A SECOND LOOK AT DUCKWORTH-LEWIS IN TWENTY20 CRICKET

1. 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

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

3. INTRODUCTION

4. 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)

5. MOTIVATION

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

7. CRICKET: THE GAME

11. DUCKWORTH-LEWIS RESOURCE TABLE

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

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

14. 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

15. 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.

16. 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 ?

17. A NEW RESOURCE TABLE FOR T20

18. 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.

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

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

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

22. The New Resource Table (NRT) for Twenty20

23. Heat map of the absolute differences between DL and NRT

24. 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

25. 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

26. REMARKS

27. 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.

28. THANK YOU

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