With Pat Burrell signing with the Rays for $8 million a year, discussion is picking up about the other big bats left on the market. Some people would like to see Adam Dunn with the Angels as full-time DH. I want to offer my justification for why Dunn actually does not make sense for this team. I do a lot of math for a living, so I can't avoid explaining myself with numbers. If you're not interested in the details, just skip to the last few paragraphs.

Note: This is not intended as a promotion of Moneyball as an organizational philosophy. According to Fangraphs, the "Mathletics" came out $21 million ahead in value last year, and the Angels were $46 million in debt, but in the standings, the Angels finished 24 1/2 games ahead. My point is that if you like Adam Dunn because of his sabermetric qualities (ISO, OBP, K/BB), you have to use sabermetrics to look at the whole picture.

If the roster doesn't change at all, here is a simplified projection of playing time at third base, left, and right:

LF: 50% Rivera, 50% Figgins

RF: 50% Guerrero, 50% Figgins

3B: 100% Wood

DH: 50% Rivera, 50% Guerrero

According to career statistics on Baseball Prospectus, this is about how I'd expect these players to do in the field:

Rivera: (14 FRAR in LF) * 50%= 7 FRAR

Guerrero: (4 FRAR in RF) * 50% = 2 FRAR

Figgins: (14 FRAR in LF) * 50% + (10 FRAR in RF) * 50% = 12 FRAR

Wood: (22 FRAR at 3B) * 100% = 22 FRAR

This adds up to 43 FRAR. At the plate, I'll assume:

Guerrero: 60 BRAR

Rivera: 30 BRAR

Figgins: 25 BRAR

Wood: 0 BRAR? 20 BRAR? 40 BRAR?

Just how well Brandon Wood will do is anyone's guess, I'll call it w. Adding it up, I get (115 + w) BRAR. Adding the offensive and defensive contributions gives (158 + w) RAR for a team without Dunn.

I'm going to suppose, like others have suggested, that the Angels would use Dunn as a full-time DH to compensate for his horrific defense. Now the playing time breaks up like this:

LF: 100% Rivera

RF: 100% Guerrero

3B: 100% Figgins

DH: 100% Dunn

I'll use the same assumptions for fielding performance (Figgins has been a slightly below average 3B in his career), which have to be adjusted for different playing times:

Rivera: (14 FRAR in LF) * 100% = 14 FRAR

Guerrero: (4 FRAR in RF) * 100% = 4 FRAR

Figgins: (17 FRAR at 3B) * 100% = 17 FRAR

The total is 35 FRAR. Now for the offensive numbers:

Guerrero: 60 BRAR

Rivera: 30 BRAR

Figgins: 25 BRAR

Dunn: 35 BRAR

This assumes that Dunn repeats his performance last year. This adds up to 150 BRAR, and the total of both offensive and defensive contributions is 185 RAR. The amount of production that Dunn adds to the team is:

185 RAR - (158 + w) RAR = (27 - w) RAR

The general rule is that 10 extra runs equals 1 marginal win, and 1 marginal win is worth $5 million to a franchise. Adam Dunn's total worth to the Angels would be:

(27 - w) RAR * (1 win/10 RAR) * ($5 million/1 win) = $(13.5 - w/2) million

Actually, it's about $450,000 less than that, because I'm assuming that Wood stays on the roster as a backup even if the Angels sign Dunn.

For fun, I'll make this more complicated. Scioscia likes to cycle Guerrero in and out of the DH spot because of his injury risk. I'll suppose that for every game Guerrero spends in the outfield, there's a 0.1% chance he sustains a season-ending injury. This means there's an 15% chance he gets hurt for some period of time if he plays 162 games in the outfield, and an 8% chance if he plays 81 games--believable numbers to me. If Vlad goes down, GMJ plays right field, who I will (very generously) say is an average hitter and average defender. That's a loss of 40 BRAR and a gain of 10 FRAR, so it's a 30 run hit in total: the equivalent of $92,500 per game in value. Adding up all of the risks (I'm skipping the math) means that playing Vlad as a full-time outfielder carries about $900,000 in risk. The price of the risk comes off of Dunn's salary. Rounding it off, I have:

Value = $(12 - w/2) million

This formula is a quick way to decide Dunn's worth depending on Brandon Wood's performance. He cannot be worth more than $12 million, because w cannot be negative (if Wood hits below replacement level, he gets replaced). If Wood has a good rookie season and hits about average (w = 20), then Dunn's value drops to $2 million. If Wood does great (w = 40), then Dunn should pay $8 million to play for the Angels.

So how much faith do you have in Wood? To get a sense of what this means for Dunn, I'll suppose that Wood has a 40% chance of totally flaming out, a 40% chance of doing well, and a 20% chance of doing really well. If I got to play next season 1000 times over, how much money should I bet on Adam Dunn and expect to come out ahead?

($12 million) * 40% + ($2 million) * 40% - ($8 million) * 20% = $4 million

Now, inventing all of these numbers may seem silly, and I've arbitrarily chosen what factors to consider and what to disregard (like the effect of Dunn behind Vlad in the order, which I believe is minimal). That's why I'm just a fan posting on a blog, not an actuary or an investment banker. But if Tony Reagins came to me and asked how much Adam Dunn was worth to the Angels, I would tell him about $4 million. Spend any more money than that, and you're playing a losing game. There's only one trial, so you might luck out, but I don't like the odds.