Moving on from an analysis of starting pitchers, we move to relievers.

Relief pitchers happen to be the easiest group of players to project as their final salary is nearly entirely driven by saves although for non-closers, holds become very important to differentiate between setup men (who make slightly more) and middle relievers.

For a RP who is arbitration-eligible for the first time, here are the statistics that correlate most with eventual salary:

Career SV: 83.28%

Platform SV: 79.07%

Career WPA: 38.15%

Career SV%: 35.60%

Career fWAR: 35.18%

Platform SV%: 27.06%

Platform SO: 25.75%

When initially looking for player comps, these are statistics we are going to focus on. Keep in mind that although ERA is not listed, it is nonetheless important as ERA is still one of the default statistics used during a hearing and one of the first bases for comparison.

Note: WPA and Shutdowns (SD) have strong correlations, however those two stats are not widespread enough to be used during a hearing. My model includes WPA, but does not include SD as the inclusion of SD de-emphasized the importance of saves while it inflated the salaries of situational relievers. While ideally that should be the way salaries are determined, that does not happen in practice so it made sense to omit SD from the model.

Let’s use Indians closer, Cody Allen, as an example of a first-year-eligible reliever. Cody Allen is arbitration-eligible for the first time going into 2016 with 3 years and 76 days of service time (3.076). In his platform season (2015), Allen recorded 34 saves with a 89.47 SV%, 99 SO and a 2.99 ERA. Over his career, Allen has compiled 60 saves with a 84.51 SV%, 4.19 WPA, 5.0 fWAR and a 2.64 ERA. The objective here is to find the players who avoided arbitration by signing a 1-year contract with statistics that are most similar to Allen’s. The more recent, the better. The best way to do that is to set a floor and a ceiling and then work your way towards the middle.

First, let’s look at David Aardsma’s 2009 platform season (old, but still useful). Like Allen, Aardsma was an effective closer with high save totals and a strong ERA. Aardsma recorded 38 saves, 80 SO with a 2.52 ERA. Over his career, Aardsma had compiled 38 saves with a 80.85 SV%, 2.25 WPA, 1.5 fWAR and a 4.38 ERA. Although the platform stats are very similar, Allen’s career numbers are far superior. Therefore, we can definitively state that Allen should receive more than Aardsma did. As such, Aardsma’s 2010 salary of $2.75 million should be the floor.

Next, let’s look at Greg Holland’s 2013 platform season. Like Allen, Holland was an effective closer with high save totals and a very strong ERA. Holland recorded 47 saves with a 94.0 SV%, 111 SO and a 1.21 ERA. Over his career, Holland had compiled 67 saves with a 88.16 SV%, 7.87 WPA, 6.9 fWAR and a 2.41 ERA. Although their career numbers are relatively close, Holland had a dominant platform season that surpassed Allen in every way. Therefore, we can definitively state Allen should receive less than Holland did. As such, Holland’s 2014 salary of $4.675 million should be the ceiling.

Given the above, Cody Allen is likely to receive somewhere between $2.75 million and $4.675 million. Now that we have a range, let’s find someone towards the middle.

In 2013, Ernesto Frieri recorded 37 SV with a 90.2 SV%, 98 SO and a 3.80 ERA. Over his career he recorded 60 saves with an 89.55 SV%, 5.62 WPA, 2.3 fWAR and 2.76 ERA Those numbers are quite similar across the board with both players having an identical career save total and only 3 more platform saves. Frieri’s 2014 salary was $3.80 million so we can determine Allen will receive a similar amount. Andrew Bailey ($3.9 million in 2012) is a decent comp as well.

As for my model, Allen projects to receive $3,595,732 +/- $130,998 which is perfectly in line with the comps above. MLBTradeRumors projects him at $3.5 million so both of our models are very close here (and will be most of the time).

For a player who has already been through the arbitration process before, the valuation is completely different as career statistics are no longer used the 2nd, 3rd, 4th, etc. time around (except in a few rare cases).

For a RP who has previously been through the arbitration process, the stats that correlate most with eventual salary are:

(1) Platform SV: 70.40%

(2) Platform fWAR: 41.36%

(3) Platform RA9-WAR: 36.58%

(4) Platform SV%: 34.79%

(5) Platform WPA: 34.34%

(6) Platform SO: 30.04%

For example, let’s look at Reds closer Aroldis Chapman who is arbitration-eligible for the third time going into 2016. As an Arb-2 going into 2015, Chapman received a $8.05 million salary. That figure includes everything he had done in his career up to that point. Thus, when determining his 2016 salary, we don’t need to focus on previous seasons. We need only determine what his 2015 season was worth and give him a raise. In his platform season (2015), Chapman recorded 33 saves with a 91.67 SV%, 116 SO, 1.99 WPA, 2.4 fWAR, 2.7 RA9-WAR and a 1.63 ERA. We want to find the players whose stats are most similar to Chapman.

