Even Stevens

According to Cricinfo, eight of the eleven “questionable” decisions in Sydney went against India. Is this statistical proof of umpiring bias against the visitors?

I quickly did a one-tailed binomial test (check it online) under the null hypothesis that the two teams were equally likely to get the benefit of every error committed by the officials. The probability that eight or more of these errors will go against India is 11.3%. The null hypothesis of unbiased umpiring errors cannot be rejected at 10% level of significance, but it comes darn close. If Bucknor were judging it, he might rule himself out caught.

Of course there are severe sampling bias issues. This game was selected precisely because it was controversial for its one-sided decisions. If reliable tallies of umpiring errors are kept for every test match, it will be interesting to run a test on larger samples. It is not clear how to group the sample, though (e.g., by umpire, by country, by home team, etc.). If it is true that mistakes are tending to add up in the Aussies’ favor of late, there are a number of possible causes to consider – home country bias, strong team bias, etc. and each will have different predictions for the data.

Legal disclaimer: One-tailed tests have been brought up purely for statistical purposes. It is not a reference to the primatological status of any player, official or fan.