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Did the Mets overpay for Juan Soto?

tomisphere2 Comments

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.

There shouldn’t be a consensus pick for AL Rookie of the Year, but it seems there is

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So by now (late October 2024), all votes are in for 2024 AL and NL Rookies of the Year, so at this point anything I say in this article is me ranting and complaining about something that I think has already happened, but won’t know for certain has happened until three weeks from now. Nothing I can do to change it now!

But if you read articles like this one, you get the idea that Colton Cowser is the consensus pick to be AL Rookie of the Year for 2024. Or at least it’s down to him and Luis Gil.

Then there’s this betting odds line from when there were 5 days left in the season. It had Luis Gil with a greater than 50% chance to win, with Colton Cowser and Austin Wells also having good chances, and Wilyer Abreu being an extreme longshot, with a less than 2% chance to win it.

Luis Gil and Colton Cowser. Why these two? It seemed to me like there was a crowded field of top candidates in this race.

Well, someone in that article mentioned WAR as part of their reasoning. And though WAR isn’t the be-all end-all criterion for choosing Rookies of the Year and MVPs, I think it’s a great first step in creating a pool of top candidates to ponder and consider, to compare and contrast. So I considered it. I considered it in 16 different ways, in fact.

So it was interesting to learn in this assessment of the WARs that AL rookies accumulated in 2024, that Gil maybe shouldn’t even be in the mix. I have him as just outside the 6 strong contenders, who are, in alphabetical order:

Wilyer Abreu
Colton Cowser
Wyatt Langford
Mason Miller
Cade Smith
Austin Wells

How did I come to that conclusion? Well let’s start by looking at the top WARs of AL players. Note that there are two different commonly used ways of calculating WAR, that are scaled to be a similar size, but can produce quite different answers for individuals. One of these ways comes from Baseball-Reference.com, and it is often labeled bWAR for clarity. Here are the AL rookies with the highest bWARs for 2024:

There are Gil and Cowser, but they’re in the third and fourth spots. Yet they’re both within 1 WAR of the leaders, Wyatt Langford and Wilyer Abreu, which is not considered a truly significant difference.

What does the other WAR look like? It is calculated by FanGraphs.com, and it is often labeled fWAR for short. Here are the AL rookies with the highest fWARs for 2024:

Ah, there’s Cowser at the top. But Gil is in 7th place? And of the 8 players appearing on both lists, none of them are in the same place as before. Also, as with bWAR, a lot of guys are within 1 fWAR of each other.

Some of these differences are surely indicative of the inherent inaccuracies of estimating the value of a player’s performance. That said, WAR is our best current tool for objectively attempting to measure the overall value of a player’s performance. We just must recognize the approximate size of those inaccuracies, and as others have said before me, we must use WAR as a conversation starter, not a conversation ender.

But hey, maybe we can squeeze a little more accuracy out by averaging the bWAR and the fWAR? That looks like this:

Colton Cowser on top again (thanks to his high fWAR), but the top 6 guys all within one WAR of each other! And a new top 2. This makes things look even tighter.

But maybe it would be better to look at each player’s peak assessment – their highest WAR attained between the two systems?

The same top 4 and top 5 as with the average WAR, though a different top 3. But no … maximum can be completely influenced by one system having a very inaccurate high assessment. Having a high minimum WAR between the two systems only happens if both systems rate you highly – we should therefore have more confidence in a high minimum WAR than a high maximum WAR. Here’s what that looks like:

Well that shook things up a bit! A new name on top.

But looking over all five lists, there are four names always hanging out near the top – (alphabetically) these are Wilyer Abreu, Colton Cowser, Wyatt Langford, and Austin Wells. Perhaps we should declare these four in a dead heat as far as WAR is concerned, and focus on these four in determining, using other measures, which one should be AL Rookie of the Year. But Luis Gil is not part of that group. Why is he such a frontrunner for Rookie of the Year, then? I’ll share some thoughts on that later.

