=BINOMDIST(hits,ab,avg,TRUE) gives you the probability of the lower tail

=1-BINOMDIST(hits,ab,avg,TRUE) gives you the probability of the upper tail

Sorry about that.

Actually, the Excel formula for the binomial probability distribution is a more elegant way to do it:

=BINOMDIST(,,,TRUE) gives you the probability of the lower tail

=1-BINOMDIST(,,,TRUE) gives you the probability of the upper tail

The probability of 227 (or fewer) hits in 750 ABs for a “true” .331 hitter = BINOMDIST(227,750,.331,TRUE) = .0528. If Ichiro hits less than .303 over 750 ABs, the probability of it being merely random is 5.3%.

But you can probably also do better with taking a season’s worth of data, considering the player’s performance before that year, and adding in some regression to the mean. That’s basically what PECOTA and all the other player forecast systems do. (I would also argue that’s basically what all talent evaluators do.)

It sort of goes back to the distinction between value and skill. If a player hits .300/.400/.500 over 600 PA, there’s value in that. But if there are underlying reasons to believe his skill level won’t allow him continue to do that, then you might say that he was lucky over those 600 PA. Going forward, you expect more skilled players to be more valuable than less skilled players, but when assessing past performance, it is possible that over a 600 PA time frame, the less skilled player happened to be more valuable than the more skilled player, thanks to luck or other things outside the players’ control.

Which is a long-winded way of saying that if all you care about is past value, then you don’t need to bother worrying about whether or not a player was lucky. If you want to know about future value, though, knowing whether or not a player was lucky in the past is important.

Bobo Holloman. Pitched a no-hitter in his first career start, played only 1 season (not surprisingly):
K/9: 3.44
BB/9: 6.89
FIP: 5.17

“This game would prove to be one of only three major league wins that Holloman achieved, against seven losses, all in 1953. Bill Veeck, then-owner of the Browns, in his autobiography described the 27 outs of Holloman’s no-hitter as consisting of hard-hit ground balls, screaming line drives, and deep fly balls.”

For what it’s worth, Charlie Hough had at least 6 seasons in his 25 year major league career where his K/9 was below 5. He only pitched 17 innings in one of those seasons and roughly 925 over the other 5. Here’s those 6 seasons in the context of his career:

career: 216-216; K/9: 5.59; BB/9: 3.94; ERA: 3.75; FIP: 4.72;

K/9 less than 5.00: 45-52; K/9: 4.53; BB/9: 4.30; ERA: 4.42; FIP: 5.21;

K/9 grater than 5.00: 171-164; K/9: 5.95; BB/9: 3.83; ERA: 3.59; FIP: 4.38;

I think most people would take the Hough that had a K/9 greater than 5.

For what it’s worth, Charlie Hough had at least 6 seasons in his 25 year major league career where his K/9 was below 5. He only pitched 17 innings in one of those seasons and roughly 925 over the other 5. Here’s those 6 seasons in the context of his career:

career: 216-216; K/9: 5.59; BB/9: 3.94; ERA: 3.75; FIP: 4.72;

K/95.00: 171-164; K/9: 5.95; BB/9: 3.83; ERA: 3.59; FIP: 4.38;

I think most people would take the Hough that had a K/9 greater than 5.

Well, he has a major league job despite some of the crappiest performances in MLB history. And he’s going to get paid 8 million to do it, regardless of whether or not he succeeds or fails from this point onwards. I’d say that’s a pretty big break.

Weaver has allowed close to 150 runs in his last 200 IP (outside of the playoffs). His K rates are cratering from his days in Detroit, and his velocity is around 88-90. I think he’s coasting on the fumes of when he had decent stuff the same way Pineiro is.