The Cubs' acquisition of Aroldis Chapman was probably the biggest news of the trade deadline (though the Rangers' and Indians' moves mean their potential World Series rivals got more ferocious). One reason is, obviously, Chapman's suspension for domestic violence, which I've written about at some length.

On the field, or at least in the front office, it was big news for what it did to the market, and what the Cubs gave up for a couple months of his time—including Baseball America's 27th-best prospect, Gleyber Torres. Torres is just 19 but a potential star headed in the right direction, as Eric Longenhagen details at Fangraphs. The Yankees also got a former Cubs top prospect who's been something of a disappointment, Billy McKinney; Rashad Crawford, who Longenhagen describes as a "low-level lottery ticket"; and Adam Warren, who was disappointing for the Cubs but fine during his previous stint with the Yanks from 2012 to 2015.

That's four players for three months of Aroldis Chapman—three very important months, but still. "It looks like the kind of return we might’ve expected for two-and-a-half reasonably priced years of [Andrew] Miller, [the Yankees' other star left-handed-reliever]. It’s the kind of return that forces us to once again re-evaluate our perception of a reliever’s trade value," August Fagerstrom wrote. (A few days later Miller was traded for a better package to the Indians—a slightly higher-ranked prospect than Torres, another top-100 youngster, and a couple promising, though not high-profile, potential bullpen arms.)

About the same time, the Nationals, who wouldn't pay the Yankees' toll for Chapman or Miller, got three months of Mark Melancon for a cheap young major-league reliever and a young minor-league reliever. Melancon isn't nearly as sexy as Chapman—his fastball is about eight or nine miles per hour slower—but his stats have been almost as good as Chapman's.

It's an interesting example of how quickly the conventional wisdom, and the market, can change in baseball. The Cubs traded for Chapman, and it looked like everyone had underestimated the price of a good reliever. Then the Indians and Nationals traded for Andrew Miller and Mark Melancon, and it looked as if the Cubs had overestimated it.

(Of course, to an extent the Cubs were forced into overpaying. Melancon is a righty, and the Cubs already have two excellent right-handed relievers in Pedro Strop and Hector Rondon. Their biggest weakness, arguably their only real weakness, was left-handed relief pitching, and the Yankees cornered the market on top-tier left-handed relievers. So Chapman is a bigger upgrade over Melancon for the Cubs than he would be for any other team, and the Yankees knew that. Nonetheless, the price the Cubs paid has surprised most observers.) 

I started thinking about Melancon versus Chapman because Ben Lindbergh and Sam Miller, authors of the wonderful book The Only Rule Is It Has to Work and hosts of Baseball Prospectus's "Effectively Wild" podcast, brought him up on a recent episode. As they discussed, Melancon has been really, really good in recent years. His ERA in the past three years has been 1.90, 2.23, and 1.48, compared to 2.00, 1.63, and 2.00 for Chapman. Melancon's strand rate, critical for a high-leverage reliever, has been 80.4 percent, 75.7 percent, and 81.2 percent, compared to 76.8 percent, 88.5 percent, and 76.3 percent for Chapman. Chapman's advanced stats, FIP and xFIP, have been reliably better than Melancon, but Melancon was worth more Win Probability Added ("a complicated concept and a stupidly easy concept") than any reliever in baseball from 2013-2015. They're both really good.

But Melancon came a lot cheaper than Chapman.

So they got to wondering: is Chapman really worth it? He's good because he throws over 100 miles per hour and, over the past three years, has struck out 38 to 53 percent of batters. He used to walk too many people (12 percent in 2014 and 2015), but he's brought that down to six percent this year.

Melancon only strikes out about a quarter of the hitters he faces. He's good because, while he can be hit, it's hard to hit him well. In 2014 Drew Fairservice called him the most unheralded reliever in baseball: "He isn't the flashiest pitcher in the league… He doesn't have the same gaudy strikeout rates of some of the higher profile relievers in the game, but Melancon absolutely belongs in their company."

But let's say it's the bottom of the eighth inning in a World Series game, with one out and guy on third in a one-run ballgame. Melancon's more likely to allow a ball in play. It might not be a hit, but that doesn't matter if the game gets tied. Maybe that's when you want the guy with the 100-mile-per-hour fastball who strikes out forty percent of batters.

To find out how that might play out, I went to Baseball Reference's lovely Play Index, which allows you to search every play in baseball by specific scenarios. In this case, I looked at every time Chapman and Melancon have been in a high-leverage situation with runners in scoring position in the past three seasons.

For Chapman, that's been 98 plate appearances. He's struck out 41, walked 11, and allowed a .169 batting average, giving up 22 runs. That comes out to .22 runs per plate appearance.

For Melancon, that's been 114 plate appearances. He's struck out just 23, walked 10, and allowed a .163 batting average, giving up 31 runs. That comes out to .27 runs per plate appearance.

Let's try narrowing it down even farther—high leverage with a runner on third.

For Chapman, that's been 39 plate appearances. He's struck out 17, walked two, and allowed a .182 batting average, giving up 15 runs. That's .38 runs per plate appearance.

For Melancon, that's been 45 plate appearances. He's struck out eight, walked four, and allowed a .194 batting average, giving up 22 runs. That's .49 runs per plate appearance.

These are both very small samples, obviously, over a long period of time. But they do at least suggest that Chapman might have some additional value over Melancon in a critical situation. In high-leverage situations with a runner on third, for example, Chapman allowed four runs on groundball or flyball outs; Melancon allowed eleven.

Another way to look at it: this year Chapman has thrown 599 pitches and allowed contact 80 times; Melancon has thrown 616 pitches and allowed contact 123 times. Melancon is great at forcing hitters into bad contact, and over the course of a season, that works out about as well for him as preventing contact works for Chapman. But even bad contact can end badly for a team, as Cubs fans, Alex Gonzalez, and Steve Bartman know.

How much is it worth avoiding contact in a high-leverage situation—or the highest leverage situations that baseball can create? It's very hard to put numbers on that. The Cubs may not find themselves in the late innings of a critical playoff game with a runner on third, and the price they paid for Chapman might be for naught. Or it could be Game Seven in the same situation, and a strikeout there might make Torres and the lesser pieces seem well worth giving up.

We're getting down to the rarest moments in baseball, and nothing drives up prices like scarcity, fear, and hope.