analysis of different parameters in game of cricket

Akshat Aggarwal (105011)

Ronit Arora (105016) Shrawan Arya (105044) Kunwar Preet Singh (105046)

P Ganesh (105054) Nikhil Bansal (105067) Anmol Jain (105076)

Deepak Kataria (105080)

ANALYSIS OF DIFFERENT PARAMETER

IN THE GAME OF CRICKET

`

DECLARATION

This is to certify that the material embodied in this present project is based on our original

research work. Our indebtedness to other works, studies and publications have been duly

acknowledge at the relevant places. This project work has not been submitted in part or in full

for any other diploma or degree in this or any other university.

Project Supervisor : Mrs Manisha Rao

Group Members

Akshat Aggarwal (105011)

Ronit Arora (105016)

Shrawan Arya (105044)

KunwarPreet Singh (105046)

P Ganesh (105054)

Nikhil Bansal (105067)

Anmol Jain (105076)

Deepak Kataria (105080)

`

INDEX

SR. NO TOPIC PAGE NO

1. Acknowledgement 1

2. Introduction –

Aim 2

Objective 2

3. Review Of Literature 3

4. Hypothesis 1 5

5. Hypothesis 2 23

6. Hypothesis 3 36

7. Hypothesis 4 45

8. Conclusion 56

9. Limitations and Further Scope 57

10. Bibliography 58

1

ACKNOWLEDGEMENT

The satisfaction and euphoria that accompany the successful completion of any task would be

incomplete without mentioning the people who made it possible, whose consistent guidance

and encouragement crowned the effort with success.

First of all, we are thankful to our Computer Teacher – Mr Hitesh Sachdeva, under whose

guidance we are able to complete our project. We are wholeheartedly thankful to him for

giving us his valuable time & attention & for providing us a systematic way for completing our

project in time.

We must also make special mention of Mrs Manisha Rao, our Project Supervisor for her co-

operation and assistance in making of the project. We would thank all lab maintenance staff for

providing us assistance in various problem encountered during the course of the project.

Also, we will like to thank our collegues, friend and everyone who has helped us in completing

this project.

Thank You

`

2

INTRODUCTION

AIM

To understand and compare the different parameters in the field of cricket with the help of

Statistical Software like Microsoft Excel and SPSS, and check whether there is any relation

between them.

OBJECTIVE

For carrying out the project, the following objectives have been formulated:

To do a literature review in order to learn from the past studies already done on the

topic.

To learn the use of software for doing statistical analysis.

To prepare various hypothesis in order to compare different parameters in the field of

cricket to check:

o A relation between the strike rate of the player in One day International (ODI)

matches & Test matches,

o A relation between mean economy rate of a fast bowler & a spinner in ODI’s,

o A relation between the team winning the Toss, and the team eventually wining

the match,

o A relation between the no. of wickets taken and 3 things bowling average, strike

rate and economy rate.

3

REVIEW OF LITERATURE

An attempt was made in order to learn from the similar studies done in the past, the following

sub-section summarises the major findings of the project.

LITERATURE 1

In the study done by Silva B.M. and Swartz T.B. (1994), statistical analysis of 427 one-day

international cricket matches playe during the 1990s was done. Two general conclusion were

obtained (1) Contrary to widespread opinion, winning the coin toss at the outset of a match

provides no competitive advantage ( 2 ) the advantage of playing on one’s home field increases

the log-odds of the probability of winning by approximately 0.5

LITERATURE 2

In the study done by Staden P.J (2012), comparison of cricketer’s batting and bowling abilities

was done with very basic performance measures. More sophisticated measures

were been proposed, but were generally not used due to a variety of reasons, including

the statistical illiteracy of those involved in cricket, the way cricket data is captured

and presented for bowlers and for batsmen and the different rules applicable for the

various formats of the game. Graphical displays for comparisons have not featured

prominently. In this paper a graph, originally proposed for comparing bowlers, was

presented and adapted for comparing batsmen and all-rounders. The construction

and interpretation of the graphs was illustrated with cricket records from the recent

Indian Premier League (IPL)

4

LITERATURE 3

In a study done by Gill P.S, Beaudoin D, a test was conducted in search for optimal or nearly

optimal batting orders in one-day cricket. . A search was conducted over the space of

permutations of batting orders where simulated annealing was used to explore the space.

A non-standard aspect of the optimization was that the objective function (which is the mean

number of runs per innings) was unavailable and was approximated via simulation. The

simulation component generates runs ball by ball during an innings taking into account the

state of the match and estimated characteristics of individual batsmen.

`

6

Null Hypothesis: Average strike rate of a player in ODI matches is

equal to average strike rate in TEST matches.

Alternative Hypothesis: Average strike rate of a player in ODI

matches is not equal to average strike rate in TEST matches.

Null Hypothesis: Variation in strikes rate of a player in equal in

TEST and ODI matches.

Alternative Hypothesis: Variation in strike rates of a player is

different in TEST and ODI matches.

We will test the above Hypothesis using the Stats of two players,

that are – Virendre Sehwag (India ), and Sachin Tendulkar ( India )

`

7

First, we will apply different test on the Stats of Virendr Sehwag.

Score of Virendre Sehwag(Ind) in 50 random innings of his test career and their Strike rate.

