BOWLING STRATEGY BUILDING IN LIMITED OVER CRICKET MATCH : AN - PowerPoint PPT Presentation

BOWLING STRATEGY BUILDING IN LIMITED OVER CRICKET MATCH : AN APPLICATION OF STATISTICS Akash Adhikari Rishabh Saraf Rishikesh Parma

About the game • Cricket is a bat and ball game, and is one of those sports which has been evolving with time . • The format of the game include test cricket which can go as long as five days, One day International (ODI) comprising of 50 overs and T20 which limits to 20 overs. • With the introduction of new rules like batting and bowling powerplay (a field restriction where only limited number of fielders are allowed outside the 30 yard circle) have made the game an interesting one .

Introduction • Implementation of new approach to analyze bowler’s performance in limited over cricket match. • Current format of the game largely depends on bowling performance. • Application of statistics. • The statistics mainly used to decide bowler’s performance are bowling average, economy rate, and strike rate. However these statistics are individually deficient as they do not adequately account for overs, wickets and runs respectively. •

Data • The data of every ball bowled by a bowler in his career during the years 2007-2016 has been used in the analysis. • R script programming is used to extract data from www.espncricinfo.com. • All the analysis and statistical operations has been done in microsoft excel.

Parameters Runs between wickets (r i ) : runs conceded in between fall of consecutive wickets in a spell of a respective bowler . Balls between wickets (b i ) : balls delivered in between fall of consecutive wicket in a spell of a respective bowler .

Bowling analysis Analysis of bowler has been done separately for the first 30 overs (SET 1) and the last 20 overs (SET 2) . 30 different bowlers were analyzed, out of which five best rated fast-arm seamers and slow-arm spinners (as per ICC ODI rankings 2016) is mentioned .

Fast Arm Seamers MA Starc (Australia) • TA Boult (New Zealand) • DW Steyn (South Africa) • M Morkel (South Africa) • TG Southee (New Zealand) •

Slow Arm Spinners Imran Tahir (South Africa) • SP Narine (West Indies) • Shakib Hasan (Bangladesh) • R Ashwin (India) • RA Jadeja (India) •

Probability model The probability for a bowler to take wicket given the number of runs he may concede P(r n ) is defined as, P(r n ) = F(r n )÷w t + P(r n-1 ) Here, w t = total number of wickets taken by the bowler, r n = n {0 ≤ n ≤ max (r i ) } Frequency of (r n ), F(r n ) = number of occurences of r n among all the values of r i .

The probability for a bowler to take wicket given the number of balls to be bowled by him P(b k ) is defined as, P(b k ) = F(b k )÷w t + P(b k-1 ) Here, w t = total number of wickets taken by the bolwer, b k = k {1 ≤ k ≤ max (b i ) }, P(b 0 ) = 0, Frequency of (b k ), F(b k ) = number of occurences of b k among all the values of b i .

Procedure • The value of P(r n ) and P(b k ) are calculated independently, considering the effect of only one parameter at a time . • Since the permitted balls for a bowler in ODI cricket is 60, so the value of P(b k ) is calculated for the domain [0,60] . • Assuming that the maximum runs a bowler may concede in an ODI cricket match is 80, the value of P(r n ) is calculated for the domain [0,80] .

R ASHWIN ANALYSIS

Analysis in SET 1 ( 1-30 overs) Matches 92 Runs Conceded 2663 Overs 616.2 Wickets 67 Extras 110

Calculated values of P(b k ) b k P(b k ) 10 0.1194 20 0.2537 30 0.3582 40 0.5074 50 0.6119 60 0.6865

Calculated values of P(r n ) r n P (r n ) 0.0298 0 0.2089 10 0.4179 20 0.5522 30 0.5970 40 0.7611 50 0.8208 60 0.8656 70 0.8805 80

Analysis in SET 2 ( 31-50 overs) Matches 95 Runs Conceded 1721 Overs 329 Wickets 76 Extras 80

Calculated values of P(b k ) b k P(b k ) 0.2666 10 0.4800 20 0.6400 30 0.8266 40 0.8800 50 0.9600 60

Calculated values of P(r n ) r n P (r n ) 0.0533 0 0.3600 10 0.5733 20 0.6666 30 0.8000 40 0.9066 50 0.9600 60 0.9733 70 0.9999 80

• Similar analysis has been done for all the bowlers mentioned before . • Separately for fast-arm seamers and slow-arm spinners. • The calculated probabilities is compared with the help of dominance curve.

DOMINANCE CURVES

SLOW-ARM SPINNERS

Bowlers Indicators Imran Tahir SP Narine Shakib Al Hasan R Ashwin RA Jadeja Dominance curve of different spinners for SET 1 Dominance curve of different spinners for SET 1 and with P(b k ) as ordinate and b k as abscissa. and with P(r n ) as ordinate and r n as abscissa.

Bowlers Indicators Imran Tahir SP Narine Shakib Al Hasan R Ashwin RA Jadeja Dominance curve of different spinners for SET 2 Dominance curve of different spinners for SET 2 and with P(b k ) as ordinate and b k as abscissa. and with P(r n ) as ordinate and r n as abscissa.