First, let’s discuss Juan Carlos Oviedo’s (formally known as Leo Nunez) 2011 platform season where he recorded 36 saves with an 85.70%, 55 SO, 1.07 WPA, 0.1 fWAR, 0.2 RA9-WAR and a 4.06 ERA. Although Oviedo was fortunate enough to record more saves, Chapman was the far better player overall; so much so that, despite having fewer saves, we can determine that Chapman will definitely receive a larger raise than the $2.35 million raise Oviedo received going into 2012. Therefore, we can consider a raise of $2.35 million to be his floor. Oviedo is the perfect example of how important saves are (for arbitration purposes) when it comes to relievers.

Next, let’s look at Heath Bell’s 2010 platform season (again old, but useful still) where he recorded 47 saves with a 94.0 SV%, 86 SO, 4.49 WPA, 2.3 fWAR, 2.6 RA9-WAR and a 1.93 ERA. Like Chapman, Bell was an All-Star closer with virtually identical numbers except for WPA and SV, where Bell clearly outproduced him. Moreover, Bell was named the NL reliever of the year. As such, Bell’s raise of $3.5 million going into 2011 should be the ceiling.

Given the above, Aroldis Chapman is likely to receive a raise somewhere between $2.35 million and $3.5 million for a final salary between $10.4 million and $11.55 million.

Chapman is a perfect example of why first determining a range is important as Chapman represents a type of player who just has not been through the arbitration process in this service group before. Since 2006, there has not been a closer who recorded less than 40 saves with dominant numbers. Looking at saves we have Chris Perez (39 saves – $2.8 million in 2013), Brandon League (37 saves – $2.75 million in 2012), Jonathan Papelbon (37 saves – $2.65 million in 2011) and Joel Hanrahan (36 saves -$2.94 million in 2013). Somewhere around those numbers and perhaps a bit higher is what we should expect.

My model projects that Chapman should receive a raise of $2,743,587+/- $152,366 for a total 2016 salary of $10,793,587+/- $152,366, although I think my projection underestimates the impact his dominant numbers will have despite the lowish save totals (due the lack of comps). I would expect a raise of around $3 million. MlbTradeRumors is projecting a raise of $4,850,000 for a total salary of $12,900,000, which not only surpasses Heath Bell’s raise, but shatters Jim Johnson’s record-setting raise for a non-first-year reliever of $3,875,000 when he recorded 51 of 54 saves in 2012. Given the importance of saves and the relative unimportance of the other stats, I don’t see how such a high number is possible. Nonetheless, Chapman is a very interesting case study as he has the potential to change the way relievers are viewed during the arbitration process.

Next up: position players.

My name is Rich Rieders and I am a 2015 graduate of Rutgers Law School. Over the winter, I participated in Tulane University’s 9th Annual Baseball Arbitration Competition and we finished in 2nd place overall out of 40 teams.

In order to prepare for the competition, I created a database (going back to 2008) consisting of all arbitration awards and players who signed 1-year contracts avoiding arbitration along with their respective statistics. Using regression analysis, I was able to determine which statistics correlate most with salary. In turn, I have created a projection system that can accurately predict arbitration salaries. My projections are more accurate than the ones featured on MLBTradeRumors.

I will be releasing my 2016 projections once the season is over and all awards are announced.

The goal of this article is to properly explain how arbitration salaries are determined and how to choose the best comparative baseball salaries (comps) as outlined in Article VI, Section E, Part 10(a) of the CBA. You can think of the comps as legal precedent. The closer the comps are to the player’s stats, the more comps you have and the more recent those comps are, the stronger your argument.

First and foremost, the purpose of the arbitration process is to compensate the player for his actual results on the field, not to give him a salary based on what we expect he will produce in the upcoming season. We concern ourselves with only the traditional stats. I know this is a complete departure from the way we normally think here on FanGraphs, but salary arbitration is a completely different animal. In essence, arbitration salaries are determined by the accumulation of traditional counting stats.

For our purposes, there are six types of players who are up for arbitration in a given offseason and each type has its own separate valuation. The six types of players are:

(1) First-year-eligible SP

(2) SP who have previously been through the arbitration process

(3) First-year-eligible RP

(4) RP who have previously been through the arbitration process

(5) First-year-eligible position player

(6) Position players who have previously been through the arbitration process.