Virendra Sehwag test matches

INNINGS RUNS SCORED

NO. OF BALLS FACED

STRIKE RATES

1 84 96 87.5

2 61 65 93.84

3 195 233 83.69

4 309 375 82.4

5 76 82 92.68

6 254 247 102.83

7 201 262 76.71

8 76 89 85.39

9 180 190 94.73

10 65 75 86.66

11 151 236 63.98

12 319 304 104.93

13 201 231 87.01

14 90 122 73.77

15 66 69 95.65

16 92 107 85.98

17 83 68 122.05

18 131 122 107.37

19 293 254 115.35

20 52 51 101.96

21 109 139 78.41

22 165 174 94.82

23 109 118 92.37

24 99 101 98.01

25 109 105 103.8

26 59 54 109.25

27 173 119 86.93

28 96 120 80

29 54 54 100

`

8

30 74 73 101.36

31 55 46 119.56

32 55 55 100

33 60 65 92.3

34 67 83 80.72

35 62 53 116.98

36 105 173 60.69

37 147 206 71.35

38 47 50 94

39 173 244 70.13

40 44 48 70.9

41 50 52 91.66

42 56 63 96.15

43 47 41 88.8

44 38 33 114.63

45 45 51 115.15

46 135 221 88.23

47 88 118 70.13

48 44 44 100

49 36 28 128.57

50 63 90 74.57

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

INNINGS

STR

IKE

RA

TE

Inning Wise Strike Rate Of Virendre Sehwag in

50 Innings of his Test Career.

`

9

Score of Virendre Sehwag(Ind) in 50 random innings of his ODI career and their Strike rate.

odi matches

INNINGS RUNS SCORED

NO. OF BALLS FACED

STRIKE RATES

1 58 54 107.41

2 100 70 142.86

3 55 43 127.91

4 51 58 87.93

5 82 62 132.26

6 71 65 109.23

7 42 36 116.67

8 126 104 121.15

9 59 58 101.72

10 114 82 139.02

11 108 119 90.76

12 112 139 80.58

13 66 76 86.84

14 82 81 101.23

15 43 44 97.73

16 130 134 97.01

17 90 102 88.24

18 99 101 98.02

19 109 105 103.81

20 59 54 109.26

21 173 119 145.38

22 96 120 80

23 54 54 100

24 74 73 101.37

25 55 46 119.57

26 55 55 100

27 60 65 92.31

28 67 83 80.72

29 62 53 116.98

30 105 173 60.69

31 147 206 71.36

32 47 50 94

33 173 244 70.9

`

10

34 44 48 91.67

35 50 52 96.15

36 56 63 88.89

37 47 41 114.63

38 38 33 115.15

39 45 51 88.24

40 155 221 70.14

41 70 52 134.62

42 74 40 185

43 48 22 218.18

44 75 65 115.38

45 77 62 124.19

46 78 44 177.27

47 119 95 125.26

48 49 33 148.48

49 60 36 166.67

50 114 87 131.03

0

50

100

150

200

250

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

INNINGS

STR

IKE

RA

TE

Inning Wise Strike Rate Of Virendre Sehwag in

50 Innings of his ODI Career.

`

11

This is how we get the above results. Using

Formulas in Excel.

TEST MATCHES ( Strike Rate )

ODI MATCHES ( Strike Rate )

AVERAGE 92.679

AVERAGE 111.2774

VARIANCE 242.9632622


CORRELATION 0.040662259

CORRELATION 0.040662259

CV 16.81%

CV 27.70%

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12

t-Test: Two-Sample Assuming Unequal Variances

Variable 1 Variable 2

Mean 92.679 111.2774

Variance 242.9632622449 955.08869310204

Observations 50 50

Hypothesized Mean Difference 0

Df 72

t Stat -3.79946772730192

t Critical two-tail 1.99346353904453

F-Test Two-Sample for Variances


Mean 92.679 111.2774

Variance 242.9632622449 955.08869310204

Observations 50 50

Df 49 49

F 0.254388167297612

F Critical two-tail 0.622165466996477

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13

VIRENDER SEHWAG

1. THE AVERAGE STRIKE RATE IS 92.679 IN TEST AND 111.2774 IN ODI. THIS

SUGGEST THAT THIS IS NOT AS SIGNIFICANT AS COMPARED TO SACHIN AND

OTHER PLAYERS. THIS IS DUE TO HIS BATTING STYLE/

2. THE CV IN TEST IS 16.81 IN TEST AND 27.7 IN ODI . IT SUGGEST THAT THE

VARIATION IS HIGH IN BOTH THE CASES.

3. THE CV IS LESS IN TEST THAN ODI . IT SUGGEST THAT SEHWAG IS MORE

CONSISTENT IN TEST THAN ODI.

4. THE CORRELATION COFFICIENT IS 0.04. IT IMPLIES THAT THER IS VERY LOW

DEGREE OF ASSOCIATION (ALMOST NO) BETWEEN STRIKE RATES IN BOTH THE

FORMATS.

`

14

HYPOTHESIS TESTING

LET U1 AND U2 THE AVERAGE STRIKE RATES OF A PLAYER IN TEST AND ODI

RESPECTIVELY

NULL (H0):U1=U2

ALTERNATIVE (H1):U1 ≠ U2

The test statistic value -3.79 is less than critical value -1.99. Therefore we have

sufficient evidence to reject null at 5% significance level.

CONCLUSION

SO WE CONCLUDE THAT THERE IS SIGNIFICANT DIFFERNCE BETWEEN AVERAGE

STRIKE RATES OF SEHWAG IN BOTH THE FORMATS.

Let σ12 and σ2

2 be the variance in strike rates of a player in TEST and ODI

matches respectively.

Null (Ho): σ12 = σ2

2

Alternative (H1): σ12 ≠ σ2

2

CONCLUSION:

The F-Test shows that “Test statistic value” (0.254) is less than “Critical value”

(0.622), So we do not reject Null at 5% significance level.

So we conclude that Variation in strike rates of Sehwag is same in both the

formats.

`

15

Now, we will apply different test on the Stats of Sachin Tendulkar. Score of Sachin Tendulkar(Ind) in 50 random innings of his test career and their Strike rate.

