Friday, November 11, 2011

What is Pujols Worth?

Albert Pujols is a free agent. As a St. Louis Cardinals fan, hearing that may be difficult to swallow, but I finally came to the realization he may not be back next season after hearing he will be visiting with the Miami Marlins.

The Cardinal Virtue and Fungoes pointed out there is a limited market for a premier first baseman, but there is still a gap between the 9 year $200 million the Cardinals had allegedly offered and the 10 year $300 million contract Pujols supposedly wants. The Cards got a bargain when he agreed to his previous 7 year $100 million contract, that's for certain, but it will not and should not play any role in these current negotiations.

Sabermetricians have been tinkering with the discussion of whether a player's value is linear or exponential. Dave Cameron from FanGraphs wrote about it once in February and again in November. CC Sabathia recently signed a 6 year $142 million extension and Cameron showed in his most recent calculations the possibility of it being justified. His linear dollar-per-win model assumed a decline of 0.5 WAR per season from a 5.5 WAR starting point and 5% inflation in the dollar per win rate each year, which actually hit the value almost exactly: 6 years $142.12 million.

Using the same linear concept, perhaps I can predict Albert's next contract, but it is more complicated than just a simple mathematical plug and chug. Interestingly enough, Pujols and Sabathia made both their major league debuts in 2001, so it is somewhat easy to compare them against each other even though they play different positions.

Albert Pujols (red/blue) versus CC Sabathia (navy/white)
Pujols has been an outstanding player ever since he first appeared in the Majors in 2001 and has been superior to Sabathia every season aside from 2011. He has performed fairly consistently over the course of his entire career, though you can see a steep decline since 2009 (since 2008 if you really want to argue a difference of WAR from 9.1 to 9.0 is really a decline).

He has averaged a seasonal WAR of 8.0 over the past 11 seasons, but there is a slight downward trend. Sabathia started slowly, as does most players do in baseball, but has since improved to one of the best pitchers in the game. His average WAR is 5.2, so Cameron's initial projection starting at 5.5 in 2012 makes sense.

So how should we value Pujols? It depends on if you feel he should be judged from his average (8.0) or current WAR (5.1). In other words do you feel his production will be similar to Jose Bautista or Matt Holliday? Both are still excellent results, but a difference of three wins is still pretty significant. Just ask the Red Sox or Braves.

Albert Pujols WAR Projections (Max/Min)
Albert Pujols Salary Projections (Max/Min)
Year $/Win Max WAR Max Value Min WAR Min Value
2012 5.00 8.0 $40.00 5.1 $25.50
2013 5.25 7.5 $39.38 4.6 $25.50
2014 5.51 7.0 $38.59 4.1 $24.15
2015 5.79 6.5 $37.62 3.6 $22.60
2016 6.08 6.0 $36.47 3.1 $18.84
2017 6.38 5.5 $35.10 2.6 $16.59
2018 6.70 5.0 $33.50 2.1 $14.07
2019 7.04 4.5 $31.66 1.6 $11.26
2020 7.39 4.0 $29.55 1.1 $8.13
2021 7.76 3.5 $27.15 0.6 $4.65
- - 57.5 $349.01 28.5 $166.63

A linear regression starting from 8.0 compared to 5.1 is substantial, to say the very least. The total maximum WAR and salary is over twice as high compared to the minimum WAR and salary. A 9 year $200 million contract falls closer to the minimum projection with a 5.8 WAR starting point, while the 10 year $300 million contract Pujols is seeking would be comparable to a 7.2 WAR introduction.

I am not sure exactly why he would seek a salary so outrageously high except to prove he is the best baseball player of all time. In other words, if he nets a more expensive contract than Alex Rodriguez (10 year $275 million), then everyone will know he is the best. I honestly hope my way of thinking is wrong because I do not want to see a charitable human being like Pujols classified with a symbol of greed, like A-Rod and the New York Yankees.

What is Pujols worth? If he nets a 10 year contract, then he should earn somewhere between $166 and $349 million. I apologize for the non-definitive answer, but it depends on how harshly you judge his decline to "sub-stardom."

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