Clearly, some people in the Yankees front office did not listen to my advice. There are so many angles from which to approach the fallacy of the signing of Rafael Soriano that I can hardly decide where to begin. The New York Yankees just agreed to pay an average of over $16 million per year (including competitive balance tax) for a reliever not named Mariano Rivera, allow said reliever the option of opting out of the deal after either of its first two seasons, and give up a first-round pick in a deep draft in the process. Most business-minded baseball analysts would argue that giving up that kind of money, leverage, or future value for a reliever is a bad idea. The combined loss of all three is simply staggering.
It seems as if this s not the timeliest of signing reactions, so I have already overheard pieces of others’ reactions. Some sabermetric analysts, not entirely unlike me, are inclined to look at this contract in a vacuum and conclude rather uniformly that there is no rational justification. More casual or intuitive observers who support the deal have a more varied set of arguments, most of which, frankly, are a bit too casual or intuitive and mostly serve to distract from this analysis.
To those who claim that the Yankees added 2010’s best closer as a bridge to the best of all time, you might be looking at the wrong numbers. Soriano’s performance last season is amazing to those who value his 1.73 ERA and 45 saves. His more predictive FIP and xFIP combo of 2.81 and 3.81—ERA-scaled numbers based on pitchers’ most consistent outcomes, strikeouts, walks, and home runs—is a bit underwhelming. That inflated xFIP number is symptomatic of a large number of fly balls that were not home runs in 2010—but very well could be in 2011, especially in Yankee Stadium. (Joba Chamberlain’s numbers, you ask? 2.98 FIP, 3.34 xFIP. Watch for the convergence.)
To those who claim that the Yankees have found the heir to Mariano Rivera, you need to analyze the contract and its incentive scheme. For one thing, Soriano is only under contract for one year longer than Rivera; a 33-year-old Soriano with one year left on his deal sounds very little like an heir. That assumes, of course, that he even remains under contract that long. Assuming Soriano does not opt out of his contract after the first year, and pitches well in 2012, he will have a choice to make. Option A is to assume the Yankees’ closer role at a salary of $13.5 million for just one year. Option B is to opt out of the last year of the contract and fish for a new multi-year deal, either from the closer-less Yankees or elsewhere. Either way, though Option B seems much more likely—think like Scott Boras for a second—the Mariano Rivera replacement attempt is far from finished.
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The one argument that seems to actually stand up in my mind, as strange as it may seem, is that the Yankees have so much money that they can afford a contract that would be insane for any other team. The WAR valuation method I previously used to recommend a maximum bid of three years and $16 million uses a “market value” for wins in the free agent market. However, the Yankees clearly have the financial resources, available revenue streams, and place on the marginal win curve that make wins worth more than the going market rate. Due to the market in which they play, wins are simply worth more money to the Yankees than they are to other teams, which is why the Yankees can get away with paying more than other teams for those wins. Even though I expressed my opposition to the contract earlier, I just have not been able to shake the intuitive sense that the Yankees—as astronomical as the financial cost may seem—will not be severely inhibited from pursuing other players, so the situation is worth another look.
Economist J.C. Bradbury, author of The Baseball Economist and Hot Stove Economics, developed a method of determining a player’s value (as a marginal revenue product, for you economists) that does a better job of considering the Yankees’ unique situation. Bradbury’s work involves multiple regression analysis and other calculations that are unnecessary to show here, but the concept is that an average team produces a fixed amount of revenue, and an average player who plays X% of the time (by plate appearances or total batters faced) produces X% of that revenue. Then, any runs scored or prevented beyond the contribution of that average level of play continue to add (or reduce) revenue, and the amount of revenue increases as the quality of the team, represented by run differential, increases. This is the concept of the marginal win curve.
Using Bradbury’s findings about leverage and the percentage contribution of pitchers in Hot Stove Economics (and skipping several steps here), I determined that Soriano saved the Rays 18 runs in 2010 while pitching to only 3.8% of their total batters faced—about 11 runs above average for that percentage of TBF. Bradbury’s book also explains that the 9th inning is 2.5 times as influential as innings 1 to 6, and the 7th and 8th innings are twice as influential as the first six. Thus, we need to adjust Soriano’s runs prevented value by the appropriate factor. Using Bradbury’s runs-to-revenue formula and the assumption that Soriano will pitch almost exclusively in the 7th and 8th innings, we can see what that same performance (an optimistic assumption) would be worth for the 2011 Yankees, conservatively assuming a 130-run differential before the addition of Soriano and assuming that Soriano himself is replacing an average performer (likely David Robertson).
In other words, Soriano’s 2010 performance, if repeated in 2011, would be estimated to be worth $11.6 million for the Yankees. Even if the Yankees started off as better than a 130-run differential team—say, a 160-run differential team, as they were last year—that performance would only be worth $14.8 million. By similar calculations, a duplication of Soriano’s 2009 performance with the Braves, when he pitched better innings and more of them, would be worth $19 million or $24 million for each of those respective run differentials, 130 and 160, respectively.
So what have we learned? When the leverage of the innings Soriano will pitch and the Yankees’ place on the marginal win curve are taken into account, Soriano has a chance to be worth the $16 million the Yankees will pay for him in each of the next three years. However, that possibility assumes that he stays healthy and replicates the best seasons of his career. Given the obvious risk that this will not be the case, the opt-out clauses the Yankees put in the contract, the fact that Robertson is likely to be better than an average pitcher, and the loss of the 31st overall draft pick in a deep draft class, this is still an overpay by the Yankees. At least now, though, maybe we can see where they were coming from. Maybe.
The author extends a special thanks to J.C. Bradbury himself for his clarification of certain processes outlined in his book, Hot Stove Economics.
Lance Gurewitz is currently a freshman at the Wharton School of Business at the University of Pennsylvania. He also serves as the MLB Trade Rumors Florida Marlins Team Coordinator. You can read and discuss his baseball analysis and other sports musings in 140 characters or less by following @LanceWG42 on Twitter
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