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Hardy's weird hitting streak


Frobby

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A .250 hitter has a 68.36 percent chance of getting at least one hit per game assuming 4 at bats per game and independent draws. So the odds of a .250 hitter having a 15 game hit streak are about 300 to 1 (since 0.6836 to the 15th power is roughly 0.003).

But the odds of a .250 hitter getting only 16 hits while sustaining a 15 game hit streak are presumably much lower. Someone who is better at applied probability theory than me might be able to figure this out.

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Ok, here goes...the probability of a .250 hitter getting exactly one hit in a four at bat game is 0.25, assuming independent draws.

The probability of a .250 hitter getting exactly one hit in 14 out of 15 games and at least one hit in the 15th game is 0.25 to the 14th power, times 0.6836, which comes out to odds of...about 785 million to one.

So yeah, this is freaky.

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Ok, here goes...the probability of a .250 hitter getting exactly one hit in a four at bat game is 0.25, assuming independent draws.

The probability of a .250 hitter getting exactly one hit in 14 out of 15 games and at least one hit in the 15th game is 0.25 to the 14th power, times 0.6836, which comes out to odds of...about 785 million to one.

So yeah, this is freaky.

Correction. 392 million to one. Had a 2 in my spreadsheet where I should have had a one. Still pretty freaky.

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Ok, here goes...the probability of a .250 hitter getting exactly one hit in a four at bat game is 0.25, assuming independent draws.

The probability of a .250 hitter getting exactly one hit in 14 out of 15 games and at least one hit in the 15th game is 0.25 to the 14th power, times 0.6836, which comes out to odds of...about 785 million to one.

So yeah, this is freaky.

What about a .240 hitter? ;)

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But remember that each at bat is actually a singular event having no relation to any previous at bats, either from prior games or from the same game. So essentially the odds of getting a hit at any "at bat" for Hardy is roughly 1 in 4 assuming his average is .250.

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Ugh. I get dumber as I get older. The probability of a .250 hitter getting exactly one hit in a game is not 0.25, it's 0.421875.

So the probability of getting exactly one hit in 14 games and then at least one hit in the fifteenth is 0.421875 to the 14th power, times roughly 0.68. It looks like the odds are 258600 to 1. Still very unlikely, but no longer astronomically unlikely.

But getting less likely by the day.

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