A few days ago, a fan at a baseball game caught two home run
balls hit by consecutive batters, as has been widely reported.
Calib Lloyd’s amazing day at the Cincinnati Reds’ game
earlier this week had me wondering what the odds were, but there were no
mentions that I could find of anyone else having this happen.
That does not mean we cannot give an estimate of the likelihood
of the event, it just suggests that the estimate will be lousy. Anyway here’s my take:
There are 2430 regular season games per season, and maybe ≈5,000
seats or so in the outfield, and each team averages roughly ≈1 home run/game. Last year it was .94 HR/team/game, whereas in
2000, the steroids era, it was 1.17 (STATS LLC). Then, using Poisson to inform us the
likelihood of various numbers of home runs by a team in a game is simple.
There are about 40 plate appearances per team per game
(baseballgurus.com). A little bit of math tell us the number of consecutive
home runs in a game per team would be about 0.013.
We guess the odds of a ball being caught by someone is ≈0.8,
since some leave the stadium and some land in the bullpens or in the area in
center field where there are no seats.
Thus, in a given game, the odds that this might happen to
someone is about
So, in a hundred years of baseball (yes, there were formerly
fewer games per year, but this will only affect the calculations by a factor of
two at most probably) this would happen roughly once. That it would happen to you at a game would be about 1.5 billion to 1.
Of course I am not the only one to ask this question, so we can
compare it to others’ calculations:
Here, using an slightly higher average number of home runs
per game and a different methodology gave about twice the likelihood of its
occurance. That is not atypical for this
type of calculation, and either calculation does suggest that there is a good
chance that Caleb Lloyd is the only person to ever catch home runs hit by consecutive
batters.
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