Probability and Kings' Birthdays, seriously...

In Sunday's fit of boredom, I added a column for birthdays to the Kings reserve list (the master list that contains all the players under contract plus unsigned draft picks and players playing in Europe whose rights are controlled by the team). I decided it would be useful to have that information next to the waiver and draft data. In Monday's fit of boredom, I made a list of birthdays by month and day only (you know, for all of those birthday parties we like to throw here at SBN).

There are 68 players on the list (actually now there are only 65, but I put this together pre-Ersberg and a couple other deletions). How many do you suppose share a birthday with another player on the list? Not talking about years here, just month and day.

(Yes, this is a math problem. No, it has nothing to do with hockey. This is what happens when you have four days off.)

Sixty-eight players with sixty-eight birthdays. How many have a birthday on the same day as another player in the Kings organization?

Would you believe 18? Slightly better than 1/4. Here's the list, chronologically by birthday:

The most common illustration of this effect: take any group of 23 people (e.g. the active roster of one NHL team, or a classroom of kids). The odds of any two people in a group of 23 sharing the same birthday is just better than 50%. That is, half the time, if you check the birthdays on the roster of a sports team (if they have 23 players or more), you will find at least one pair of players who share a birthday. Try it next time you're looking at your $10 program between periods. 

With 57 people, the odds are higher than 99% that there will be at least one match. So it's not probably/possibly not so surprising that the Kings reserve list of 68 has 18 different matched pairs. I say it's not surprising, but I am still surprised by it every time. 

If you're interested in getting into the numbers, the gist is described by Wikipedia as The Birthday Problem.