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A SECOND LOOK AT DUCKWORTH-LEWIS IN
TWENTY20 CRICKET
Harsha Perera
Department of Statistics and Actuarial ScienceSimon Fraser University
Joint SFU-UBC Student Seminar in StatisticsFall 2011
CONTENTS
• Introduction
• Motivation
• Cricket : The Game
• Duckworth – Lewis Resource Table
• A New Resource Table for Twenty20
• Remarks
INTRODUCTION
• 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)
MOTIVATION
• Twenty20 cricket differs from One-Day cricket.
• Duckworth-Lewis Resource Table designed for One-Day cricket matches but applied to Twenty20 matches.
CRICKET: THE GAME
DUCKWORTH-LEWIS RESOURCE TABLE
• First developed by two British academics, Frank Duckworth and Tony Lewis in 1998.
• Updated in 2004.
• Improvement over the run rate method.
Scaled Duckworth- Lewis (DL) Resource Table for Twenty20 cricket
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.
uwbwZwuZ )(exp1)(),( 0
)(0 wZ
)(wb
),( wuZ
• 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 ?
A NEW RESOURCE TABLE FOR T20
Data CollectionFirst innings data from 388 T20
matches were collected from www.cricinfo.com for 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:
n
iiinini
n
inii rrrrrr
iii1
20,19,,,1
,20, |..........|,......,1
1
0.1,0.1~2 maInverseGam
2,1,1,1,, ,~|1,,
uiui wuwuuiuiui rNrr
The full conditional distributions are:
Subject to the constraints;
for and
2/)2(,1~.| ,,2 wuwu mmmaInverseGam
)2/(,~.| ,2
,, wuwuwu mNormal
),min(),max( 1,,1,1,,1 wuwuwuwuwu
19,.....,1u 9,....,1w
where
is the number of matches that pass through , and
The sum is taken over all matches
that passes through .
wum ,
),( wu
i),( wu
1,1, ,11,,,11,,
,, 2
1uiui wuuiuiwuuiui
wuwu rrrr
m
The New Resource Table (NRT) for Twenty20
Heat map of the absolute differences between DL and NRT
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
REMARKS
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.
THANK YOU
Abbreviated version of the Duckworth- Lewis (DL) Resource Table
(Standard Edition for One-Day cricket)
