This article was cross-posted on FanGraphs Community on April 22, 2014, and was selected by the site's editors as one of the best posts of the week.
Last month, Dave Cameron published a brilliant yet simple free-agent pricing model. Using only projected 2014 WAR (ZiPS and Steamer projections are averaged) and the assumption that one incremental win is worth $5 million, it accurately projects the contract length and cost of last offseason’s free agents. Cameron also made some minor tweaks to his model to project 2015 free agent contracts. Both articles are absolutely worth checking out in full.
It’d be fun and easy to extend Cameron’s model to predict what David Price (2016), Chris Davis (2016), and Giancarlo Stanton (2017) would make on the free agent market. (If you’re curious, Price would get 6/$136, Crush would get 6/$112, and Stanton would get 9/$260, assuming that the value of an incremental win increases annually by $500,000.)
But the recent slate of massive contract extensions illustrates the folly of this exercise. Savvy front offices lock up top talent before it hits free agency, usually at a discount relative to the free agent market. Young players often prefer an immediate certain payday rather than rolling the dice in free agency, when their future value will be far more unpredictable. A model that predicts the value of contract extensions would thus be a useful counterpart to the free agent pricing model. You’re in luck, because I just built one.
I kept the basic contours of Cameron’s model in place; as before, the only inputs are projected 2014 WAR and an estimated value of an incremental win. This gives us the contract length (projected 2014 WAR times a multiplier that scales up depending on the WAR projection) and average annual value (projected 2014 WAR times $5 million).
To test the accuracy of this approach, I compared the extension model’s output to 32 contract extensions that have been signed since July 1, 2013. I excluded players projected to produce less than 1 WAR this season. I estimated the value of an incremental win produced by a closer as $10 million, which lines up with what closers earned in free agency last offseason. If a player’s extension kicks in after the 2014 season, I counted the remainder of his current contract as part of the extension.
The initial results are mixed. The model comes very close to the actual average extension contract length (prediction of 5.1 years vs. actual of 4.8 years), but badly overshoots the actual AAV. Again, this is because GMs pay more for a win on the free agent market than for a win produced by a player already on their roster. To account for this, I set the value of an incremental win at $3.7 million, the average WAR / $ of the 30 non-closers’ contract extensions. (For closers, I used $7.4 million.)
With the adjustment to $/WAR, the results look much better. The predicted average AAV ($11.3 million) is now only 6% higher than the actual average ($10.6 million.) For the 31 players on the list (excluding Mike Trout, an outlier if there ever was one), the model projects a total of 147 years and $1.87 billion in contracts; the actual sums are 146 years and $1.67 billion. Not perfect, but decent.
The model misses very badly for unusual situations. Jason Heyward and Ian Desmond are projected as 8/$121 and 6/$70 respectively, but they both signed 2 year contracts worth less than $20 million last offseason. Both players were unable to come to terms with their teams on longer deals. This is probably because they are the odd men out on teams that have either just made it rain on prodigious young talent (Kimbrel, Freeman, Simmons) or will do so in the near future (Strasburg, Harper). Instead, Heyward and Desmond opted for shorter contracts in order to avoid arbitration and set themselves up for 2016 free agency.
Mike Trout is a unique case. The fishy outfielder signed a 7 year, $146 million extension last month, which looks like a massive underpay compared to the 17 years, $541 million (!!!) the model says he is worth. Don’t get me wrong: for the Angels, the Trout signing is still the best deal since the Louisiana Purchase. But it’s unrealistic to conclude that the Angels saved $395 million, since nobody would wait until Chelsea Clinton’s second term to test free agency, least of all someone who is currently breaking baseball.
Despite these shortcomings, the model can still evaluate the wisdom of recent extensions. Plotting the 32 players on a 2×2 matrix (the x-axis is the difference between actual and projected AAV, and the y-axis is the difference between actual and projected contract length) shows which front offices overpaid and which got steals.
The extensions fall into four groups: locked-in bargains, short-term bargains, “win now” splurges, and albatrosses.
Finally, the model can estimate how much your team should pay to extend your favorite young star.
Last month, Dave Cameron published a brilliant yet simple free-agent pricing model. Using only projected 2014 WAR (ZiPS and Steamer projections are averaged) and the assumption that one incremental win is worth $5 million, it accurately projects the contract length and cost of last offseason’s free agents. Cameron also made some minor tweaks to his model to project 2015 free agent contracts. Both articles are absolutely worth checking out in full.