But hang on. There’s an important factor we haven’t considered here: playing time. Among the highest performers, WAR acts like a counting statistic – the more you play, the more WAR you accumulate. So in comparing top players, it may be more appropriate to turn WAR into a rate stat by dividing it by some measure of playing time. So let’s do that.

For position players, I like to use plate appearances as the measure of playing time, as plate performance has an outsized effect on overall WAR.

For pitchers, I like to use batters faced instead of innings pitched, because it’s the number that is most relatable to the position player’s plate appearances. In fact, if you add up all players’ plate appearances over all of MLB for an entire year, you get exactly the same number as you get when totaling batters faced in the same way.

But pitchers as a whole don’t get as much WAR as position players do. Probably rightly so, because position players can add to the run values of their batting contributions with their defense and/or baserunning; pitchers can only add value by reducing the run contributions of the batter. Because major league players collectively will do better than replacement-level players at baserunning and fielding, on average these will add a positive amount of WAR on top of their batting contributions. Pitchers only have access to the run values available in the pitcher/batter interaction.

So since there’s less WAR to go around for pitchers, to assess how good their play was against position players, we must grant them more opportunity by allowing them to accumulate WAR over a larger number of batter/pitcher interactions. Looking at the numbers from 2023 and 2024, I found a pretty consistent trend: position players get a little over 40% more fWAR per batter/pitcher interaction than pitchers do, and a little over 50% more bWAR. To be a little conservative about it, I used the 40% and 50% adjustments. So we calculate WAR per 500 plate appearances for position players, fWAR per 700 batters faced for pitchers, and bWAR per 750 batters faced for pitchers. These numbers were chosen to get into the vicinity of one season’s worth of plate appearances.

The results of this adjustment for all five tables we made before can be found below.

Now you may object to my adjustment, and insist that position players and pitchers should be evaluated based on equal numbers of batter/pitcher interactions. Okay, to humor you, I also did the same five tables as before that way – WAR per 500 PA for position players, and WAR per 500 BF for pitchers. So now we have 10 new tables to show you.

But before we do, we have one more adjustment to make. Because we’re dealing with rate stats now, players with a lower number of chances will be able to ride a “hot streak” of good luck to achieve higher rates than a player with more chances is able to access. So we insist on a minimum number of chances – 400 for each. If a player has below 400 PA or BF, we divide their WAR total by 400 instead of by their actual, lower number. It’s like we’re assuming that a player with 300 PA would have accumulated 0 WAR over their next 100 PA.

With that adjustment, now we’re ready. Here are the five tables using WAR per 500 PA and WAR per 700 or 750 BF:

Wow, Cade Smith and Mason Miller completely took over the top of the lists!

But here are the five tables using WAR per 500p PA/BF. Will they stay atop those?

They’re not atop these, but still placing higher than before, as are David Hamilton and Parker Meadows. But the new dominant pair on these five lists are Wilyer Abreu and Austin Wells. And Luis Gil has nearly disappeared from them!

All these lists, all 15 of them looked at collectively, tell a tale of ambiguity. These 15 lists have 14 different top 3s. There are nine different players occupying top 3 positions. There are five different players occupying the top position of a list. There is no clear cut frontrunner here!

But surely some are appearing near the top moreso than others. Here’s one thing we can do to sort those out: for each player, find their highest position on any list, and their lowest position on any list. Here is what that looks like:

And there we see the two runaway favorites to win AL Rookie of the Year coming in behind five other guys. And looking at their numbers, I can see that a good case could be made to vote for Wilyer Abreu, Cade Smith, or Wyatt Langford over Colton Cowser or Luis Gil. Maybe even Austin Wells too.

So why are Cowser and Gil so favored to win?

Is it because they’re from major markets? No, because Wilyer Abreu is from a major market.

Is it because most of the others played less? I think that is a factor, especially for Cade Smith, who as a reliever doesn’t face nearly as many batters as starting pitchers do. And a little bit for Wilyer Abreu, who missed part of the middle of the season due to injury.

