Tuesday, March 15, 2011

QUARTER FINALS PROBABILITIES

Another 8 matches remain before the Group stage of the ICC Cricket World Cup 2011 comes to an end. Amidst all the speculation of Quarter final lineups, I have decided to use the good old method of probability to find out the most probable QF lineup.

NOTES:

1. Out of the 8 remaining matches, 2 will have no impact on the Quarterfinals lineup - Ireland v. Netherlands and Kenya v. Zimbabwe

2. I have assumed that Australia will beat Canada in their match on 16th March 2011 at M. Chinnaswamy Stadium, Bangalore.

3. I have also assumed none of the matches will be washed out, even though the weather forecasts state that there will be scattered thunderstorms over Colombo on the day of Australia v. Pakistan match.

4. In all the matches, equal probabilities have been given for each side to emerge as the winner (even though, in my opinion, South Africa should be given a higher probability of winning against Bangladesh).

5. Lastly, I have assumed that the NRR of the teams will not change significantly over the remaining matches, and therefore, in case of a tie of points, the team with the higher NRR as of present has been ranked higher.

RESULTS:

The following 8 Quarter-finals combinations have the highest probability (6.25% each):

A. SL v. WI; Pak v. SA; NZ v. Bang; Aus v. Ind
B. SL v. WI; Aus v. SA; Pak v. Bang; NZ v. Ind
C. Pak v. WI; NZ v. SA; SL v. Bang; Aus v. Ind
D. NZ v. WI; Aus v. SA; SL v. Bang; Pak v. Ind
E. SL v. SA; Pak v. Ind; NZ v. WI; Aus v. Bang
F. SL v. SA; Aus v. Ind; Pak v. WI; NZ v. Bang
G. Pak v. SA; NZ v. Ind; SL v. WI; Aus v. Bang
H. NZ v. SA; Aus v. Ind; SL v. WI; Pak v. Bang

There are 16 other Quarter-finals combinations that have a probability of 3.125% each.

However, to get a clearer picture, let us look at the probability of individual teams and their Quarter-final opponents.

GROUP A:

Australia -

Chances of playing Bangladesh in QFs: 25%
Chances of playing England in QFs: 12.5%
Chances of playing India in QFs: 25%
Chances of playing South Africa in QFs: 25%
Chances of playing West Indies in QFs: 12.5%

New Zealand -

Chances of playing Bangladesh in QFs: 21.875%
Chances of playing England in QFs: 6.25%
Chances of playing India in QFs: 25%
Chances of playing South Africa in QFs: 25%
Chances of playing West Indies in QFs: 21.875%

Pakistan -

Chances of playing Bangladesh in QFs: 21.875%
Chances of playing England in QFs: 6.25%
Chances of playing India in QFs: 25%
Chances of playing South Africa in QFs: 25%
Chances of playing West Indies in QFs: 21.875%

Sri Lanka -

Chances of playing Bangladesh in QFs: 18.75%
Chances of playing England in QFs: 0%
Chances of playing India in QFs: 25%
Chances of playing South Africa in QFs: 25%
Chances of playing West Indies in QFs: 31.25%

GROUP B:

Bangladesh -

Chances of playing Australia in QFs: 25%
Chances of playing New Zealand in QFs: 21.875%
Chances of playing Pakistan in QFs: 21.875%
Chances of playing Sri Lanka in QFs: 18.75%
Chances of not qualifying for QFs: 12.5%

England -

Chances of playing Australia in QFs: 12.5%
Chances of playing New Zealand in QFs: 6.25%
Chances of playing Pakistan in QFs: 6.25%
Chances of playing Sri Lanka in QFs: 0%
Chances of not qualifying for QFs: 75%

India -

Chances of playing Australia in QFs: 25%
Chances of playing New Zealand in QFs: 25%
Chances of playing Pakistan in QFs: 25%
Chances of playing Sri Lanka in QFs: 25%
Chances of not qualifying for QFs: 0% (because of NRR better than that of England)

South Africa -

Chances of playing Australia in QFs: 25%
Chances of playing New Zealand in QFs: 25%
Chances of playing Pakistan in QFs: 25%
Chances of playing Sri Lanka in QFs: 25%
Chances of not qualifying for QFs: 0%

West Indies -

Chances of playing Australia in QFs: 12.5%
Chances of playing New Zealand in QFs: 21.875%
Chances of playing Pakistan in QFs: 21.875%
Chances of playing Sri Lanka in QFs: 31.25%
Chances of not qualifying for QFs: 12.5%

However, like I have already said, I think these percentages above do not reflect a true picture because I have assumed equal chances of winning for both South Africa and Bangladesh in their match as well as the fact that I have assumed that the NRR will remain pretty much the same till the group stages finish. The worst affected due to these two assumptions is England.

I will keep updating the changes in these percentages above after the end of every match from hereon (except the ones that have no effect on these probabilities as mentioned in Notes 1 and 2 above).

2 comments:

knowledge_eater said...

Good Work this. :)

If I assume SA to win against Bangladesh, India to beat WI, WI to beat England, then India will be B2 will compete with A3.

and

If I assume Australia to win next 2, Lanka to win against NZ, then NZ will be A3.

So, after all, it's all good. :)

Australia will play Bangladesh
Srilanka will play Westindies
Pakistan will play South Africa

If India do not win to West Indies, there is no doubt we will be B3.

So, unless BD doesn't beat SA. We will either be B2 (if we win against WI) or B3(if we lose to WI). But we will never be B4 for sure, seeing our Run-rate will always be higher than England or Bangladesh.

Cheers. It's fun.

Shridhar Jaju said...

The only bit that I could understand from your comment was "So, after all, it's all good. :)".

My head is so full of numbers right now that I am incapable of understanding anything else! :)

Sadly, Ireland got knocked out today. But because of their defeat to South Africa, I felt that now I can do this probability computation... otherwise, it would have been a bigger headache with 6 teams from Group B in contention!

SAVE OUR TIGER!