It’d be fun and easy to extend Cameron’s model to predict what David Price (2016), Chris Davis (2016), and Giancarlo Stanton (2017) would make on the free agent market. (If you’re curious, Price would get 6/$136, Crush would get 6/$112, and Stanton would get 9/$260, assuming that the value of an incremental win increases annually by $500,000.)
But the recent slate of massive contract extensions illustrates the folly of this exercise. Savvy front offices lock up top talent before it hits free agency, usually at a discount relative to the free agent market. Young players often prefer an immediate certain payday rather than rolling the dice in free agency, when their future value will be far more unpredictable. A model that predicts the value of contract extensions would thus be a useful counterpart to the free agent pricing model. You’re in luck, because I just built one.
I kept the basic contours of Cameron’s model in place; as before, the only inputs are projected 2014 WAR and an estimated value of an incremental win. This gives us the contract length (projected 2014 WAR times a multiplier that scales up depending on the WAR projection) and average annual value (projected 2014 WAR times $5 million).
To test the accuracy of this approach, I compared the extension model’s output to 32 contract extensions that have been signed since July 1, 2013. I excluded players projected to produce less than 1 WAR this season. I estimated the value of an incremental win produced by a closer as $10 million, which lines up with what closers earned in free agency last offseason. If a player’s extension kicks in after the 2014 season, I counted the remainder of his current contract as part of the extension.
Free Agent Model vs. Actual Contracts
| Player | Team | 2014 WAR | Proj Yrs | Proj Amount | Proj AAV | Act Yrs | Act Amount | Act AAV | $/WAR |
| Mike Trout | Angels | 8.6 | 17 | $731 | $43 | 7 | $146 | $21 | $2.4 |
| Miguel Cabrera | Tigers | 6.0 | 12 | $357 | $30 | 10 | $292 | $29 | $4.9 |
| Clayton Kershaw | Dodgers | 4.7 | 8 | $186 | $23 | 7 | $215 | $31 | $6.6 |
| Dustin Pedroia | Red Sox | 4.6 | 9 | $207 | $23 | 8 | $110 | $14 | $3.0 |
| Andrelton Simmons | Braves | 4.5 | 9 | $200 | $22 | 7 | $58 | $8 | $1.9 |
| Jason Heyward | Braves | 4.1 | 8 | $164 | $21 | 2 | $13 | $7 | $1.6 |
| Matt Carpenter | Cardinals | 3.6 | 7 | $126 | $18 | 6 | $52 | $9 | $2.4 |
| Freddie Freeman | Braves | 3.5 | 7 | $121 | $17 | 8 | $135 | $17 | $4.9 |
| Jason Kipnis | Indians | 3.5 | 7 | $121 | $17 | 6 | $53 | $9 | $2.5 |
| Ian Desmond | Nationals | 3.2 | 6 | $95 | $16 | 2 | $18 | $9 | $2.9 |
| Jose Quintana | White Sox | 3.1 | 5 | $78 | $16 | 5 | $27 | $5 | $1.7 |
| Starling Marte | Pirates | 3.1 | 6 | $92 | $15 | 6 | $31 | $5 | $1.7 |
| Chase Utley | Phillies | 3.0 | 4 | $59 | $15 | 2 | $25 | $13 | $4.2 |
| Coco Crisp | A’s | 3.0 | 4 | $59 | $15 | 3 | $30 | $10 | $3.4 |
| Yan Gomes | Indians | 3.0 | 4 | $59 | $15 | 6 | $23 | $4 | $1.3 |
| Brett Gardner | Yankees | 2.8 | 4 | $55 | $14 | 5 | $58 | $12 | $4.2 |
| David Ortiz | Red Sox | 2.7 | 2 | $27 | $14 | 2 | $31 | $16 | $5.7 |
| Jordan Zimmermann | Nationals | 2.7 | 4 | $54 | $14 | 2 | $24 | $12 | $4.4 |
| Jedd Gyorko | Padres | 2.7 | 4 | $54 | $14 | 6 | $35 | $6 | $2.2 |
| Homer Bailey | Reds | 2.6 | 4 | $51 | $13 | 6 | $105 | $18 | $6.9 |
| Hunter Pence | Giants | 2.4 | 4 | $48 | $12 | 5 | $90 | $18 | $7.5 |