Sachin Tendulkar test matches

INNINGS RUNS SCORED

NO. OF BALLS FACED

STRIKE RATES

1 88 266 33.08

2 119 189 62.96

3 148 213 69.48

4 114 161 70.8

5 111 270 41.11

6 73 208 35.09

7 165 296 55.74

8 104 161 64.59

9 96 140 68.57

10 179 322 55.59

11 122 177 68.92

12 177 360 49.16

13 74 97 76.28

14 169 254 66.55

15 92 147 62.58

16 139 266 52.25

17 155 191 81.15

18 113 151 74.83

19 136 273 49.81

20 44 39 112.82

21 217 344 63.08

22 116 191 60.73

23 97 163 59.5

24 74 128 57.89

25 155 184 84.23

26 88 144 61.11

27 103 197 52.28

28 176 316 55.69

29 117 260 45

30 92 113 81.41

`

16

31 193 330 58.48

32 176 298 59.06

33 241 436 55.27

34 194 348 55.74

35 248 379 65.43

36 94 202 46.53

37 109 196 55.61

38 64 130 49.23

39 101 159 59.76

40 122 226 53.98

41 154 243 63.37

42 153 205 74.63

43 109 188 59.97

44 103 196 52.55

45 160 260 61.53

46 100 211 47.59

47 105 166 63.25

48 143 182 78.57

49 100 179 55.86

50 106 206 51.45

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

INNINGS

STR

IKE

RA

TE

Inning Wise Strike Rate Of Sachin Tendulkar in

50 Innings of his Test Career.

`

17

Score of Sachin Tendulkar(Ind) in 50 random innings of his ODI career and their Strike rate.

ODI matches

INNINGS RUNS SCORED

NO. OF BALLS FACED

STRIKE RATES

1 84 107 78.5

2 110 130 84.61

3 115 136 84.55

4 105 134 78.35

5 112 137 104.67

6 127 138 92.02

7 137 137 100

8 100 11 90.09

9 118 140 84.28

10 110 138 79.71

11 114 126 90.47

12 104 97 107.21

13 117 137 85.4

14 91 87 104.59

15 100 89 112.35

16 143 131 109.16

17 134 131 102.29

18 100 103 97.08

19 128 131 97.7

20 127 130 97.69

21 141 128 110.15

22 118 112 105.35

23 124 92 134.78

24 140 101 138.61

25 120 140 85.1

26 186 150 124

27 122 138 88.4

28 146 153 95.42

29 139 125 111.2

30 122 131 93.12

31 105 108 97.22

32 113 102 110.78

`

18

33 152 151 100.66

34 98 75 130.66

35 97 120 80.83

36 141 135 104.44

37 123 130 94.61

38 141 148 95.27

39 99 143 69.23

40 99 112 88.39

41 117 120 97.5

42 163 133 122.25

43 200 147 136.05

44 120 115 104.34

45 111 101 109.9

46 85 115 73.91

47 96 104 92.3

48 91 121 75.2

49 99 91 108.79

50 84 80 105

0

20

40

60

80

100

120

140

160

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

INNINGS

STR

IKE

RA

TE

Inning Wise Strike Rate Of Sachin Tendulkar in

50 Innings of his ODI Career.

`

19

This is how we get the above results. Using

Formulas in Excel.

TEST MATCHES

ODI MATCHES

AVERAGE 60.8028

AVERAGE 99.2836



CORRELATION - 0.094141578

CORRELATION -0.094141578

SKEWNESS 1.10005858 SKEWNESS 0.5789129

CV 22.07%

CV 16.26%

`

20

t-Test: Two-Sample Assuming Unequal Variances

Variable 1 Variable

2

Mean 60.8028 99.2836

Variance 180.07475 260.8007

Observations 50 50


df 95

t Stat -12.95899




Mean 60.8028 99.2836

Variance 180.0747471 260.80067

Observations 50 50

df 49 49

F 0.690468876

F Critical one-tail 0.622165467

`

21

1. THE AVERAGE STRIKE RATE IN TEST MATCHES AND ODI MATCHES DIFFERS

SIGNIFICANTLY. IT IS HIGH IN ODI AND LOW IN TEST.

2. THE COFFICIENT OF VARIATION IS 22.07% IN TEST AND 16.26% IN ODI. IT SUGGEST

THAT VARIATION IN STRIKE RATES IS HIGH IN BOTH THE CASES.

3. CV IS HIGH IN TEST THAN IN ODI. IT SUGGEST THAT THERE IS MORE VARIATION IN

TEST MATCHES IN STRIKE RATES. IT MAY BE BECAUSE DURATION OF TEST MATCHES

IS MORE THAN OF ODI AND DUE TO BATTING STYLE

4. THE CORRELATION COFFICIENT IS -0.09, IT IMPLIES THAT THERE IS ALMOST NO

CORRELATION (OR LOW DEGREE OF NEGATIVE CORRELATION) BETWEEN THE STRIKE

RATES IN 2 FORMATS.

5. THE COFFICIENT OF SKEWNESS IN TEST MATCHES IS 1.1 OF THE SAMPLE TAKEN .

THIS IMPLIES THAT THE DATA IS HIGHLY POSITIVELY SKEWED. IT IS 0.57 IN ODI

MATCHES , THIS IS ALSO POSITIVELY SKEWED BUT APPROXIMATELY NORMAL.

`

22

HYPOTHESIS TESTING

Let u1 and u2 the average strike rates of a player in test and odi respectively

Null (ho): u1=u2

alternative (h1): u1 ≠ u2

Level of signicance=5%

The test done shows that test statistic value (-12.95) is less than crtical value(-

1.985). Therefore we reject null at 5% significance level.

CONCLUSION We conclude that there is significant differnce between average strike rates of

sachin in ODI and test. The average strike rate is more in ODI than test.

Let σ12 and σ2

2 be the variance in strike rates of a player in TEST and ODI

matches respectively.

