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Calculating MLB Arbitration Percentages

How did Antonio Bastardo do in free agent relative to his modeled arbitration salaries? Photo by Matt Kartozian-USA TODAY Sports

How did Antonio Bastardo do in free agent relative to his modeled arbitration salaries?
Photo by Matt Kartozian-USA TODAY Sports

Next week, TPOP is going to rolling out our updated Prospect Surplus Values model.  As with any model, it must constantly be tweaked as new information comes available and tested for legitimacy.  I’m examining every aspect of the model, from front to back.

While discussing the project with Dave Cameron of Fangraphs, he mentioned that I may want to look into the arbitration percentages for players in their arbitration years.  Previously, I used the rule-of-thumb 40-60-80% of potential free agent value that had been widely accepted and propagated.  Considering how key of an aspect these rates are in the surplus value formula, I felt it was worth the time and effort.

To do this, I used the indispensable Cot’s Contracts and combed through each franchise’s roster.  I pulled out every player that went through arbitration all three times (or four, I did this for Super 2, as well) and then signed a free agent contract after.  Any player that started out in arbitration, but then signed an extension that bought out free agent years was ruled out, as these extensions are meant to suppress both arbitration year costs and especially free agent year salaries.

I found 38 such players, which isn’t a huge sample but it’s large enough to have a degree of confidence in the results.  Those results are tabulated below.  The first three columns after the player’s name are the salaries they received during arbitration years. The next column is the average annual value of their free agent contract.  The final three columns are the percentages of the arbitration years, as they relate to the free agent contract.

Standard
Player Arb 1 ($, in M) Arb 2 ($, in M) Arb 3 ($, in M) FA Avg Value ($, in M) Arb 1 % of FA Arb 2 % of FA Arb 3 % of FA
Melvin Upton 3 4.825 7 15.05 0.2 0.32 0.47
Chris Davis 3.3 10.35 12 23 0.14 0.45 0.52
Shin-soo Choo 3.975 4.9 7.375 18.57 0.21 0.26 0.4
Jacoby Ellsbury 2.4 8.05 9 21.86 0.11 0.37 0.41
Carlos Beltran 3.5 6 9 17 0.21 0.35 0.53
Brett Gardner 2.8 2.85 5.6 13 0.22 0.22 0.43
Matt Weiters 5.5 7.7 8.3 15.8 0.35 0.49 0.53
Jose Bautista 1.8 2.4 2.4 13 0.14 0.18 0.18
Marco Estrada 1.955 3.325 3.9 13 0.15 0.26 0.3
David Robertson 1.6 3.1 5.215 11.5 0.14 0.27 0.45
Anibal Sanchez 1.25 3.7 8 16 0.08 0.23 0.5
Francisco Rodriguez 3.775 7 10 12.33 0.31 0.57 0.81
Jason Vargas 2.45 4.85 8.5 8 0.31 0.61 1.06
Phil Hughes 2.7 3.2 7.15 8 0.34 0.4 0.89
Colby Rasmus 2.7 4.675 7 8 0.34 0.58 0.88
Luke Gregorson 1.55 3.2 5.065 6.133 0.19 0.52 0.83
CJ Wilson 1.85 3.1 7 15.5 0.12 0.2 0.45
Joe Smith 0.87 1.75 3.15 5.25 0.17 0.33 0.6
Jed Lowrie 1.15 2.4 5.25 7.66 0.15 0.31 0.69
Seth Smith 2.415 3.675 4.5 6.5 0.37 0.57 0.69
Michael Bourn 2.4 4.4 6.845 12 0.2 0.37 0.57
Erick Aybar 2.05 3 5.075 8.75 0.23 0.34 0.58
Emilio Bonifacio 2.2 2.6 3.5 4 0.55 0.65 0.88
Alejandro de Aza 2.075 4.25 5 5.75 0.36 0.74 0.87
Antonio Bastardo 1.4 2 3.1 6 0.23 0.33 0.52
Jerry Blevins 1.1 1.675 2.4 4 0.28 0.42 0.6
Max Scherzer 3.75 6.725 15.525 30 0.13 0.22 0.52
Jonathan Papelbon 6.25 9.35 12 12.5 0.5 0.75 0.96
Daniel Murphy 2.925 5.7 8 12.5 0.23 0.46 0.64
Miguel Montero 2 3.2 5.9 12 0.17 0.27 0.49
Jon Jaso 1.8 2.3 3.175 4 0.45 0.58 0.79
Neftali Feliz 2.9 3 4.125 3.9 0.74 0.77 1.06
Mike Leake 3.06 5.925 9.775 16 0.19 0.37 0.61
Jorge de la Rosa 1.025 2 5.6 10.75 0.1 0.19 0.52
Gerardo Parra 2.35 4.85 6.237 9.133 0.26 0.53 0.68
Fernando Rodney 1 1.7 2.7 5.5 0.18 0.31 0.49
Carlos Villaneuva 0.95 1.415 2.278 5 0.19 0.28 0.46
Jeff Samardzija 2.64 5.345 9.8 18 0.15 0.3 0.54
0.25 0.4 0.62

A couple notes of interest:

  • Jason Vargas and Neftali Feliz both signed free agent contracts that were lower than their last year of arbitration, mostly due to injury/ineffectiveness.  I contemplated tossing them out, but felt it would be disingenuous to the data, so they remain as a counterbalance to some of the other lower deals.
  • Jose Bautista appears to be criminally underpaid in his arb years, but remember that things didn’t click for him in Toronto until the very end of his arb-2 year.  By that time, his body of work suppressed his arb-3 award.

