## Ichiro’s Body Armor July 8, 2011

Posted by tomflesher in Baseball.

In the previous post, I looked at Kevin Youkilis and his uncanny ability to be hit by pitches during the regular season. This time, I’d like to go in the opposite direction – who’s started the year with the fewest times hit by a pitch? That’d be Ichiro Suzuki, who’s gone 87 games (he had one night off this year) and 389 plate appearances without being plunked yet this year. Last year he was hit three times in 732 plate appearances, or about 4 in every 1000 plate appearances, for a rate of .004. Assuming his batting and league pitching haven’t changed, that means that any given streak of 389 plate appearances had a probability of occurring of

$(1-p)^n = .996^{389} = .21$

or roughly one in five. Ichiro has played eleven seasons in the US majors and made 7728 plate appearances, so it’s totally unsurprising that he’d have such a streak without being hit.

In fact, Ichiro is currently on a streak that started on July 7, 2010, of 155 games with at least one plate appearance that don’t involve being plunked. In order to make sense of this, let’s normalize his stats to per-game rather than per-plate-appearance. Over his career, Ichiro has been hit 47 times in 1675 games, meaning that on average he gets hit .028 times per game, or once every 35.6 games. Equivalently, the probability that he does not get hit is (1-.028) = .972. The likelihood of a streak of 155 games, then, is

$.972^{155} = .012$

It’s highly unlikely to occur, but assuming Ichiro is the same batter he always has been, and assuming he plays the remaining 74 games, the likelihood that he won’t be hit at all is

$.972^{74} = .122$

Using the binomial distribution, we can determine that there’s about a 26% chance he’ll be hit once in his next 74 games, and about a 27.4% chance he’ll be hit twice. After that, it drops off sharply. Finally, the probability that he’ll be hit in all 74 games remaining is 1.229e(-115), or so small as to be equivalent to zero for our purposes. (It’s about 1 behind a decimal point and 114 zeros.