| Julio Teheran | Braves | 2.3 | 3 | $34 | $11 | 6 | $32 | $5 | $2.4 |
| Tim Lincecum | Giants | 2.0 | 2 | $20 | $10 | 2 | $35 | $18 | $9.0 |
| Will Venable | Padres | 1.9 | 2 | $19 | $9 | 2 | $9 | $4 | $2.3 |
| Jose Altuve | Astros | 1.9 | 2 | $19 | $9 | 4 | $13 | $3 | $1.7 |
| Craig Kimbrel | Braves | 1.8 | 7 | $123 | $18 | 4 | $42 | $11 | $6.0 |
| Ryan Hanigan | Rays | 1.6 | 2 | $16 | $8 | 3 | $11 | $4 | $2.3 |
| Michael Brantley | Indians | 1.6 | 2 | $16 | $8 | 4 | $25 | $6 | $4.0 |
| Chris Archer | Rays | 1.5 | 2 | $15 | $8 | 6 | $26 | $4 | $2.9 |
| Martin Perez | Rangers | 1.5 | 2 | $15 | $8 | 4 | $13 | $3 | $2.2 |
| Charlie Morton | Pirates | 1.4 | 1 | $7 | $7 | 3 | $21 | $7 | $5.2 |
| Glen Perkins | Twins | 1.0 | 4 | $40 | $10 | 4 | $22 | $6 | $5.5 |
The initial results are mixed. The model comes very close to the actual average extension contract length (prediction of 5.1 years vs. actual of 4.8 years), but badly overshoots the actual AAV. Again, this is because GMs pay more for a win on the free agent market than for a win produced by a player already on their roster. To account for this, I set the value of an incremental win at $3.7 million, the average WAR / $ of the 30 non-closers’ contract extensions. (For closers, I used $7.4 million.)
Extension Model vs. Actual Contracts
| Player | Team | 2014 WAR | Ext Yrs | Ext Amount | Ext AAV | Act Yrs | Act Amount | Act AAV | $/WAR |
| Mike Trout | Angels | 8.6 | 17 | $541 | $32 | 7 | $146 | $21 | $2.4 |
| Miguel Cabrera | Tigers | 6.0 | 12 | $264 | $22 | 10 | $292 | $29 | $4.9 |
| Clayton Kershaw | Dodgers | 4.7 | 8 | $138 | $17 | 7 | $215 | $31 | $6.6 |
| Dustin Pedroia | Red Sox | 4.6 | 9 | $153 | $17 | 8 | $110 | $14 | $3.0 |
| Andrelton Simmons | Braves | 4.5 | 9 | $148 | $16 | 7 | $58 | $8 | $1.9 |
| Jason Heyward | Braves | 4.1 | 8 | $121 | $15 | 2 | $13 | $7 | $1.6 |
| Matt Carpenter | Cardinals | 3.6 | 7 | $93 | $13 | 6 | $52 | $9 | $2.4 |
| Freddie Freeman | Braves | 3.5 | 7 | $89 | $13 | 8 | $135 | $17 | $4.9 |
| Jason Kipnis | Indians | 3.5 | 7 | $89 | $13 | 6 | $53 | $9 | $2.5 |
| Ian Desmond | Nationals | 3.2 | 6 | $70 | $12 | 2 | $18 | $9 | $2.9 |
| Jose Quintana | White Sox | 3.1 | 5 | $57 | $11 | 5 | $27 | $5 | $1.7 |
| Starling Marte | Pirates | 3.1 | 6 | $68 | $11 | 6 | $31 | $5 | $1.7 |
| Chase Utley | Phillies | 3.0 | 4 | $44 | $11 | 2 | $25 | $13 | $4.2 |
| Coco Crisp | A’s | 3.0 | 4 | $44 | $11 | 3 | $30 | $10 | $3.4 |
| Yan Gomes | Indians | 3.0 | 4 | $44 | $11 | 6 | $23 | $4 | $1.3 |
| Brett Gardner | Yankees | 2.8 | 4 | $41 | $10 | 5 | $58 | $12 | $4.2 |
| David Ortiz | Red Sox | 2.7 | 2 | $20 | $10 | 2 | $31 | $16 | $5.7 |
| Jordan Zimmermann | Nationals | 2.7 | 4 | $40 | $10 | 2 | $24 | $12 | $4.4 |
| Jedd Gyorko | Padres | 2.7 | 4 | $40 | $10 | 6 | $35 | $6 | $2.2 |
| Homer Bailey | Reds | 2.6 | 4 | $38 | $9 | 6 | $105 | $18 | $6.9 |
| Hunter Pence | Giants | 2.4 | 4 | $36 | $9 | 5 | $90 | $18 | $7.5 |
| Julio Teheran | Braves | 2.3 | 3 | $25 | $8 | 6 | $32 | $5 | $2.4 |
| Tim Lincecum | Giants | 2.0 | 2 | $14 | $7 | 2 | $35 | $18 | $9.0 |
| Will Venable | Padres | 1.9 | 2 | $14 | $7 | 2 | $9 | $4 | $2.3 |
| Jose Altuve | Astros | 1.9 | 2 | $14 | $7 | 4 | $13 | $3 | $1.7 |
| Craig Kimbrel | Braves | 1.8 | 7 | $91 | $13 | 4 | $42 | $11 | $6.0 |
| Ryan Hanigan | Rays | 1.6 | 2 | $12 | $6 | 3 | $11 | $4 | $2.3 |