As you can see by the bottom line, the averages come out to 25/40/62%, a far cry from the rule-of-thumb of 40/60/80%.  For simplicity purposes, I’ll be referring to the rates going forward as 25/40/60.

I repeated the same exercise for the Super 2 players.  As you can imagine, there are far fewer samples to choose from.  But there’s still 14 and we’ve gone this far down the rabbit hole, so let’s examine these as well:

Super 2
Player Arb 1 ($, in M) Arb 2 ($, in M) Arb 3 ($, in M) Arb 4 ($, in M) FA Avg Value ($, in M) Arb 1 % of FA Arb 2 % of FA Arb 3 % of FA Arb 4 % of FA
Chase Headley 2.325 3.475 8.575 10.525 13 0.18 0.27 0.66 0.81
David Price 4.35 10.1125 14 19.75 31 0.14 0.33 0.45 0.64
Rick Porcello 3.1 5.1 8.5 12.5 20.625 0.15 0.25 0.41 0.61
JJ Hardy 2.65 4.65 5.1 5.85 7.42 0.36 0.63 0.69 0.79
Mike Napoli 2 3.6 5.8 9.4 16 0.13 0.23 0.36 0.59
Jordan Zimmerman 2.3 5.35 7.5 16.5 22 0.1 0.24 0.34 0.75
Luke Hochevar 1.76 3.51 4.56 5.21 5 0.35 0.7 0.91 1.04
Ricky Nolasco 2.4 3.8 6 9 12.25 0.2 0.31 0.49 0.73
Carlos Gomez 1.15 1.5 1.9625 4.3 8 0.14 0.19 0.25 0.54
Shawn Kelly 0.6 0.935 1.765 2.835 5 0.12 0.19 0.35 0.57
Matt Garza 3.35 5.95 9.5 10.25 12.5 0.27 0.48 0.76 0.82
Boone Logan 0.59 1.2 1.875 3.15 5.5 0.11 0.22 0.34 0.57
Andre Ethier 3.1 5.5 9.25 10.95 17 0.18 0.32 0.54 0.64
Hunter Pence 3.5 6.9 10.4 13.8 18 0.19 0.38 0.58 0.77
Angel Pagan 0.575 1.45 3.5 4.85 10 0.06 0.15 0.35 0.49
0.18 0.33 0.5 0.69

In this case, the precursor rule-of-thumb of 20/40/60/80% was a little bit more on target with our results, but it still will be referred to (by me, at least) as 20/33/50/70% for Super 2 players.

So to utilize this information, select a player entering in the arbitration process and guesstimate how many WAR you think that player will be worth at the potential age of his free agency.  Multiply that by $8M/WAR and then calculate backwards his potential arbitration salary accordingly.  Naturally, that just gets you a ballpark figure, as you’ll want to establish a set of comparable players for him, too.

It can also be used in reverse.  Let’s use everyone’s favorite pitcher, Jeff Locke, who was recently awarded a shade over $3M in arbitration.  By this metric, Locke would be worth $12M on the open market as a free agent.  Yes, that seems outrageous, but #4-level pitchers routinely gets $12M/year on the market nowadays, especially with the inflated cost of pitching.  Chris Young signed with the Royals for 2 yr/$23M ($11.5M/year) and JA Happ signed for 3 yr/$36M ($12M/year).  Number 3-level pitchers, such as Mike Leake, now get $16M/year.  A true arms race, indeed.  Going back to Locke, using that $12M baseline, we can pencil in his last two arbitration years as potentially $4.8M (40% of $12M) and $7.2M (60% of $12M).  If you thought people got their hackles up over Locke at $3M, imagine the sturm and drang over those salaries.

About Kevin Creagh (300 Articles)
Nerd engineer by day, nerd writer at night. Kevin is the co-founder of The Point of Pittsburgh. He is the author of Creating Christ, a sci-fi novel available on Amazon.

2 Comments on Calculating MLB Arbitration Percentages

  1. On the same day that you published this piece, I wrote this piece (http://camdendepot.blogspot.com/2016/02/say-goodbye-to-40-60-80-rule.html), in which I looked at all players that hit arbitration from 2011-2015 and compared their salary in that arbitration year to their production.

    Despite the different methodologies, we ended up with similar results. My results were 29/41/58 compared to your 25/40/62.

    That stated, I’m not sure why you wouldn’t use actual salaries to determine prospect production, as you’ve done that for this example.

    • Kevin Creagh // February 15, 2016 at 3:02 PM //

      Because sifting through salary data for 756 total players over a 13 year period (going back to late 90’s when salary info not as easy to find) is a herculean effort. That’s why this is a model.

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