What Did Teams Pay per Win in Free Agency?

How do projected wins translate into salaries in free agency? That’s a fundamental question that front offices have to answer and, in fact, have had to answer ever since free agency opened up baseball’s labor market after the 1976 season. No, no GM back then was using Wins Above Replacement or fancy-pants computers spitting out ZoRPs or Stonker projections. But decisions are always based on some kind of projection, whether that exercise is explicit or not. When Grizzled Greg the GM went after a player for X hundreds of thousands of dollars after the 1976 season, he was still estimating how the player would play in the future and whether that benefit was worth the cost. Heck, I’ve never made a taco-based projection system. Still, when I see a taco, I’m projecting whether or not the DAR (Deliciousness Above Refrigerator) is worth the dollars that will be debited from my bank account.

Naturally, one of the ways we estimate player salaries has been a linear relationship between dollars and wins above replacement. There’s still a debate over whether player salaries should be treated in this way. Many analysts have argued that the price of wins should not be linear because of the efficiency of getting a lot of wins from a single player. After all, there’s a limit on roster size and utilization; you can’t just sign five one-win first basemen and combined them into a horrifying amalgamation whose twisted, fear-inducing form approximates a Freddie Freeman season. And even if you could, I wager that the MLBPA would file some kind of grievance about players being used for twisted medical experimentation. Well, at least players on the 40-man roster.

Matt Swartz is probably the most prominent advocate for the opposite view, that worrying about whether to add a four-win player instead of a pair of two-win players don’t really come up in the real world all that often. I’ve come to side more strongly with the majority in recent years than I used to, simply because I believe — though I can’t prove it conclusively — that good teams are becoming better at not leaving as many obvious holes. For teams like the Rays, Dodgers, and Padres, as well as other teams that prize serious depth, replacement level is probably higher than replacement level.

Wherever you stand on how wins ought to be valued, the conclusion about what has actually happened has been the same: In free agency, teams have acted as if wins are linear. This was true when Andrew Zimbalist looked at it in Baseball and Billions, remained true over decades of analysis, and still looked true when my colleague Craig Edwards checked up on the issue last year.

With most of the signings for this winter complete, and it looking rather unlikely that an enormous Rick Porcello payday will shatter baseball’s assumptions, I thought this was a good time to check up on free agency in the time of cholera COVID-19.

Summed for an entire free agent class, there tend to be a larger number of projected wins than actual wins when looking back in hindsight. I’d actually argue that this is not an error. When you’re signing a player, you’re not actually signing a player to play them; you’re signing a player for the option to play them. For teams that aren’t the Colorado Rockies, players tend to lose playing time long before they reach replacement level. If you have a one-win player under contract for another season and you bench them because your hot new prospect is coming to the majors, you still have the one-win player even if you choose not to use him. These differences generally aren’t massive, but you shave a few missing wins here and there, and it adds up to a real monetary difference.

Since 2021-2025 hasn’t happened yet — if it has where you are, let me know because I’d like to buy some stats from you — we have to go with the projected wins. Looking back at the last two offseasons, I projected an implied value per win in free agency of $7.4 million after 2019 and $7.1 million after 2020. In light of the shortened 2020 season and its undeniable financial consequences, I’ve generally been using $7.0 million this year based on, well, a wild-ass guess.

The WAG appears to have been too high. Ignoring split contracts, which have their own complexities, and free agents from overseas leagues, who are trickier for teams to evaluate, I get $1.39 billion in guaranteed future salaries. Tacking on an additional $6 million apiece for the two players with qualifying offers, using the same methodology that Craig used, I get $1.41 billion for 240.4 projected wins or approximately $5.87 million per win in free agency. As Craig did, I’m also assuming, given the general roughness, that the issues of inflation and discount value more or less come out in the wash; we only have a 130-some player sample size, so errors in the margins don’t make the list of our top problems.

How much of this is 2021’s economic environment? The answer appears to be: a lot. While teams typically get the best-projected deals early in contracts, the implied year-by-year value of a win from these contracts is much steeper than typical.

You expect to see that slope, but it’s much higher than I’ve gotten in past seasons. In both of the previous two offseasons, I got a value per win in the fourth year 40-45% higher than in the new contracts’ first year. This time, the difference is 84%! The caveat, of course, is that there are only a handful of players who got three or more years in their contracts. Looking only at the players who received multi-year deals, ZiPS comes up with $962.85 million and 140.7 WAR, or $6.84 million, closer to what I expected coming into this winter. That left the players on one-year contracts getting paid a projected $4.37 million per win.

For a linear model, I used $563,500 + $4.78 million x WAR, with a $209,000 standard error and the model’s 5% and 95% for that multiplier at $4.36 million to $5.19 million.

There’s a lot of heteroskedasticity here, meaning that the error is not consistent across the range of the input variables (the projected wins). That’s not a big deal given how weak our data set is, but it should at least be mentioned. Looking at wins from a discrete standpoint, by treating each win in a projection as a discrete variable (first win, second win, third win), the model does appear to be less linear. I’m also only using 2021 salary and WAR to keep any issues from teams evaluating wins as significantly more valuable in the future from being a confounding variable.

That certainly looks non-linear, but there’s are a few significant problems. We still have a very small sample, and the result isn’t very robust; the r-squared does not improve! The second is that even if we’re only looking at 2021, teams may simply be more willing to pay a player more per win in 2021 than otherwise because it enables the team to secure that player’s services in future seasons.

So, what does this all mean?

From this spotty data, there are a couple broad conclusions I think we can draw. First, teams are generally reducing how much they value 2021 wins. Second, wins might be becoming more non-linear, but if they are, the effect is likely still very small. And lastly, while there are storms ahead due to the upcoming CBA negotiations, I at least consider it a promising sign that in the few contracts that go for several years, the valuations are far less bleak than in the one-year contracts. Perhaps being optimistic is a risky frame of mind to be in given the league’s unending ability for self-inflicted damage, but I’ll be happy to take any small indication that the pandemic won’t be used as a permanent drag on salaries.