I will explain, in detail, how to properly choose player comps for each of the six group of players. In this segment, we will focus just on the starting pitchers.

For a SP who is arbitration eligible for the first time, here are the statistics that correlate most with eventual salary:

Platform IP: 60.83%

Platform GS: 57.59%

Platform SO: 54.41%

Platform W: 53.12%

Career IP: 50.56%

Career SO: 47.45%

Career W: 42.76%

Career GS: 37.10%

When initially looking for player comps, these are statistics we are going to focus on. Keep in mind that although ERA is not listed, it is nonetheless important as ERA is still one of the default statistics during a hearing and the first basis for comparison. Note that rate stats almost always have a very low correlation since rate stats do not take into account playing time.

Let’s use Atlanta Braves starter, Shelby Miller, as an example of a first-year-eligible SP.

Shelby Miller is arbitration-eligible for the first time going into 2016 with 3 years and 30 days of service time (3.030). In his platform season (2015), Miller made 33 starts recording 6 wins, 171 SO with a 3.02 ERA in 205.1 IP. Over his career, Miller has compiled 575 IP, 32 W, 483 SO with a 3.22 ERA in 96 GS. The objective here is to find the players who avoided arbitration by signing a 1 year contract with statistics that are most similar to Miller’s. The more recent, the better. The best way to do that is to set a floor and a ceiling and then work your way towards the middle.

From Miller’s perspective, let’s look at Miguel Gonzalez’s 2014 platform season. Like Miller, Gonzalez posted a low win total despite a very strong ERA. Gonzalez made 26 starts, recorded 10 wins, 111 SO with a 3.23 ERA in 159 IP. Over his career, Gonzalez compiled 69 starts, 30 wins, 308 SO with a 3.45 ERA in 435.2 IP. Although their ERA and win totals are extremely close, Miller bests Gonzalez in all the most important categories and has significantly more playing time and strikeouts. Therefore, we can definitively state Miller should receive more than Gonzalez did. As such, Gonzalez’s 2015 salary of 3.45 million should be the floor.

From Atlanta’s perspective, let’s look at Chris Tillman’s 2014 platform season. Like Miller, Tillman pitched a similar amount of innings and games with a pretty low ERA. In his platform season, Tillman made 34 starts recording 13 wins, 150 SO and a 3.34 ERA in 207.1 IP. Over his career, Tillman compiled 45 W, 680.1 IP, 511 SO with a 4.00 ERA in 118 GS. Although Miller has the better ERA, Tillman is superior in all the other major categories. Hence, we can conclude that Miller will receive less than Tillman. We can use Tillman’s 2015 salary of $4.315 million as the ceiling.

Given the above, Shelby Miller is likely to receive somewhere between $3.45 million and $4.315 million. Now that we have a range, let’s find someone towards the middle.

In 2011, Justin Masterson made 33 starts with 12 W, 158 SO, 3.21 ERA in 216 IP. Over his career he made 87 starts, with 28 W, 485 SO, 3.92 ERA in 613.2 IP. Those numbers are quite similar across the board with Miller having a better ERA, but fewer IP. Masterson’s 2012 salary was $3.825 million. Alex Cobb ($4.0 million in 2015),  Travis Wood ($3.9 million in 2014) and Steven Strasburg ($3.975 million in 2014) are all good comps as well.

As for my model, Miller projects to receive $3,859,816 +/- $145,351 which is perfectly in line with the comps above. MLBTradeRumors projects him at $4.9 million, which is not only significantly higher than the above comps, but would beat the record for a first-year player by nearly 600K.

For a player who has already been through the arbitration process before, the valuation is completely different as career statistics are no longer used the 2nd, 3rd, 4th, etc. time around (except in a few rare cases). This group of players are the most difficult to project since we use fewer variables due to the exclusion of career stats and how there are fewer SP across the league than relievers or position players. Nonetheless, we can still get a pretty good idea what their eventual salary will be.

For an SP who has previously been through the arbitration process, the stats that correlate most with eventual salary are:

(1) Platform W: 69.12%

(2) Platform RA9-WAR: 64.04%

(3) Platform SO: 60.97%

(4) Platform fWAR: 58.93%

(5) Platform IP: 58.34%

(6) Platform GS: 49.75%

For example, let’s look at Angels SP Garrett Richards who is arbitration eligible for the second time going into 2016. As a Super-2 going into 2015, Richards received a $3.2 million salary. That figure includes everything he had done in his career up to that point. Thus, when determining his 2016 salary, we don’t need to focus on previous seasons. We need only determine what his 2015 season was worth and give him a raise. In his platform season (2015), Richards made 32 starts recording 15 wins, 176 SO, 3.65 ERA, 2.5 fWAR and 2.8 RA9-WAR in 207.1 IP. We want to find the players whose stats are most similar to Richards.

