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Adam Lind is proud of being so valuable despite being a full-time DH at 26.

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The designated hitter position is a funny thing. Not so much "funny haha" or "funny strange" but "funny interesting." Teams just sort of, have them, but it is hard to know  -- either in terms of runs, wins, or, most importantly, money, how much they are worth. Are DHs paid enough? Too much? Just right?

How well does a DH need to hit to earn his paycheck? This article goes team-by-team through the AL to find out.

In an earlier post, I explored the idea of measuring just how bad a player has to be at defense to be "better off as a DH." This is something very different, and addresses the "DH question" from the other end. Sort of.

The positional adjustments I usually use are those that Tom Tango came up with, and most commonly associated with FanGraphs. Per season/150 games/whatever number of plate appearances (FanGraphs prorates over 600 PAs), one adjusts the players wins above/below average (or replacement level) by this many runs (technically, this should be wins, but I'll just assume 10 runs to the win for simplicity). Of course, some people don't like this way of doing positional adjustments, or these particular adjustments, but for the sake of this post, we'll just go with the:

+12.5 C
+7.5 SS
+2.5 2B/3B/CF
-7.5 LF/RF
-12.5 1B
-17.5 DH

How does one arrive at this designated hitter adjustment?

The replacement level player (a heuristic notion of a player who is freely available at the league miniumum) is defined as 2.25 wins (22.5 runs) below average. Tango notes that " league average hitter who cannot (or is not expected to) play the field is the very definition of a replacement-level player." While a league average player is very valuable not easy to find (and thus the need for replacement level as a baseline), a league average hitter isn't that hard to find if you ignore his (in)ability to play defense. That would seem to make the DH adjustment -22.5. However, there is also research (such as that found in The Book) that shows that it is more difficult to hit off the bench, so we give 5 run/0.5 wins as a "bonus." So the adjusment comes to -17.5 runs/1.75 wins.

In a recent discussion about DHs, I commented about how few players seem to be able to be "above average" (average being 2-2.25 WAR [wins above replacement] per season). Someone remarked to the effect that this shows that the -17.5 DH adjustment is unfair. That's an interesting point. However, when looking at the 20008 FanGraphs AL leaderboards for hitters, out of 68 qualified hitters, 25 hit for more than 17.5 runs above average (wRAA) over the season. I hardly think one would say that it is unfair to expect a player whose only job it to hit should be an above average hitter. More than one third of qualified AL hitters would have "beat" the adjustment -- just because only a few of them were actually near full-time DHs doesn't make DHs more valuable. If anything, it shows how little intrinsic value the DH "position" has, or, perhaps, how the position is being misused by teams.

But again, the point of "replacement level" is that players can be value even if they are below average. And part of that point is to get a sense of what players should be paid. Are teams paying their DH's appropriately? Let's find out.

The following chart lists each player who is is listed by  baseball-reference as their primary 2009 DH on each to find out who has been each team's page. The 2009 salaries listed are taken from Cot's. The value field lists what the team is "really paying" by adjusting non-FA year contracts according to the pre-arb/arb rules of thumb (40/60/80 for each arb year, and I used 20% for the one pre-arb player).  Using $4.5M as the dollar amount per win above replacement level, I determine how many WAR for which the player is being paid (xWAR). From there, I factor in replacement level (+20 runs/600 PAs, like FanGraphs) and the DH adjustment (-17.5/600) to figure out how many runs above average the player will have to produce on offense to achieve the WAR, or "earn his money" over 600 PAs (xRAA).  Finally, I convert that amount to wOBA (assuming something like last year's run environment for wOBA Scale, for those curious) to see what sort of wOBA the player will have to hit to meet that expectation (xwOBA).

+ Player is pre-arbitration.

* Player is in his first arbritation season.

# Player is in his second arbiration season

I first should note that not all of these guys are full-time DHs -- Vladimir Guerrero is playing a fair bit there because of injuries, Marcus Thames might have played some in the field (and is now hurt anywhere), etc. So some guys are going not get get the "full" DH adjustment this year because of time they spend at first base, outfield, or elsewhere. This just gives a sense of what they'd be worth, in these cases, if they were full time DHs. And remember, the point here is the monetary value of each player when they are DHing.

Adam Lind may or may not be good enough to play the field over Travis Snider, but for the money they're paying him, he certainly looks like he'll hit well enough. Luke Scott certainly does play the outfield well, but given the other options (Pie, Markakis, etc.), he does just fine at DH, and for the right price. Jack Cust is pretty much the blueprint for how to use the DH spot: a so-called "AAAA" hitter with power and walks, who can't play D for anything, but can hit the heck out of the ball. He's great value for the money. It probably isn't too fun to be 30 and in your first year of arbitration, but it beats slugging homers in Sacramento, I'll bet.

Despite David Ortiz's rough spot, the projection systems see him as paying off this season. Boston had better hope this isn't the beginning of the end a la Mo Vaughan. The other old guys on the list don't fare so well. Matsui looks like a mistake, unless you think his current pace is sustainable. Jim Thome is still a very good hitter, but not enough, given his contract. Somehow, even Junior's small contract doesn't seem so great.

The older guys aren't the only DHs who seem a bit overpaid. Jason Kubel is projected to earn his cash by some systems, not others. Although this year of the deal might look okay so far, we'll see how things turn out by the end, and the second year might be the kicker. Mike Jacobs' salary isn't too onerous, but once one adjusts for arbitration values, one realizes just how unlikely it is that he'll hit well enough to "earn" it.

This isn't the last word, of course. In the case of arbitration salaries, perhaps it's worth it for teams who might not have better options given their budget (Minnesota, Kansas City). That's worth debating. Perhaps some of these guys are just playing DH because their position slots are full (Luke Scott). What is pretty clear from this list is that younger, cheaper players are almost always the better bet, because even the best players at the position get awfully risky the older they get (Matsui, Ortiz, Hafner, etc.).

One shouldn't necessarily take this as a "final judgment" of whether these players are going to be worth their 2009 salary or not. it assumes a linear model of payroll, which I like for its simplicity, but which others argue about. Also, for some teams, it may be worth paying too much for an arb year rather than paying more in free agent dollars -- I'm not sure about that myself, but it's worth discussing. Still, for others, they may simply not have enough slots to put a player in the field even if he is able to player there (like Scott or maybe Lind) where he would be more valuable.

Discussion is welcome on these or any topics. Enjoy! And remember: money is the currency of baseball.

Update, April 30: Tom Tango linked to this post and made the correct and helpful point that when determining what a team is valuing a player at in terms of $, the replacement level salary of $0.4M should be subtracted, which I forgot to do in the original post (Thanks, Tango).  I have amended that, along with the RAA/WAR/wOBA required. He is also correct that it is futile to try to determine the "value" of a pre-arb contract like Lind's, but since I was going about this from the "money end," well, I just left stuff up there and crossed out.  Independently, I decided to I also took the chance to remove "current" column since it wasn't really helpful only 3 weeks into the season and only cluttered the chart up. I also tweaked some of my comments.