First of all, let me reiterate that, as most people who actually pay any attention will concede, dWAR is, to put it gently, a crock of ****. This is particularly troubling when trying to compare a guy who was basically a career DH to a guy who played nearly his entire career in the field using total WAR. But again, as I mentioned pages ago, I do agree that in a perfect calculation of the number of wins a player was worth vs. replacement level, Martinez was probably worth at least a little bit more, in terms of WAR, than Bernie. I'm not disputing that.
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The problem is that in the past decade too many people have taken the famous Moneyball quote about buying wins as too close to gospel. That's not entirely the way it works, at least not on the single-player level. If you're trying to build a championship caliber team, you would hope that your contingency plan is NOT replacement level. And the likely contingency plans at DH are typically going to be far, far better than the available contingencies in CF. You think the Yankees would have traded Bernie Williams for Edgar Martinez in 1998? Not a chance. He's far too hard to replace at anything similar in terms of overall value.
Thought of in a different way, if you were to rebuild MLB from the bottom up, just throw everybody into a draft pool and start repicking the teams, you have to figure that early in both guys' primes - say 1996-1998 - both of these guys are probably 2nd rounders, 3rd at worst (particularly for Edgar, who, as I mentioned earlier, was actually pretty old before he really started hitting). At that point in an all-players draft, you're not drafting relative to replacement level. You're drafting relative to what you can get in the 3rd round, or the 5th, or maybe the 10th. And certainly you're thinking, at least on some level, that you can find a couple of guys with enough bat to platoon at DH at the end of the draft. You can't even find quality platoon CFers that late. The reality is that in 1998 there are probably no more than 8 CF guys you're at all happy about if you're trying to be a serious contender. Sure, you can compete for a title with 1 really weak spot. But not many more than that, and you don't just want to toss CF to a glove-only guy if you can avoid it. Probably love to save that option for SS. So I think in that situation Bernie undeniably goes ahead of Edgar.
The real issue highlighted to me in both of these scenarios is that in many, many scenarios, the sort of AAAA replacement level considered by WAR isn't entirely realistic when weighing FA options. In many cases, at least for competitive teams, a much more relevant consideration might be value relative to the guy you're likely to be able to sign in January for $3 or $4 million. I think Bernie wins that battle hands-down. The available market for contingency CF is never strong, and the time when these guys were at their best was not a great period for CF depth. On the other hand, it's a great era for general offensive depth. Steroids were certainly prolonging careers, and throughout the '90s and early 2000s there were always old guys available who could no longer field worth a damn but who could still swing the stick. Darryl Strawberry's DHing years for the Yankees are a great illustration of this (happened to come into my head when I was considering whether the Yankees would even entertain an offer of Edgar for Bernie). Not a great bat, certainly. Not going to do much of an Edgar Martinez impression. But still putting up OPS+ numbers comfortably north of 100 (121 over 779 PAs total with the Yanks, almost all as a DH). For that production he was paid under $3 million total. You think you could find a guy to give you an 80 OPS+ in CF for that money? Doubtful to me...
Just trying to buy wins works if you're just trying to compete, drag yourself out of the cellar. But if you're trying to make the playoffs and win World Series, you need to think in different terms. Maybe if I'm the Rays in 1998 I'd rather have Edgar Martinez. But if I'm the Yankees or the Indians or the Red Sox, and trying to win the AL, I take Bernie in a hearbeat. And this is another part to what I meant when I said the best player isn't necessarily the most valuable. Yes, clubhouse presence can be a part of it, as someone (sorry I don't remember who it was) alluded to a bit ago. But it's not the only factor. And positional value can be a big part of the equation, which in the case of elite teams is certainly undervalued by WAR.