The Cost of a Win in Free Agency in 2020
After a few cold, dreary, quiet hot stove seasons, free agency picked up its pace this winter. While Manny Machado and Bryce Harper got $300 million deals last offseason, it took until nearly spring to get those contracts finalized. This offseason, we’ve seen Gerrit Cole, Stephen Strasburg, Anthony Rendon, and Zack Wheeler sign for more than $100 million, and with the new year just eight days old, only a handful of decent free agents remain. While large deals and total spending near $2 billion have captivated us this offseason, it’s worth exploring what has made this winter different from years past. Is it just timing? Is it this class of free agents? Have teams changed their spending habits? Is the cost of a win still linear? A useful tool when examining those issues it to try to determine how much teams are paying for a win above replacement in the free agent market.
While putting dollar figures on players isn’t the most feel-good task, it’s helpful for framing conversations about costs in free agency. From the front office perspective, it helps to determine which free agents are good values and a worthy investment of resources compared to other free agents and veteran players. It also helps frame the value of younger players who have yet to reach the full six years of service time necessary to hit the market by showing the alternative cost to obtaining similar production. On the player side, these types of valuations tend to show how underpaid players are prior to reaching free agency, given the low cost of their tremendous on-field value compared to similarly productive free agents.
There are a variety of ways to go about determining how much teams are paying per win on the free agent market. Matt Swartz, having found that projections tended to overweight free agent player production and playing time when considered in the aggregate, instead considered actual production of past results to determine how much teams were paying for a win. He also used all players with at least six years of service time to account for players aging over the course of a contract. He acknowledged that there might be issues with including players on extensions. To be clear, Swartz wasn’t wrong about the way he formulated his dollars per win, but another approach can be helpful, and, if we are to look at the current offseason, necessary.
In trying to keep things as simple as possible, I looked at free agent contracts and current projections and used simple aging curves to try to determine the current cost of a win on the free agent market. The aging curve essentially removes half a win (0.1 WAR for relievers) every season after a player’s age-30 season, and three-quarters of a win (0.2 WAR for relievers) after their age-37 season. And while aging curves are rarely used for these purposes because there are rarely free agents who are that young, the projections were increased by one quarter of a win through the age-27 season. Inflation, coupled with discount rates, presents an interesting problem, but rather than having them cancel each other out by increasing values over time for inflation and then decreasing them because money is worth more now than it would in the future, I opted to leave both aside. Since offseasons appear to change from year to year, this method isolates a single free agent class at a time without concern for how players were paid in prior offseasons.
Essentially, I took the total projected WAR over the life of the contract and divided that number into the total dollars paid over the life of the contract for a non-adjusted dollars per WAR figure, which we see below. Later, I will adjust those figures to account for the qualifying offer and the likelihood that projections are overrating playing time and production. To provide some comparisons, I’ve included the last two winters as well:
| Offseason | Cost of a Win in Free Agency |
|---|---|
| 2018 | $8.1 M/WAR |
| 2019 | $6.8 M/WAR |
| 2020 | $8.0 M/WAR |
A quick note on the years listed above: because offseasons span two calendar years, the years listed above correspond to the latter of the two. So 2018 above refers to the offseason following the conclusion of the 2017 season. We’ll make the necessary adjustments in a moment, but first look at how the last few offseasons have gone. Last offseason stands out. I was concerned that Manny Machado and Bryce Harper’s contracts might have unduly skewed the numbers, but removing them made no difference. What we see is similar spending after the 2017 and 2019 seasons when we look at the value teams paid.
The difference between the two classes is that teams have spent about 40% more in total this offseason because the free agent class was much better. If teams had spent on a dollar per WAR basis in 2019 like they did in 2018 and 2020, the free agency totals from last year would have been slightly higher than this offseason so far, though this year will still likely be higher after Josh Donaldson, Marcell Ozuna, and Nicholas Castellanos sign. Some form of lack of competition suppressed free agent prices a year ago, and that hasn’t been present this season. Even so, we are still only back to 2018 levels, when the winter was also a slow one.
The table below adds in the value of the qualifying offer, which I’m estimating at $6 million based on prior draft pick valuation research. In addition, I’m estimating that projections overshoot the mark on the whole by 10%, which is less than Swartz found, but I want to be a little more conservative. That yields the following results:
| Offseason | Cost of a Win in Free Agency |
|---|---|
| 2018 | $9.3 M/WAR |
| 2019 | $7.8 M/WAR |
| 2020 | $9.1 M/WAR |
This winter has certainly been better than the last one. Teams paid more for wins in 2018 than they have this winter, but that winter’s class was of a considerably higher quality. When the last three years are taken together, the cost of one win on the free agent market is $8.6 million. That lines up pretty well with a similar study that also examined the 2017 class. Given that overall payroll hasn’t moved during that time, it shouldn’t be a huge surprise that the cost of a win on the free agent market has remained relatively stable. In the introduction, I raised questions regarding the linearity of a win, and if spending habits by teams have changed depending on their financial or competitive circumstances. I’ll explore those issues in the days to come.