First let’s discuss Matt Garza’s 2010 platform season (a bit old, but still useful) where he made 32 starts recording 15 wins, 150 SO, 3.91 ERA, 1.9 fWAR and 2.8 RA9-WAR in 204.2 IP. Other than the strikeout numbers, we have a virtually identical season. As such, Richards is likely to receive a raise higher than Garza’s $2.6 million raise going into 2011. We can consider a raise of $2.6 million to be his floor.

Next let’s look at C.J. Wilson’s 2010 platform season (again old, but useful still) where he made 33 starts recording 15 wins, 170 SO, 3.35 ERA, 4.1 fWAR and 5.1 RA9-WAR in 204 IP. Wilson has the same amount of wins and virtually the same number of SO although Wilson has a clear advantage in fWAR and RA9-WAR with a slightly better ERA so it’s pretty safe to say that Richards is likely to get a raise lower than Wilson’s $3.9 million raise. The $3.9 million should be the ceiling.

Homer Bailey’s 2012 platform season is a great final comparison. Bailey made 33 starts recording 13 wins, 168 SO, 3.68 ERA, 2.7 fWAR and 2.8 RA9-WAR in 208 IP. Both players are virtually identical statistically. Bailey received a raise of $2.925 million so Richards is likely to receive a very similar raise himself. Shaun Marcum ($3.1 million in 2011), Jordan Zimmerman ($3.050 million in 2011) and Max Scherzer ($2.975 million in 2013) are all good comps as well.

Therefore, we can be certain that Richards will receive a raise somewhere between $2.6 million and $3.9 million. As for my model, Richards projects to receive a raise of $2,923,484 for a total salary of $6,123,484+/- $336,500 and, unsurprisingly, that is perfectly in line with the comps above. MlbTradeRumors is projecting a raise of $3.6 million for a total salary of $6.8 million which I think is a bit generous given the comps we have at our disposal, but not unreasonable.

Next up: Relief Pitchers.

My name is Rich Rieders and I am a 2015 graduate of Rutgers School of Law. Over the winter, I participated in Tulane University’s 9th Annual Baseball Arbitration Competition and we finished in 2nd place overall out of 40 teams. The arbitration cases used in the competition were Jenrry Mejia v. New York Mets, Lorenzo Cain v. Kansas City Royals, and Mark Trumbo v. Arizona Diamondbacks. My team represented the Royals, Mets and Mark Trumbo in those cases. It was a great experience and I learned a tremendous amount. Those of you who are in law school should absolutely participate. Being in New Orleans is an amazing bonus as well! You can read more about the competition from Tulane’s website and Jerry Crasnick’s ESPN article.

Instead of explaining how arbitration works, I highly recommend reading this article as it will give you an excellent basis for understanding the arbitration process. Just ignore the part about free agency since that’s been done away with now.

In order to prepare for the competition, I created a database (going back to 2008) consisting of all arbitration awards and players who signed 1-year contracts avoiding arbitration along with their respective statistics (Note multi-year contracts are not allowable as player comps for arbitration purposes). Using regression analysis, I was able to determine which statistics correlate most with salary.

Here on FanGraphs we pride ourselves on the use of metrics and the abandonment of traditional stats. That all goes out the window for the arbitration process. The arbitrators jointly selected by league and the union have a background in labor law, not baseball. And those that are baseball fans probably aren’t avid FanGraphs readers and their exposure is likely to be limited to Wins, Losses, ERA, H, HR BB, SO, etc. Each side gets 30 minutes to present their case, plus another 15 minutes of rebuttal. You simply don’t have time to teach the panel sabermetrics and argue your case at the same time. And as I will discuss later, the use of predictive stats largely fall outside the scope of an arbitration hearing anyway. However, by using regression analysis we can pinpoint exactly which stats correlate most with eventual salary and which ones don’t.

• SP: W (.6099), IP (.5401), SO (.5368), RA9-WAR (.5166), GS (.4598)
• RP:  SV (.7302), SD (.4980), SV% (.3237), SO (.2716), WPA (.2491)
• Hitter: XBH (.7318), RBI (.7188), R (.6382), HR (.6031), PA (.5934)

These stats correlate among the least with future salary:

• SP: ERA (.1018), FIP (.0592), xFIP (.0765), BB% (.0202), HR/FB (.0046)
• RP: ERA (.0202), FIP (.0846), xFIP (.0962), BB% (.0218), LOB% (.0406)
• Hitter: BB% (.0175), BABIP (.0346), Z-Contact% (.0113), UBR (.0035), Def (.0202)

Now that’s not to say only the stats with the highest RSQ matter. Traditional rate stats like K/9 and ERA are still important. Try arguing to a casual fan that a pitcher with an ERA of 2.50 was not as productive as pitcher with an ERA of 4.00 ERA and see how that goes.