FAST-ARM SEAMERS

Bowlers Indicators MA Starc TA Boult DW Steyn M Morkel TG Southee Dominance curve for different seamers for SET Dominance curve for different seamers for SET 1 and with P(b k ) as ordinate and b k as abscissa. 1 and with P(r n ) as ordinate and r n as abscissa.

Bowlers Indicators MA Starc TA Boult DW Steyn M Morkel TG Southee Dominance curve for different seamers for SET Dominance curve for different seamers for SET 2 and with P(b k ) as ordinate and b k as abscissa. 2 and with P(r n ) as ordinate and r n as abscissa.

Discussions • The probability of a bowler to take a wicket given the number of balls he can deliver P(b k ) or the number of runs he can concede P(r n ) does not entirely support each other . • There may be instances where an exclusive preference for either of the parameter does not exists . • So we defined a new function ‘Striking score’ to include the effect of both the parameters.

STRIKING SCORE AND DOMINANCE FACTOR

Striking score (Y) of a bowler as a function of b k is defined as, Y = P + b k ÷r n Given b k , P is equal to P(b k ), and r n is equal to that value for which P(b k ) = P(r n ).

Striking score (Y) of a bowler is a more accurate value to analyze his performance, which includes the effect of both b k and r n in line with the probability to take wickets .

• Striking score is discrete values which depends on b k . • For analysing overall performance, Dominance factor is defined, which is the weighted average of striking score (Y) with respect to b k . D.F. = {∑(Y* b k ) } ÷ {∑b k }

Striking score and Dominance factor of R Ashwin b k Striking Score b k Striking Score (Y) (Y) 10 10 1.9333 2.1194 20 20 1.8133 1.7921 30 30 1.7511 2.1229 40 40 1.7357 1.8867 50 50 1.9216 1.8314 60 60 1.9944 1.8314 D.F. D.F. 1.8729 1.9391 SET 1 SET 2

Striking score and Dominance factor for SET 1 (Spinners) b k IMRAN SP NARINE S HASAN R ASHWIN R JADEJA TAHIR 10 2.6694 2.7244 2.7043 2.1194 1.3111 20 1.8079 2.6303 1.8264 1.7921 1.9589 30 1.9823 2.5102 2.2485 2.1229 1.9153 40 2.1589 2.5170 2.1158 1.8867 2.0461 50 2.3287 2.2563 2.2903 1.8314 1.9128 60 2.4264 2.4217 2.3208 1.8314 1.9535 D.F. 2.2414 2.4474 2.2353 1.9391 1.9259

Striking score and Dominance factor for SET 2 (Spinners) b k IMRAN SP NARINE S HASAN R ASHWIN R JADEJA TAHIR 10 2.0797 1.5765 1.9166 1.9333 1.5664 20 1.6304 2.1360 1.6407 1.8133 1.8143 30 2.0000 2.4381 1.7476 1.7511 1.8329 40 1.8854 1.9315 1.8311 1.7357 1.7224 50 2.1413 2.2460 1.9814 1.9216 1.9476 60 2.1592 2.3001 1.9773 1.9944 1.9575 D.F. 2.0259 2.1867 1.8826 1.8729 1.8603

Striking score and Dominance factor for SET 1 (Seamers) MA STARC TA BOULT DW STEYN M TG b k MORKEL SOUTHEE 5.2941 2.7820 2.1891 2.1645 2.2133 10 2.1372 2.0256 1.8204 1.9182 2.2315 20 2.0364 1.9790 2.1936 2.1603 2.1789 30 2.0655 1.8547 2.2477 2.3751 2.2666 40 2.2602 2.1025 1.8526 2.0977 2.1488 50 2.4985 2.0962 2.0528 2.0487 2.2634 60 2.3920 2.0609 2.0467 2.1316 2.2192 D.F.

Striking score and Dominance factor for SET 2 (Seamers) MA STARC TA BOULT DW STEYN M TG b k MORKEL SOUTHEE 2.0866 1.4761 1.5069 1.8085 2.8148 10 1.9700 1.8730 1.6984 1.6423 1.5711 20 1.9000 2.2380 1.8214 1.8300 1.7222 30 1.8723 2.2364 1.9484 1.7895 1.8674 40 1.8064 2.1868 1.9579 1.9604 1.9675 50 1.9677 1.6185 2.1479 2.1120 2.0158 60 1.9073 1.9775 1.9447 1.9150 1.9298 D.F.

• Higher the Dominance factor higher will be the chance to take wicket for a bowler, given the number of balls (here, b k ) . • SP Narine has highest Dominance factor among the considered Slow-arm spinners . • MA Starc has the highest Dominance factor among the Fast-arm seamers .

Conclusion • Within the limits of this study , the paper seeks to highlight the tremendous scope that exists to improve and develop on the measures currently used to describe the performances of cricket players in general and bowlers in particular. • The attempt of the paper is not to arrive at a model to rank the utility of the players, it is just an approach to have an efficient bowling strategy for a match.