The Baseballsphere Blog

Two years ago I wanted to estimate the market values of some of the free agents coming out of the 2022 MLB season. So I did some analysis then comparing the expected annual bWAR of recently signed free agents to the average annual salary they got in their contracts. It gave me interesting insights on what to expect in free agent contracts that year.

Just over a week ago I wanted to see if Juan Soto was about to be overpaid, based on the same analysis. I updated a lot of things about my previous analysis, and learned that yes, he was indeed about to be overpaid. But before I could publish this article about it, he actually did sign. So now I’m here to tell you that he was overpaid, and what I’m basing that on.

It’s not based on Steve Cohen’s ability to pay. The owner of the Mets’ pockets are so deep, this kind of money barely affects him.

No, this is about whether the average annual value of his contract is in line with other recent free agent contracts for the most talented players in the game, given his age and the value he provides.

All the players used for comparison in this analysis are position players, with the partial exception of Shohei Ohtani. For him, I added his pitching WAR to his position player WAR.

For the table and charts below, instead of using just Baseball-Reference’s WAR (bWAR) as I did the first time, I averaged it with Fangraphs’ WAR (fWAR). When adding in Ohtani’s pitching WAR, I weighted bWAR more heavily, as I trust it more (it considers all of the pitchers’ results, and not just 37% of them like fWAR does).

I didn’t usually use all the WAR accumulated over the player’s entire career for this. It was always the last few years, as of the time of their signing. How many of those last few years to use was a judgement call -whatever span of seasons I felt best represented who the player was as a player at that moment. In the second and third columns of the table you can see the years I picked, and so can cross examine my choices if you want.

To get WAR per 150 games, I got their WAR totals over the chosen years, divided by the number of games played, and multiplied by 150. I only used players for whom this value was at least 3. Below that, in my judgement, WAR starts behaving less like a cumulative statistic, and more like a rate statistic, and so the assumptions on which this analysis are based start to break down.

The next column is the first year of “free agent” pay. I put “free agent” in quotes because I’ve included some players who signed extensions that overlap their free agent years. For those players, the year in this column isn’t the year the extension begins, but the year their free agency would have begun. We only consider the portion of the extension that overlaps what would have been free agent years, because the previous parts of the extension will usually provide much lower salaries, and that would skew these results. As it happens with the players in this list, this year is never more than a year delayed.

In next to last columns, you’ll see me convert into 2024 dollars the annual amount paid to the player per WAR. In most cases I’m moving past amounts forward in time, but in the case of Shohei Ohtani’s almost entirely deferred $700 million contract, I’m first bringing that deferred money back to 2023 dollars, which results in the $460 million estimated value that they’re using for the purposes of the Competitive Balance Tax. Then I move that forward one year to 2024 dollars. When you do that, you get that the Ohtani contract is actually a pretty good deal. (This devaluing effect of deferred money makes it wrong to directly compare the dollar totals of the Ohtani contract to those of the Soto contract.)

That last column is the one I’m plotting in the chart below. I got it by dividing the average annual salary of the contract by the player’s evaluated WAR per 150 games. So you have millions of dollars per WAR. This I plotted against the season after which they signed the contract or extension. Each data point is labeled with the player’s name, their age on June 30 of the first year of their contract, and their age on June 30 of the last year of the contract. The results are as follows:

There are a few things to note here. One is that, over time, the range of values you get each year is about the same, once you make the inflation adjustments. That gives me confidence in comparing 2018’s free agents against 2024’s.

So that makes it easier to look at this chart and decide yes, Juan Soto was overpaid. He’s a clear outlier.

But not so fast. Look at the ages that follow each name. If you focus on the first number, you’ll notice that the top of the chart is populated almost entirely by players who were 28 or younger in their first contract year, whereas below that almost everyone is over 28. Youth appears to be a factor in accessing higher dollars per WAR.

We can get a clearer view of the age trend by plotting millions of dollars per WAR against age as of the first contract year. I have intentionally left Juan Soto out of the plots below, because the idea is to compare his result to what the market had done before him. (Ages are not rounded in this next plot; they are precise to the day as of June 30 of the first year of the player’s contract.)

