08 February 2016

Say Goodbye To The 40-60-80 Rule

Update: I originally included DFA'd players with players that signed extensions because neither set of players went through arbitration. This was poor logic on my part and therefore I'm editing this post to take into account players that were DFA'd and players that signed extensions.

Most baseball fans with an interest in baseball arbitration are familiar with the 40-60-80 rule. The argument is that on average, a player with between 3 and 4 years’ service time will receive 40% of his value, between 4 and 5 years will receive 60% and between 5 and 6 years will receive roughly 80% of his value. The problem is that this rule was actually created in 2007 and therefore is nearly a decade old. Does it still have any validity?

Cot’s Baseball Contracts has developed a spreadsheet with the service time for all players from 2007-2015. By combining that spreadsheet with salary information from the Lehman Database, free agent win costs via Lewie Pollis and RA9_WAR values from Fangraphs, it is possible to determine the cost per win for the categories of players listed above. MLBTR has an arbitration tracker for 2011-2015 that indicates which players went through arbitration/settled on a one year deal in those years and thereby implying which players agreed to long term extensions. This information can be used to determine the cost per win for each of the above categories for both arbitration and extension players during those years.

The chart below shows the amount players from 2007-2015 in each category earned as a function of the cost of a free agent win regardless of whether a given player went through arbitration or signed an extension for either one or multiple years. On average, first year players just earned 25% of their value, second year players earned 38% of their value and third year players earned 54% of their value.

This graph shows how this has changed over time. The amount that second and third year players earn seems to be increasing. It is difficult to tell whether this is a real trend or merely normal variance.

The next chart shows how much a team ultimately paid for players in each category from 2011-2015 as a function of the cost of a free agent win grouped by whether the player signed a multi-year extension or went through arbitration or agreed to a one year deal. The numbers are slightly different as overall players earned slightly more from 2011-2015 then they did from 2007-2015.

Arbitration players earned 29% in their first year, 41% in their second year and 59% in their third year, while Super Two players earned 23% indicating that the rule now is 25-30-40-60. Players that went through arbitration also earned more than players that didn’t. First year players saw a 50% increase, while second and third year players had a 20% increase. Given that this ignores the benefits of controlling a player for a longer time period, this indicates that signing quality team-controlled players to extensions is a good way of saving money.

In general, hitters were cheaper than pitchers regardless of whether they signed extensions or went through arbitration as well as service time. This could possibly be because teams are worried about signing veteran arms due to attrition. It’s almost certainly due in part to the fact that the arbitration process overvalues relievers. In any event, teams pay only a fraction of the cost for a team-controlled position player whether or not they sign an extension or go through arbitration. It isn’t the case for pitchers though. Once pitchers go through arbitration for their third season, they’re roughly earning market value.

This next table shows the cost of relievers and starters. There aren’t many relievers that sign an extension in their first year of arbitration and therefore that number has little meaning. But relievers start getting extremely expensive by their second year and starters get expensive by their third year. In fact, teams actually pay a premium to keep a reliever in arbitration by the time he has five years or more of service time. This sounds weird but makes sense because it allows teams to commit only one year to a questionable asset rather than being forced to give a multi-year contract. It also in part explains why the Orioles were willing to offer Matusz a contract for $3.9M this offseason. It is hard to find deals for relievers once they have been in the league for more than four years and therefore it is cost effective to maintain a minor league pipeline of potential quality relievers.

Likewise, teams pay close to market value for starting pitchers once they are in their third year of arbitration. For example, Bud Norris isn’t a particularly good starter, but earned $8.8M in his last year of arbitration. The value of tendering a starting pitcher in that third year isn’t due to the cost savings, but the fact that he only needs to be signed for one year. The difference between Jimenez and Norris is that Jimenez was signed as a free agent and therefore the Orioles needed to offer him four years (and still have him on their payroll) while the Orioles could offer Norris a one year term and cut him when he failed to produce.

There is only a minimal premium for going to arbitration with a starting pitcher rather than signing him to an extension before the third year. This indicates that the benefit that a team receives from signing a pitcher to an extension comes solely from the last year of arbitration and any discounts they receive on future free agent years. If a starting pitcher is unwilling to trade away free agent years in return for an extension, then it may make sense to just go to arbitration.

Players earn considerably less in arbitration than the 40-60-80 rule suggests they should. This shows that they’re an even bigger bargain than originally considered and further shows the value of team controlled players. It also indicates that teams don’t save a large amount of money from extensions, but primarily benefit from having players under control for larger periods of time. It is also interesting that position players are better deals than both starting and relieving pitchers, perhaps indicating that it makes more sense to grow the bats and buy the arms.


Anonymous said...

I wonder who will give Mark Trumbo 20 million bucks a year.

Matt Perez said...

Fair enough.

But Fowler and Davis got $9.5M and $12M last year. Things average out.

Anonymous said...

So who are the guys who really got jacked? Davis made half and Fowler made like 75%. Who are the 30 and 40% players in their last year?

Matt Perez said...

Fowler was worth 3.2 fWar @ 8M per WAR or 25.6M. He earned 9.5M. That's in the 30-40% range. CD was worth 5.6 fwar @8M or 44.8M while earning 12M. That's in the 25-30% range.

I'll have access to my data table later today if you'd find a list of the five largest bargains or something.

Matt Perez said...

I wonder if I did a poor job explaining the metric I wanted to use. Would there have been a clearer way to define actual cost/production (cost of free agent WAR * fWAR)?

Anonymous said...

Survivorship bias? Are dfas in the dataset? Extended arms that are paid but not on rosters?

Matt Perez said...

Players like Mike Minor, Alex Cobb and Aaron Crow (all 2015) were included in the dataset. I consider them to have contributed 0 fWAR (as they were injured the entire season).

DFA'd is a good point. I included them in the extended group because I didn't think to remove them. I should have put them into a separate group. I expect that will have a minimal impact on the results though as those players will contribute minimal WAR and minimal salary. But yeah, good point.

I don't see the difference between survivorship bias and extended arms that are paid but not on rosters. What's the difference between a player that's injured all year and one that's in the minors all year?

Bill said...

This does not take into account how the market factors in risk. If we said that the market pays about 70% of production, then the overall numbers fall out as 40/60/80. There would still be positional differences, but that would seem to be what happens.

My bet is that the free agent market pays 70% of the year production as well.

Matt Perez said...

Bill - I don't think you understand the methodology.

Lew Pollis measures the cost of a Free Agent Win by taking the salaries for all free agents and dividing by all WAR produced by free agents in a given year. So, suppose a player was signed to a five year deal at $15M per year as a free agent in 2012. And suppose we wanted to find his value in this methodology for 2015. We would divide his salary ($15M) by whatever production he produces.

Defined as such, the market pays out 100% of production because it only defines the value of a win after the fact.

Since it only measures actual values that have already occurred there is no risk. It is a fact that Chris Davis earned 12M in 2015 and produced 5.6 fWAR. Now that it is 2016, there's no risk that his performance will retroactively change.

Bill said...

A contract signed in 2012 might have nothing to do with how well the guy does three or four years later. Those are different markets. With Davis, they did not pay him to be a 5.6 fWAR player. They could not know that when the market was present.

Matt Perez said...

Bill - This is a retrospective look. In order to determine the quality of a model, you need to know what actually happened. Looking at actual results is a good way to do that.

Bill said...

You are not looking at what happened. You are looking at what would happen as opposed to what was thought to happen.