During the IPL, there used to be a commercial aired by Parle 20-20 (clever spin on the name from 50-50 to 20-20) in which the team was awarded the cup on the win of the toss, trying to emphasize the “short me niptao” tagline of Parle 20-20. I personally liked the hindi commentator commercial of Parle 20-20 though.

The Parle 20-20 commercial kindled an old curiosity of mine to understand the effect of outcome of a toss on the outcome of the match. Of course, then I was not acquainted to the statistical methods, and even if I did I wonder where I would have obtained the data from; and so had no way to figure out the answer. Anyway, this time around with the superpower of statistics and cricinfo with me, I set out on the quest for the truth.

I chose the IPL2 dataset wherein it is said that anything can happen. This is what I found.

The 3 matches with no results were the 2 abandoned matches and 1 match which was tied and had to be resolved in a super-over. So, 33/56 = 59% of the time the match winner wins the toss. In terms of statistical probability, we can thus say that there is 59% chance that if a team wins the toss, it will win the match.

If a game has to be fair, all outcomes must be equally likely. The two most likely outcomes of a match are that Team A wins or Team A loses. I know of the tie outcome, but how many limited overs cricket games have been tied ever, less than even a 0.1% of all games? So, Team A wins or Team A loses is equally likely implies there should be a ½=50% chance of either happening. But, in cricket the toss changes the odds significantly towards the winner of the toss. Now, that is not fair. I really wish I had worked this math out before the bets I placed in T20 world cup – had to give a good number of chocolates to a friend.

On further analysis, I found something very interesting. Two of the four teams, which made it to the semi-finals of IPL2, were leading the tally in terms of toss-winnings also.

But then this could be one of those spurious correlations like the Redskins Rule. The real question is whether, the variables winning a match and winning the toss are independent or not. Of course, a more rigorous analysis is needed.

So, I googled and found this interesting paper: To bat or not to bat: An examination of match outcomes in day-night limited overs cricket which finds that winning the toss and batting first increases the probability of winning. The study conducted over day-night matches over 1979-2005 uses logit regression to prove the point. Though this does not actually address the toss-win implies match-win hypothesis and does not cover the entire ODI spectrum but does partly address the problem. I did not find a comparable study for test matches.

The cricket fans who ardently believe that “anything can happen in cricket” will argue about the role of strategic decision making on every ball, pitch & weather conditions, team composition, selection criteria, politics in cricket, racist attitude towards Asian teams, yada yada yada on the outcome of the match. To all ye, I say, prove it statistically!

I have to agree these results are not enough to make a generic statement that “Cricket is an unfair game”. But I have instinctive feel that any study would return toss outcome as the topmost factors that affect the outcome of the match. And hence on basis of my hunch, I claim: Cricket is an unfair game.

P.S. I hope I have the freedom of speech to make such a statement. These days, anything can happen: big media (proponents of free speech) can legally ask a blogger to remove his post, political parties can ask award juries to award only "deserving" people. Who knows, BCCI might take offence to this non-trivial albeit somewhat naive analysis of IPL2 or cricket and I might be sued to take it off blogosphere!


Lakshminarasimhan said... @ June 21, 2009

the 50-50 stats is over a very large dataset(like over the course of 2-3 years)..since there are a very few matches considered the probab is varied is usually a mistake by statisticians who tend to take a very selective or small dataset..hence the argument seems incorrect!

Lakshminarasimhan said... @ June 21, 2009

Oops ignore earlier comment..thought you had taken only IPL matches into account saw the paper later...seems odd!

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