Arbitration Projection Model

In the past couple days, I have been discussing some of the factors that play into arbitration salaries and the new model that I have developed for MLBTR to predict them. Yesterday, I discussed what gets a hitter paid. Today, we’ll look at pitchers.

One thing that advanced statistical analysis of pitchers has taught us is that luck, teammates, and opportunity play large roles in a pitcher’s success. A good defense can end rallies and convert a sure extra-base hit into an out, while a good offense can put you in the position to get a win or a save. The free agent market has clearly adjusted to this knowledge—Cliff Lee had just 12 wins and finished 21^st in ERA in 2010. He still got $120MM as a free agent, because his peripherals indicated he was a better pitcher than that—his SIERA was 3^rd in the league. This year, his ERA was 3^rd in the league too and he got 17 wins, thanks to more support from his teammates. Even recent Cy Young Awards have gone to Zack Greinke, Felix Hernandez, and Tim Lincecum, who fell far short of the standard 20-win Cy Young Award winner. However, arbitration panels have not made these same adjustments. The statistics that matter to panels remain IP, W, and ERA for starting pitchers, and IP, ERA, saves and holds for relief pitchers.

Playing time is crucial for pitchers’ arbitration salaries, just as it was for hitters. Accumulating innings gets you a big raise, even with a mediocre season. Joe Saunders got a $1.8MM raise last year, with 203 1/3 IP despite a 4.47 ERA and a 9-17 record. This year, we project Mike Pelfrey to get a $1.9MM raise to about $5.8MM for his 193 2/3 IP, despite a 4.74 ERA and a 7-13 record. Both pitchers will get raises for bad performance, since IP reign supreme.

Wins are pretty important as well. Jorge de la Rosa had 16 wins in 2009, despite a 4.38 ERA, which got him a $3.6MM raise. Our model predicts that for each four wins a pitcher gets, he will receive about a 10% larger raise, even with all of his other statistics unchanged. For example, our model has Cole Hamels getting $14.0MM in arbitration this winter with a solid ERA but only 14 wins. On the last day of the season, Phillies skipper Charlie Manuel used Hamels as a reliever in the 5^th inning with the hopes that he could back into his 15^th win. It didn’t work, but our model says that if it had, he could have expected an extra $200K in arbitration with a little help from his teammates during his throw day.

Relievers get paid by role. An elite closer with a history of saves gets paid far more than a set-up man, who gets paid far more than a middle reliever, even with similar performances. Andrew Bailey is slotted for $3.5MM this winter, but turn his 24 saves into 24 holds and he’d only get $2.1MM with the same elite ERA of 2.07, even with his 51 career saves prior to 2011 still on his record. Take all those saves and holds away, and he’d get under $1.0M with 174 career IP of a 2.07 ERA. Tyler Clippard had 38 holds this year for the Nationals, which boosts him up to a $1.7MM salary estimate. Take away 33 of those 38 holds to make him a middle reliever, and he only projects to get $1.3MM.

Even more so than hitters, one of the best ways for a pitcher to woo an arbitration panel is to have good teammates and a manager that puts him in a position to accumulate the right statistics. He’ll get more wins, saves, and holds with an offense that puts him in front, and more IP with a lower ERA with a defense that turns hits into outs.

Yesterday, I discussed the model that I developed for MLBTR to predict arbitration salaries. The model uses similar information to that which arbitration panels use to determine salaries, and generates an estimate for players that is very close to the actual salary the players earn. Today, I’ll talk a little bit about the salaries of hitters.

One of the most important determinants of a hitter's salary is playing time. For position players, this comes in the form of plate appearances. While it shouldn't be surprising that back-ups make less than regulars, position players who make it onto the field every day get paid more. For example, Hunter Pence got a $3.4MM raise last year for hitting .282 with 25 HR and 91 RBI, but with 658 PA. Adam LaRoche hit .270 with 25 HR and 85 RBI in 2009, but only got a $2.15MM raise for his 554 PA. This year, we predict Nelson Cruz only managing a $2.1MM raise despite 29 HR and 87 RBI, due to his 513 PA, while we have Hunter Pence getting a $4.2MM raise with 22 HR and 97 RBI, in part due to his excellent 658 PA. Getting onto the field matters to panels, both because you can accumulate bigger counting stat totals and because playing time is just important. Take Pablo Sandoval as another example. He has a career .307 batting average coming into his first year of arbitration, and has averaged over 20 HR per season. Our model projects him for just $3.2MM due to his 466 PA this season. Give him the same career rates of AVG, HR, RBI, and SB but with 650 PA in 2011, and he would get about $4.7MM.