Null (Ho): σ12 = σ2

2

Alternative (H1): σ12 ≠ σ2

2

CONCLUSION The F- Test shows that “Test statistic value” (0.699) is greater than “Critical

value” (0.622), So we reject the null at 5 % significance level.

So we conclude that variation in strike rates of “Sachin” is different in both the

formats.

`

24

The statistical test presented here is to analyze the relationship between economy rates in odi’s

of fast bowlers and slow bowlers in their respective last 10 matches.

The sample is taken from five most active countries playing odi’s i.e. India, Australia, Sri lanka,

Pakistan and South Africa. From each team we have selected one main fast bowler and one

slow bowler in order to test whether or not there is any significant difference between their

economy rates.

The sample size is taken of 50 for each in order to cater to the normality assumption

Null Hypothesis: Average Economy Rate of the Fast Bowler and

the Slow Bowler is equal.

Alternative Hypothesis: Average Economy Rate of the Fast Bowler

and the Slow Bowler is not equal.

Null Hypothesis: Variance in Economy Rate of the Fast Bowler and

the Slow Bowler is equal.

Alternative Hypothesis: Variance in Economy Rate of the Fast

Bowler and the Slow Bowler is not equal.

`

25

DATA

Economy Rate of Top 2 Bowler’s from Different countries in 10

random ODI matches

South Africa

Dale Styne ( Fast Bowler )

Overs Mdns Runs Wkts Econ Opposition

9 2 24 2 2.66 v England

9.4 0 47 2 4.86 v England

7 0 32 1 4.57 v England

7 2 28 0 4 v New Zealand

10 1 37 1 3.7 v New Zealand


10 0 55 1 5.5 v Sri Lanka

9 1 54 1 6 v Sri Lanka

3 0 7 1 2.33 v Sri Lanka

10 0 44 1 4.4 v Australia

RE van der Marwe ( Spinner )


10 1 27 1 2.7 v West Indies

10 0 47 2 4.7 v India

10 0 62 1 6.2 v India

6 0 50 0 8.33 v England

9 0 55 0 6.11 v England

8.3 0 27 3 3.17 v Zimbabwe

9 0 67 0 7.44 v England


10 0 42 0 4.2 v Sri Lanka


http://stats.espncricinfo.com/ci/engine/player/47492.html?class=2;orderby=overs;template=results;type=bowling;view=innings

http://stats.espncricinfo.com/ci/engine/player/47492.html?class=2;orderby=maidens;template=results;type=bowling;view=innings

http://stats.espncricinfo.com/ci/engine/player/47492.html?class=2;orderby=conceded;template=results;type=bowling;view=innings

http://stats.espncricinfo.com/ci/engine/player/47492.html?class=2;orderby=wickets;template=results;type=bowling;view=innings

http://stats.espncricinfo.com/ci/engine/player/47492.html?class=2;orderby=economy_rate;template=results;type=bowling;view=innings

http://stats.espncricinfo.com/ci/content/team/1.html










`

26

Australia

bret lee ( Fast Bowler )


2.2 1 12 0 5.14 v England

10 0 58 0 5.8 v England

10 1 57 1 5.7 v England

3 1 10 2 3.33 v Ireland



9.4 1 52 1 5.37 v West Indies



8 0 59 3 7.37 v Sri Lanka

Brad Hogg ( Spinner )


7 0 38 1 5.42 v India

10 1 33 1 3.3 v Sri Lanka

9 0 62 1 6.88 v India

4.3 1 15 0 3.33 v Sri Lanka

8 1 30 2 3.75 v India

10 1 41 2 4.1 v Sri Lanka

6 1 17 1 2.83 v Sri Lanka



8 0 40 0 5 v India































`

27

India

Zaheer Khan ( Fast Bowler )


9 1 53 1 5.88 v Sri Lanka

6 0 36 0 6 v Sri Lanka

10 0 39 2 3.9 v Sri Lanka

6 0 39 0 6.5 v Sri Lanka

10 0 63 1 6.3 v Sri Lanka

9 0 61 1 6.77 v Sri Lanka



10 1 44 2 4.4 v Sri Lanka

10 3 60 2 6 v Sri Lanka

R Ashwin ( Spinner )


9 0 37 0 4.11 v Sri Lanka

10 1 46 2 4.6 v Sri Lanka

10 0 50 0 5 v Sri Lanka

5 1 18 1 3.6 v Sri Lanka

10 1 46 2 4.6 v Sri Lanka

10 0 56 1 5.6 v Pakistan

10 0 56 1 5.6 v Bangladesh

9 0 39 3 4.33 v Sri Lanka

10 0 52 0 5.2 v Sri Lanka

















`

28

Pakistan

Umar Gul ( Fast Bowler )


10 1 43 0 4.3 v Sri Lanka

8 1 51 1 6.37 v Sri Lanka

9 0 58 0 6.44 v Sri Lanka

9 2 24 3 2.66 v Sri Lanka


8.5 0 65 2 7.35 v India

8 1 20 2 2.5 v Sri Lanka

9.1 0 58 3 6.32 v Bangladesh

7 0 59 0 8.42 v England

7 1 43 0 6.14 v England

Saeed Ajmal ( Spinner )




10 0 30 3 3 v Australia

10 1 50 2 5 v Sri Lanka

10 0 49 1 4.9 v Sri Lanka

10 2 40 2 4 v Bangladesh

9 0 49 1 5.44 v India

8.4 1 27 3 3.11 v Sri Lanka


10 0 62 3 6.2 v England
















`

29

Sri Lanka

Lasith Malinga ( Fast Bowler )



10 0 64 3 6.4 v India

8 1 41 1 5.12 v India

10 0 60 2 6 v India

7.3 0 36 2 4.8 v India

10 0 83 0 8.3 v India

10 1 52 1 5.2 v Pakistan

7 0 30 2 4.28 v Pakistan

3 0 9 1 3 v Pakistan

8 1 40 2 5 v Pakistan

Ajantha Mendis ( Spinner )


