Does Size Matter?

I wrote an article for The Hardball Times Thursday examining how player performance varies by size. If you have yet to read it, check it out! Anyways, there were a bunch of questions that followed, so I’ve decided to just answer them all here.
How many players were in each category?
I mentioned that Kirby Puckett made up more than half of the “pudgy” sample, which led to a lot of questions about the significance of my samples. Here they are, for each category:
Big = 657 players; 644,886 PAs
Lanky = 10 players; 3,011 PAs
Pudgy = 7 players; 12,404 PAs
Small = 462 players; 652,722 PAs
Now obvioulsy the samples for the Big and Small groups are much greater, and for obvious reasons. There are plenty of guys that are tall and heavy or short and light, because those two characteristics are proportionate. It is much harder to find a disproportionately sized player. Nevertheless, I think that both the “lanky” and “pudgy” samples are large enough to be significant.
Tom Tango suggested on The Book blog that I make the breakdown such that my samples are all the same size, and I may yet take that suggestion. One e-mailer suggested that I use BMI, and that might be a pretty good idea as well.
My one worry is that I want to use just extreme players. If I start expanding the requirements for the “lanky” and “pudgy” categories, my samples might increase, but I’m not sure that the players I’ll be including will actually be guys that are lanky or pudgy rather than slightly under- or over-weight.
Shouldn’t you be adjusting for era?
Some suggested that players are bigger nowadays, and I should adjust that. Actually that’s not really the case. Players have gotten slightly taller (about an inch) and slightly heavier (about five pounds) over the past 50+ years. I don’t think that’s significant enough to merit adjusting for.
Okay, so big players are better hitters, what does that tell us about how big players develop?
Well, to get that answer, you’ll have to wait for part two. My interest in writing part one was to examine the differences between the categories. In part two, I’ll look into how size affects development.

Is David Ortiz a clutch hitter?

Jess Sussman says no. Seth Mnookin (and pretty much the rest of the world) says yes. One of the most astonishing numbers quoted in the David-Ortiz-is-a-clutch-hitter arguments is that Ortiz has come to plate 19 times since the end of the 2004 regular season, and gotten on-base in 16 of those plate appearances. In his 14 official at-bats in that time span, Ortiz has 11 hits. If this seems like statistical cherry-picking, it is, and I’ll get back to that in a second. But are these numbers statistically significant?
The short answer is yes. The probability that Ortiz would have 11 hits in 14 at-bats just by random chance alone is one in 34,365 (assuming that he is a .295 hitter). The chances that he would get on-base in 16 of 19 plate appearances are just as slim if we assume that Ortiz will generally get on-base 39.5% of the time — one in 30,269. The National League has eight hitters per team and 16 teams, which is 128 hitters. The American League has nine hitters per team, and 14 teams — that’s 126 hitters. Combined, that’s 254 hitters. We would expect them to hit as well as Ortiz has in walk-off situations just once every 120 or so years. That’s pretty significant.
But the cherry-picking problem is a big one. There are of course plenty of players who go through 11 for 14 streaks in their careers — that’s nothing special. The reason that those streaks are not particularly significant is because they can start with any at-bat, as long as there are 13 more at-bats left in the season. If the average player gets 620 at-bats a year, that’s 607 opportunities a season to start such a streak. With 254 hitters, we expect four or five such stretches a year. Still rare, but no longer in the realm of statistically unlikely. What we’ve done with Ortiz here, however, is said that such a streak must have started in one specific moment (at the end of the 2004 regular season). Why not count the 2004 regular season? Why not count his whole career? By doing it this way, we’re limiting the number of eligible hitters, and using his best-possible clutch streak.
So is David Ortiz a clutch hitter? The answer is, I don’t know. What I do know is that clutch or not, I’m happy he plays for my Boston Red Sox.