innings data from 388 T20 matches were collected from www.cricinfo.comfor the period February 17, 2005 to May 28, 2011. • Included 146 ICC T20 matches and 242 IPL matches over four seasons.
The likelihood of the first innings data is: • Key modelling assumptions are:
The full conditional distributions are: Subject to the constraints; for and
where is the number of matches that pass through , and The sum is taken over all matches that passes through .
COMPARISON 1 • Match 1: England vs West Indies, 15th 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
COMPARISON 2 • Match 2: England vs West Indies, 03rd 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
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.
Abbreviated version of the Duckworth- Lewis (DL) Resource Table (Standard Edition for One-Day cricket)