Analysis of the D/L method. The analysis proves that it is inherently unfair and should not be used.

1. Analysis of the D/L Method Used
for Target Resetting in Interrupted
Limited Over Cricket Matches
Rohan de Silva PhD
CQUniversity Sydney Campus,
Faculty of Engineering and Technology
Australia
r.desilva@cqu.edu.au
Proceedings of IMBIC, Volume 2 (2013), ISBN 978-81-925832-1-1

2.  Introduction
 Review of the D/L Method
 Analysis of the D/L Method
 Statistical Analysis
 Conclusion
Presentation Road Map
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
2

3.  In one day internationals and T20 cricket matches, interruptions may reduce
the number of balls allocated to one or both teams.
 Thus, the runs that should be scored by the team batting second in order to
be in par with the team batting first (par score) has to be calculated.
 Various methods have been developed to calculate the target score (par
score +1)
 The (D/L) method introduced in 1998 was adopted by ICC in 1999.
 But the D/L method can produce target scores that are questionable in
practice.
 It has been shown via simulations that D/L method does not produce a fair
outcome most of the time when innings of the team batting second has to
be terminated at 30th over due to an interruption.
 The aim of our work is to analyse the D/L method using graphical and
mathematical methods and find out the root cause of this unfairness.
Introduction
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
3

4. Review of the D/L Method
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
4
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
%ResourcesAvailable
Over Number
Fig. 1: Resources graphs of D/L Method
W=0
W=1
W=2
W=3
W=4
W=5
W=6
W=7
W=8
W=9

5. Analysis of the D/L Method
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
5
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
PercentageScore
Over Number
Fig.2: Expected Scoring Patterns of D/L Method
W=0
W=1
W=2
W=3
W=4
W=5
W=6
W=7
W=8
W=9
Linear Scoring

6.  We can construct the expected scoring pattern of a
team if the instances of falling of wickets are known.
 In Fig. 3, we have constructed the two graphs for the
cases where a wicket falls after every 5 completed
overs (called W-5) and after every 10 completed overs
(called W-10).
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
6
Analysis of the D/L Method (contd.)

7. Analysis of the D/L Method (contd.)
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
7
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
PercentageScore
Over Number
Fig. 3: Expected Scoring Patterns in D/L Method with a Wicket Loss After Every 5 Overs
and 10 Overs
Linear scoring
Expected Scoring-Wicket after 5 Overs (W-5)
Expected Scoring-Wicket after 10 Overs (W-10)

8.  These graphs reveal an important fact; if a team batting second
scores in a linear fashion to reach the set target but loses a
wicket after each 5 overs, then they are likely to lose the game if
their innings is terminated after about 20 or more overs.
 This is an alarming fact hidden in the D/L method.
 Thus, to guarantee its win when batting second under
interruptions, a team has to ensure that its performance
characteristics should be better than that dictated by the D/L
method.
 This is an unfair requirement as if there was no abrupt end, the
team could have reached the target score following its usual
scoring pattern and won the match.
Analysis of the D/L Method (contd.)
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
8

9.  The loss of a wicket puts the new partnership in unduly
stress because they are expected to compensate for the
loss of the wicket by adding quick runs.
 The new partnership is further stressed by requiring them
to perform above the expected scoring pattern dictated by
the D/L method as the match may be terminated at any
point due to the change in weather condition.
 Each team has its own performance pattern and is not
capable of performing to stay always above the expected
scoring pattern specified by the D/L method though they
could win the game if it was not interrupted.
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
9
Analysis of the D/L Method (contd.)

10.  We also analysed the D/L Method using actual
average performance patterns of world teams.
 We obtained the average scoring patterns of world
teams by using the data of 36 unshortened one day
internationals played between May 2010 and 2012 by
each of the teams, Australia, Bangladesh, England,
India, New Zealand, Pakistan, South Africa, Sri Lanka,
West Indies and Zimbabwe.
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
10
Analysis of the D/L Method (contd.)

