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Baseball has been trying to figure this problem out since free agency began. Baseball players are free actors and may sign with whomever they choose—and that usually corresponds to whoever happens to offer the most money. Some teams have more money than others. How to keep the big money *cough*Yankees*cough*Dodgers*cough* teams from simply buying championships and ruining all the fun for everyone else?

In the past few collective bargaining agreements, we’ve seen various attempts to solve this problem, with the most recent iterations being that teams would lose high draft picks (usually a first or second rounder!) in the next year’s draft as punishment for signing a free agent. Not just any free agent mind you. If teams were forfeiting first rounders for every single free agent that they signed, that would be chaos. Instead, baseball has made a conscious decision that this punishment should be exacted only for signing “good” free agents. Everyone else can roam where they please. It’s worth saying that we will not question the wisdom of having some sort of free agency loss compensation in this article, but there’s a case to be made that such compensation ends up having some very unfortunate unintended consequences.

For example, how to define who’s “good” and who’s not? Prior to this current CBA, there was the Type A and Type B free agent system in which the Elias Sports Bureau came up with a ranking of who’s who in baseball based on cutting edge stats like batting average, win-loss record, and fielding percentage. Of course, that system had its problems, especially as teams started realizing just how valuable a high draft pick is. It left some players, notably relievers who were tagged with the “burden” of being a Type A free agent out of luck, as everyone knew that they were good, but not give up my first round pick good. There are some things that one would do but that are reserved for a Klondike Bar.

And so we entered the era of the qualifying offer. If teams were so torn up at the thought of losing Maicer Izturis to free agency, they needed to put their money where their mouth was. To be exact, this year, they needed to put $15.8 million of their money near their jaw on a one-year commitment. This solves the problem of defining who was a marquee free agent by letting teams do the work themselves. It also allowed would-be free agents to have a guaranteed contract that they could say yes to. Got stuck by the draft pick tag? You had an offer in front of you! It’s your fault.

In the CBA, the owners and players union somehow hit upon the idea that the price tag for a qualifying offer should be the average of the top 125 salaries in MLB for the previous year. In 2015, this year’s $15.8 million number would have placed a player in 50th place in baseball on the “highest salary” list, between David Ortiz and John Danks. (Yes. That John Danks.) By extending the qualifying offer, a team would have to essentially say that they believed that the player was among the top 50 players in all of baseball.

For some, that’s easy. The Dodgers had already paid Zack Greinke $27 million in 2015, so offering him $15.8 million was actually offering him a pay cut, and the Dodgers would be delighted if he accepted their offer. Like any line that is demarcated in “yes” or “no” though, there are always cases along the borderline that mess everything up. But it’s the borderline cases that are the most interesting. They show us where MLB has (consciously or unconsciously) drawn the line as to what a good player is.

And let’s back up a second. There were twenty players who received qualifying offers this offseason. Colby Rasmus even made trivia (side note: We as a culture need to become more comfortable with the phrase “made trivia.” History is something that people will still care about in two weeks) by becoming the first QO offeree to take up his team (the Astros) on the offer. But you’re telling me that by random chance there just happened to be 20 of the 50 best players in baseball who are all free agents this year? Hooray baseball! It seems that if the goal was to only attach draft pick compensation to players who were in the top echelon of performers, the CBA has swung and missed.

There’s a big problem in how the qualifying offer system is put together, mostly that a team is only mandated to give a one-year offer. Combining a one year deal and the average price for the top 125 players in baseball is actually a bit of a mismatch. In fact, looking over that top salary list again, we see most of those top 125 players are actually signed to multi-year deals.

There’s a well-known practice in the free agent market that teams will sign players to deals that are longer than they should be. The team gets a “discount” up front on the deal, but as Father Time inevitably claims yet another notch on his perfect record, the contract eventually becomes an albatross. In exchange for the ability to cost-shift, players get security and, even if they blow out an elbow, a guaranteed salary for a few years. If all players were forced to accept a one-year deal in some bizarre parallel universe suitable for Wednesdays on Effectively Wild, they would be able to demand more up front, because teams couldn’t cost-shift and players wouldn’t get their security.

At the risk of sounding obnoxious, and starting a sentence with “if a win is worth $7 million on the free agent market” then anyone who projects to be worth a little more than two wins next year—in other words, anyone who’s an average-ish regular player—is worth the $15.8 million. But since it’s a one-year commitment, you don’t have to think about the long-term risk. And the fact that you’re making a QO decision probably means you’re going to have to find someone for that spot anyway. If you like the guy you have, why not make him the offer and hope he sticks around? If he takes it, great! If not, you get a draft pick.

I’m not sure if the people who designed the QO system had this in mind, that the level at which draft pick compensation would be triggered would be at the Dexter Fowler (he got one!) line. It seems that they had something a little grander in mind, although I guess it’s possible that Dexter Fowler was what they planned all along. But, I’m going to assume that the CBA was really supposed to limit draft pick compensation to those who were among the elites in the game. In other words, if we’re going to stick with a one-year offer, how can we set a number that would actually do what the CBA theoretically set out to do?

