A (not actually very quick) thought: WAR and positional adustments

Every year, there are a few players whose defensive problems or injuries lead to discussions about when they’ll need to move to another position. This year, there’s been talk about moving Joe Mauer, Buster Posey, and Matt Kemp, just to name the most famous. With all of these discussions comes the inevitable mention about how much less valuable the player would be at their new position. With Mauer and Posey, this reasoning is obvious: both are considered to be good “gamecallers” and Mauer, at least, has a reputation for being a very good defensive catcher in other respects. Those skills would be useless at first base.

With Kemp, I’m less convinced. Despite the Gold Glove, Kemp has a reputation as a poor centerfielder. By Fangraphs, he has been poor this year, though his -6.5 fielding runs has nothing on the -25.7 that he recorded last year. Given his defense, one might suppose that Kemp would be more valuable at a corner position, especially since the Dodger regularly roll out Tony Gwynn Jr. in left. At least according to a traditional understanding, Gwynn’s plus fielding numbers would be much better used in center. And while the Dodgers might not gain even a win or two in what is already a lost season, switching their two outfielders would probably improve their team. Kemp, as such, might have more value in left to the Dodgers in left than he does in center.

So far, though, Kemp’s case seems like a semi-unique one, which can be expressed by saying that when a player’s defense improvement from a switch outweighs the change in replacement value, he will have more value at the second position. Or: (d2-d1)+(rv2-rv1) = net gain (assuming that the position change does not impact the offense that the player provides).

But I think that positional part of replacement value is misleading in other situations as well. Right now, for example, Lance Berkman and Albert Pujols have played almost the same number of games (105 to 107) and have almost the same fWAR (3.7 to 3.8). For the sake of argument, however, let’s assume that the teammates have been identical offensively and on the basepaths. Just for example, let’s say that, in a whole season, they will both create exactly fifty runs offensively and be neutral runners. Continuing our imaginary world, we’ll assume that the positional difference between RF and 1B is 10 runs this season, and that Pujols is about 5 runs better defensively than Berkman when both are playing first and 10 runs better when Berkman is playing RF. Here’s how WAR would determine their value, assuming that each plays a full season:

	Bat	Running	Fielding	Replacement	Positional	RAR	WAR
Imaginary Pujols	50	0	5	24	-15	64	6.3
Imaginary Berkman	50	0	-5	24	-5	64	6.3

WAR is, of course, a theoretical measure. But we would, nevertheless, assume that either of these players getting injured (as both have been this season) would deprive the club of the same amount of value. This is not true. Let’s assume Berkman goes down for sixteen games. He’s replaced by Allen Craig, who’s hitting pretty well right now. We’ll say Craig is the same defensively  in RF and on the bases, and give him about three runs generated in those sixteen games from his bat. Now say Pujols gets hurt for the same time. Berkman fills in at first and Craig plays RF instead of Berkman. Our comparison for the two results looks like this:

	Bat	Running	Fielding	Replacement	Positional	Runs Lost
Without Pujols	-2	0	-.5	0	0	-2.5
Without Berkman	-2	0	0	0	0	-2

Now, there’s not a huge difference there. But there is one, because both are essentially replaced by the same player offensively, but the replacement situation for theoretical Pujols is worse defensively over that 1/10 of a season.

It may be clearer to say it this way: real replacement/positional value is team-dependent. Team-dependency, of course, is kryptonite to anyone in the sabermetrics community; rbis and runs are terrible way to judge true talent level, and thus true value. What I’m saying is that WAR, as currently constructed isn’t judging true value added either. This may be obvious to some, and the distinction I’m about to introduce may seem trivial; but the “positional” part of WAR is valuable not on the field but in the general manager’s office. Troy Tulowitzki and Dustin Pedroia are extremely good players to build a team around right now (and who, as of today, lead their leagues in WAR) because they are terrific all-around players who play key defensive positions. But another terrific player—let’s pick on Derek Jeter since I’m a Red Sox fan—would likely have created more value over the last decade at a different position than shortstop, because what he contributed on the field (in terms of better defense) would have been better, regardless of whether the Yankees could have more easily found a replacement shortstop or centerfielder.

To estimate the true value that a player added to a team over their replacement, we would have to use their specific replacement, something based on their team and thus un-related to their skill level. But when we estimate that same value with WAR, we do essentially the same thing, only with a less specific measurement: a theoretical replacement level adjusted to how well other players at that position are playing. To put it another way: Jeter’s skills had nothing to do with the those of the other shortstops between 1997-2003. Judging him on the fact that (most) of his prime coincided with the “Golden Age of Shortstops,” a historical circumstance, is just as “inaccurate” as judging him based on the historical circumstance of who he came to bat in front of or the park he played in.[1]

To sum up, a middle-of-the-order hitting shortstop or second baseman is (or should be) like candy for general managers. Having a good hitter who can also play a prime defensive position allows you to have a better offense overall because normally you expect to have not very good hitters at those positions. However, that expectation doesn’t mean that said player creates more value on the field than your first baseman who couldn’t dream of playing short. That determination requires adding up the various things the player brings to the field and maybe some bonus points because short ends up having a greater defensive impact than first. Determining which player is a better one to sign—i.e., which one you can replace more easily—is an entirely different question. Maybe there’s no one who hits like your first baseman does, and maybe every short stop in the league has hit free agency at the same time.

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[1] A side note: had Albert Pujols or Jeff Bagwell come along in say, 1977, the relative position scarcity at first base would have made them seem even more impressive than they seem today. But the fact that there were a lot of great-hitting first basemen—for various reasons—in the last couple decades lessens that impact.