11. Analysis of the D/L Method (contd.)
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
11
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
PercentageScore
Over Number
Fig. 4: Average Scoring Patterns of World Teams
WI
BAN
IND
ENG
SA
AUS
ZIM
NZ
SL
PAK
Expected Scoring W-5
Expected Scoring W-10

12.  The graphs in Fig. 4 reveal that there is a marked difference between the
scoring patterns of England and Australia.
 The performances of the other teams lie between the performances of
these two teams. As we can see, the performances of all world teams lie
below the expected performance graph of D/L method approximately after
over 20 for W-5.
 This implies that all teams would be under pressure if they happen to bat
second in a game that is threatened to be stopped at any time due to bad
weather conditions and lose a wicket after every 5 overs.
 However, England is under much less pressure as their scoring pattern lies
above or closer to the expected scoring pattern most of the time and
Australia is under highest pressure as their scoring pattern lies below and
farther from the expected scoring pattern most of the time.
Analysis of the D/L Method (contd.)
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
12

13.  To investigate further, we performed a chi-square test for similarity.
 We used the same data of 36 unshortened one day internationals.
 Though the second innings of these matches were not interrupted,
we predicted the expected score calculated by the D/L method if
each of these innings had to be terminated abruptly at the end of
each over.
 We used a level of significance of 0.05.
 H0: The expected scoring pattern of the D/L method and the scoring
pattern of the world team under consideration are similar.
 H1: The expected scoring pattern of the D/L method and the scoring
pattern of the world team under consideration are different.
Statistical Analysis
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
13

14.  In each innings, there were at most 50 data points.
 Thus, the degrees of freedom was less than or equal to 49. For
this value of the degrees of freedom, the upper tail critical value
was found to be 66.339 from the Chi-Square Tables.
 If the number of data points in an innings is less, then, the
degrees of freedom will be less and the upper tail critical value
will be less than 66.399. As we can see, most of the test
statistics values in Table 1 are greater than 66.399 and we reject
the null hypothesis and conclude that the expected scoring
pattern of the D/L method and the scoring pattern of any team
under consideration are different.
Statistical Analysis (contd.)
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
14

15.  We have shown the reason for the unfairness of the D/L method.
 It was found to be due to the inherent nature of the D/L method that use
graphs produced using past statistics of all teams of the world.
 The expected performance specified by those graphs deviate considerably
from the actual performance of the teams.
 It will not be possible to remove this unfairness by any modification to the
curves of the D/L method as they will never match completely with actual
performance of the teams.
 The cricket playing nations and the ICC should seriously consider removing
the D/L method for target score adjustment and explore other avenues.
 The recently introduced Planned Performance Method may be a better
alternative for one-day internationals and T20 cricket matches.
Conclusion
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
15

16. Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
16
Questions

17.  [1] Duckworth, FC & Lewis, AJ, A fair method of resetting the target in interrupted one-day cricket
matches, Journal of the Operational Research Society, vol. 49, no. 3, pp. 220-227, 1998.

 [2] Bhogle, S, Is Jayadevan's proposed method better than the Duckworth/Lewis method?,
http://www.rediff.com/cricket/2001/may/21srini.htm, 2001, 2001.

 [3] Bandulasiri, A, Predicting the Winner in One Day International Cricket, Journal of Mathematical
Sciences and Mathematics Education, vol.3, no. 1, pp. 6-17, 2008.

 [4] Jayadevan, V, A New Method for the Computation of Target Scores in Interrupted Limited-Over
Cricket Matches, Current Science, vol. 83, no. 5, pp. 577–586, 2002.

 [5] de Silva, R, A Fair Target Score Calculation Method for Reduced-Over One day and T20
International Cricket Matches, Journal of Mathematical Sciences & Mathematics Education vol. 8, no.
2, pp. 6-19, 2013.

Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
17
References

18.  [6] Duckworth, FC & Lewis, AJ, Duckworth/Lewis Method of Re-calculating the Target Score in an
Interrupted Match, http://static.icc-cricket.yahoo.net/ugc/documents/DOC_1F1135280
 40177329F40FE47C77AE2_1254317757686_695.pdf.

 [7] Swartz, TB, Gill, PS, Beaudoin, D & de Silva, MB, Optimal batting orders in one-day cricket,
Computers & Operations Research, vol. 33, no. 7, pp. 1939–1950, 2006.

 [8] Norman, JM & Clarke, SR, Optimal batting orders in cricket, Journal of the Operational Research
Society, vol. 61, pp. 980-986, 2010.

 [9] de Silva, MB, Pond, GR & Swartz, TB, Estimation of the magnitude of victory in one-day cricket,
Australian and New Zealand Journal of Statistics, vol. 43, pp. 259-268, 2001.

 [10] Lemmer, HH, The single match approach to strike rate adjustments in batting performance
measures in cricket, Journal of Sports Science and Medicine, vol. 10, no. 4, pp. 630-634, 2010.
Analysis of the D/L Method Used for Target Resetting in
Interrupted Limited Over Cricket Matches – Rohan de Silva
18
References (contd.)