8 0 54 1 6.75 v South Africa

9.1 0 49 3 5.34 v Australia





8 2 24 1 3 v Scotland

9.5 0 35 3 3.55 v New Zealand

10 0 34 1 3.4 v England

6 0 24 2 4 v New Zealand

`

30

FAST BOWLERS ECONOMY RATE IN ODIs

MATCHES SA AUS IND PAK SL

1 2.66 5.14 5.88 4.3 3.9

2 4.86 5.8 6 6.37 6.4

3 4.57 5.7 3.9 6.44 5.12

4 4 3.33 6.5 2.66 6

5 3.7 4.66 6.3 6.5 4.8

6 4.11 7.2 6.77 7.35 8.3

7 5.5 5.37 4.6 2.5 5.2

8 6 4.62 4.6 6.32 4.28

9 2.33 3.57 4.4 8.42 3

10 4.4 7.37 6 6.14 5

VARIANCE

2.107397714

MEAN ECONOMY RATE

5.1768

COEFFICIENT OF VARIATION

0.28042186

SKEWNESS

0.043348757

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31

SLOW BOWLERS ECONOMY RATE IN ODIs

MATCHES SA AUS IND PAK SL

1 2.7 5.42 4.11 4.11 6.75

2 4.7 3.3 4.6 3.2 5.34

3 6.2 6.88 5 3 4.42

4 8.33 3.33 3.6 5 4.75

5 6.11 3.75 4.6 4.9 3.83

6 3.17 4.1 5.6 4 5.33

7 7.44 2.83 5.6 5.44 3

8 3.5 8.16 4.33 3.11 3.55

9 4.2 4.9 5.2 4.5 3.4

10 4.4 5 4.5 6.2 4

VARIANCE

1.763029755

MEAN ECONOMY RATE

4.6678

COEFFICIENT OF VARIATION

0.284457626

SKEWNESS

0.900545694

`

32

HYPOTHESIS TESTING

Testing for equality of average ECONOMY RATES

t-Test: Two-Sample Assuming Equal Variances


Mean 5.1768 4.6678

Variance 2.107397714 1.763029755

Observations 50 50

Pooled Variance 1.935213735


df 98

t Stat 1.829461683


TESTING FOR EQUALITY OF VARIANCES IN ECONOMY RATES



Mean 5.1768 4.6678

Variance 2.107397714 1.763029755

Observations 50 50

df 49 49

F 1.195327367

F Critical two-tail 1.607289463

`

33

1. The average economy rate of fast bowlers and slow bowlers in ODI’s are

calculated as 5.18 and 4.67 respectively. It shows that there is almost no

significant difference between economy rates of fast bowlers and slow bowlers.

2. The COEFFICIENT of VARIATION is 28.04% in economy rates of fast bowlers and

28.44% in economy rates of slow bowlers in ODI’s. It implies that the variation is

high in both the economy rates of fast bowlers and slow bowlers and more

importantly they are almost equal which shows that the variation in economy

rates is almost similar.

3. The coefficient of skewness in economy rates of fast bowlers and slow bowlers is

0.04 and 0.90 respectively. The values show that the economy rates are positively

skewed for both the cases and they are approximately normal as well.

4. The COEFFICIENT of CORRELATION between the economy rates is -0.051.It

implies that there is low degree of negative linear correlation between the

economy rates.

`

34

HYPOTHESIS TESTING

(1) LET µ1 and µ2 be the average economy rates of fast bowlers and slow bowlers

in ODI’s respectively. Our purpose is to check whether there is any significant

difference between the average economy rates of the fast bowlers and slow bowlers

in ODI’s or not.

Null Hypothesis (H0): average economy rates are equal i.e. µ1 = µ2

Alternative Hypothesis (H1): average economy rates are not equal i.e.

µ1≠ µ2

LEVEL OF SIGNIFICANCE = 5%

INFERENCE:

The T-test here done shows that the TEST STATISTIC VALUE of 1.829 is less than

the 5% critical value of 1.984.

Therefore we have insufficient evidence to reject null hypothesis at this

level of significance and conclude that the average economy rates of fast

bowlers and slow bowlers is equal in ODI’s.

(2) Let σ12 and σ2

2 be the variance of economy rates in ODI’s of fast bowlers and

slow bowlers respectively. Our purpose is to check whether there is any significant

difference between the variance of economy rates of the fast bowlers and slow

bowlers in ODI’s or not.

Null Hypothesis (H0): Variances are equal i.e. σ12 = σ2

2

Alternative (H1):

Alternative Hypothesis (H1): Variances are not equal i.e. σ12 ≠ σ2

2

LEVEL OF SIGNIFICANCE = 5%

`

35

INFERENCE:

The F-test here done shows that the TEST STATISTIC VALUE of 1.195 is less than

the 5% critical value of 1.607.

Therefore we have insufficient evidence to reject null hypothesis at this

level of significance and conclude that the variance of economy rates, in

ODI’s, of fast bowlers and slow bowlers is equal.

`

37

We will test the above Hypothesis using the Stats of 18

Countries that have played 294 matches starting from 1975

ODI World Cup to 2007 ODI World Cup

Null Hypothesis: In long run, Number of times a team won the

toss is equal to number of wins, when a team wons the toss.

Alternative Hypothesis: In long run, Number of times a team won

the toss is not equal to number of wins, when a team won the

toss.

