# ICC WORLD TWENTY ( WORLD CUP-2014 )- A CASE STUDY

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2 8 BHAVIN PATEL AND PRAVIN BHATHAWALA I these two examples, whe the umber of customers i the system is reached to N, o more arrivals are allowed i the system. Thus, we have,,,1, 2,..., N 1, N, N 1,...,,1, 2,... Usig, the probability of customers i the system is p p, N, N The value of is determied from the equatio p 1, which gives p (1 2. N ) 1 or p 1, 1 N 1 1 1, 1 N 1 Thus, (1 ), 1 N 1 1 p,,1,..., N 1, 1 N 1 The value of eed ot be less tha 1 i the case of Twety2 match, because arrivals at the system are cotrolled by the system limit N. This meas that eff is the rate which matters i this case. Because customers will be lost whe there are N i the system, p eff lost pn (1 pn ). I the case of Twety2 match, eff.. Sice 1, eff The expected umber of customers i the system is determied by lost N

3 ICC WORLD TWENTY-2, 214 (WORLD CUP-214)- A CASE STUDY 9 p L p N s ( N ) N p ( N ) 1 N( N 1) N 1 2 N LS. 2 EXPECTATION IN TWENTY2 MATCH: I Twety2 match, utilizatio factor = 1 ad the umber of customers (wickets) fallig is N =1 i each iigs. Therefore, the expected umber of customers (wickets) i each iigs or expectatio of customers (wickets) is That meas i each iigs, o average 5 wickets are fallig. It may vary earer 5 to i.e. 4 or 6 wickets i each iigs. We applied queuig model to Twety2 cricket i particular to the ICC World Twety As a result, firstly we got the expected umber of wickets durig World Cup-214. The actual record of the World Cup-214 is as uder: Match No. Of Wkts No. Of Wkts Average Match No. of Wkts No. Of Wkts Average Sr. No. i 1st I. i 2d I. No. Of Wkts Sr. No. i 1st I. i 2d I. No. Of Wkts Total: No. = umber Wkts = Wickets I. = Iigs Actual Expectatio is wickets. This data shows that, durig ICC World Twety2-214, the average umber of wickets that has bee falle is 6. This average is close to the ideal average 5. This is the real applicatio of queuig models i the real world.

4 1 BHAVIN PATEL AND PRAVIN BHATHAWALA CALCULATION OF PROBABILITIES IN TWENTY2 MATCH Secodly, we seek to fid the probability that the team battig first will wi a Twety2 match ad the probability that the team battig secod will wi. We eglect the tied Twety2 matches, ulike ODIs, because i that case, the super over comes i the frame ad gives the result of the match. For this, we defie the evets of team battig first ad team battig secod. At the start of the game, the coi is tossed to decide which team will bat first. Let B 1 be the evet that the team battig first ad B 2 be the evet that the team battig secod. 1 P( B ) P( B ) Let I be the evet that the 1 st iigs is completed, irrespective of the umber of wickets fallig i the iigs. P( I ) P( 1 i the 1 st iigs) (11 times ) P(I) = 1.. Now, Let I 1 be the evet that the team battig first wi ad I 2 be the evet that the team battig secod wi. The, the probability of I 1 is determied by P( I 1) The probability of I 2 is determied by = P(B 1 )P(I) + P(B 2 ) P( = 1 i the 2 d iigs) = 1 (1) d P(I 2 ) = P( B2 ) P( 9 i the 2 iigs) = (1 times) = This meas that, out of Twety2 matches 12 matches are wo by team battig first ad 1 matches are wo by team battig secod. This ca be verified from the data of the ICC World Twety The actual record is as uder: Match Sr. No. 1st I. Wi 2d I. Wi Match Sr. No. 1st I. Wi 2d I. Wi 1 L 1 W 13 L 1 W 2 1 W L 14 1 W L 3 1 W L 15 1 W L 4 1 W L 16 1 W L 5 L 1 W 17 1 W L 6 1 W L 18 1 W L 7 L 1 W 19 L 1 W Table Cot d

5 ICC WORLD TWENTY-2, 214 (WORLD CUP-214)- A CASE STUDY W L 2 1 W L 9 1 W L 21 1 W L 1 L 1 W 22 L 1 W 11 L 1 W 23 L 1 W 12 L 1 W Total:23 13 W 1 W meas Lost(L) ad 1 meas Wo(W) The above table shows that durig the ICC World Twety2-214, out of 23 Twety2 matches 13 matches have bee wo by team battig first ad 1 have bee wo by team battig secod. We observe that the theoretical probabilities match with the actual probabilities. CONCLUSION We coclude that, i T2 game of cricket, out of 22 Twety2 matches12 matches are wo by team battig first ad 1 matches are wo by team battig secod. That is, the probability that team battig first wi is ad the probability that team battig secod wi is I other words, it meas that out of 1 Twety2 matches 55 matches are wo by team battig first ad matches are wo by team battig secod. Durig ICC World Twety2-214, the probability that team battig first wi is ad the probability that team battig secod wi is This shows that the theoretical probabilities match with the actual probabilities. Moreover, durig ICC World Twety2-214, the actual expectatio of wickets fallig is wickets. REFERENCES [1] H.A. Taha, Operatios Research-A Itroductio. 8 th Editio, ISBN Pearso Educatio, 27. [2] J.D.C. Little, A Proof for the Queuig Formula:, Operatios Research, 9(3), 1961, pp , doi:1.237/ [3] Cooper RB (1972). Itroductio to Queuig Theory. McMilla: New York. [4] Tijms HC (1986). Stochastic Modellig ad Aalysis. A Computatioal Approach. Wiley: Chichester. [5] K. Rust, Usig Little s Law to Estimate Cycle Time ad Cost, Proceedigs of the 28 Witer Simulatio Coferece, IEEE Press, Dec. 28, doi:1.119/wsc [6] Worthigto D ad Wall A (1999). Usig the discrete time modellig approach to evaluate the time-depedet behaviour of queuig systems. J Opl Res Soc 5: [7] Steveso WJ (1996). Productio/Operatios Maagemet, 6 th ed. Irwi, McGraw-Hill, USA.

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