The Cubs are the champions. There’s a rule about champions: the end justifies the means. There are no regrets, and, given a time machine, there’s nothing the team would want to undo, because every event, every decision led up to that final, most beautiful inning. A championship season is a delicate thing, and if you go back to adjust or remove one Jenga block, there’s no telling what causes a tower collapse. The Cubs won, so they’ll embrace how they came to win, for all of the good and all of the weird.

With that being said, we’ve seen something remarkable. *I* think it’s remarkable, anyway — your mileage might vary. Near the end of July, the Cubs made a low-profile trade, adding lefty Mike Montgomery from the Mariners. At the time, it looked like the Cubs might’ve gone for a cheap alternative to the premium-priced elites. A few days later, they paid said premium price for an elite, adding lefty Aroldis Chapman from the Yankees. The Chapman move was the more celebrated one, as all the championship dreams would go. With Chapman, the Cubs looked almost invulnerable. He could be the piece to put them over the top.

Yet in the end, Montgomery proved more valuable. By at least one measure, anyway. Chapman wasn’t what he was supposed to be. The Cubs won almost despite him.

For these purposes, I have only the playoffs in mind. Chapman, without question, was fantastic after he first arrived. Montgomery was fine, but Chapman recorded 16 saves. He allowed four runs and 12 hits over 28 regular-season games with Chicago. The Cubs got what they thought they were getting, but really, all that did was give them some extra confidence going into the playoffs. Because the Cubs were pretty much always going to win the division no matter what. Montgomery was acquired on July 20. Chapman was acquired on July 25. Here’s a plot of the Cubs’ chances of winning the NL Central:

At the time of the Montgomery trade, the Cubs were up 7.5 games on the Cardinals. At the time of the Chapman trade, the margin was identical. The Cubs were great, and they projected to be great. Even without any moves, the Cubs were going to win the division. Roster modifications were made essentially with October and October alone in mind.

So let’s just get to that. Win Probability Added — WPA — isn’t great for analysis, but it’s a lot of fun for hindsight. According to Baseball-Reference, Chapman had a playoff WPA of +0.31. Montgomery had a playoff WPA of +0.41. According to our own numbers we have here, the figures were +0.17 and +0.27, respectively. I don’t know why there are differences, but the gaps are the same. Overall, folding in the ups and the downs, Montgomery was on the mound for a better group of events. Chapman, obviously, is the better pitcher. He’s one of the best per-inning pitchers on the planet. He simply didn’t generate enough of those results. It’s one of the things that made these playoffs so bizarre.

Chapman was anything but bad. He had his heroic outings, like World Series Game 5, when he got the final eight outs. He had four pretty spotless saves, and in all he pitched 13 times. Even in Game 7, he recovered from a nightmare eighth inning to manage a 1-2-3 ninth. If the ninth had gone worse, the season would’ve gone worse. Yet the ninth sure tried to suck. And Chapman was on the mound for three memorable events in particular. I sorted all the Cubs pitching events by WPA. The third-most damaging event was Adrian Gonzalez‘s game-tying single off Chapman in NLCS Game 1. The second-most damaging event was Rajai Davis‘ game-tying homer off Chapman Wednesday night. The single-most damaging event was Conor Gillaspie’s go-ahead triple off Chapman in NLDS Game 3. Those were the three most harmful events by a sizable margin, and you wouldn’t think Chapman would allow any of them to happen.

In this plot, you see Chapman’s 13 appearances, and Montgomery’s 11 appearances, in descending order of WPA. Chapman’s record was a bit more extreme in both directions.

It’s not so much that Montgomery was a star. He was just fine, one of few Cubs relievers Joe Maddon could trust. It did end up being Montgomery who threw the final pitch of the Cubs’ championship season. This is more about Chapman getting saves in four of seven opportunities. During the season, he recorded saves in 36 of 39 opportunities. Three blown saves in each. Certain memories will be hard to forget.

So who cares? It’s a worthwhile question. The Cubs won anyway, and maybe without Chapman, the replacements would’ve done even worse. We all noticed that Maddon didn’t trust Hector Rondon or Pedro Strop. Perhaps Chapman’s very presence in the bullpen somehow allowed for the Cubs to win as often as they did. Again, no champion would want to change a thing. The Cubs are happy to have exchanged Gleyber Torres for an ahead-of-schedule trophy.

I think there are two considerations. One, there’s a lesson in here about midseason trades. The Indians would tell you they’re thrilled with the trade they made for Andrew Miller, and then some. Miller was a crucial part of what got them as far as they got. Yet trading for an elite reliever is no guarantee of anything, especially if you’re already sitting in a pretty regular-season position. The playoffs can be just that unpredictable. For Chapman, the Cubs gave up a top-30 prospect, and still more pieces. Arguably the more valuable reliever wound up being the one they got for Dan Vogelbach. Navigating the trade market is hard. It’s impossible to know what might actually be worthwhile.

The other consideration is a soft one. Chapman’s presence on the Cubs provoked, for so many fans, something of an ethical dilemma. I don’t know how many times I saw a Cubs fan saying they’d feel a little weird if it was Chapman on the mound celebrating the final out. Obviously not everybody felt the same way, and you are how you are, but this worked out well in the end for a significant part of the Cubs fan community. The championship was deservedly won, but Chapman wasn’t so vital to the effort. If anything, he tried his damnedest to lose. It could’ve played out in a more psychologically challenging way.

As it played out, the Cubs won, as they were supposed to. But they also didn’t win how they were supposed to. You’ll never get this game figured out. Nobody will. Even Theo Epstein and the Cubs don’t have it figured out. They just get to shrug the happiest shrugs.