Craig Edwards can be found on twitter @craigjedwards.
The cynic in me suspects that the speed of this offseason’s FA market signings was due to collusion by owners to stave off anticipated arguments in the upcoming labor negotiations. I find it highly suspicious that after two years of foot dragging and preposterously lowball deals for players owners suddenly opened their wallets (somewhat) just before the CBA expires.
I can’t wait for Apple, Microsoft, and Google to collude in order to sell me a cheaper computer.
You joke, but Apple and Google were among many silicon valley companies who literally were colluding with each other to drive down the price of labor.
https://en.wikipedia.org/wiki/High-Tech_Employee_Antitrust_Litigation
Beat me to it. Those companies literally colluded to suppress the price of labor!
I find it difficult to imagine that the owners would do this. For one, exactly how do they pick the teams who have to spend more? It seems more likely that there were more teams that were desperate.
I don’t think there are any CBA effects here, but if there were, I’d look to what the owners expect the CBA will look like after negotiations happen. If they expected free agent salaries to increase as a result of the CBA changes (which, IMO, is probably less useful to the membership than arbitration expansion/reform), then they might want to spend more now.
The league and teams already collude on arbitration. Though it’s more of a gray area. It’s not a stretch that they communicate in a similar, more secretive way for free agency. Not like they haven’t done it before!
This is possible–that they colluded before and now they just stopped. The problem is that before, it would have taken an unprecedented level of cooperation, because before it was them just all agreeing behave a certain way (don’t offer FA contracts to other team’s FAs, keep the length under a certain amount). Those are easy decision rules that don’t require a lot of cooperation. The previous FA markets didn’t lend themselves to an easy decision rule like that.
It’s orders of magnitude easier to collude then it ever has been. The front offices are all run by people schooled off using the same “analytics” to rate players.
Then we can always go to the next level where I give you my PGP key and you give me yours and we communicate through free email accounts.
Ah, I guess we found AEC/JimmieFoxx’s new username, given the sudden surge in downvotes for anyone who disagrees with him (and upvotes here).
maybe I’m just cynical but I don’t think teams can keep a lid on that kind of thing. Like in sadtrombone’s theoretical, the owner of the Pirates wouldn’t throw a public shit fit when they get a turn at the “you have to spend money this year sorry” spot? These guys stink at keeping their mouths shut as it is, let alone a company like Liberty Media exposing themselves to SIGNIFICANT downside risk if they get caught hiding something from shareholders.
Two years ago, it was a perfect storm of a weak free agent class, too many tanking teams, and only the Red Sox willing to surpass the luxury tax line. Last year is harder to explain, but there are still reasons behind it other than collusion such as smarter front offices being less willing to pay top dollar for players in their late 30’s (or beyond). This offseason is more of an expected return to form rather than an outlier.
Or could it be that this year we had superstar free agents coming off incredible years who had few question marks about historic performance and personality issues, while last year was headlined by one “superstar” who had exactly one superstar-level season 4 years earlier, and one who admitted himself that he is lazy, is known to be a dirty player, and who had very good but not outstanding offensive numbers, and declining defense?
The reason I’m glad you did this (and why I find the last couple paragraphs so frustrating) is because the method here is, contrary to what Craig writes here, a far superior way to estimate the cost of a win. When you go to the donut store and you order a dozen donuts, you know there will be 12 donuts inside. When teams go shopping on the free agent market, they don’t really know what they’re going to get. Their expectations are based on projections. Teams are paying for projections.
So when someone says that the projections “overshoot the mark by 10%”, it should be totally irrelevant to the exercise unless we assume that the proprietary team projections are somehow coming up with outcomes for free agents that are, in aggregate, 10% higher. That’s a pretty big logical leap and since we can’t actually use the team projections in future analyses, it’s sort of a waste of time to go for that anyway unless you increase every free agent projection by 10% now and forever.
There’s a seemingly widespread misconception out there that because a team paid X dollars for a player, and they got Y wins, then the team decided they were going to pay X to get Y. That’s obviously ludicrous; the Angels are not paying this much money to Albert Pujols for that level of production. What that measures is return on investment, not expectations. Let’s put that old, flawed definition of the cost of a win to rest in the new decade, shall we?
Mmmm. Donuts
May those ill-gotten donuts be forever on your head!
Well, building on this a bit, you’re paying more for the first donut you eat that will provide significantly more utility to you (WAR), in theory, than the 12th donut, which will probably just make you sick. It’s actually a perfect analogy for the Pujols contract, except donuts 8-12 were inedible and everyone told you so.
Building in nonlinearity of WAR allows you to say that the back end of a big contract is basically a loan on the WAR you got on the front end I don’t even think you need to think about the marginal value of WAR as nonlinear for this to work- but you can specify that parameter from the data!
Well, except it’s likely the opposite here. You buy 12 wins in a single year that’s way more valuable than buying 1 win in 12 consecutive years. 1-win players are just way more common. That’s part of the reason why Pujols got that huge contract in the first place, was the expectation he was going to deliver 6-win seasons regularly.
