Did Buehrle get overpaid?

Usually, it’s pretty easy to tell a good signing from a bad one. Now sure, there will be some disagreement—after all, for a deal to get done, some general manager, who, no matter what criticisms we level against him, does know quite a bit about baseball, has to decide that it’s worth it—but for the most part, reasonable observers will fall on the same side when evaluating a free agent contract.

But sometimes, there is a stark divide between the mainstream media and us sabermetric analysts. It may be because a player hits for a high average but neither walks nor hits for power, or because his gaudy stolen base totals are counterbalanced by his perennial stay atop the caught stealing leaderboard, or because he is an absolute out machine hitting at the top of the lineup. Or it could simply be that he is a pitcher.

One of the amazing findings in the statistical analysis community has been that big free agent signings are rarely a good deal, and that big free agent pitcher signings are never a good deal. While hitters may accidentally get injured, pitching injuries are no accident; rather, they are part of the job description.

The stress and tension that a pitcher puts on his arm every time he throws a pitch eventually results in injuries and loss of effectiveness. It’s about as certain as death and taxes—if you pitch for long enough, you will get injured.

That propensity for getting hurt is what, in general, makes pitchers such bad free agent targets. A player’s value is largely tied up in his ability to, well, play, and betting on a pitcher lasting a long-term deal without an injury is almost as foolish as betting on the Pirates to win the World Series (sorry, Pirates fans—I understand the suffering).

That’s why when Mark Buehrle signed a 4-year, $56 million extension this week, the reaction from the sabermetric corner of the world was not very positive. While the mainstream media commended the White Sox for signing Buehrle to a significantly below-market deal, more statistically-oriented fans replied with more caution and outright condemnation.

Take, for example, the comments provided by Mitchel Lichtman, author of The Book: Playing the Percentages in Baseball, and a former consultant to the St. Louis Cardinals:

More than 25% [of pitchers comparable to Buehrle] are not pitching at all in 4 years… you expect that on average Buehrle will pitch only 100 IP or so in 4 years…including the times he does not pitch at all… even with good, historically durable pitchers, you still can expect to lose 10-15% in quality/quantity per year.

Lichtman’s analysis foresees a bleak future for Buehrle. A one-in-four chance of being out of the major leagues by the end of his contract, double-digit decreases in innings pitched every year…it’s no wonder that stat-heads would be condemning this contract. But I can’t help but wonder if we’re digging deep enough in our analysis. Buehrle has stayed remarkably healthy throughout his major league career; I wonder if that trait portends continued success.

Luckily, that’s a question that can easily be answered. Buehrle is 28, and he has thrown at least 200 innings in each of the past six seasons. There have been 37 pitchers in baseball history who likewise from the ages of 22 to 27 pitched at least 200 innings each year, and 32 of those threw at least 115.7 innings at 28, which is how many Buehrle has at this point in the season.

We can look at these 32 pitchers’ career paths over the next four seasons to figure a reasonable expectation for Buehrle. In percentage terms relative to this year, here is how we expect Buehrle’s numbers to progress from next year to the end of his contract:

Year	%IP	%ERA	
2008	0.81	1.08	
2009	0.73	1.01	
2010	0.64	1.03	
2011	0.50	1.09

In other words, we expect Buehrle’s innings to drop 19% next year, and his ERA to rise 8%. By the end of his contract, we expect Buehrle to pitch only half as many innings as he does this season, and with an ERA that is 9% higher to boot.

How does that translate into real numbers? Here, we have to make a couple assumptions. First, I assumed that Buehrle will simply continue to pitch as much as he thus far this season, so his innings were pro-rated to 218. His ERA should rise a bit as Buehrle has been lucky this, so I simply assigned him a 3.68 ERA, which is in-line with his career numbers, adjusted for park and league.

I then translated all his numbers into Wins Above Replacement (WAR) for a handy measure of total value. Here is how Buehrle’s projection over the next four years looks:

Year	IP	ERA	WAR
2008	177	3.96	2.99
2009	159	3.71	3.16
2010	140	3.78	2.66
2011	109	4.01	1.76

That’s not very pretty. Buehrle’s ERA remains very good over the course of the deal, but his innings decline sharply despite his history of longevity. In fact, as Lichtman pointed out, pitchers who throw so many innings don’t just have a reputation for durability; they also have a lot of mileage on their arms.

Nonetheless, our sense of Buehrle’s value in terms of dollars—and after all, that’s what we really care about when we debate whether his contract was a good deal or not—still isn’t all that clear. Buehrle is a specific player who signed a specific contract with a specific team, and all those particulars must be taken into account when evaluating his value to the White Sox.

To help me with that, I turned to Vince Gennaro, author of Diamond Dollars: The Economics of Winning in Baseball and a consultant to a major league baseball team. Gennaro has developed a complex system for evaluating each team’s individual revenue levels at any given win total.

By looking at a team’s expected revenues with and without a given player, Gennaro can calculate the player’s value; for example, if the White Sox are a 70-win team without Mark Buehrle, but a 73-win team with him, Buehrle’s value to the club is the difference between its expected revenue streams with 73 wins and its expected revenue with 70 wins.

I asked Gennaro to look at Buehrle’s value to different-quality White Sox teams over the next four years using my projections. Gennaro found that given his expected performance, Buehrle would be worth just $7 million to an otherwise 70-win White Sox team (which is how good the Sox roster minus Buehrle is right now). Even in the best case scenario, a 90-win roster for which Buehrle could be the difference between making the playoffs and sitting at home in October, Buehrle would still only be worth $39 million.

In other words, given even the most optimistic expectations about the White Sox—expectations, by the way, which are in no way justified—Buehrle will still be overpaid by almost $20 million over the life of his contract! More likely, his value to Chicago’s bottom line will be minimal, though through no fault of his own, and his cost exorbitant.

This is a signing that simply cannot be justified. Buehrle’s reputation for handling large workloads is essentially worthless, and his expected decline is sharp.

My gut instinct in this case was wrong, but I’m still glad that I took the time to investigate. Both mainstream analysts and sabermetrically-inclined commentators attempted to apply universal truths to a very specific situation which deserved individual treatment. Yes, Buehrle signed a below-market deal, both in terms of dollars and years. And yes, pitchers get injured at incredibly high rates as they age. For us to pretend that we know which of these facts is more important would just be foolhardy.

This time, however, the stock sabermetric principle won out.