Since pretty much the beginning of the offseason, I've wanted to do this series where I take a close look at one stat I like to use (or maybe that I don't like) -- what it is, why I like it, what its strengths and weaknesses are. The idea is, basically, that I know little or nothing about math, but I'm really obsessed with baseball statistics, so I'd have a different perspective than your average statistician and might make it a little easier to digest. Eventually, I'd have kind of a primer for interested sabermetric neophytes (and there are a few lurking around here, believe it or not).

It may or may not actually become a series. This could well be a one-shot deal.

Either way, today I'm going to cover the "plus" stats, which (in the case of OPS+ and ERA+, anyway) are kind of the backbone of ground-level sabermetric discussion right now. I don't really expect the usual commenting crowd to spend a lot of time on this one -- this is more for your ground-floor baseball stathead (though of course comments and suggestions are always appreciated, and the last point below is an important one many people don't think enough about).

Quickly, some layperson's definitions.
(click here to read more)

A "plus" stat attempts to measure how far above or below average a player is, where 100 is average, above 100 is better than average and below 100 is worse. In essence, if a player's number in a given plus stat is 125, he's 25% better than average; if 75, he's 25% below average. For instance, Babe Ruth's 207 OPS+ means he was a little more than twice as good as average; Daniel Cabrera's 88 ERA+ means he's 12% worse than average. More specifically:

OPS+ has become every internet dweeb's favorite way of quickly evaluating hitters; how much better or worse than average is his on base percentage plus slugging percentage? If life were simple, the calculation would be

((Player's OBP / League OBP) + (Player's SLG / League SLG) - 1) * 100

So if a player put up a .400 OBP and .500 SLG in a league that averaged .350/.425, it would be

((.400/.350 [1.14]) + (.500/.425 [1.18]) - 1) * 100 = 132

meaning that player's OPS was 32% better than the average hitter. But of course, it's not that simple. The version of OPS+ that's almost always used is actually called Adjusted OPS+, from Baseball-Reference.com, and includes an adjustment based on the relative hitter-friendliness of the hitter's home park, plus some other adjustments that, frankly, I can't figure out. That's the basic idea, though.

OPS+ is great because it's right there on BBREF, which makes it very easy to compare two fairly similar hitters across periods of similar lengths -- one season or several consecutive seasons -- to get a rough idea of who was the better hitter. Or just to take a quick look at one guy's career and get a quick idea of how he stacked up to his peers.

It's not so great for comparing two very different hitters: OPS+, like OPS, treats on-base percentage and slugging percentage as equals, when in reality, OBP is the considerably more important component (before more advanced stats were readily available, people figured things like OPS' = 1.4*OBP + SLG). For instance, if you've got two hitters who are more or less peers, and Guy A has a 119 OPS+ and a .323 OBP while Guy B has a 123 OPS+ and a .385 OBP, Guy B is likely a better hitter by considerably more than those four little "points" of OPS+ would lead you to believe, by virtue of that OBP.

ERA+ is the same thing, but for pitchers; percentage that the pitcher's ERA, given his home park, was better or worse than average. Works like OPS+ and not like ERA, in that a higher number is better. (ERA/League ERA)*100, adjusted for the pitcher's park. It's also almost entirely a creation of Baseball-Reference.com.

It's good for the exact same thing OPS+ is. The drawback is that ERA isn't really a great indicator of how well a pitcher actually pitches; pitchers have a lot of control over how many unearned runs they give up, too, and little control over whether balls fall in for hits or are hit right at somebody. But it's a very good quick-and-dirty measure, just like OPS+.

wRC+ is a new stat, explained in mathtastic detail here, and available only on FanGraphs.com. It's on the same scale as OPS+, and aims to fix that stat's flaws. It's based on another FanGraphs-specific stat called wOBA, which measures the same things as OPS+, but more accurately assigns values to the various things a hitter can do (so it gets rid of the undervaluing-OBP problem). The drawbacks to it are (a) it's very, very hard to understand -- I can't break it down to even an oversimplified equation like I did with the others above -- so you just have to kind of trust that it works (which, as far as I can determine, it really does); and (b) it's only available on FanGraphs, which doesn't give you nearly the user-friendliness of BBREF, or the ability to easily come up with averages for a number of consecutive seasons.

Finally,

THE ONE THING PLUS STATS ABSOLUTELY, POSITIVELY CANNOT DO

This is the point I really wanted to make all along: the one thing plus stats really can't do is the thing that it seems to me people most often try to make them do: compare two players over their entire careers, when those careers have different lengths. Recently, somebody tried to tell me that sabermetrics was junk because by OPS+, John Kruk (133 career OPS+) was a better hitter than Tony Gwynn (132). Of course, Kruk played parts of ten injury-riddled seasons and got 4603 plate appearances in the big leagues, while Gwynn played parts of 20 seasons and got 10232 plate appearances. OPS+ will tell you they were basically the same hitter, if you want to misuse it that way; taking a look at it realistically will tell you that Gwynn's value as a hitter was equivalent to what John Kruk's would be if he played two and a quarter times longer at the exact same level. All those extra years should help Gwynn, right, even if he wasn't quite playing as well as he did at his very best? But by OPS+, he gets punished for them. Obviously doesn't work.

It's misused just as often by people who do like statistics, though. I've had people try to tell me that Greg Maddux couldn't be that great because he's only got the 33rd best ERA+ of all time, behind guys like Noodles Hahn and Roy Oswalt. Of course, Maddux pitched considerably more innings than both of those guys combined. Makes a difference.

My favorite example ever is Maddux against Whitey Ford. Of course Ford was a fine pitcher, a deserving Hall of Famer. He has a 133 ERA+ to Maddux's 132. Looks awfully similar. But check this out:

Ford pitched a total of 3170 innings in his career, almost all between ages 24 and 36. If we take Maddux's age 24 to 36 seasons against Ford's whole career, we get this comparison:

Ford: 3170 innings, 133 ERA+
Maddux: 3076 innings, 159 ERA+

So if Maddux's career had covered only the same ages and innings as Ford's, he'd vault into second place on the all-time ERA+ list, behind only Mariano Rivera, who has only barely topped the 1000-career-innings threshhold required to make the list. And Maddux would still have more career innings than Pedro Martinez, who'd be right behind him at 154. So, Maddux isn't Ford at all. Not even close. He's Pedro Martinez, plus two really good seasons before age 24 (he was 37-20, 121 ERA+ at ages 22 and 23) and six average seasons after age 36. With the exception of his terrible first full season before he was really ready, those eight years where he was a good pitcher but just not quite Greg Maddux [yet/anymore] were still very valuable, and they make him a better pitcher, not a worse one. Yet, ERA+ makes him look like Whitey Ford, which is great -- just not nearly as great as the Pedro Martinez++ that he really was.

So...don't use it that way. Plus stats are great little things for one season, or three or five consecutive seasons, or two careers that happen to be almost identical lengths (like Raines and Dawson above, or Jim Rice and Edgar). But it only goes so far.

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