`

38

0.0000.1000.2000.3000.4000.5000.6000.7000.800

AU

STR

ALI

A

BA

NG

LAD

ESH

BER

MU

DA

CA

NA

DA

ENG

LAN

D

IND

IA

IREL

AN

D

KEN

YA

NET

HER

LAN

D

NA

MIB

IA

NEW

ZEA

LAN

D

PA

KIST

AN

SOU

TH A

FRIC

A

SCO

TLA

ND

SRI L

AN

KA

UN

ITED

AR

AB

…

WES

T IN

DIE

S

ZIM

BA

WE

p(winning match)

p(winning match)

COUNTRIES TOTAL NUMBER OF MATCHES

PLAYED TOTAL NUMBER OF

MATCHES WON P(WINNING MATCH)

AUSTRALIA 69 52 0.754

BANGLADESH 19 5 0.263

BERMUDA 3 0 0.000

CANADA 12 1 0.083

ENGLAND 58 36 0.621

INDIA 56 32 0.571

IRELAND 8 2 0.250

KENYA 25 6 0.240

NETHERLAND 14 2 0.143

NAMIBIA 6 0 0.000

NEWZEALAND 61 34 0.557

PAKISTAN 54 30 0.556

SOUTH AFRICA 39 25 0.641

SCOTLAND 8 0 0.000

SRI LANKA 54 24 0.444

UNITED ARAB EMIRATES 5 1 0.200

WEST INDIES 56 36 0.643

ZIMBAWE 41 8 0.195

588

COUNTRIES

PR

OB

AB

ILIT

Y

`

39

\

0.0000.1000.2000.3000.4000.5000.6000.7000.800

AU

STR

ALI

A

BA

NG

LAD

ESH

BER

MU

DA

CA

NA

DA

ENG

LAN

D

IND

IA

IREL

AN

D

KEN

YA

NET

HER

LAN

D

NA

MIB

IA

NEW

ZEA

LAN

D

PA

KIST

AN

SOU

TH A

FRIC

A

SCO

TLA

ND

SRI L

AN

KA

UN

ITED

AR

AB

…

WES

T IN

DIE

S

ZIM

BA

WE

p(winning match when toss won)

p(winning matchwhen tosswon/winning toss)

COUNTRIES TOTAL NUMBER OF

TOSS WON P(WINNING TOSS)

TOTAL NUMBER OF TIME TEAM WON

MATCH WINNING THE TOSS

P(WINNING MATCHWHEN TOSS

WON)

AUSTRALIA 37 0.536 26 0.703

BANGLADESH 5 0.263 1 0.200

BERMUDA 1 0.333 0 0.000

CANADA 7 0.583 1 0.143

ENGLAND 34 0.586 20 0.588

INDIA 26 0.464 13 0.500

IRELAND 3 0.375 2 0.667

KENYA 12 0.480 2 0.167

NETHERLAND 7 0.500 2 0.286

NAMIBIA 3 0.500 0 0.000

NEWZEALAND 34 0.557 18 0.529

PAKISTAN 25 0.463 11 0.440

SOUTH AFRICA 17 0.436 9 0.529

SCOTLAND 4 0.500 0 0.000

SRI LANKA 28 0.519 13 0.464

UNITED ARAB EMIRATES 4 0.800 1 0.250

WEST INDIES 26 0.464 15 0.577

ZIMBAWE 21 0.512 3 0.143

COUNTRIES

PR

OB

AB

ILIT

Y

`

40

Countries total number of toss won

total number of time team won match winning the toss

AUSTRALIA 37 26

BANGLADESH 5 1

BERMUDA 1 0

CANADA 7 1

ENGLAND 34 20

INDIA 26 13

IRELAND 3 2

KENYA 12 2

NETHERLAND 7 2

NAMIBIA 3 0

NEWZEALAND 34 18

PAKISTAN 25 11

SOUTH AFRICA 17 9

SCOTLAND 4 0

SRI LANKA 28 13

UNITED ARAB EMIRATES 4 1

WEST INDIES 26 15

ZIMBAWE 21 3

0

5

10

15

20

25

30

35

40

AU

STR

ALI

A

BA

NG

LAD

ESH

BER

MU

DA

CA

NA

DA

ENG

LAN

D

IND

IA

IREL

AN

D

KEN

YA

NET

HER

LAN

D

NA

MIB

IA

NEW

ZEA

LAN

D

PA

KIST

AN

SOU

TH A

FRIC

A

SCO

TLA

ND

SRI L

AN

KA

UN

ITED

AR

AB

EM

IRA

TES

WES

T IN

DIE

S

ZIM

BA

WE

total number of toss won

total number of time team wonmatch winning the toss

COUNTRIES

Res

p. F

igu

res

`

41

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.94530

R Square 0.89361

Adjusted R Square

0.88696

Standard Error

4.22770

Observations 18

ANOVA

df SS MS F Significance F

Regression 1 2402.02 2402.02 134.3904161 3.38759E-09

Residual 16 285.97 17.8734

Total 17 2688

Coefficients Standard Error

t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 5.31561 1.37703 3.86017 0.001385289 2.39641864 8.2348 2.3964 8.23480

X Variable 1 1.44758 0.12487 11.5926 3.38759E-09 1.182870478 1.7122 1.1828 1.71229

`

42

We analyse the relationship between the winning of toss and winning of a match . herein we take regression analysis taking: Y: DEPENDENT VARIABLE: total number of time team won match winning the toss

X: INDEPENDENT VARIABLE: total number of toss won

Regression Statistics

Multiple R 0.945309601 R Square 0.893610242 Adjusted R Square

0.886960882

Standard Error 4.227703795 Observations 18

Multiple R: The correlation between the two variables is 94.53%. A high level of correlation

which approaching +1 denotes that the two variables are positively linearly

correlated

R Square: it means that 89.36% of the variation in the Y(total number of matches won when

toss is won), is explained by the independent variable X( total number of tosses won)

Adjusted R Square = 1 - (Total df / Residual df)(Residual SS / Total SS)

Used to test if an additional independent variable improves the model.

