## Estimating Trevor Story

Trevor Story, of course, became the first player to homer in each of his first four MLB games.  Obviously this is pretty improbable, so let’s estimate how improbable.

First we need the chance for Story to hit a home run in a given plate appearance.  I’ll use the FanGraphs depth chart projections, so that would be 15 HR in 490 PA, or about 3% per PA.

Story actually got 6, 4, 4, and 5 PAs in his first four games, so I’ll just look at games with 4-6 PAs.

For 4 PAs in one game, there’s an 11.7% chance that Story hits at least 1 HR.  For 5 PAs, 14.4%, and for 6 PAs a 17.0% chance.

For the number of PAs Story actually got, this gives a 1 in about 2984 chance to homer in all of his first four games.  This is somewhat sensitive to the actual PA distribution, but it seems the chance is somewhere in the neighborhood of 1 in 2500 to 1 in 3000 or so, if you get that total number of PAs.  Obviously, very improbable … for any individual player.

It’s a little less astonishing that this happened when you realize that there have been somewhere around 18000 major league baseball players in history.  Using the FanGraphs leaderboards, I get a total of 7417 non-pitchers who have recorded at least 20 PAs since 1900.

It’s … a lot of work to figure out the actual probability of some major league player homering in his first four games of his career.  So I don’t have a good actual estimate for the chance of this happening.  But I think that it’s not terrifically unlikely that some player would have, by this time, homered in his first four major league games. It’s probably reasonably likely after accounting for what I’ve seen called the Wyatt Earp effect; in short, large populations are almost certain to have a few large outliers just by chance.

Still, this is certainly a remarkable start to any individual player’s career.  Congrats to Trevor Story for a resoundingly successful major-league debut; he’s been the fifth-best position player in the majors so far this year, by FanGraphs.