What are the real odds that Aaron Judge hits his 62nd home run in game 162 like I think is most likely? This is something we can actually figure out.
The Yankees have five games left this season, including a doubleheader. Although Judge had a couple of at-bats left in today’s game when I published my post, I’ll let that slide and just pretend I made my prediction with five games left.
Judge has hit 61 home runs in 152 games played this year. Normally, I would take the number of plate appearances he averages in each game to determine how likely he is to homer, but that’s not really how his power seems to work. Judge’s power often comes in bursts, and 11 of the 50 games he has hit home runs in have been 2-homer games.
This means he has hit a home run in ~32.9% of the games he’s played. In order to figure out how likely my prediction is, we need to multiply the percentage of games he doesn’t hit a home run in by four, the number of games we need him to go homerless for. ~67.1% × 4 = 20.3%
Now we can multiply 20.3% by the likelihood that he will hit a home run, 32.9%.
This gives us a product of 6.7%, or about 1 in 15
Since 22% of the games he homers in are 2-homer games, this gives us a ~1.46%, or about 1 in 69 (heh).