Analysis of different parameters in game of cricket

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Analysis of different parameters in game of cricket

  1. 1. 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
  2. 2. ` 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)
  3. 3. ` 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
  4. 4. 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
  5. 5. ` 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.
  6. 6. 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)
  7. 7. 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.
  8. 8. ` 5
  9. 9. ` 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 )
  10. 10. ` 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
  11. 11. ` 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 STRIKERATE Inning Wise Strike Rate Of Virendre Sehwag in 50 Innings of his Test Career.
  12. 12. ` 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
  13. 13. ` 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 STRIKERATE Inning Wise Strike Rate Of Virendre Sehwag in 50 Innings of his ODI Career.
  14. 14. ` 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 VARIANCE 955.0886931 CORRELATION 0.040662259 CORRELATION 0.040662259 CV 16.81% CV 27.70%
  15. 15. ` 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 Variable 1 Variable 2 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
  16. 16. ` 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.
  17. 17. ` 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 σ1 2 and σ2 2 be the variance in strike rates of a player in TEST and ODI matches respectively. Null (Ho): σ1 2 = σ2 2 Alternative (H1): σ1 2 ≠ 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.
  18. 18. ` 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
  19. 19. ` 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 STRIKERATE Inning Wise Strike Rate Of Sachin Tendulkar in 50 Innings of his Test Career.
  20. 20. ` 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
  21. 21. ` 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 STRIKERATE Inning Wise Strike Rate Of Sachin Tendulkar in 50 Innings of his ODI Career.
  22. 22. ` 19 This is how we get the above results. Using Formulas in Excel. TEST MATCHES ODI MATCHES AVERAGE 60.8028 AVERAGE 99.2836 VARIANCE 180.0747471 VARIANCE 260.8006725 CORRELATION - 0.094141578 CORRELATION -0.094141578 SKEWNESS 1.10005858 SKEWNESS 0.5789129 CV 22.07% CV 16.26%
  23. 23. ` 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 Hypothesized Mean Difference 0 df 95 t Stat -12.95899 t Critical two-tail 1.985251 F-Test Two-Sample for Variances Variable 1 Variable 2 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
  24. 24. ` 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.
  25. 25. ` 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 σ1 2 and σ2 2 be the variance in strike rates of a player in TEST and ODI matches respectively. Null (Ho): σ1 2 = σ2 2 Alternative (H1): σ1 2 ≠ 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.
  26. 26. ` 23
  27. 27. ` 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.
  28. 28. ` 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 9 0 37 1 4.11 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 ) Overs Mdns Runs Wkts Econ Opposition 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 1 35 2 3.5 v New Zealand 10 0 42 0 4.2 v Sri Lanka 10 0 44 2 4.4 v Australia
  29. 29. ` 26 Australia bret lee ( Fast Bowler ) Overs Mdns Runs Wkts Econ Opposition 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 3 42 3 4.66 v West Indies 10 0 72 2 7.2 v West Indies 9.4 1 52 1 5.37 v West Indies 8 1 37 1 4.62 v West Indies 7 1 25 1 3.57 v West Indies 8 0 59 3 7.37 v Sri Lanka Brad Hogg ( Spinner ) Overs Mdns Runs Wkts Econ Opposition 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 6 1 49 3 8.16 v New Zealand 10 1 49 1 4.9 v New Zealand 8 0 40 0 5 v India
  30. 30. ` 27 India Zaheer Khan ( Fast Bowler ) Overs Mdns Runs Wkts Econ Opposition 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 0 46 1 4.6 v Australia 10 0 46 1 4.6 v Australia 10 1 44 2 4.4 v Sri Lanka 10 3 60 2 6 v Sri Lanka R Ashwin ( Spinner ) Overs Mdns Runs Wkts Econ Opposition 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 10 0 45 0 4.5 v Australia
  31. 31. ` 28 Pakistan Umar Gul ( Fast Bowler ) Overs Mdns Runs Wkts Econ Opposition 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 10 2 65 2 6.5 v Bangladesh 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 ) Overs Mdns Runs Wkts Econ Opposition 9 1 37 3 4.11 v Australia 10 0 32 4 3.2 v Australia 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 45 2 4.5 v Bangladesh 10 0 62 3 6.2 v England
  32. 32. ` 29 Sri Lanka Lasith Malinga ( Fast Bowler ) Overs Mdns Runs Wkts Econ Opposition 10 0 39 2 3.9 v New Zealand 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 ) Overs Mdns Runs Wkts Econ Opposition 8 0 54 1 6.75 v South Africa 9.1 0 49 3 5.34 v Australia 7 0 31 0 4.42 v Australia 8 0 38 1 4.75 v Australia 6 0 23 0 3.83 v Australia 6 0 32 1 5.33 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
  33. 33. ` 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
  34. 34. ` 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
  35. 35. ` 32 HYPOTHESIS TESTING Testing for equality of average ECONOMY RATES t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 5.1768 4.6678 Variance 2.107397714 1.763029755 Observations 50 50 Pooled Variance 1.935213735 Hypothesized Mean Difference 0 df 98 t Stat 1.829461683 t Critical two-tail 1.984467455 TESTING FOR EQUALITY OF VARIANCES IN ECONOMY RATES F-Test Two-Sample for Variances Variable 1 Variable 2 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
  36. 36. ` 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.
  37. 37. ` 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 σ1 2 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. σ1 2 = σ2 2 Alternative (H1): Alternative Hypothesis (H1): Variances are not equal i.e. σ1 2 ≠ σ2 2 LEVEL OF SIGNIFICANCE = 5%
  38. 38. ` 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.
  39. 39. ` 36
  40. 40. ` 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.
  41. 41. ` 38 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 AUSTRALIA BANGLADESH BERMUDA CANADA ENGLAND INDIA IRELAND KENYA NETHERLAND NAMIBIA NEWZEALAND PAKISTAN SOUTHAFRICA SCOTLAND SRILANKA UNITEDARAB… WESTINDIES ZIMBAWE 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 PROBABILITY
  42. 42. ` 39 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 AUSTRALIA BANGLADESH BERMUDA CANADA ENGLAND INDIA IRELAND KENYA NETHERLAND NAMIBIA NEWZEALAND PAKISTAN SOUTHAFRICA SCOTLAND SRILANKA UNITEDARAB… WESTINDIES ZIMBAWE p(winning match when toss won) p(winning matchwhen toss won/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 PROBABILITY
  43. 43. ` 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 AUSTRALIA BANGLADESH BERMUDA CANADA ENGLAND INDIA IRELAND KENYA NETHERLAND NAMIBIA NEWZEALAND PAKISTAN SOUTHAFRICA SCOTLAND SRILANKA UNITEDARABEMIRATES WESTINDIES ZIMBAWE total number of toss won total number of time team won match winning the toss COUNTRIES Resp.Figures
  44. 44. ` 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
  45. 45. ` 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 .
  46. 46. ` 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
  47. 47. ` 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. 59.11 124.0 0447.1ˆ 1 11 ˆ 1      SE BB tB )ˆ( ˆ j j j S t   
  48. 48. ` 45
  49. 49. ` 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.
  50. 50. ` 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. 51. ` 48
  52. 52. ` 49
  53. 53. ` 50
  54. 54. ` 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 .749 a .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 ANOVA b 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 Coefficients a 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
  55. 55. ` 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).
  56. 56. ` 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
  57. 57. ` 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
  58. 58. ` 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
  59. 59. ` 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.
  60. 60. ` 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.
  61. 61. ` 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.

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