Hardy's weird hitting streak

[Frobby]

JJ Hardy now has a 15-game hitting streak.

He has a total of 16 hits during the streak.

[isestrex]

That's Hall of Fame talk to Jim Hunter right there...

[weams]

That's Hall of Fame talk to Jim Hunter right there...

No longer modest.

[TonySoprano]

That's Hall of Fame talk to Jim Hunter right there...

a mere 41 games behind DiMaggio.*

*Hunter gets out his calendar and notes J.J. can tie him at home vs. Boston on September 15.

[Three Run Homer]

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.

[Three Run Homer]

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.

[Three Run Homer]

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.

[square634]

I think you would need to multiply by 15p1 = 15 (since there are 15 permutations of where the multihit game can occur within the streak), but that still leaves you with < 1/20 million.

[TonySoprano]

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?

[ChipTait]

You guys never cease to amaze me!

[jaege]

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.

[bobmc]

a mere 41 games behind DiMaggio.*

*Hunter gets out his calendar and notes J.J. can tie him at home vs. Boston on September 15.

But if he could only bat ninth so he could turn the lineup over.....:cussing:

[jerseyosfan]

I'm in no way the best person at math but if he is a .250 hitter that would mean that the probability of him getting a hit in a single at bat is .25 meaning if he gets 4 at bats in one game it is a 1:1 ratio that he gets a hit in each game.

[Three Run Homer]

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.

[O's84]

a mere 41 games behind DiMaggio.*

*Hunter gets out his calendar and notes J.J. can tie him at home vs. Boston on September 15.

Look out Joltin' Joe.