The Red Sox have had a sad start to the offseason, even by the standards of baseball’s recent payroll doomsaying. While some teams have intimated that they won’t increase payroll, the Sox have gone further; owner John Henry announced that they plan on dropping below the luxury tax threshold for 2020, setting the tone for a strange winter where cutting salary might matter more than the eventual product on the field.

Viewed through that lens, it’s somehow a bad development when one of the best hitters in baseball chooses to stay on your team. J.D. Martinez was the 16th-best qualified hitter by wRC+ last year, and that was a down year. He elected not to opt out of his current contract, and is slated to make $23.75 million next season — a steal if he hits his Steamer projection, and a useful piece for a team with no other DH options. And yet, when you set artificial salary constraints on yourself, things tend to snowball.

With Martinez in the fold, things took an even weirder turn. The offseason rumor mill seems increasingly convinced that the Sox will offload Mookie Betts to save the last year of his salary and avoid an appropriately costly extension, reaping some prospects in return and cutting payroll in the bargain. I’ll attempt to quantify what this might do to the team, but let me say upfront: this seems like an obviously bad choice to me. Dan Shaughnessy hit pieces aside, Betts is probably the best non-Trout player in baseball. You don’t trade someone like that and take a step forward.

But okay, fine, let’s go through the math of trading Betts. We’ll do the grim calculus of turning player contracts into cash amounts first: if you value a win on the free market at $8 million, Betts’ 6.6 WAR projection is worth $52.8 million. If Betts earns his projected arbitration salary of $27.7 million, that works out to $25 million in surplus value. That sounds reductive, and it is. Mookie Betts isn’t an asset worth $25 million to the Red Sox; he’s one of the best players in baseball, and also a great bowler in his spare time. But if we’re doing the math, that’s the starting point.

With that surplus value in mind, we can think about what the team might get in return. Per Craig Edwards’ research, a 50 FV position player prospect is worth roughly $28 million in present value, while a 50 FV pitcher is worth $21 million. Someone like Seattle outfielder Julio Rodriguez, say, since all trade examples should include a Mariner for Dipoto purposes.

But that return feels impossibly light for Betts. Indeed, stars tend to go for a bit more than that. One recent point of comparison is the Paul Goldschmidt deal from last winter. The Cardinals acquired Goldschmidt with one year left until free agency. Steamer projected him for 4.1 WAR, and his salary was $15.5 million, which put his excess value at around $17.5 million; Betts-range, though lower. In return, Arizona received Carson Kelly, Luke Weaver, Andy Young, and a competitive balance pick. That works out to something like a 50 FV position player, a 45 FV pitcher, and two 40 FV position players, though the specific deal wasn’t quite that, as neither Weaver nor Kelly had rookie eligibility.

If you assume the Red Sox will also target players who can contribute immediately, this seems like a good framework for a trade. Think of it in the abstract, and it might look something like this: the Red Sox trade away Betts’ 6.6 WAR in 2020 as well as his salary. In return, they get 1.65 WAR in 2020, 2021, 2022, and 2023 between the prospects they receive in return and the money they can redeploy elsewhere (though in practice, it seems like they might just pocket the money).

That’s a very simplistic analysis, and that return still feels light — again, we’re talking about the position player who, since he came up in 2014, is second only to Trout in WAR (37.2 to Trout’s 52.5) versus an amalgam of wins your brain has now shaped into a weird Carson Kelly/Luke Weaver/et al composite. We haven’t even accounted for all the non-baseball benefits (ticket and merchandise sales, fan engagement, outfield dance celebrations) that come from having a Mookie Betts on the roster. But it’s useful for our purposes. If you want to evaluate the cost and benefit of trading Betts, you need to assume a realistic return. Would the Red Sox trade Betts for Juan Soto? Of course! They can’t get Soto, but they’d do it in a heartbeat. There’s no point in evaluating that trade, though — so we’ll evaluate a theoretical trade in which the team neither gains nor loses WAR in expectation.

From there, we can approximate how good the team will be in each of the next four years. A very, very early cut of the math puts the Red Sox at a projected 96.6 wins next year (I worked this out by adding up WAR. As Dan Szymborski will tell you, that’s not a foolproof method). That’s with Betts; subtract him and add back his return in trade, and it gets you to 91.65 wins.

We’re getting quite speculative in projecting future years, but let’s call each of the 2021-2023 squads 89 win teams without either the prospects or Betts. There’s plenty of room around that projection, but it will do as a baseline. Next I also projected the other AL East contenders for the next four years; this is rocky math at best, but necessary for the next step. It looks like this:

Boston’s Competition Team 2020 Wins 2021 Wins 2022 Wins 2023 Wins Yankees 94 94 94 94 Rays 92 92 91 90 Wild Card Contender 1 90 90 90 90 Wild Card Contender 2 88 88 88 88

The generic Wild Card contenders aren’t any one specific team; rather, they’re approximations of the talent level necessary to contend for a Wild Card. Maybe they’re the A’s, or the Indians — the point is, they’re good but not overpowering.