| Michael Brantley | Indians | 1.6 | 2 | $11 | $6 | 4 | $25 | $6 | $4.0 |
| Chris Archer | Rays | 1.5 | 2 | $11 | $6 | 6 | $26 | $4 | $2.9 |
| Martin Perez | Rangers | 1.5 | 2 | $11 | $6 | 4 | $13 | $3 | $2.2 |
| Charlie Morton | Pirates | 1.4 | 1 | $5 | $5 | 3 | $21 | $7 | $5.2 |
| Glen Perkins | Twins | 1.0 | 4 | $30 | $7 | 4 | $22 | $6 | $5.5 |
With the adjustment to $/WAR, the results look much better. The predicted average AAV ($11.3 million) is now only 6% higher than the actual average ($10.6 million.) For the 31 players on the list (excluding Mike Trout, an outlier if there ever was one), the model projects a total of 147 years and $1.87 billion in contracts; the actual sums are 146 years and $1.67 billion. Not perfect, but decent.
The model misses very badly for unusual situations. Jason Heyward and Ian Desmond are projected as 8/$121 and 6/$70 respectively, but they both signed 2 year contracts worth less than $20 million last offseason. Both players were unable to come to terms with their teams on longer deals. This is probably because they are the odd men out on teams that have either just made it rain on prodigious young talent (Kimbrel, Freeman, Simmons) or will do so in the near future (Strasburg, Harper). Instead, Heyward and Desmond opted for shorter contracts in order to avoid arbitration and set themselves up for 2016 free agency.
Mike Trout is a unique case. The fishy outfielder signed a 7 year, $146 million extension last month, which looks like a massive underpay compared to the 17 years, $541 million (!!!) the model says he is worth. Don’t get me wrong: for the Angels, the Trout signing is still the best deal since the Louisiana Purchase. But it’s unrealistic to conclude that the Angels saved $395 million, since nobody would wait until Chelsea Clinton’s second term to test free agency, least of all someone who is currently breaking baseball.
Despite these shortcomings, the model can still evaluate the wisdom of recent extensions. Plotting the 32 players on a 2×2 matrix (the x-axis is the difference between actual and projected AAV, and the y-axis is the difference between actual and projected contract length) shows which front offices overpaid and which got steals.
Scatterplot of Contract Extensions
The extensions fall into four groups: locked-in bargains, short-term bargains, “win now” splurges, and albatrosses.
- Locked-in bargains are the best kind of extension: these contracts are cheap and relatively long. Yan Gomes is a good example; the model thinks he’s worth $11 million a year for 4 years, but the Indians locked him down for $4 million a year for 6 years. Initially, I felt bad that Yan missed out on an extra $20 million, but then I remembered that he’s a millionaire in his mid-20s who probably sleeps well at night, whereas I am a non-millionaire in his mid-20s who does not play a sport for a living.
- Short-term bargains are contracts that are cheap but shorter than projected. According to the model, Andrelton Simmons is worth $16 million a year for 9 years; the Braves signed him for $8 million a year for 7 years. So the Braves paid a below-market AAV for Simmons, but deprived themselves of controlling him for two more years (at least in theory). One caveat here: as explained earlier, Heyward and Desmond fit into this quadrant because their teams were unwilling to pay out for longer contracts, and Trout is simply a freak show.
