By Andrew Puopolo
Rhys Hoskins has been off to quite a tear to start his MLB career. 9 Home Runs in his first 54 at bats, 11 in his first 64 and he’s currently at 12 HR in 85 at bats. That got me thinking, how unlikely is it to hit 11 home runs in any 64 at bat sequence?
To measure this, I decided to calculate the cumulative distribution function of a binomial random variable with 64 trials and at least 11 home runs. I used quite a few different probabilities for the chances of hitting a Home Run in a particular at bat. As follows, they were:
1.) The average number of home runs per at bat for all MLB players in 2016 (5610 Home Runs in 165561 at bats)
2.) Mark McGwire’s 1987 rookie season (record number of Home Runs for a rookie in a season, 49 in 557 at bats)
3.) Barry Bonds 2001 season (73 in 476 at bats)
4.) Mark McGwire career (best HR/AB ratio in MLB history, 583 Home Runs in 6187 at bats)
Assuming that every at bat is independent and identically distributed, the probabilities for each of these players hitting at least 11 Home Runs in any 64 at bat cycle were:
While this does exhibit how absurd Barry Bonds’ 2001 season was, it does show that even for the best players of all time, the probability of this event happening is still extremely rare.
Looking at the average MLB player though shows how absolutely astonishing this feat is. For the average MLB player, we would expect this to happen once in every 104779 sequences of at bats. Assuming the average MLB player takes 600 at bats in a season, this means that for any one player this would happen approximately once every 174 years.