If you’ll recall, the Red Sox will look like one of these:

Boston’s Two Options Team 2020 Wins 2021 Wins 2022 Wins 2023 Wins Keep Betts 96.6 89 89 89 Trade Betts 91.65 90.65 90.65 90.65

From there, we can simulate things out to see how often the Red Sox make the playoffs in each case. Sprinkling in a bit of variance to each team’s projection (here’s a lovely article on variance), I simply simulated each season a million times in each of the two scenarios.

If the Sox keep Betts, they project to win the AL East 1.13 times in the next four years and a Wild Card 1.28 times. That’s extremely front-loaded — they’re 46% to win the East in 2020 and 34% to win a Wild Card. After that, it’s scraps and variance.

What if they trade Betts? Their odds of winning in 2020 decline, of course. If you trust my method, the post-Betts Red Sox would be 28.7% to win the East and 34% to win a Wild Card. The team is better in 2021-2023, but not by quite enough to make up for the shortfall in 2020. All in all, my model gives them an average of 1.09 AL East titles and 1.33 Wild Card berths in the next four years. The two scenarios are indeed mostly equivalent, but the team would prefer the scenario with Betts in the fold marginally, as it’s essentially picking up .04 AL East titles at the cost of .05 Wild Card berths.

The gap is extremely small, such that the return the team gets for Betts is far more important than going all-in for 2020 or pushing the window of contention back. And this result holds even if you think Boston is slightly better or slightly worse than my forward projections. But there’s something missing: the teams that win the East with Betts are better. To wit: in the scenario where the Sox keep Betts, their East-winning teams average 99.7 wins. In the scenario where they trade him, they average only 98.9 wins. Meanwhile, the Wild Card records are roughly identical.

In essence, the Red Sox are more likely to have a juggernaut by keeping Betts, which makes total sense. They might break even on playoff berths by spreading out the wins, but they’ll be doing it, on average, with worse teams. What looks like roughly an even tradeoff skews the way of keeping Betts, because their odds in the playoffs are better with him.

The differences are marginal, of course. That’s always going to be the case when you assume a player gets traded for an exactly offsetting amount of WAR. But the direction is clear. When you’re in a division with a perennial beast like the Yankees, a natural boom-bust cycle is a good way to maximize your odds of winning a World Series.

There’s a second reason that trading Betts for parts doesn’t add up. Imagine the Red Sox trade Betts for a right fielder who projects for 1.65 WAR in each of the next four years, to make the math as easy as possible. Also imagine that the team has two minor league outfielders of exactly replacement level, who might continue to develop or regress.

We can apply a rough estimate to that development or regression by applying a random variable to their future projections. If they’re projected for 0 WAR in 2020, they might be projected for 0.8, or -0.8, in 2021, and so on. I’ve done some work on this in the past, and I applied a rough model to work out a projected right field WAR in each of 2021, 2022, and 2023.

With Betts, the math is pretty simple. In 2020, the team has Mookie Betts in right. That’s a 6.6 WAR projection, per Steamer. From there, it plays whichever of its two anonymous prospects is projected to be better. That works out to the next four years of right field looking like this:

Red Sox Right Field WAR Choice 2020 2021 2022 2023 Total Keep Betts 6.6 0.45 0.64 0.78 8.47

Why does the projection increase every year? Because there’s more time for the two players to separate, for one of them to get good. Right now, they might both be replacement level, and indeed, if the team only had one replacement level player, their average production would always be 0. But having two increases the odds of getting lucky with one player’s development.

Let’s do this again, this time with our hypothetical Betts replacement in right. In 2020, the team gets his 1.65 WAR from the spot. From there, it looks like this:

Red Sox Right Field WAR Choice 2020 2021 2022 2023 Total Keep Betts 6.6 0.45 0.64 0.78 8.47 Trade Betts 1.65 1.72 1.86 2.01 7.24

As you can see, future year WAR also increases in this scenario, because sometimes the replacement level players pass our 1.65 WAR man in expected production. They increase by less, though, which is only natural; the vast majority of the time, the new acquisition remains the best bet in right.

But in aggregate, Boston picks up more expected WAR by getting Betts’ full brilliance in 2020 and then letting replacement level players duke it out after that. The compounding effect of uncertainty is a good way to produce players just a bit above replacement level, but that effect isn’t worth as much if you have average players already filling those spots. Trading a star for an average player, in other words, decreases the value you get from prospect variance.

These two effects are small. One is worth something like .05 division titles, and one is worth 1 WAR over four years. But they’re real effects nonetheless, and they point in the same direction. If Boston is making a baseball decision, trading Mookie Betts doesn’t make sense, even if they get a “fair” return in WAR.

There are, no doubt, many assumptions in this analysis you could question. They probably won’t get a league average right fielder in exchange for Betts; they’ll probably get someone who could be either much better or much worse than that. Maybe they could actually acquire 15 projected WAR in trade, which makes my analysis moot. Maybe there aren’t actually two replacement level outfielders in the system waiting to get better or worse at random. All that could be true. But I stand by my analysis. Trading Betts, even if the cold hard surplus value math balances, doesn’t make sense. The Red Sox should stick to their guns and try to spike a World Series in 2020, then figure out what to do in 2021 later.