Warning! Gory Mathematical Details Ahead!

First, let’s look at the top 125 salaries in baseball for 2015. Taking a look at the terms of each contract, only 15 of them are one-year deals. Here’s a breakdown:

Contract Term (years)

Number of Contracts Among Top 125 Salaries

1

15

2

12

3

9

4

27

5

22

6

13

7

12

8+

16

The mean number of years in those contracts is 4.7, the median is 4.5. All of those 125 salaries are based on the idea of a four- or five-year contract. If we really wanted teams to match the terms of the top 125 salaries, then they should be offering $15.8 million over four years, which would be $63.2 million of total outlay.

We’re going to assume that teams price their contracts to their estimation of the total value that a player will grant them over the course of the contract. To take Clayton Kershaw’s contract as an example, a contract which will pay him $215 million over seven years, we’ll assume the old $7 million/win standby and that the Dodgers project that they will get 30.7 wins worth of value from Kershaw over the life of his contract. (For the initiated: Yes, I know that’s a bit slapdash. “Net present value.” “Factoring in inflation.” Happy?) or an average of 4.4 wins per year. But knowing what we know about aging, the Dodgers more likely to see the 7-win type seasons up front and the 2-win seasons on the back end. If the Dodgers had paid Kershaw for the 7-win season he had (and that everyone knew was coming), they’d have to pay him $49 million. But they got a bargain at $30 million for this year. Call us in five years.

But now let’s see what sorts of free agents-to-be are getting qualifying offers. The list of the offerees, along with their ages next year:

The mean age is 30.7, with the median and mode both checking in at 30. Our “average” qualifying offeree is 30. If he’s a pitcher, he’s a starter. If he really is worthy of one of the top 125 salaries in baseball, we know that those generally come attached to a four- or five-year deal. We expect that because hitters tend to peak on average around age 27 (it’s a little more complicated for pitchers, but roughly the same age) it’s all going to be downhill from here, on average.

But let’s look at players who played between ages 30 and 33 (what a four-year contract would cover) and see how much of their value between those years is concentrated in their age-30 season. I used Baseball-Reference’s WAR figures from 1999 to 2015 and took only players who played significant time (either 250 PA or 50 IP) in each season (ages 30-33).

The results:

Age

Total WAR for all hitters in sample

Percentage of WAR in timeframe

Total WAR for all pitchers in sample

Percentage of WAR in timeframe

30

472.4

30%

184.0

29%

31

443.9

28%

174.8

27%

32

381.1

24%

171.2

27%

33

268.7

17%

111.5

17%

Total

1566.1

100%

641.5

100%

It looks like about 30 percent of the total value that a player is going to produce between the ages of 30 and 33 will be produced at age 30. Since we’re assuming that the actual total outlay for this “contract” should be $63.2 million (four years at $15.8 million), ponying up for just the one year (age 30) in which they could expect 30 percent of the production of he next four years would mean that a team should spend just shy of $19 million ($18.96 million, to be precise).

The other nice thing about “forcing” a player to sign a one-year contract (if you’re a team… it’s not so nice if you’re a player) is that if a player gets injured or suddenly loses effectiveness, you’re only on the hook for one year. In theory, though, if we’re going to model the actual cost of what a one-year contract would really cost a team, we need to account for the risk that comes from having to live year-to-year when, in baseball, the spectre of a significant injury is always the 10th man in the lineup.

Among players who notched at least 2 WAR in both their age 28 and 29 seasons since 1999, six out of 137 (4.4 percent) ended their careers before age 31. Yikes! Because the qualifying offer artificially forces them to give up the security of what we assume should be a four-year contract, we need to price that risk into the salary as well. If we assume that after his age-30 season, our player would be at liberty to go out on the free agent market again and get paid for his 31-33 seasons, presumably recouping the rest of the $43.8 million that he is foregoing by being forced to take a one-year deal for his age-30 season, we have to account for the fact that there’s a 4.4 percent chance that, by virtue of playing his age-30 season, something would happen that would render his earning power for ages 31 to 33 to $0.

Using expected value theory, a player should ask for 4.4 percent of that $43.8 million or $1.92 million. Add that to what we found earlier and we get something just shy of $21 million for a one-year offer.

Would You Pay $21 Million for One Year of Howie Kendrick?

That’s really the question, isn’t it? If the qualifying offer system is going to continue to be based on a one-year offer, and we want to limit free agent compensation to those who are in the top 50 or so players in baseball, then the price tag needs some adjusting, probably to about $21 million. Again, sticking with the $7 million per win rule of thumb, a player would need to be worth three wins to merit this sort of salary, which is an above-average regular.

And that would have cut down on the number of offerees, almost by definition. I suppose the definition of what players are “good enough” for draft pick compensation is as much aesthetic as it is empirical, but I’m wondering if the people who wrote the CBA really intended it to attach draft pick compensation to Howie Kendrick. Maybe the next time the CBA is being negotiated, a few minor adjustments might make for a better system.