The 40-60-80 Arbitration Rule

What could McCutchen earn as a Super Two player?

Over the last few days I’ve been looking at the possible benefit of being a Super Two eligible player.  It started when I noticed that Andrew McCutchen was at risk of being a Super Two player following the 2011 season, which I speculated could add $10 M to his potential earnings.  Matt Bandi at Pittsburgh Lumber Company followed up by pointing out that Super Two players received 21.8% of their free agent values during the 2008/2009 off-season.

This was significant, as it is assumed that players go on a 40/60/80 scale for arbitration, which means they earn 40% of their free agent values in year one of arbitration, 60% in year two, and 80% in year three (free agent value can be found by multiplying the player’s WAR by $4 M).  If Super Two players received close to 20%, then that meant they went on a 20/40/60/80 scale, which means that someone like McCutchen would only get an additional $3 M by being a Super Two, since the only difference between being a Super Two and a regular scale would be that you get a year with 20% of your free agent value, rather than going on some sort of 40/60/80/100 scale.

After seeing Matt’s research, I had one problem: how accurate is the 40/60/80 scale?  I looked at this yesterday, and noticed that first year arbitration eligible players in the 2008/2009 off-season (the same that Matt looked at), received around 26.49% of their free agent value.  That was closer to the 21.8% that Super Two players received than it was to the assumed 40% that first year arbitration eligible players should have received.  From there, I wanted to study that off-season group to see what second and third year arbitration eligible players received.

After figuring out that players made 26.49% of their free agent value in year one of a normal arbitration scale, I proceeded to year two.  I looked at all of the players who had 4.000-4.171 years of service time in the 2008/2009 off-season, as well as what they received through arbitration.  Just like my original study, I excluded the following:

-Super Two players in their third arbitration years

-Closers (the value of saves in the arbitration process really changes the results for closers)

-Players with less than a 0.5 fWAR (FanGraphs WAR) in 2008

Here are the results (click on the image to enlarge):

In year one of a normal arbitration scale, I found that players received 26.49% of their free agent value, rather than the 40% assumption.  The above chart shows that year two arbitration eligible players received 48.09% of their free agent value, rather than the assumed 60%.  Year one was a difference by about 13.5%, while year two was a different by about 12%, both lower than the assumed values.  What’s even more interesting is that I went back to look at the Super Two players who were in their second year of arbitration:

The Super Two players in the 2008/2009 off-season received 21.8% of their free agent value, according to Matt.  The players in that same off-season who were previously Super Two players, and in their second arbitration year received 49.07% of their free agent value.  So far we have the following from the 2008/2009 off-season:

Super Two Players, 1st Year: 21.8%

Normal Arbitration Players, 1st Year: 26.49%

Super Two Players, 2nd Year: 49.07%

Normal Arbitration Players, 2nd Year: 48.09%

That’s much different from the 40/60/80 scale so far.  As of now, it’s looking like a 25/50 scale for the first two years of arbitration under a normal scale.  However, the third year is where I ran in to a problem.

This can’t make sense.  Players in the 08/09 off-season received 48.09% of their free agent value during their second year of arbitration.  There’s no way that the standard can be 47.34% of free agent value in the third and final year of arbitration.  The problem I see here is very simple.  The free agent value that we’ve been using is based on the 2008 fWAR numbers, and the 2009 salaries.  Let’s think about the arbitration process for a second.

Arbitration values aren’t just based on what the player did during the previous season.  They’re based on the career body of work by the player.  Take Adam LaRoche, for example.  LaRoche received 103.68% of his 2008 value, with an fWAR of 1.7.  However, LaRoche put up a 2.5 and a 2.6 fWAR in his previous two seasons (he also proceeded to put up a 2.6 fWAR in 2009).  With a 2.5-2.6 fWAR, LaRoche’s value goes from 103.68% to around 70%.

There’s also the flip side.  Marlon Byrd received 25.5% of his value.  In 2008, Byrd had an fWAR of 3.0.  He had a 2.1 fWAR in 2007, but prior to that he was under 1.0 for the previous three seasons, including a negative in 2004.  Byrd’s average fWAR through the 2008 season was closer to a 1.0 than a 3.0.  Using a 1.0 as his fWAR, we see that he received a 76.5% value, rather than the extremely low 25.5% value.

