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)