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:

Non-Adjusted Cost of a Win in Free Agency Offseason Cost of a Win in Free Agency 2018 $8.1 M/WAR 2019 $6.8 M/WAR 2020 $8.0 M/WAR Does not include adjustments for qualifying offers or potential overestimation of playing time.

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:

Estimate of the Cost of a Win in Free Agency 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.