What’s the best pitcher in the world worth?

The Boston Red Sox exercised Pedro Martinez‘s 2004 option on Monday, locking him in at a $17.5 million salary. That figure represents not only the most that a team has paid to pick up an option year, but also the highest single-year salary that will have ever been paid to a pitcher, just beating out Randy Johnson‘s new extension, and the highest-priced seasons of the Mike Mussina and Kevin Brown contracts. (Mike Hampton could blow Pedro out of the water if the Braves pick up his $20 million option in 2009, but we’re guessing that AOL/Time Warner’s solvency problems get in the way of their better judgment).

Let’s imagine for a moment that Pedro was right now putting his 2004 services up on the open market. Of course, that’s not what he’s doing–but indulge me for a moment.

Earlier this winter, I conducted an analysis of this year’s free agent market, in an attempt to come up with an equation to predict a player’s salary from a reasonable expectation for his performance. In order to get a read on what Pedro’s market value would be, I’ve updated that study for the purposes of this article. I won’t rehash all of the methodology here, but there’s a couple of important differences this time around:

  • I’ve considered only starting pitchers, and not relievers, or position players.

  • I’ve included contracts signed since the date that the original article was posted, most notably the Greg Maddux settlement.

  • I’ve evaluated pitchers by means of their PECOTA forecast, rather than their historical performance as judged by their WARP scores. This provides for a couple of important advantages: We’re able to account for the effects of aging, and more importantly, we’re able to use the PECOTA five-year forecast to evaluate each year of performance for a pitcher signed to a multi-year contract. We can also use the five-year forecast to get an idea of what Pedro’s 2004 performance is worth right now.

The study included a total of 30 contracts signed during the past off-season, including 29 deals that will begin in 2003, and Johnson’s two-year extension that covers 2004 and 2005. I excluded pitchers like Jon Lieber and Chris Carpenter, who are attempting to recover from substantial injuries.

Free Agent Contracts to Starting Pitchers, Winter/Spring 2003

Pitcher	  Term	  Wins*     Cost*
Clemens	  2003	   4.0	 $   7.17 
Johnson	  2004-05  3.7	 $  15.04 
Maddux	  2003	   3.5	 $  14.45 
Moyer	  2003-05  2.4	 $   4.72 
Byrd	  2003-04  2.3	 $   4.53 
Rogers	  2003	   1.9	 $   1.70 
Wakefield 2003-05  1.8	 $   3.83 
Williams  2003-04  1.8	 $   6.92 
Castillo  2003	   1.7	 $   0.50 
Loaiza	  2003	   1.7	 $   0.20 
Valdes	  2003	   1.6	 $   2.20 
Glavine	  2003-05  1.3	 $  10.74 
Estes	  2003	   1.3	 $   2.70 
Haynes	  2003	   1.1	 $   2.20 
D'Amico	  2003	   1.0	 $   0.45 
Tracshel  2003-04  1.0	 $   3.58 
Reynolds  2003	   0.9	 $   0.70 
Person	  2003	   0.9	 $   0.00 
Baldwin	  2003	   0.8	 $   0.28 
Anderson  2003	   0.8	 $   1.20 
Daal	  2003-04  0.8	 $   3.36 
Bere	  2003	   0.6	 $   0.70 
Hamilton  2003	   0.6	 $   0.55 
Nagy	  2003	   0.5	 $   0.20 
Sturtze	  2003	   0.5	 $   0.70 
Hermanson 2003	   0.4	 $   0.60 
Parris	  2003	   0.3	 $   0.10 
Tavarez	  2003	   0.3	 $   0.45 
Mlicki	  2003	   0.2	 $   0.45 
Wright    2003	   0.1	 $   0.43 
TOTAL		  39.6	 $  90.65

Cost is the marginal price of a pitcher, calculated as his average annual salary over the life of the deal in millions, with future years discounted at a 5% rate, and the $300,000 minimum salary subtracted. Wins is PECOTA’s expectation for the average number of wins above replacement he’ll contribute annually over the same period.

There are a couple of ways to browse through the data, both of which lead back to the same conclusion: Even in a down market, pitching is expensive, and it’s likely that major league teams aren’t doing a good enough job of accounting for the extra risk associated with just about every starting pitcher. There are some good storylines buried in the table. The Tom Glavine contract looks foolhardy, the Johnson extension premature, the Kenny Rogers deal a good bargain–but let’s keep the focus on Pedro.

