1. Validation Of Players Inclusion Into
The National Cricket Team
Chetan Reddy Mitta

2. Introduction :What is Cricket?
• Cricket is a sport played by two teams of eleven
players each, which takes turns to bowl a hard-leather
ball
• similar to baseball, with players striking a ball and
trying to score as many runs as possible

4. Batting :
• Batting is the act or skill of hitting the cricket ball with
a cricket bat to score runs or prevent the loss of one's
wicket
• The terms batsman or specialist batsman are also used
generically to describe players who specialize in batting
• The main concerns for the batsmen are not to lose their
wicket and to score as many runs as quickly as possible.
• The main statistic for batting is the batting average,
the mean score achieved by the batsman over his career

5. A Batsman

6. Problem Definition:
• Evaluate the performances of four Indian Batsman
using the parametric control chart
• Compare the performances and make a decision
• Compare the decision with the selector‟s decision and
justify

7. Methodology :
• Bracewell and Rugiero in their paper “A Parametric
Control Chart for batting performances In cricket”
have proposed a distribution model for the batting
scores
• This is an application of the above paper

8. • Ducks and runs distribution has been proposed
• Inspired from the sport
• Score and Contribution are two important performance
measures
• A beta distribution is used to model the zeros
• Zeros-final score of a batsman at the end of the innings is “0”
• And geometric distribution is modeled for non zero runs (final
score of a batsman at the end of the innings is > 0) part of the
distribution
Methodology:

9. Methodology:
• The probability density function for contribution follows
a beta distribution and is given as:
• C is the contribution made by a batsman in an innings
• Here we consider it to be 0.01

10. Methodology:
• Probability for non-zero is obtained from geometric distribution
• P(S=s) =d if s=0 and 0≤d≤1
• = (1-d)*r*
• S- The number of runs scored by an individual batsman
• r- The probability of a non zero score is obtained from the probability
mass function of a geometric distribution.
• r= reciprocal of the non zero mean score
• Here, the not outs (i.e., if a batsman has to end the innings not because he
was out but for any other reason) are considered as the end of the innings

11. Control Chart :
• provides us with the information related to the player‟s
form, which is a prime factor for them to be included in
the team
• Traditional control charts fail to give us any information
as they are unsuitable for cricket data
• Assumption of normality is violated. It is necessary that
we keep extreme scores as they indicate their performance
• A control chart is proposed based on the Quartiles. The
properties of ducks and runs distribution is derived to
theoretical quartiles since the sample sizes are small

12. Methodology:
• First Quartile:
• Median:
• Quartile 3:
• Where D=1-d; R=ln(1-r)
• These are used to define the control lines

13. Zone Rules :
• With the three control lines, chart is divided into 4 zones
• The situations designed for use are set with 95%
confidence limits
• H0: There is no change in the form
• H1: There is change in the form
• Six run rules have been proposed and have to satisfy
•

14. Situations :
Situation Description(points lying) Number of
points(consecutive)
a zones 4 or/and 1 5
b zones 2& 3 5
c any one zone 3
d above or below median
(zone1&2 or 3&4)
5
e Points increasing/decreasing 4
f Avoiding zone 1/4 11

15. Method II : Bayesian Approach
• a player who comes late to batting might end up with low not
out score‟s which would affect his overall performance chart
• we would like to estimate the score he would have gone on to
score if he was not out for that particular innings
• Grk = 0 if Rk< Rj and
• = 1 if Rk >= Rj for k = 1,2,….j-1
• nj = Σ Grk
• Ck = 0 if Rk< Rj and
• = Rk If Rk >= Rj for k = 1, 2,….j-1

16. Methodology:
• The estimate of the number of runs that the „not-out‟ batsman would
have gone on to score is
• then given by:
• Ej = Σ Ck / nj
•
• Rk =scores of a player i in each innings of k=1 to j-1
• Rj = Score of the innings in which a player is not out in jth innings
• Ej= Estimate score of a particular not out innings

17. Results:
Four players are :
• Rohit sharma
• Virat Kohli
• Robin Uthappa
• Suresh raina

19. Situation :
Situation Yes No
a X
b X
c X
d X(above)
e X(Dec)
f X(avoid 1)

20. Virat Kohli :
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Upper Q
Scores
Lower Q
Median
Innings
R
u
n
s

21. Situation:
Situation Yes No
a X
b X
c X(zone 4)
d X
e X(INC)
f X(avoid 1)

22. Robin Uthappa :
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Scores
Lower Q
Upper Quartile
Series4
R
u
n
s
Innings

23. Situation:
Situation Yes No
a X
b X
c X
d X(above)
e X(inc)
f X(avoid 1)

24. Suresh Raina :
0
20
40
60
80
100
120
140
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 53 55 57 59 61 63 65 67 69 71 73
Scores
Lower Q
Median
Upper Q
Innings
R
u
n
s

25. Situation:
Situation Yes No
a X
b X
c X(zone 4)
d X
e X(INC)
f X

26. Who should be selected ?
• Suresh Raina and virat kohli have to be given more
chances
• Selectors Decision:
• Virat Kohli and Suresh Raina have been both
selected into the national squad for the series against
South Africa 2010. In the two matches, virat kohli
scored 31 & 57 and suresh raina scored 58&49.

27. Using Method II :
• Rohit :
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Scores
Q1
M
Q2

28. Situation:

29. Virat:
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Estimated score
Q1
M
Q2

30. Situation:

31. Robin :
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
scores
Q1
M
Q2

32. Situation:

33. Rohit :
0
20
40
60
80
100
120
140
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 53 55 57 59 61 63 65 67 69 71
scores
Q1
M
Q2

34. Situation:

35. Comparison :
Player’s Name Positive Sign Negative Sign
Rohit Sharma 5 0
Virat Kohli 5 0
Robin Uthappa 5 0
Suresh Raina 8 4

36. Conclusion :
• This result is similar to the parametric control chart
method without estimation. But by applying this we
get the bigger and better picture of each player.
Rohit Sharma had 10 not outs in total which made
him look to be the last choice but when you estimate
the not out scores we can see a significant
improvement in his parametric control chart

37. References :
• Bracewell.J,Ruggiero.K (2009) A Parametric Control
Chart for Batting performances In cricket, Journal of
Quantitative Analysis in Sports ,5(3),art 5
• Damodaran,Uday (2006) Stochastic Dominance and
Analysis of ODI Batting Performances: The Indian
Cricket Team, 1989-2005, Journal of Sports Science and
Medicine, 5, 503-508

38. Questions ?