All 15 home teams win! What are the odds?

All 15 home teams win! What are the odds?

My dad just sent me an article saying that yesterday was the first time in the modern history of Major League Baseball that all 15 home teams won in a single day. Seems pretty incredible, right? To get 15 of 15 winners in a 50/50 contest is a 0.5^15 = 1-in-32,768 shot. To get a better sense of just how rare an event this is, we need to know two things: 1. how often is it possible for it to happen (i.e. all 30 teams play in a day), and 2. when it’s possible, what is the probability of it happening (i.e. all 15 home teams winning).

Both are pretty easy to figure out: This guy makes a convenient csv-formatted version schedule of all regular season MLB games. A couple lines of R code tells us that, for 2015 at least, all 30 teams play on the same day 128 times. [Aside: That seems crazy to me, that of each team’s 162 games, 4/5 of them fall on a day when every other team plays. It’s a busy season (And there’s probably some bias to the weekends, but anyway…)].

And as to the home team advantage, this guy has answered that question. You can’t get complete data from that site without a paid subscription, but eyeballing from his graph, I’m estimating that home teams win with an average of 54.2% over the long run.

So, when all 30 teams play, we should expect all 15 home teams to win 0.542^15 = 1 in every 9,773 times. And with 128 such days per year, we should expect to this happen once every 9,773 / 128 = 76 years.

So really, it was about time.