What we can take away from this is that:

1. Traditional stats have a strong correlation, metrics do not.
2. Counting stats have a strong correlation, rate stats do not.
3. Offense, particularly power have a strong correlation and defense and baserunning do not.
4. The more playing time you receive (PA, IP, G), the more money you are likely to make.

In essence, the overarching principal behind baseball arbitration is that salary is almost wholly dependent on the accumulation of traditional counting stats with traditional rate stats used to highlight the difference between the comparable players and serves in my formula to help prevent outliers.

Individual awards also matter a great deal. In my hearing, it was extremely difficult to try and argue against Lorenzo Cain when he won the ALCS MVP with his breakout postseason fresh in everyone’s mind. Those type of factors are extremely difficult to overcome. For a real-life example, I heard a story from one of our judges that the Giants were planning on going to arbitration with Tim Lincecum in 2010. Lincecum showed up with a Cy Young Award under each arm and within a few hours, a two-year contract was agreed upon.

Also keep in mind that for players going through arbitration for the first time, we also consider their career numbers as well. The correlations are fairly similar for career stats, but with slight improvement for career rate stats. For players going through the process for a second, third or fourth time, we pretty much ignore career statistics.

Before I introduce the model, I want to stress the importance of understanding the purpose of the baseball arbitration process. During the final round in Tulane, we represented the Kansas City Royals against Lorenzo Cain. One of our principal arguments was that Lorenzo Cain had an unsustainable .380 BABIP (highest in MLB mind you) which is why he batted .300 and that his BA (and the rest of his offensive numbers) would likely regress towards his career averages. The expected regression along with his low walk rate would limit his value to the club going forward. An argument most of us on FanGraphs would surely have made at the time, but Lorenzo Cain’s awesomeness is a topic for another day.

While this type of logic works perfectly well for free-agent signings or whether to acquire the player via trade, it does not work for arbitration purposes. The underlying purpose of the arbitration process is to compensate the player for his performance in the previous season, NOT to compensate him based on what we expect he will do the following season. This is absolutely critical. Hence, for arbitration purposes, the fact that a player was lucky, his performance was unsustainable or anything along the lines of “he won’t be as good as he was last season” is not permissible. This works the same for underachievers too as teams will get the benefit at arbitration when a player was “unlucky.”

Keeping all this in mind, what I have been able to do is determine which statistics (and other factors) matter the most when it comes to arbitration salaries and have created a formula that can accurately predict the salaries of future players by plugging in certain statistics. You may have seen similar work featured on MLBTradeRumors.com, however, the raw numbers produced by my formula are more accurate and contain less variance than their model’s adjusted projections. The 2015 arbitration projections on MLBTradeRumors featured an average error of $303,061 with a standard deviation of $334,102. My unadjusted projections yield an average error of $283,094 with a standard deviation of $255,174. Not to mention that my formula does not have any built in restraints or adjustments, which would certainly help increase its accuracy even more.

You can see a side-by-side comparison of the results here.

While these projections aren’t perfect, we can get a pretty good idea of what arbitration-eligible players will receive. Using these projections we should be able to not only predict a player’s salary for the upcoming season, but with good long-range statistical modeling, we can reasonably project a player’s subsequent arbitration salaries as well.

1. How much will Matt Harvey earn before he reaches free agency? How many millions will TJS wind up costing him?
2. Should Kris Bryant sign an extension this winter or should he try to reach free agency as early as possible? What should each side do? What about someone coming to arbitration for the first time like Nolan Arenado?
3. How much money does a team stand to save by avoiding Super-2 or delaying free agency by a year? Should the type of hitter/pitcher influence the decision?
4. Were the Reds or Todd Frazier better off by agreeing to a 2-year, $12-million deal this winter instead of going through arbitration twice? What about a defense-first player like Juan Lagares?
5. How much money is a rebuilding team like the Phillies costing themselves over the next few years by using Ken Giles as a closer instead of as a “high-leverage reliever?” Should the Marlins not make Carter Capps their closer in 2016?
6. Which teams do the best when it comes to arbitration? Which ones do the worst? (More on that next time). What about the agencies?

Using my formula, these are the questions we can begin to answer now.