Adding together the total expenditures for our group of pitchers and dividing by the total number of wins suggests that teams were paying just about $2.3 million in present day value for the expectation of an additional win. Running a simple linear regression on the same dataset results in a slightly higher estimate, a marginal cost of about $2.6 million per pitcher win. There are more sophisticated forms of analysis that would be more econometrically appropriate for handling this particular set of data, but they do not change the results significantly, and for a working estimate, a range of $2.3-$2.6 million per win contributed should work fine.

What then would Pedro be worth? It’s tough to say exactly because he’s so far ahead of anyone else on the list. PECOTA values Pedro at 7.1 wins above replacement in 2004; pitchers that might have looked nearly as attractive on the open market–like Maddux and Glavine–are thought by the system to be considerably riskier investments. But running with the numbers as we have them, Pedro’s 2004 expectation translates into a market price of between $16.3 and $18.5 million. Discounting the $17.5 million the Red Sox will pay him to the present day results in an annual salary of around $16.7 million, which places him securely within that range.

So…Pedro’s happy, Theo’s happy, Dan Shaughnessy’s happy, the CITGO sign is happy, and the math worked out just right. Everything’s just peachy, right?

Well, not quite. In the consulting world, a tidy result like that would deserve a prominent placement on your performance review, but in this case, things are a bit more complicated. For one thing, the terms of Pedro’s contract required a $2.5 million buyout payment in 2004 if his extension hadn’t been exercised. That’s a sunk cost, which means that the marginal price of exercising his option is “just” $15.0 million, and a little less still in terms of present value. By our metrics, Pedro looks like a little bit of a bargain at that price.

Still, two essential questions are left unanswered:

  • Forget the open market–what is Pedro worth to the Red Sox?

  • What is the cost of executing the option now instead of at the end of the season?

It’s the latter question that has received more attention, but the former might be just as important. Even if Pedro has made some veiled threats to the contrary, this isn’t a case in which every team has a chance to bid on his services; the Red Sox had the sole discretion to lock him in at that price. While the intuitive sentiment is to look at the Red Sox’s fat revenue stream and Pedro’s popularity with the fan base, and conclude that he’s worth more in Boston than anywhere else, there are good arguments that cut both ways. As Gary Huckabay pointed out in a spirited debate on the BP authors list, Red Sox attendance has a long history of showing almost no response to changes in team quality. It’s an argument more frequently put forth in the case of the Cubs, but Fenway is the closest thing to a guaranteed sellout in the big leagues, with enough excess demand for much of the schedule to fill the small ballpark thrice over.

On the other hand, you can make a pretty good argument that the Red Sox have been very smart about responding to excess demand by raising ticket prices. According to Doug Pappas’ data, the Red Sox have increased ticket prices by an average of 17 percent per year since 1995. Assuming a full season of sellouts, the price hike increases the Red Sox’s revenue stream by somewhere in the neighborhood of $20 million each year. Could you justify such an increase to Sammy Somerville and Bobby Brookline in the same season in which Pedro signed with the Yankees? Well, actually I think you could, but it’s easy to see why the Red Sox want to maintain the goodwill of their fan base.

Which brings us back to the question of the timing of the deal. I won’t try and deconstruct the supposed benefits of signing Pedro early, since Joe Sheehan has done a better job of that than I ever could. But I can tell you something about the cost.

I’ve mentioned before that PECOTA tends to take an actuarial view of the universe. Risk is an inherent part of life, and for someone who already is performing at as an elite a level as Pedro, it’s a lot more likely that something will happen to decrease his value rather than to increase it.

PECOTA quantifies the risk in terms of the difference between Pedro’s 2003 and 2004 expected value forecasts; it values him at 8.4 wins above replacement in 2003, versus 7.1 in 2004, a decrease of about 15%. Note that PECOTA doesn’t expect any decrease in the quality of Pedro’s performance: the difference is accounted for by his injury risk.