But I think the biggest factor is that Colton Cowser and Luis Gil played for playoff contenders, and except for Cade Smith and Austin Wells, most of the rest didn’t. And the fact that that’s probably true really makes me sad.

Why should otherwise equal players be judged differently based on the performance of the other players on their teams? That makes no sense, and should not factor at all into the voting. But I fear it does. It’s looking like Wilyer Abreu and Wyatt Langford will be cheated of Rookie of the Year votes due to not playing on contenders, and Cade Smith will be cheated out of votes for lack of playing time.

Here’s hoping the prognosticators got it wrong, and we see Cade Smith, Wilyer Abreu, and Wyatt Langford finish with strong scores in the Rookie of the Year voting.

Who was the “most .500” team of 2024?

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Of course, one could say that the “most .500” Major League Baseball team in any given year is the one whose record is closest to .500, or 81-81 in a full season. But even a hypothetical team that always had exactly a 50% chance of winning would sometimes end up, by luck of the “coin flip”, a few games away from .500.

And what about a team that’s great for the first half of the season, then awful for the second half, ending up with a .500 record? They weren’t really a .500 team at any point in the season, in that their chance of winning games wasn’t actually close to 50% at any point, nor were they winning about half their games in any given week.

So here are a few different ways to measure how .500 a team was, along with the top teams by each method.

Final Record

We can just look at a team’s final record and see how many games away from .500 it was, above or below.

The Boston Red Sox had the only .500 record, but several other teams were close.

Run Differential

This was mentioned in Sarah Langs’ 2020 article What does a true .500 team look like?

The run differential of a team is the runs it scores over the entire season minus the runs it allowed in that same time. A small run differential is a good predictor of a team that will have a record near .500. (There is even a stat called Pythagorean expectation which estimates what record a team should have based on it totals of runs scored and runs allowed.)

Whose run differential was closest to 0 in 2024?

Four teams had a run differential close to 0. Of these, again, the Boston Red Sox were the closest to 0, just barely. It seems we have a frontrunner.

Number of times at .500

A team that plays “a .500 brand of baseball” throughout the season is likely to have a winning percentage of exactly .500 at several times during the course of the season. The most times this could possibly happen is 81, though even for a hypothetical team that always has a 50% chance of winning, the odds of that happening 81 times are over 2,000,000,000,000,000,000,000,000 to 1 against. The most times it’s ever been done, at least before 2020, is 35 by the 1959 Chicago Cubs.

The Tampa Bay Rays came close to that this year, tying for 3rd most. The Padres, Red Sox, and Cardinals also had a lot.

For fun: consecutive times at .500

This last one is more about the luck of streaks than anything else. But there was an interesting streak this year in this regard, so I thought I’d throw it in.

When a team is at .500 in the middle of the season, the next game they play takes them off of .500; it’s only 2 games later that they can be back at .500 again. So a streak of consecutive times at .500 means that at the end of every 2 games played after being at .500, they’re back at .500 again.

The Red Sox were at 26-26 on May 25, 2024 – 26 wins and 26 losses. Two games after that they were 27-27, then 28-28, 29-29, and so on up to 35-35. That’s ten times in a row at .500. The likelihood of that happening, once a team has reached a .500 record, is more than 500-to-1 against.

Here are the longest such streaks in the majors in 2024:

The “Winner”

It’s gotta be the Boston Red Sox as The Most .500 Team of 2024. They top every list except number of times at .500, and they did pretty well there, too. Runner up goes to the Tampa Bay Rays.

Interestingly, these two teams played each other in their last 3 games of the season, with the Rays winning the first two but losing the final game. Had they won it, they would have replaced the Red Sox atop the Final Record list, probably solidified the Red Sox hold on the Run Differential list, but strengthened their own position atop the Times At .500 list. That game was something of a battle for Most .500 Team of 2024. Congratulations, Red Sox, on your “victory”!