There is a trend there to be seen, which the R² of 0.33 confirms as a moderate relationship. But it is not as obvious to the eye as it might be. It is easier to see if we group together all players of the same age in years, and average their numbers. Here is what that looks like:

A definite downward trend. Note that there are much fewer players contributing to the average at the extremes of age, especially just one each for the age 33 and 34 player groups. Those few players could really alter the slope of the fitted line. So I made multiple versions of both plots, some with those players at the extreme ends left out, some with Juan Soto put back in. The line was pretty similar in all of them. I picked one that had a slope that was in the middle of the pack, and I used that line in my next step. (For the curious, the line used is y = -0.3248x + 15.51 where x is the player age and y is the millions of dollars per WAR they make.)

That line provided me the expected average value of millions of dollars per WAR that players of a certain age in their first contract year would make. I then just subtracted that from each player’s actual number to get an amount, in millions of dollars per WAR, above or below this average that the player made. Here is the new version of the first plot when redone in this way, to remove age as a factor:

So that changes things a bit. Juan Soto is no longer an isolated outlier on the high end, but only the third worst overpay after Anthony Rendon in 2019 and Freddie Freeman in 2021. Yet it’s the 15-year duration of that overpay that will make it worse in the end. Freeman’s contract is 6 years long, Rendon’s 7. Neither contract goes past their age 37 season; Soto’s goes all the way to his age 40 season. He’ll surely have been relegated to a full-time DH well before then, and will rack up a great many years underperforming his contract.

I’d like to do another analysis along these lines that considers the contract’s duration as well. Maybe by looking at overall contract value? Or perhaps overall amount of risk? This could get complicated – I’d probably have to get into aging curves to handle that properly. My point being that such an analysis would probably make the Soto contract even more of an outlier, more of an overpay.

Another thing we can see on this chart that many people may find shocking is that Shohei Ohtani may actually have been underpaid. Because future dollars are worth less than today’s dollars, and he’s paid almost exclusively in future dollars, his $70M per year sounds like more than it really is. Plus, he’s been consistently producing over 9 WAR each of the last 4 years (only the first 3 of those counted in this analysis). Not even Mike Trout in his prime was that consistent. He produces more value than anyone else on this list. His 9.44 WAR/150 G is more than 50% higher than 5th place Juan Soto’s 6.21. Heading into the 2024 season, when he knew he wouldn’t be able to contribute with his pitching, Ohtani turned himself into an elite baserunner by putting in a lot of work on learning that craft. The guy just finds a way to excel and provide value, whatever his circumstance. If future injuries don’t tank his value the way they did for Trout, he’ll be worth every penny.

As a Red Sox fan, there are a couple of other data points on this chart that are interesting to consider. One is Rafael Devers. I have always thought of his 2022 extension as a big overpay, 50% higher than what he should have gotten. But in this new chart, though he is still on the high end of things, I’d say he’s a little shy of being an overpay.

Finally, there’s that Mookie Betts contract. We’ve now learned that had the Red Sox just offered him the contract that the Dodgers eventually did, he’d have signed and would still be a Red Sox today. But the Red Sox were really down on big contracts at that time, and wouldn’t offer Betts what he wanted. Well, here we see that Betts’ contract with the Dodgers is actually one of the biggest bargains in the game. The Red Sox were wrong in their offers, Betts was right to reject them, and my favorite team let my favorite player get away because they were just so excessively stingy. It’s hard to forgive that.

They’ll have some chances soon here at a do-over, though. Jarren Duran is the real deal, and should get paid a lot. Not just for his great results on the field, but for how his constant hustle inspires his entire team to try harder. And I am expecting upcoming prospects Roman Anthony and Kristian Campbell to become as valuable as Betts was. The Red Sox can pay them what they’re worth, or they can offer what they’re comfortable paying, and watch them all walk. Please, Red Sox, learn the lesson from your mistakes with Mookie Betts. You could have a great team for the next decade if you just pay your stars what they’re worth.