Standard Error: The Standard Error is the error you would expect between the predicted and actual dependent variable. Thus, 4.22 mean that the expected error for a team winning the match after

winning the toss prediction is off by 4.22.

Observations: The number of observations we have taken is 18 as the number of countries are 18 .

`

43

ANOVA

df SS MS F Significance F

Regression 1 2402.02433 2402.02433 134.3904161 3.38759E-09

Residual 16 285.97567 17.87347938 Total 17 2688

The ANOVA (analysis of variance) table splits the sum of squares into its components.

Total sums of squares

= Residual (or error) sum of squares + Regression (or explained) sum of squares.

REGRESSION:

DF: Degrees Of Freedom=Number of Independent Variable =1

SS: Regeression Sum of Squares= 2402.02

MS:Regression SS/ Regression Df=2402.02

F= Regression MS / Residual MS=134.39

SIGNIFICANCE F = Probability that independent variable does NOT explain the variation in y, i.e.

that any fit is purely by chance. This is based on the F probability

distribution. If the Significance F is not less than 0.1 (10%) you do not have a

meaningful correlation. Since we have significance F which is nearly

approaching zero it means we have a meaningful correlation, there exists a

valid relation between the two variables.

RESIDUAL DF = residual degrees of freedom = Total df - Regression df = n - 1 - number of

independent variables =16

RESIDUAL SS = sum of squares of the differences between the values of y predicted by analysis

and the actual values of y. If the data exactly fit equation 1, then Residual SS

would be 0 and R2 would be 1 which is equal to 285.97

RESIDUAL MS = mean square error = Residual SS / Residual df which is equal to 17.87

TOTAL DF = total degrees of freedom = n – 1=18-1=17

TOTAL SS = the sum of the squares of the differences between values of y and the average y

`

44

= (n-1)*(standard deviation of y)2 =17* (12.57)2 =2688

Coefficients Standard Error

t Stat P-value

Intercept 5.315610915 1.37703901 3.860174531 0.001385289 X Variable 1 1.447583967 0.124870432 11.59268804 3.38759E-09

COEFFICIENTS = Values which minimize the Residual SS (maximize R2).

The Intercept Coefficient is 5.31

And independent variable coefficient is 1.44

STANDARD ERROR= intercept: 1.37

Independent variable=0.12

T stat = = Coefficient for that variable / Standard error for that variable

P-value = 3.38759E-09

Consider test H0: β1 = 0 against Ha: β1 ≠ 0 at significance level α = .05

P value (β1 )= 3.38759E-09

Reject the null hypothesis at level .05 since the p-value is < 0.05.

59.11124.0

0447.1ˆ

1

11ˆ1

SE

BBt

B

)ˆ(

ˆ

j

j

jS

t

`

46

Null Hypothesis: There is a relationship exists between the no. of

wickets taken and 3 things bowling average, strike rate and

economy rate.

Alternative hypothesis: there is no relationship exists between

them.

`

47

PLAYER NO.OF MATCHES PLAYED

RUNS CONCEDED

BOWLING AVERAGE

STRIKE RATE

WICKETS TAKEN

ECONOMY RATE

Irfan pathan 24 618 22.07 16.5 28 8.62

Harbhajan singh 25 573 26.04 24.5 22 6.36

Shane watson 36 715 20.42 17 35 7.19

Mitchell johnson 28 724 20.11 16.8 36 7.14

Umar gul 49 1153 18.59 16 62 6.95

Saed ajmal 48 1092 15.82 15.4 69 6.13

Dwayne bravo 32 617 25.7 18 24 8.56

Tim southee 31 654 25.47 18.1 36 8.41

Struat broad 43 1113 23.18 18.9 48 7.34

Albie morkel 42 734 33.36 25 22 7.99

Johan botha 40 823 22.24 20.9 37 6.37

Dale steyn 28 636 17.18 16.2 37 6.36

Nuwan kulusekra 25 637 25.48 20.8 25 7.33

Lasith malinga 40 1025 21.35 17.1 48 7.48

Shahid afridi 56 1312 21.16 20.4 62 6.22

`

51

Model Summaryb

Model R R Square Adjuste

d R

Square

Std. Error of

the Estimate

Change Statistics

R Square

Change

F

Change

df1 df2 Sig. F

Change

1 .749a .561 .441 11.446 .561 4.678 3 11 .024

a. Predictors: (Constant), Economy Rate, Bowling Srike Rate, Bowling Average

b. Dependent Variable: Wickets

Taken

ANOVAb

Model Sum of

Squares

df Mean Square F Sig.

1 Regression 1838.574 3 612.858 4.678 .024a

Residual 1441.026 11 131.002

Total 3279.600 14

a. Predictors: (Constant), Economy Rate, Bowling Srike Rate, Bowling Average

b. Dependent Variable: Wickets Taken

a. Dependent Variable = Wicket Taken

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) 228.628 102.607 2.228 .048

Bowling Average 3.280 4.632 .924 .708 .494

Bowling Srike Rate -6.689 5.697 -1.304 -1.174 .265

Economy Rate -19.032 13.793 -1.068 -1.380 .195

`

52

Descriptive Statistics

Mean Std. Deviation N

Wickets Taken 39.40 15.305 15

Bowling Average 22.5447 4.31333 15

Bowling Srike Rate 18.7733 2.98340 15

Economy Rate 7.2300 .85887 15

Correlations

Wickets Taken Bowling

Average

Bowling Srike

Rate

Economy Rate

Wickets Taken Pearson Correlation 1.000 -.690** -.501

* -.510

*

Sig. (1-tailed) .002 .028 .026

N 15.000 15 15 15

Bowling Average Pearson Correlation -.690** 1.000 .806

** .528

*

Sig. (1-tailed) .002 .000 .022

N 15 15.000 15 15

Bowling Srike Rate Pearson Correlation -.501* .806

** 1.000 -.054

Sig. (1-tailed) .028 .000 .424

N 15 15 15.000 15

Economy Rate Pearson Correlation -.510* .528

* -.054 1.000

Sig. (1-tailed) .026 .022 .424

N 15 15 15 15.000

**. Correlation is significant at the 0.01 level (1-tailed).

*. Correlation is significant at the 0.05 level (1-tailed).

