One of the side effects of spending way too much time on Twitter is that you find some interesting questions about baseball to write about. Today’s comes from Jerry Mackinnem, who asked a good question about valuing trade chips at the deadline. Normally for big trades, good analysis would use future projections of WAR/$ (essentially, valuing players at the going rate of $9 million per WAR they expect to put up) and compare that to prospect valuations to try to work out fair trade value. The wrinkle that Jerry adds is an interesting one: how do you value a low WAR player at the trade deadline? Obviously someone like Shane Greene isn’t going to post gigantic WAR totals, but he’s a coveted trade chip. Can we do the math to figure out what he’s actually worth?

More after the cut

The answer is yes, and to do so, we need to get a bit more complicated. To do so, we need to understand the win curve. Put simply, all wins are not equal. The Tigers, who project to win around 50 to 60 games this year, aren’t going to get as much value for their wins than, say, the Chicago Cubs, currently fighting in a pennant race. Fangraphs, via The Hardball Times, has done significant work on establishing monetary value for each win along the win curve, and you should go read that piece to better understand exactly what the win curve is.

But the short version is that wins 85-95 possess significantly more value to a team than normal wins. Intuitively, this makes sense- if you’re in a tight division race, and the difference between making the playoffs is 90 wins versus 89 wins, you’ll pay out the nose for that extra win.

As a result, that leads to different valuations of players at the trade deadline. The updated win curve article, published in 2017, includes a chart laying out the value of each additional win and its value to a team at the trade deadline. This is where things get fun for prospect watchers. If the Tigers trade a player at the deadline, both teams value that player higher, in part because you can reduce uncertainty and guarantee that the win you’re picking up has more value. For the Cubs, for instance, that means acquiring Nicholas Castellanos leads to a better shot of winning game 90, which greatly increases their odds of making the playoffs.

Armed with this knowledge, let’s go ahead and make some projections about the value of Nicholas Castellanos, Shane Greene, and Matthew Boyd at the trade deadline. For these projections, we’ll assume the average value of a marginal win is $10 million. That’s at the top end of the 2017 projections for value, but that’s probably ok for a best case scenario considering that the Tigers possess leverage in a selling market and given that we’re working with a (slightly) outdated set of values. On top of that, we can assume that each win is worth $9 million on the open market, meaning each win that a player contributes in 2019 is worth $19 million in surplus value as opposed to $9 million (the going WAR/$ rate). For additional cost-controlled years, we can assume a standard $9 million/WAR (that ignores inflation, but let’s keep it simple). We’ll compare that to Fangraphs’ Prospect Valuation Chart so we have a going reference, and I’ll intersperse the math with some analysis and comparable trades.

Nicholas Castellanos, Outfielder

Remaining salary: ~4 million (2019)

Expected WAR for 2019: 1 WAR

Expected Value: $19 million

Surplus Value: $15 million

Castellanos is a great test case, because he nicely illustrates how teams value rental bats at the deadline. The short version is that despite his offensive potential, Castellanos doesn’t have all that much surplus value.

Fangraphs values a 50 FV (future value) pitching prospect at $21 million in value, and a 50 FV position prospect at $28 million. That difference reflects the risk a young arm has over a young position player. Castellanos is not going to bring back a 50 FV player, which translates to a back-end top 100 prospect.

That said, Castellanos is still worth something, and probably something pretty nice. At best, he might bring a fringe top-120 prospect back, but I think it’s safe to assume that the package looks more like the JD Martinez deal, in that the Tigers get one or two 40/45 FV prospects back. While fans never liked that particular trade, it’s worth noting that, as Dan Szymborski observes, that’s about the going rate for a premium bat with poor defensive value. Bats just don’t fetch much of a return at the deadline. The real value comes from relief pitching. Speaking of…

Shane Greene, Relief Pitcher

Remaining Salary: ~1.5 million (2019), ~6 million (2020- via arbitration)

Expected WAR for 2019: 0.5 WAR

Expected future WAR: 1 WAR

Expected Value: $19 million

Surplus Value: $11.5 million

Here’s where the wheels tend to fall off when it comes to the math. On paper, it looks like Greene’s worth even less than Castellanos is, despite the extra year of control. After all, he won’t contribute all that much to a team’s total wins this year, and an extra year of control from a good, not great, relief pitcher is only about $9-$10 million. And yet Greene’s going to invariably return more than Castellanos. What gives?

Well, there are a couple factors working in the Tigers’ favor when dealing an above average relief pitcher. First, the worst reliever in the bullpen is almost always the worst pitcher on the roster, and is very often the worst overall player on the roster. To put it another way, if the Cubs upgrade their outfield by acquiring Castellanos, they substitute out Albert Almora, which is an upgrade of about half a win.

Meanwhile, if they trade out their worst relief pitcher, they take a zero win scrub and turn him into a 1 win player. That’s huge in terms of roster upgrades. The value of that 25 man roster spot skyrockets, meaning the Cubs not only add Greene’s value, but add by subtracting whomever they call up from AAA to fill in as a middle reliever.

Second, teams tend to overvalue relievers at the deadline, especially ones with cost control. That’s in part because virtually every team can use a reliever, whereas the number of teams that actually need, say, a right-handed outfielder who plays defense like Matt Stairs is significantly lower. Not only is a team like the Cubs trying to add a relief pitcher to get that $11.5 million in marginal value, but they’re trying as hard as they can to stop the Milwaukee Brewers from doing the exact same thing.

So relief trades tend to blow up the value chart. They range from the Brad Hand/Adam Cimber blockbuster to the Justin Wilson trade from 2017. The Tigers can probably expect a return a bit closer to that Wilson trade, but that’s still a couple back-end top 100 prospects. Add to that the fact that as few as eight teams are selling players, the fact that the relief market consists of Ian Kennedy, Jake Diekman, Paul Fry, Matt Shoemaker, Austin Adams, Alex Colome, and Shane Greene (with maybe a couple others), and… wow, that looks real bad for a contender. Adams is probably the best pitcher on the market, but there’s a real case for Greene being a strong #2. Expect a return that at least includes a back-end top 100 prospect or two in the 50 FV range, and don’t be shocked if the Tigers manage to pull off a 55 FV prospect.

Matthew Boyd, Starting Pitcher

Remaining Salary: ~1 million (2019), 7 million (2020), 10 million (2021), 12 million (2022)

Expected WAR for 2019: 1.5 WAR

Expected future WAR: 12 WAR

Expected Value: $136.5 million

Surplus Value: $106.5 million

Ah, here we get into real value. If we project Matthew Boyd out as a 4 WAR starter going forward (think Dallas Keuchel having a good year), he’s worth serious surplus value. Bear in mind the Tigers, with significant leverage given Boyd’s three years of team control, are likely treating him as such on the trade market.

I fudged the arbitration values a bit because it’s hard to track down comparables, but even calling it $100 million in surplus value considering his value to a team right now and in the future is astronomical.

To put that into perspective, a 70 FV position prospect is worth $112 million and a 70 FV pitching prospect is worth $90 million. If the Tigers are using roughly the same math that I am, that means a Matthew Boyd for Wander Franco deal would be very close to fair value. That, of course, is a total pipe dream, given teams’ propensity to hoard top prospects. But if you go down a bit, you could easily grab a 60 FV position prospect valued at $60 million and a 55 FV position prospect valued at $55 million (worth noting my previous post detailing potential options). After running the numbers, it’s easy to see why Detroit is pursuing top-flight offensive prospects in any trade for Boyd, and frankly, given their leverage and his monster year, they deserve that return.