If Pedro makes it through this season healthy, that will not only help the Red Sox to compete with the Yankees, but it will also provide them with valuable information about the sturdiness of Pedro’s right arm. To put it another way, 15% is a reasonable estimate of the premium that the Red Sox have paid to exercise Pedro’s extension now. Multiply that by the $15 million that the extension will cost the Red Sox, and the price of Pedro’s propriety is around $2.3 million bucks. While I’m not quite as down on the deal as Joe is, that’s a lot to pay for goodwill.

Six in Six

Eight hundred miles west, the Detroit Tigers, a franchise that was once held in the same esteem as the Red Sox, wishes it had Pedro-like problems on its hands. For the second year in a row, the Tigers have started out the year by losing their first six games. More remarkable still is their offensive ineptitude: In spite of having faced such luminaries as Josh Stewart, Esteban Loaiza, and Kyle Lohse, the Tigers are batting just .133 through their first six games, and have scored just six runs. While I don’t want to devote an entire column to the matter–the Tigers are my boyhood team, after all–the question has arisen whether the string of low-run scoring is historically significant, and the answer is a resounding yes.

Between 1993 and 2002, there were just nine streaks of six consecutive games in which a team scored six runs or fewer, including a couple of overlaps that I’m double-counting. With an assist from the fantastic streaks analyzer put together by Sean Forman and Retrosheet, I’ve reproduced the list below:

Fewest runs scored in six consecutive games, 1993-2003

Orioles    8/24/01 - 8/30/01   4 runs 
Reds       8/10/93 - 8/16/93   5 
Orioles    4/03/02 - 4/10/02   6 
Phillies   9/08/99 - 9/13/99   6 
Phillies   9/9/99  - 9/14/99   6 
Rockies    1/7/97  - 1/6/97    6 
Blue Jays  9/13/96 - 9/18/96   6 
Marlins    9/10/93 - 9/16/93   6 
Marlins    9/11/93 - 9/17/93   6 

Focusing only on streaks in the first six games of the year, the Tigers’ accomplishments look even more remarkable. No team has scored as few runs to start the year since the 1963 Mets, about whom the best thing you can say is that they weren’t the 1962 Mets:

Fewest runs scored, first six games, 1963-2002

Mets        1963   6 
Orioles     1988   7 
White Sox   1968   7 
Padres      1969   8 
Indians     1973   8 
Dodgers     1968   9 
Royals      1985   9 (14 RA, 2-4 record) 
Phillies    1982   9 
Padres      1974   9 (52 RA)

How did those sluggish starters fare the rest of the way?

Team			W	L	RS	Avg
1963 Mets		51	111	501	3.09
1988 Orioles	        54	107	550	3.42
1968 White Sox	        67	95	463	2.86
1969 Padres		52	110	468	2.89
1973 Indians	        71	91	680	4.20
1968 Dodgers	        76	86	470	2.90
1974 Padres		60	102	541	3.34
1982 Phillies	        89	73	664	4.10
1985 Royals		91	71	687	4.24
AVERAGE		        68	94	558	3.45

A couple of the teams weren’t so bad–the Phillies were competitive in 1982, and as Rany Jazayerli will fondly remember, the ’85 Royals won the World Series. But also included on the list are some of the worst offensive clubs of all time, including the expansion Mets, the 1988 Orioles, and the early, fast-food-uniformed Padres. The nine teams on the list averaged just 558 runs for the full season.

I think the Tigers will do a little bit better than that. Carlos Pena and Eric Munson at least look like real hitters, and the frigid weather in the weekend series against the White Sox didn’t help. The Tigers wind up closer to their PECOTA estimate of about 650 runs on the season. But at some point, one has to wonder whether bad hitting isn’t contagious.

I’m not talking about SARS or team chemistry or anything, but the first step in the Tigers’ recovery is an improvement in their plate discipline. In watching them struggle over the weekend, I couldn’t shake the impression that drawing a walk and starting a big inning isn’t a little bit more difficult when you’re convinced that the next guy is going to swing at the first pitch and ground out weakly to the second baseman. Everyone’s trying to be a hero, and the result is a hack-happy procession that only compounds the problem.

It’s not clear that there’s any way out of the dilemma except for some warmer weather an abundance of patience. But if the Tigers were my team, I might place a call to the estate of one Rickey Henderson. Presumably, Rickey is still hankering to play, and whether he leads by word or example, his role as a mentor alongside Alan Trammell could be invaluable.

What, you afraid of taking a few at-bats away from Hiram Bocachica?

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