To analogize further to donuts, the free agent contract is where you are purchasing a subscription with an ironclad contract, that will deliver to your household a mystery number of donuts every single day/week/month/year. You don’t know exactly how many donuts are going to make it into the box; it could be 6, it could be 3, it could be 1. You have a sense based on how many donuts will make it into the box at the beginning but not exactly, and it will bounce around a bit at the beginning of the contract. You also know that the number of donuts declines over time (not always, it will bounce around a bit, but the trendline is down) while your subscription price stays the same.
In the Pujols case, the Angels thought they were buying six or seven donuts a year–sometimes a little higher, sometimes a little lower–and that the number of donuts would decline by, say, one every other year until it reached zero. Instead what they got was 3 donuts in year one and three, came to take donuts from you in year six, and by now has settled into a box of zero donuts. Saying that this is what the Angels thought they were buying when they signed up for that donut subscription is a bit much.
yeah, I didn’t mean it quite that way- I meant more that the first donut has a higher consumption utility (your 12 donut example in the first year) and you get diminishing consumption utility from the donuts as you eat them. Your version is better, because donuts are essentially a commodity, and some years you get more donuts than others.
In my example, sometimes the donut is freakin awesome, sometimes the donut is terrible and from Voodoo (which are bad donuts), and there’s a higher probability you get better donuts earlier on, but it’s not guaranteed.
It also appears likely that the donut salesman neglected to mention that the subscription was starting with donut 3 (by which I mean that Pujols is probably a couple years older than he lets on).
Actually, depending on the doughnut store, you might 13 doughnuts in your box instead.
In looking a little bit at recent free agents contracts, I went off on a little tangent and noticed that there were 6 mega-contacts ($150 million+) originally set to expire after the upcoming 2020 season, 3 hitters (Prince Fielder, Jacoby Ellsbury, and Troy Tulowitzki) and 3 pitchers (Clayton Kershaw, Masahiro Tanaka, and Jon Lester).
We often think of hitters aging somewhat gradually and pitchers breaking, but I find it fascinating that in this case the 3 hitters all “broke” and none of the pitchers did. Of course Tulo did first have several good years at the front end of the contract, making his deal pretty decent from a team perspective. This is also a really small sample size, so I am not claiming hitters are riskier than pitchers, but I did find this sample quite surprising.
That may be a small sample size, but I think it’s telling that WAR pitcher leaders are mostly 30 and above, and WAR batter leaders are mostly below 30. We should change our mentality that hitters age better than pitchers.
We think pitchers break more easily, but I believe that’s more for prospects, who have not yet shown the ability to throw full seasons at the intensity/frequency required in MLB. Pitching is very hard on the elbows and shoulders, but those whose bodies are capable of handling this, don’t face other injury risk as much as hitters do.
I believe that pitchers with a good injury history into their mid to late 20s, will actually have less injury risk going forward than a comparable hitter.
This makes sense because pitchers’ movements are much more predictable. They pitch, sometimes they field/hit, but they’re not expected to run, dive, or otherwise make unpredictable movements as much as hitters do.
So in a sense, pitchers like Kershaw, Tanaka, and Lester at the time they signed their big contracts were already selected based on their ability to stay relatively healthy. Elbow injuries in particular will always be some risk, but these pitchers had already demonstrated the ability to hold up.
I also think that the skills required for a hitter to stay elite don’t age as well. Reflexes, vision, flexibility for wide ranges of movements, etc.
Two words: survivorship bias
Scott Boras has already reached a billion dollars in signings. He must’ve maxed out his charisma stat
Pretty pumped to see how much the marginal value of a win increases going from win to win (i.e. a 1 WAR player might get $10 million per win or whatever, but a 2 win player probably gets $12 million per win). This has always been my biggest gripe with $/win- that amount increases in a nonlinear fashion as the amount of players at that win level decrease, but it’s an open question about what that function looks like.
This point should be emphasized over and over again.
Nobody in the history of MLB saw a non-reliever and thought “I expect 1 WAR from him” and “this guy is worth $9M” at the same time.
Nobody.
It seems that most 1 WAR players get around $3M-$5M deals. Some can’t even get major league contracts. And at the top end, players like Rendon seem underpaid compared to the $8.0M/WAR figure Craig found too. Rendon is projected for 5.6 WAR by Steamer so he “should have” gotten $44.8M/year, but actually only get $35M/year. So which class of free agents is driving up the $/WAR figure to $8.0M? I suspect it’s actually the “middle class”, which is ironic given how many articles have been written in recent years about how free agency is killing the middle class.
I don’t think $ per WAR has ever been linear. It’s always cost more for an extra win the better the talent level gets. It’s a mistake to directly compare the contracts given to superstars compared to those given to 1-2 win role players, and relievers skew the results even further.
Why would the “quality” of an offseason’s free agent class influence the $/WAR figure? That variable is controlled for with the use of WAR projections.