What were the odds of an India-Pakistan final?

After the IPL, I’ve had an overdose of limited overs cricket and haven’t been watching much of it. Not even following it on Cricinfo – haven’t even found it that interesting.

Anyways I got just a little bit of enthu for following it thanks to India’s qualification for the finals. And that led me to the tournament rules, which I find ridiculous. I mean, I don’t know what organizers of tournaments are smoking nowadays – first you had the Euro where teams from the same group ended up in the same half of the draw and now this. In fact (though this must be a coincidence), the recently concluded Euro had a number of groups where two teams which had qualified from the same qualification group ended up in the same group (Italy-France; Holland-Romania; spain-sweden;). however, the last bit can be forgiven considering that it has a reasonable statistical probability.

Coming back to the Asia Cup, let us define Hong Kong and UAE as minnows and Bangladesh as mini-minnows. I know some of you will contest the latter bit, but what were the odds that Bangladesh was going to cause another upset? Let’s leave that debate aside and continue the analysis.

The tournament had a strange format. Six teams were in two pools, with the bottom team from each pool (basically the minnows) going out. Now, the top four teams played a super league; and the points gathered by teams from their original pools were also added. So basically, if you are going to forget about the minnows, the tournament was like a one-and-a-half round robin, with two pairs of teams playing each other twice, while there was one each of the other four matches. I have a feeling they came up with this design in order to have at least two India-Pakistan matches, which was the main source of revenue.

Ok I digress again. Coming back, assume that the mini-minnow loses to all non-minnow teams (in hindsight, it has duly done this duty. Though there was a small but un-ignorable probability that this might not have happened). So, if you take Bangladesh out of the tournament, that leaves Sri Lanka with four points (two wins over BD) while India and Pakistan have two each.

So you have SL -4; Ind -2; Pak -2. And you have India and Pakistan playing each other twice and taking on Sri Lanka once each. Assuming there are no draws/ties/no results, there is only one way that Sri Lanka would have gone out of the tournament – had they lost to both India and Pakistan, and the latter had won one bilateral game each. One win for Sri Lanka and they would go through to the final. Even if SL lost both their games, and say India beat Pakistan twice, it would come down to net run rate between SL and Pak, and with the former having had more games against the mini-minnows, they would in all probability have the better net run rate!

Ok let us bring in some numbers. Let us assume that even if SL were to lose both their “major” matches, the probability that they would have a “bad” net run rate (one that would be lower than that of the loser of the two indo-pak matches) is ridiculously small. And can be ignored. Hence, the only way in which Sri Lanka can go out is for them to lose to both India and Pakistan, who beat each other once each. Assuming that a priori the three teams are evenly matched, the probability of this happening would be 1/2 (india beat SL ) * 1/2 (pak beat SL ) * 2 * 1/2 * 1/2 (india and pak beat each other once each) = 1/8.

One of three things would have happened – either the organizers over-estimated the probability of Bangladesh causing an upset (yes, it’s still an upset if they beat ind/pak/SL) or they would have just wanted to guarantee two India Pakistan games or they wanted to virtually seed Sri Lanka into the final. The most probable reason, in my opinion, is the second one. And by their greed to guarantee at least two India-Pakistan games, the organizers ensured that the chances of an India-Pakistan final would be remote.

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