Monday, May 2, 2011

Andre Ethier vs. Raul Ibanez

There are two spectacular hitting streaks going on in baseball right now. One has Andre Ethier playing strong with hits in 27 straight games. The other has Raul Ibanez going 0 for his last 34 at bats. PTI just asked which one is more impressive, and with a little help from probability I aim to answer that here.

This season the league-wide MLB batting average is .250. That's interestingly considerably below the usual league total which got as high as .269 in 2006. However since we're looking at which is more impressive (less likely) in the MLB this year, I think .250 is a good number to use.
For Ibanez, it's simple to just take .750^34 to get his odds. The chances of going 0 for 34 over any given set of 34 at bats is just 5.65*10^-5, a very small number. On the other had, with well over 5000 at bats in any given year, there are many chances, so it should happen every 3 or 4 years.
For Ethier we have to make some assumptions about his at-bats per game. He has 111 at bats over his 29 games this season (slightly less than 4 per game). While average doesn't work perfectly because it's especially hard to get a hit with just 2 or 3 at bats, some games he may have been taken out only because he already had a hit. The two cancel out, so we'll go with 111/29 at bats per game. He then has about a 2/3 chance of getting a hit in any given game, and a 1.82*10^-5 chance over any 27 game stretch. Even without compensating for few chances, that's less probable than Ibanez's streak. Overall, Ethier 27 game hit streak is less likely for an average player, and therefor more impressive.

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