Arbitration isn't fair. The one skill that really gets you paid is power—HR and RBI are far more important than other statistics. Knocking in runs matters, yet scoring them is not too important at all. In fact, once you factor in the AVG and SB that hitters do to put themselves in position to score, the actual runs scored doesn’t seem to matter much at all to arbitration panels. Even AVG and SB, however, pale in importance to almighty HR and RBI. Mike Morse had 95 RBI in the Nationals’ lineup this year, and combined with his .303 AVG and 31 HR, we have him coming in with a solid $3.9MM salary. Baseball-Reference.com estimated in August that Morse would have 50% more RBI if given the same RBI opportunities as Ryan Howard. What would Morse earn with 50% more RBI? Try $4.6MM. That’s $700K the Nationals will save on him simply by putting different guys in front of him in the lineup than the Phillies put in front of Howard.

Position does not seem to matter much either—while catchers certainly get paid a premium for their hard work behind the plate, middle infielders get paid about as well as corner infielders and outfielders. Arbitration, apparently, was built to put smiles on the faces of Mark Teixeira, Prince Fielder and Ryan Howard, who accumulate massive HR/RBI totals in potent lineups, but play easy positions. Quietly skilled players who get on base in front of them and play harder positions get paid far less for their contributions. Shortstop Elvis Andrus, for example, comes in at $2.9MM in our projections. Sabermetricians would estimate that his WAR would be about 20% lower if he produced similarly but played 1B instead of SS. However, his arbitration salary would only be about 2% lower.

You can estimate a player's salary to a certain extent using more accurate estimates of value like WAR, but a more sophisticated model that utilizes the same flawed information that arbitration panels use can pick up on these kinds of inefficiencies. Tomorrow, we’ll discuss how panels decide what to pay pitchers.

Arbitration salaries totaled about $867MM in 2011, and within a few years they will total over a billion dollars across the league, yet the arbitration process is poorly understood and rarely studied to the extent of free agent salaries. With the help of Tim Dierkes, Ben Nicholson-Smith, and other friends of MLBTR, I have fine-tuned a model for predicting arbitration salaries. By incorporating arbitration earnings from the last five years, the model is able to predict salaries using a range of related players. The model has a correlation of roughly .98 with actual salaries, and predicts actual earnings within $170K for more than half of players. 

How good is the model? Well, it works well when it already knows what all the players made and can try to fit the data perfectly. So, I decided to see how well it did if I recreated the model without data from a year and then predicted the salaries from that year using the data from the other years. So I used 2007, 2008, 2009, and 2010 statistics and salaries to predict 2011 salaries, then 2007, 2008, 2009, and 2011 salaries and data to predict 2010 salaries, and so on. The result was still a very strong prediction: it was within $320K half the time. Even the most sophisticated model using service time, career wins above replacement, and single-season WAR (and remember that WAR is an actual one-size-fits-all estimate of player value) could only get within $700K half the time. For the average player, even a simplified version of my model cuts the error in half!

The salaries of arbitration eligible players are determined by arbitration panels or by contracts signed under the shadow of potential panel decisions. This represents a lot of players. Only about a third of playing time goes to free agents, and another third of playing time goes to players not yet eligible for arbitration. The other third of playing time — and about 25% of payroll — goes to players whose salaries will be determined by an arbitration panel, unless they reach an agreement first.

In contrast to the free agent market, which now incorporates a modern understanding of baseball, arbitration relies on simple statistics such as pitcher wins and runs batted in. When advanced statistics became available, teams incorporated these into their free agent bids, and stopped paying much attention to old-school statistics. Meanwhile, arbitration panels determine a player's salary based on "comparables," players with similar basic statistics and service time. The salaries that the model produces aren't far from what an educated fan might guess, but the subtle differences are important.

In Tim Dierkes's arbitration series, he has been giving rough estimates of salaries for players based on in-season projections, but we will be releasing the model’s official salary projections for the 2012 season shortly.  The most influential factor for both hitters and pitchers is playing time. More plate appearances and innings pitched make a huge difference. For batters, unsurprisingly, home runs and runs batted in matter most to arbitration panels and our model, while stolen bases and batting average also play important roles. For starting pitchers, wins and ERA are the most important, while relief pitchers get paid mostly based on saves and holds, with a dash of ERA as well. This week, I will post another article on hitters and another article on pitchers explaining the importance of these statistics for certain players in more detail, and I will highlight a couple of unique cases for the 2012 season. Will the model miss by a lot for some players? It absolutely will. But it’s going to hit a lot more than it’s going to miss, and it can provide guidance on players that are harder to understand.