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July 27, 2006

Lies, Damned Lies

Playing Matchmaker

by Nate Silver

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How beautiful would it be to acquire Alfonso Soriano? That depends on just who the beholder is. There are probably seven teams that are legitimate contenders to acquire Soriano, or one of the two other big bats on the market--Bobby Abreu and Carlos Lee--before the trade deadline passes next week:

The Red Sox and Mets have been associated with Abreu, but have more pressing needs. The Mariners were interested too, but have just picked up a bat in Ben Broussard. So we'll focus on these seven teams for now. Which has the most incentive to acquire a corner outfielder?

We can quantify the impact of picking up a player like Soriano by comparing his projected MLVr to that of the players whom he'd be replacing. To make this projection, we'll use a combination of the player's pre-season PECOTA, and his MLVr on the season to date.

The percentage that we'll weight the season-to-date MLVr depends on the number of plate appearances that the player has had thus far in 2006. In particular, the weight assigned to the 2006 performance is determined by the formula:

    Weight(2006) = PA(2006) / 650 * .5

What this formula assumes is that if a player had a full season's worth of playing time--about 650 plate appearances--then half his projection should be determined by his performance in the current season, with the balance determined by his performance in seasons past. (This might seem arbitrary, but regression analysis shows that a 50% weight is about right for a position player's most recent season's worth of performance). So Alfonso Soriano, who has had about 450 plate appearances on the season to date, has just over one-third of his projection determined by his 2006 MLVr, with the rest based on his pre-season PECOTA.

Here are how the incumbent alternatives are projected to perform for Soriano's Seven Suitors. (Note that where more than one player is listed, we simply average the MLVr projection among each of these players.)

Tigers    Monroe (+.022), Thames (+.094), Young (+.044)         +.054
Twins     Kubel (+.064), White (-.007)                          +.028
Dodgers   Lofton                                                -.047
Yankees   Cabrera (-.069), Williams (-.051)                     -.060
Angels    Anderson (-.015), Izturis (-.113), Quinlan (-.052)    -.060
Cardinals Taguchi                                               -.074
White Sox Podsednik                                             -.081

Conversely, here are the MLVr projections for the potential replacements:

Soriano    +.105
Abreu      +.188
Lee        +.159

As should be expected, picking up any of the sluggers would benefit any of the contending clubs, but this benefit varies quite a lot from team to team. The White Sox and Cardinals are employing players who simply don't have any place in a playoff-caliber outfield. Meanwhile, the Tigers and the Twins--if PECOTA's optimistic projection for Jason Kubel is to be believed--are getting by relatively well with the status quo.

Before we proceed, I'll acknowledge that the projection for Alfonso Soriano looks a bit pessimistic; this has truly been a breakout year for him. On the other hand, these projections are not attempting to account for defense, and Soriano would represent a downgrade in the field versus players like Podsednik or Taguchi. For the purposes of simplicity, we'll assume that these two wrongs cancel out and make a right.

We can translate the MLVr projections into wins added in a couple of simple steps. MLVr measures the number of runs per game that a player is worth as compared to a league average hitter. Thus, by multiplying the difference in the MLVr projections of the incumbent and the replacement by the number of games remaining in a team's season, we come up with the number of extra runs that the replacement player should generate for his new club. We then translate this into wins added by assuming that ten runs produce one win.

For example, if the Dodgers picked up Carlos Lee…

Carlos Lee        +.159 runs/game
Kenny Lofton      -.047 runs/game
                  +.206 runs/game

X 58 games remaining

                = 11.9 runs added
                = 1.19 wins added

…we'd expect them to win an additional 1.19 games as a result. These are the results of that calculation for all combinations of new player and new team:

Wins Added
               Abreu      Lee  Soriano
White Sox      +1.61    +1.44    +1.12
Cardinals      +1.57    +1.40    +1.08
Yankees        +1.51    +1.33    +1.01
Angels         +1.48    +1.31    +0.99
Dodgers        +1.36    +1.19    +0.88
Twins          +0.95    +0.78    +0.46
Tigers         +0.79    +0.62    +0.31

But the story doesn't end with wins and losses--it ends with making the playoffs. The Royals could nominally benefit from picking up a player like Carlos Lee, but that benefit wouldn't translate into a material chance of reaching the postseason. Meanwhile, a team like the Mets is such a lock to make the playoffs that they simply don't have much incentive to reload. Of course, in saying that I'm ignoring the fact that acquiring a Soriano or an Abreu not only helps you reach the playoffs, but also helps you once you get there. Even so, if my work in Baseball Between the Numbers can be trusted, a late-season acquisition for a "lock" playoff team looking specifically to October should probably be an ace starting pitcher or closer.

One fact that can be extrapolated from this is that an acquisition is most valuable when a team is on the playoff fence--that is, when a team has a roughly equal chance of making or missing the playoffs. The function is also somewhat asymmetrical; a team with a status quo playoff probability of slightly less than 50% stands a bit more to gain than a team with a status quo playoff probability of slightly more than 50%.

I won't go into too much detail on the methodology here, which is an extrapolation of some of the work that I've done in the past, in part because this methodology is experimental. Basically, I'm trying to make inferences about how much acquiring additional wins improves a team's playoff probability based where it stands on the playoff probability curve at present. In any event, this is what I get for the increase in playoff probability for each of the seven contending clubs, based on obtaining a player that would produce one additional win from now until the end of the regular season:

Team       Playoff %    +1 win
Dodgers      9.6%       +5.0%
Twins       17.9%       +8.3%
Angels      30.0%      +10.8%
White Sox   33.4%      +11.6%
Yankees     65.5%       +9.9%
Cardinals   87.7%       +4.3%
Tigers      95.9%       +1.5%

(Current playoff probabilities are based the PECOTA version of Clay's numbers as of Wednesday morning.)

More relevantly, we can combine the wins-added calculation with the playoff probability curve to estimate the team-specific payoff of acquiring Soriano, Abreu or Carlos Lee:

Playoff Probability Added

               Abreu      Lee  Soriano
White Sox     +18.9%   +16.5%   +12.8%
Angels        +16.2%   +14.4%   +10.2%
Yankees       +14.2%   +12.6%    +9.9%
Twins          +7.8%    +6.0%    +3.4%
Dodgers        +7.2%    +5.9%    +4.1%
Cardinals      +6.1%    +5.5%    +4.5%
Tigers         +1.2%    +1.0%    +0.5%

The White Sox stand the most to gain by making an acquisition, nearly a 20% increase in their playoff odds by acquiring Abreu. This is both because they're very much on the playoff fence with their current roster, and because Scott Podsednik's performance leaves a lot of room for improvement. If the market behaved perfectly efficiently, then Abreu would go to the White Sox, Lee to the Angels, and Soriano back to the Yankees.

Still, that doesn't quite answer the question of just how much these teams should be willing to give up to acquire one of the big sluggers. My finding from Baseball Between the Numbers is that a playoff appearance is worth about $25-$30 million, meaning that the biggest plausible move on this chart--the White Sox acquiring Abreu--is worth perhaps $5-$6 million in additional revenues. That's nothing to sneeze at for a player who could play barely more than 50 games in his new uniform. Still, it isn't worth giving up someone like Brandon McCarthy, who according to his MORP ratings, will probably produce between $15-$20 million worth of value above and beyond his reserve and arbitration contracts before reaching free agency. This is especially so, of course, if a team is taking on salary in the deal. Even for a team like the White Sox that could desperately use another star player, the market price for one of these outfielders should be a second- or third-tier prospect, and not much more.

Nate Silver is an author of Baseball Prospectus. 
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