Obviously to form a better conclusion, more samples are needed.  We would have to look at several years, not just the 2008/2009 off-season.  The same goes for all of the other research done on this topic, not just the third year of arbitration.  One issue that has gone unaddressed so far is just how many players actually reach their third year of arbitration?  Players get non-tendered, they sign extensions, or they just never reach that third arbitration year.  The players who actually do reach their third year of arbitration seem to be special cases.  Perhaps they have a big boost in value, which keeps them alive in the arbitration process for another year.  Maybe they’re in a situation like LaRoche, where they’re unlikely to sign a multi-year deal to remain with the Pirates.

This all started by looking at the value of Andrew McCutchen possibly being a Super Two player.  We’ve seen that Super Two players can receive 21.8%/49.07% in their first two years of arbitration.  Like the third year arbitration players, the sample of Super Two players in their third and fourth year of arbitration is small.  That’s because most players either sign extensions before they reach those years, or they get non-tendered because they’re not deserving of the salaries during those years.

This was all brought up to see what the difference was between Super Two players and regular players in the arbitration process.  The final years are inconclusive, but the first two years are similar for Super Two/normal players, with the scale being closer to 25/50 than 40/60.  The 40/60/80 scale seems like a good guide to use to get the player’s maximum value, although as shown, the actual contract can be lower.

The important thing here is to find the values of the early years of arbitration.  If the player is worth the price, he’s going to get a raise each year.  The important question is, where do you start?  As seen above, the first two years are similar, regardless of whether the player is Super Two eligible or not.  While the third year’s value isn’t conclusive, we can assume that every player would receive the same value in their third year, regardless of Super Two status.  The Super Two eligible player would see a benefit in the fourth year by getting a raise over his third year, which could mean a big raise for McCutchen if he does reach Super Two status next off-season.

Tim started Pirates Prospects in 2009 from his home in Virginia, which was 40 minutes from where Pedro Alvarez made his pro debut in Lynchburg. That year, the Lynchburg Hillcats won the Carolina League championship, and Pirates Prospects was born from Tim's reporting along the way. The site has grown over the years to include many more writers, and Tim has gone on to become a credentialed MLB reporter, producing Pirates Prospects each year, and will publish his 11th Prospect Guide this offseason. He has also served as the Pittsburgh Pirates correspondent for Baseball America since 2019. Behind the scenes, Tim is an avid music lover, and most of the money he gets paid to run this site goes to vinyl records.

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I don’t know if you’ve seen the work I did on this at onlybucs, but looking at both the pre-2009 and pre-2010 offseasons, I found that the arb scale is basically what Tango and Matt suggest: 20/40/60/80. The differences between your study and mine were that I didn’t exclude closers, did exclude multi-year deals, and used CHONE projections rather than the previous season’s WAR (and had a bigger sample size). The projections approximate how the market sees players better than a single year of WAR data does, as you note in talking about the difference between single-year and multi-year WAR figures. I think you should exclude multi-year deals, too, as they skew the results (multi-year deals will come at a discount of presumed arb prices for obvious reasons).

The other big advantage my study had was a larger sample size. For instance, I got something similar to what you did for 2009, despite our different criteria and inputs: an average of 58% of market value for second-time arb-eligible super-twos; 62% of market value for second-time arb-eligible non-super-twos. So that’s pretty similar, as you found (my numbers are higher than yours because I didn’t exclude closers, probably). But when I added the 2010 data, the average for both years was 43% of market value for second-time arb-eligible super-twos and 55% for second-time arb-eligible non-super-twos, which looks more like the 40/60/80 scale that Tango suggests.

As with you, my numbers got a little wonky when looking at arb awards for players with 5+ years of service, mostly because the samples are so small.

This won’t affect your results much in this particular case, but you should keep your criteria the same for every sample of players. You included a closer and several players with less than 0.5 WAR in your sample of second-time arb-eligible super-twos. If you eliminate those, your result will be very close to what I got for 2009: 56%.

Anyway, the larger sample I used does reveal a pattern that approaches 20/40/60/80, but even in my study the samples for the last year probably weren’t big enough. I do think my study demonstrates that super-twos are paid according to years of service rather than times through arbitration (i.e., super-twos make less than what first-time arb-eligibles with 3+ years of service do, and previous super-twos with 3+ years of service make roughly the same as first-time arb-eligibles with 3+ years of service, etc.).

I only used two years of data because those were the only years for which I could easily get WAR projections, but I’d be interested to see what you find if you apply your method to multiple years of data.

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