Adventures in Getting Statistics Right

In a previous post of mine, I cautioned against a certain way to get mixed up in calculating the odds of certain unlikely events. The specific case was a claim of two-million-to-one odds against a child being born on Leap Day to a mother also born on Leap Day, and my basic point was that on any given Leap Day there are always lots of babies born, so there's no need to double-count the odds against a Leap Day birth. So I'm pleased to see that another instance of what looks like the same double-counting is actually a valid one. The day which is now yesterday, May 3rd, 2012, apparently featured the first game in Major League history where both opposing starting pitchers were celebrating their birthdays. Ryan Dempster of the Cubs turned 35, and he was opposed by Homer Bailey of the Reds, turning 26. Now, I happen to think yesterday was a fine day for a birthday, as it was in fact my 21st, so I find this cool. A post on a certain Mets fansite I frequent, Amazin' Avenue, suggested that the odds of this occurrence are 1-in-133,402. That latter number is simply 365 * 365, so except for that whole Leap Day thing it's a pretty good approximation if we should really expect these to be independence events. Which we should! There's no remote guarantee that one of the pitchers on a given day will be celebrating a birthday, the way there is a guarantee that there will be many babies born on a given Leap Day, so we really should be surprised to the full extent of the 365-to-1 odds for both pitchers, and these odds are roughly correct. And, as there have been around 200,000 MLB games thus far, they suggest it is not particularly shocking that this was the first time this happened.

So, congratulations to Ryan Dempster and Homer Bailey for rockin' the May 3rd awesomeness!