`

53

Correlation analysis

High degree of Positive correlation: There is high degree of positive correlation between strike

rate and bowling average, which is easily justified. As if strike rate of a bowler is high, his

bowling average is also high.

Moderate degree of positive correlation: This is between bowling average and economy rate.

Low degree of Negative correlation: this is between strike rate and economy rate.

Moderate degree of negative correlation: this is between wickets taken and strike rate, wickets

taken and bowling average, and economy rate and wickets taken, which are all true in all

formats.

Regression Analysis

The regression analysis is done to analyze the relation between total no. of wickets taken with

each of the 3 things namely bowling average, economy rate and strike rate of a bowler.

Dependent variable(Y): wickets taken

Independent variables: Bowling average(X1), Strike rate(X2) and economy rate(X3)

Multivariate linear regression model

Intercept coefficient: A1=228.628

Slope coefficients :

B1 (represent change in Y due to change in X1) =3.280

B2 (represent change in Y due to change in X2) =(-6.689)

B3 (represent change in Y due to change in X2) = (-19.032)

Regression equation:

Y = 228.628+3.280X1-6.289X2-19.032X3

`

54

Actual Values Estimated Values Residual

28 26.6 1.4

22 29.11 -7.11

35 45.05 -10.05

36 46.32 -10.32

62 50.3 11.7

69 60.85 8.15

24 29.6 -5.6

36 31.03 4.97

48 38.54 9.46

22 18.75 3.25

37 40.54 -3.54

37 55.57 -18.57

25 33.56 -8.56

48 41.91 6.09

62 43.2 18.8

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20

Series1

`

55

Appropriateness of regression model

1. R2 (Coefficient of determination) : It means the proportion of total variation in

dependent variable which is explained by independent variables( regression model).

R2 =0.561

It means 56% of total variation in no. of wickets taken is explained by variation in

Bowling average, strike rate and economy rate.

It is not high but it is good.

2. Scatterplot of residuals : from the diagram we can see that residuals are randomly

scaterred with mean approximately 0.

The above results show that our regression model is good fit.

Anova analysis

Null hypothesis (H0): B1=B2=B3=0

Alternative Hypothesis (H1): the slope coefficients are not equal to 0.

Explanation: the test statistical value (4.678) is lot higher than critical value ( values from

F- tables), so we reject the null at 5% significance level.

Conclusion: so se conclude that slope coefficients are not equal to 0. They may be

greater or less than 0.

OVERALL CONCLUSION

From all the above results we conclude that there is a good relationship exists between

the no. of wickets taken a 3 things bowling average, strike rate and economy rate and

also between each of the 3 things

`

56

CONCLUSION

After going through a lots of data and applying different statistical tools in different parameters of the

game of cricket. The following was concluded from the study –

The Strike rate of player in a ODI and Test differs from each other and there is very less

correlation between them, which is evident from the fact that there are only 50 overs to play in

ODI, but no limit in Test matches.

There do exist a relation between the economy rate of a Fast Bowler and a Spinner of same

country in a ODI match.

Contrary to widespread opinion, there is no competitive advantage of winning a toss on the

result of the match, this was proved using all the data of world cup matches starting from 1975.

There exist a relation between No. of wickets taken and Economy rate, Strike Rate and Bowling

average of a bowler.

`

57

LIMITATIONS AND FURTHER STUDY

Following limitations were encountered during the making of this report-

Data regarding results of toss of past matches was not available easily.

Accurate predictions cannot be made just by evaluating a handful of random data.

Comparing data of different time span may not be giving us a correct interpretation of result

In hypothesis of a toss eventually leading to win, one more big factor is the home advantage,

which we donot consider here, since a team playing at its home ground do have more chances

of winning, irrespective of who wins the toss.

In hypothesis of equal strike rate in ODI and Test, only Indian players were considered for

formulation of analysis, the result may change with players of other countries.

Scope of further study/research-

An analysis can be made on the relation between winning of toss and winning of match after

that in “Test” matches, at toss play more important role in Test match rather in ODI.

An hypothesis testing can be made on the relationship between the strike rate of player an ODI

and T-20, and this may come to be true.

A detailed analysis should be done on why contrary to widespread opinion, there was no

relation between winning of toss and the team eventually winning the match.

An analysis should also be done on whether there is an advantage for a team playing on its

home ground.

`

58

BIBLIOGRAPHY

The following internet sites were used for the collection of data

www.cricinfo.com

www.stats.com/cricket.asp

www.howstat.com.au/

www.icc-cricket.com/

www.thatscricket.com/statistics/

Silva B.M and Swartz T.B ( 1994 ) “A statistical look at cricket data”, in Mathematics and Computers in

Sports, Bond University, Australia pp 89-104

Stalen P.J (2012) “Comparison of bowlers, batsman and all-rounders in cricket using graphical displays”,

at Department of Statistics, University of Pretoria, South Africa

Gill P.S and Beaudoin D (2004 ) “Dynamic Programming in one-day cricket”, in Journal of Operational

Reasearch Society, RMIT University, GPO Box 2476V, Melbourne, Australia.

http://www.cricinfo.com/

http://www.stats.com/cricket.asp

http://www.howstat.com.au/

http://www.icc-cricket.com/

http://www.thatscricket.com/statistics/

analysis of different parameters in game of cricket

Sports

project supervisor

project work

present project

field of cricket

game of cricket

various hypothesis

cricket records

review of literature