Odds on pitchers facing each other on their birthday

Birthday boys Bailey, Dempster make history

That seems amazing considering the total number of games that have been played in MLB history.

But I can’t set up how to work out the odds properly. Naively, you might say that that the odds are 1 in 365 times 1 in 365 or 1 in 133,225. There have been approximately 175,000 total games played so that’s not out of line.

That won’t work, because a season is only six months long - and used to be about 5 months long - so at least half the players are immediately excluded. The odds are longer than 1 in 133,225 but not simply twice as long.

How would you work this out?

I don’t think that’s a factor. You start with the date of the game as a given - call that G, and assume that the odds of a pitcher’s birthday being on any given day are more or less equal.

The odds that the birthday of the starting pitcher for team A happens to fall on G are still approx 1 in 365. (Plus a smidge to account for leap days - the odds if G is a leap day would change dramatically.) Same for the starting pitcher for team B.

The fact that there are 180+ days in the year that are impossible values for G don’t matter, unless you can correlate the remaining days to a statistical difference in birth rates that would assume our ‘equal chances of birthdays’ assumption invalid.

Your first figure is correct. It’s irrelevant that half the players are out of contention, because the other half are that much more likely.

Your initial calculation is correct. Don’t do the exclusion you speak of (or, do it correctly and watch it cancel out!). To see this, for an extreme case, suppose that the season is a single day, and each team chooses from 365 pitchers, each with different birthdays.

A question I have is: Isn’t a pitcher likely to request his birthday be an off day? (Or maybe it works the opposite: “Friends, come celebrate my birthday by watching me pitch!” ? :dubious: )

ETA: This is the instaboard – two other correct answers appeared while I was typing.

Malcolm Gladwell’s Outliers suggests that there is in fact a hugely significant statistical aberration in professional athletes’ birthdays. They are heavily skewed toward January due to childhood leagues using calendar year as a cutoff, and the various positive-feedback loops in sports training.

I believe his case study was of hockey, and that over half of the players had birthdays in January-March. I could be wrong on the details here; it’s been a year or so since I read that book.

Given that this is the first time this has occurred, it’s not at all surprising that it occurred in early May and not late October :slight_smile:

Professional pitchers are on a pretty rigid pitching schedule - I doubt they’d do that for their birthday. Additionally, it’s not like they get to go do whatever they want on their off days - they’re still required to suit up and sit on the bench, because they’re part of the 25 man roster.

The issue is complicated by the fact that the question and the answer so far have all tried to calculate the odds that two specific pitchers share the same birthday, but the problem requires that you assume that any two pitchers share the birthday. The latter is more common.

So when you start with 1 in 365 and multiply it by 1 in 365, you get a 1 in 133,225. But assuming all teams in the league have five-man rotations, there are 16 in 365 possible birthday matchups (in the NL). And that assumes all the rotations are in sync. As the season wears on, and people skip turns or lose them, it changes and can theoretically mean you can pitch against 80 pitchers, changing the odds to 80 in 365.

It would seem very likely that there have been multiple cases of two pitchers sharing a birthday starting the same game against each other. The difference is that there is a third factor – that the two pitchers no only share the birthday, but also happen to pitch on that day.

It was hockey. In Little League the cutoff is May 1 rather than the calendar year. However, I don’t know if Little League serves as a player farm for the big league the way that youth hockey does.

The answers have not tried to calculate that two specific pitchers share the same birthday. They calculate the probability of two arbitrary pitchers who start in an arbitrary game having the same birthday. This probability must then be applied to the number of games played in history to determine the probability that it would ever happen (expected value of about 1.31 times in past history, according to the OP’s figures).

The problem does not require that you assume that any two pitchers share the same birthday. Posts 2, 3, and 4 give good answers.

A starter will play less than 40 games a season, usually a lot less. So the odds of any pitcher starting on their birthday start out pretty low.

This had more to do with the way youth hockey is run in Canada than anything else. Baseball in the US wouldn’t have that same problem.

I’ve got nothing to add except perhaps that ‘Homer’ is a most unfortunate name for a pitcher. And reading the link, I see he gave up three of them in this game, though the Cubs still won.

I present to you, Grant Balfour.

But that’s a different problem. You are answering the question, “What is the chance that for a specific pitcher, he will pitch on his birthday?” The actual question is, “What are the chances that for a given game, is it the pitcher’s birthday?”

I originally saw this point made about soccer in a SciAm article a few years ago. There was a consensus that in a wide range of activities, where there is a cut-off for a given year, there will be a bias in favour of kids born closer after that date. So unless US baseball is organized by ability and doesn’t stratify by age, the effect will most likely hold.

I think the actual question involves two pitchers. But I see what you mean. I was simply addressing the number of games played per pitcher per season. Since any pitcher may not ever pitch on his birthday, the chances of two them pitching on a shared birthday has to be pretty low.

The number of games per pitcher per season is irrelevant. For every game, there’s a starting pitcher for each team, regardless of how many starts a given pitcher may have per year.

Suppose every pitcher only got a single start per year. The odds wouldn’t change. You’d just have to have more pitchers to play a whole season of games.

CookingWithGas claims that baseball has an age cut-off as well (though in May, so my speculation about January birthdays in particular was off). Why wouldn’t the same forces play out and skew the birthdays?

Homer is just his nickname although yes thats a REALLY bad nickname for a pitcher :slight_smile:

Fortunately for me, I just read Outliers a month ago.

In Canada youth hockey, it’s more stratified. The better (older) players within the group get way more playing time and opportunity. In Little League in the US, everyone gets to play and there are, in a lot of leagues, rules that even the crappy players have to get a certain amount of playing time.

A certain amount, but an equal amount? And the better players still get to play first base, while the worse ones get to play deep right field. And the worse players probably have less fun, which makes it more likely they won’t come back next year. The better players’ parents are more likely to do extra practice with them, send them to baseball summer camps, etc. I agree there’s less feedback through the league itself, but there’s still plenty in the total ecosystem.