Is the Cost of a Win in Free Agency Still Linear?

It’s no secret that free agency has changed over the last decade. As more teams have embraced analytics by focusing on paying for future, rather than past, performance, and owners have pinched pennies, we’ve seen slower winters, and in the case of last offseason, teams paying significantly less for a win on the open market. This offseason has seen a welcome return of activity, with good players receiving top-dollar contracts. When we consider the health of free agency for players, the big deals seem to grab a lot of attention, as with Gerrit Cole, Anthony Rendon, and Stephen Strasburg‘s this season, and Manny Machado and Bryce Harper’s a year ago. Mega-deals create the impression that all is well, and the size of those deals can have an outsized affect when calculating dollars per win, as in my piece yesterday on the cost of a win in free agency. But the players who don’t receive those big contracts deserve a bit more attention because it is possible that as free agent spending has shifted, the money teams are paying for wins may no longer be linear.

When we talk about the linear cost of a win, we’re talking about there being a uniform amount teams are generally willing to pay per win on the free agent market; if the cost of a win is $9 million, a three-win player gets $27 million, a two-win player gets $18 million, and a one-win player receives $9 million. And while we recognize the three-win player doesn’t actually receive a one-year deal worth $27 million, when the money is spread over a multi-year deal and the presumed decline from aging is factored in, the wins paid for over the life of the contract come out in roughly that manner. For example, Hyun-Jin Ryu is projected to be roughly a three win player in 2020. But over the course of four seasons, he is likely to be worth closer to nine wins; he signed a contract for $80 million, which comes out to right around $9 million per win. Not every case fits so neatly, but Ryu is one example.

The question now is whether the above is still true. In 2017, Matt Swartz examined the seasons through 2016 and found that the cost of a win was still linear. Since then, a narrative has emerged of slightly lesser players getting squeezed. Heading into the 2017 season, Travis Sawchik discussed baseball’s embattled middle class as players appeared to be getting frozen out of free agency. He followed that up in 2018 after another slow winter provided more evidence of a market in dire straights. Providing further support, the crowdsourced contract estimates our readers provide as part of our annual Top 50 Free Agents exercise have generally overshot free agent contracts under $40 million the last few years.

To flesh out that narrative further, and test whether the cost of a win is linear, I separated free agents into two groups: players with projections of at least two wins, and players below that level. This demarcation separates the average to above-average players from players below that bar. Over the last three seasons, here are the cost of a win figures, adjusted for the qualifying offer and with a 10% adjustment due to projections overshooting playing time and production:

Based on the above, there’s a pretty good case to be made that WAR is still linear. We do have a slightly larger change this season than from years’ past, but it’s still not massive, and over the past three years, the difference is just a 6% drop from above-average players to below-average players. We could argue that the change this season shows a difference in the way players are valued, but given the seeming drop in pay for below average players the past few years, it is awfully odd to find that there’s actually almost no change in those offseasons. I moved the groupings around a bit in terms of projected WAR, and took different subsets of the groups above, but the above data held. But there is one major problem with the dataset that could be deceiving our totals: relief pitchers.

Setting the bar at two wins generally sets above-average players apart from below-average ones, but that’s not the case for relievers. A two-win season for a reliever means that pitcher is one of the best of his kind in baseball. A one-win relief season is a good, and even half a win is a little above average over 60 innings pitched. As a result, including relievers in the below-average group means there are a bunch of above-average players in the dataset. I took relievers out; this is what the resulting the table looks like:

Now, the difference is obvious. The $1.3 M/WAR change we observed in the previous table seems more easily explained by the lack of quality relievers in this free agent class. Once relievers are removed from all years, we see the disparity between above-average and below-average players. Because the above-average players are the ones making all of the money, the change is obscured in the total cost of a win in free agency, while relievers hide the change for below-average players. Once we separate relievers out, we see a 25% discount in the cost of a win for below-average players. The last two years, the change has been over 30% and it has the chance to continue to drop this season. There are 17 more free agents on our Free Agent Tracker with projections between 1.0 and 1.9 WAR. Only Nicholas Castellanos seems likely to do much better than the current $6.7 M/WAR figure, and many of those remaining players seem likely to do worse.

The numbers above also help explain some of the curious non-tender deadline activity from earlier in the offseason. While César Hernández actually has a projected WAR just above two, players like Kevin Pillar, Jonathan Villar, Travis Shaw, and C.J. Cron might have been decent values in a linear free agent market. That’s not the case when the alternatives in free agency are cheaper. Overall, it’s pretty plain to see that the cost of a win in free agency is no longer linear given the huge discount being applied to below-average players. As for why this is happening, there are multiple reasonable explanations, including the availability of more good, young players, good teams not adding once they’ve reached a certain expected win total threshold, and bad teams not trying at all. The win-curve and a team’s financial outlook are topics that will be explored in my next piece.