- Win now splurges are contracts that are expensive but relatively short. Clayton Kershaw fits here because he makes $14 million more per year than the model thinks he deserves, but has a 7 year contract rather than the 8 years the model would give him. One could argue that Kershaw is a potential albatross, but if he leads the Dodgers to a World Series this year, their fans, like the Honey Badger, won’t care.
- Albatrosses are exactly what they sound like: excessively long, pricey contracts that make fan bases cry. Hunter Pence and Homer Bailey are the biggest albatrosses on the list; they were paid an extra $42 million (Pence) and $67 million (Bailey) than the model says they’re worth. Miguel Cabrera really belongs in this quadrant as well. The model considers Miggy a win now splurge, but only because it thinks he deserves 12 years rather than 10. No, Tigers fans, Mike Ilitch did not help me build this model.
Finally, the model can estimate how much your team should pay to extend your favorite young star.
Extension Model for 2015-18 FAs under 30 with WAR > 2
| Player | FA Year | Age in 2014 | 2014 WAR | Ext Years | Ext Amount | Ext AAV |
| Yu Darvish | 2018 | 27 | 5.1 | 9 | $168 | $19 |
| Giancarlo Stanton | 2017 | 24 | 4.5 | 9 | $148 | $16 |
| Max Scherzer | 2015 | 29 | 4.6 | 8 | $136 | $17 |
| Jason Heyward | 2016 | 24 | 4.1 | 8 | $121 | $15 |
| Carlos Gomez | 2017 | 28 | 4.0 | 8 | $117 | $15 |
| David Price | 2016 | 28 | 4.2 | 7 | $109 | $16 |
| Pablo Sandoval | 2015 | 27 | 3.7 | 7 | $95 | $14 |
| Chase Headley | 2015 | 29 | 3.6 | 7 | $92 | $13 |
| Carlos Gonzalez | 2018 | 28 | 3.5 | 7 | $91 | $13 |
| Chris Davis | 2016 | 28 | 3.5 | 7 | $89 | $13 |
| Brett Lawrie | 2018 | 24 | 3.4 | 7 | $88 | $13 |
| Stephen Strasburg | 2017 | 25 | 3.5 | 6 | $78 | $13 |
| Carlos Santana | 2018 | 27 | 4.0 | 5 | $73 | $15 |
| Jay Bruce | 2018 | 27 | 3.2 | 6 | $70 | $12 |
| Ian Desmond | 2016 | 28 | 3.2 | 6 | $70 | $12 |
| Matt Wieters | 2016 | 27 | 3.6 | 5 | $67 | $13 |
| Justin Masterson | 2015 | 29 | 3.1 | 5 | $56 | $11 |
| George Springer | 2019 | 24 | 3.0 | 5 | $56 | $11 |
| Jason Castro | 2017 | 26 | 3.2 | 4 | $47 | $12 |
| Jonathan Lucroy | 2018 | 27 | 3.2 | 4 | $47 | $12 |
| Brandon Belt | 2018 | 25 | 2.8 | 4 | $41 | $10 |
| Desmond Jennings | 2018 | 27 | 2.8 | 4 | $41 | $10 |
| Jordan Zimmermann | 2016 | 27 | 2.7 | 4 | $40 | $10 |
| Colby Rasmus | 2015 | 27 | 2.7 | 4 | $40 | $10 |
| Yoenis Cespedes | 2018 | 28 | 2.7 | 4 | $39 | $10 |
| Pedro Alvarez | 2017 | 27 | 2.7 | 4 | $39 | $10 |
| Eric Hosmer | 2018 | 24 | 2.6 | 4 | $38 | $10 |
| Johnny Cueto | 2016 | 28 | 2.2 | 3 | $24 | $8 |
| Yovani Gallardo | 2016 | 28 | 2.1 | 3 | $23 | $8 |
| Billy Butler | 2016 | 27 | 2.1 | 3 | $23 | $8 |
| Jed Lowrie | 2015 | 29 | 2.1 | 3 | $23 | $8 |
| Brandon Morrow | 2016 | 29 | 2.1 | 3 | $23 | $8 |
| Asdrubal Cabrera | 2015 | 28 | 2.1 | 3 | $23 | $8 |
To return to our earlier examples, Chris Davis would get 7 years and $89 million, David Price would get 7 years and $109 million, and Giancarlo Stanton would get 9 years and $148 million if they signed extensions this season. Of course, it’s tough to predict who will sign an extension and who will try their luck in free agency. Build me a model that can do that, and I’ll eat my Mets hat.
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