Tuesday, May 19, 2009

IPL Mathematics





Following is the IPL team tally as of today after Bangalore taking over Delhi in today's IPL Match:


Team Matches
W L Tied N/R Pts NRR
Delhi 13 9 4 0 0 18 0.25
Chennai 13 7 5 0 1 15 0.93
Hyderabad 13 7 6 0 0 14 0.26
Bangalore 13 7 6 0 0 14 -0.25
Punjab 13 7 6 0 0 14 -0.42
Rajasthan 13 6 6 0 1 13 -0.36
Mumbai 13 5 7 0 1 11 0.40
Kolkata 13 2 10 0 1 5 -0.89


Now, the purpose is to find out competent IPL semi finalists based on the data provided and probability. ;)

Assumptions:
1.) No Tie break between Chennai V/s Punjab, Hyderabad V/s Bangalore.
2.) Current Run rate is taken into consideration.

Delhi is already qualified for the Semi Finals.

Rajasthan wins
Chennai wins & Hyderabad wins - Chennai 17, Hyderabad 16, Rajasthan 15
(out Punjab 14, Bangalore 14)
Chennai wins & Hyderabad loses - Chennai 17, Bangalore 16, Rajasthan 15
(out Hyderabad 14, Punjab 14)
Chennai loses & Hyderabad wins - Hyderabad 16, Punjab 16, Chennai 15
(out Rajasthan 15, Bangalore 14)
Chennai loses & Hyderabad loses - Bangalore 16, Punjab 16, Chennai 15
(out Rajasthan 15, Hyderabad 14)

Rajasthan loses/tie-break
Chennai wins & Hyderabad wins - Chennai 17, Hyderabad 16, Bangalore 14
(out Punjab 14, Rajasthan 13/14)
Chennai wins & Hyderabad loses - Chennai 17, Bangalore 16, Hyderabad 14
(out Punjab 14, Rajasthan 13/14)
Chennai loses & Hyderabad wins - Hyderabad 16, Punjab 16, Chennai 15
(out Bangalore 14, Rajasthan 13/14)
Chennai loses & Hyderabad loses - Bangalore 16, Punjab 16, Chennai 15
(out Hyderabad 14, Rajasthan 13/14)


In the above projection, Rajasthan's loss/tie break with Kolkata are identical. So, the probability to qualify for the semi-final is:

Chennai: 8/8 (100%)
Hyderabad: 5/8 (62.5%)
Bangalore: 5/8 (62.5%)
Punjab: 4/8 (50%)
Rajasthan: 2/8 (25%)

Based on the above probability, Semi-final would be:

Delhi V/s Bangalore (1 V/s 4)
Chennai V/s Hyderabad (2 V/s 3)

Hence, one thing is sure that Chennai and Delhi are surely going to be in Semi-Finals. Rest is purely mathematics. (Courtesy: an IPL Fan)