CHICAGO -- When the Chicago Cubs acquired closer Aroldis Chapman from the New York Yankees last week, it was looked upon as a missing-piece move, the transaction that might make the team unassailable down the stretch and into the postseason.

By introducing Chapman into a bullpen mix with former closer Hector Rondon and premier setup man Pedro Strop, team architects Theo Epstein and Jed Hoyer created perhaps the most powerful group of stoppers in the game. And then they turned the management of that group of flamethrowers over to Joe Maddon, the mad scientist of bullpen management. Maddon says he's still very much in the mode of figuring out how to maximize his relievers.

“Absolutely,” Maddon said. “There's no doubt. It really shows you what happens with the addition of just one guy, what it does for everybody else.

“OK, it's just one guy, a relief pitcher, but all of a sudden [Rondon] gets moved back, Strop gets moved back, you have to really analyze it. Because there is still Travis Wood, who does good work, and C.J. Edwards, who I continue to want to build into that moment, and Joe Nathan's throwing the ball really well right now.”

Cubs fans are mostly concerned with whether Chapman can help the team end the most famous drought in sports, a title-less streak so old I heard a White Sox fan on the train last week tell some Cubs fans, “You guys have a decent team, but you haven’t won the Series since the Ottoman Empire.” The question of just how Maddon maximizes his group of relievers with this new addition is directly related to that quest. It’s a happy dilemma.

Maddon’s bullpen philosophy has long been considered the most progressive in the game among stat-heads, and sometimes a bit head-scratching to more mainstream observers. Simply put, Maddon prefers a staff of personalities without egos: pitchers OK with a bullpen that is run by percentages and matchups and not predetermined roles.

Unlike, say, the Kansas City Royals. Their recent bullpen may be the greatest ever, and they’ve come up often this week in relation to the Cubs’ Chapman-Rondon-Strop configuration. No championship team has had a greater portion of its success come from relief pitching than the Royals. According to baseball-reference.com, from 2013 to 2015, the Royals’ trio of Greg Holland, Wade Davis and Kelvin Herrera ranked ninth, 13th and 30th, respectively, in reliever wins above replacement. They didn’t have one closer, they had three, and they were all elite.

Joe Maddon, whose bullpen philosophy has long been considered the most progressive in the game, says he's still figuring out how to maximize his blue-chip relievers. Seth Wenig/AP Photo

The Cubs have created such a mix. From the beginning of 2014 to present, Chapman, Rondon and Strop rank seventh, 11th and 27th in reliever WAR. With trades breaking up the Yankees’ bullpen, and injuries wrecking the Royals, no team can match this trio in terms of aggregate multiyear production and results from just this season. That declarative statement is no slam dunk: Baltimore fans can make an excellent argument for their guys, especially now that Darren O'Day is off the disabled list.

The White Sox were the first team to confront Maddon’s new bullpen, and manager Robin Ventura was impressed.

“You see the velocity that’s there,” Ventura said. “It’s tough, too, because you get one guy that’s right-handed and one that's left-handed, so you can use that to your advantage if you want to. You can flip it around if you really want to, depending on who’s coming up. It’s a pretty good one.”

To truly create a distinction in any best back-end bullpen debate, it may be up to Maddon. Can he extract more value from his relievers than the Orioles, or Rangers, or Dodgers, or Mets do from theirs?

Royals manager Ned Yost won two pennants and a World Series with an often maddeningly simplistic approach to deploying his biggest weapons. There was a seventh-inning guy, an eighth-inning guy, and a closer, and matchups be damned. Leverage? What in holy heck does leverage matter when you’re winning the World Series?

“What Kansas City had done was just pretty much formulaic, this guy, this guy, this guy, seven, eight, nine,” Maddon said. “And they could do that because those pitchers were pretty much neutral guys. They were good against both righties and lefties. I think Strop, Rondon and of course Chapman are the same way. But so is Travis, so is C.J.”

While we don’t yet know just how Maddon will use his bullpen, we do know it’s not going to be a Yost-like approach. In too many ways to count, Maddon is the anti-Yost, and that is not meant to slight either manager. Both have won at the highest levels by adhering to their core beliefs. But let’s face it, Maddon’s way is more fun.

“We might have a bunch of other guys who might be [righty/lefty] neutral,” Maddon said. “So the point for me might then be to not run anybody into the ground.

“On any given night, if everybody is well, everybody is rested, you probably will see the Strop-Rondon [or] Rondon-Strop seven-eight, based on what it looks like with the opposition. Then, of course, Aroldis there in the ninth.”

Any evaluation of bullpen success has to be adjusted for opportunity. Since the Cubs own by far the best run differential in baseball, high-leverage situations are relatively infrequent for them. Only the Royals, Indians and Angels have had a lower average leverage index this season, according to baseball-reference.com. (Leverage is a mathematical measurement of the pressure attached to any given situation in a game.) In that sense, bullpen success is less important to the Cubs than most any team in baseball.

The problem for the Cubs this season, insofar as a team so dominant even has a problem, has not been overall bullpen performance. It’s hasn’t even been situational bullpen performance. The Cubs have the fourth-best OPS-against in baseball in low-leverage situations, according to baseball-reference.com. In medium-leverage spots, they rank first. But those crucial high-leverage spots that so many were concerned about? The Cubs also rank first.

Those numbers are a product of not just the quality of the arms in the bullpen, but in Maddon’s proven ability to deploy them. When Maddon’s Tampa Bay Rays teams were at their best, they finished in the top two in all of baseball in high-leverage OPS-against three times. Esoteric as that statistic sounds, it’s important: The Cubs have a guy with a non-traditional approach to bullpen management with a track record of maximizing the impact of his relief staff.

Postseason games are thick with high-leverage situations, largely because each successive game means so much more in terms of obtaining the ultimate goal -- a championship. We’ve already seen what this can mean in practical terms. Chapman did not record a four-out save with the Yankees. He did so in his first appearance with the Cubs. He blew a chance for another one Saturday, but that’s not going to deter Maddon from trying it again.

Meanwhile, Rondon pitched the eighth, and only the eighth, during Chapman’s debut. According to ESPN Stats & Info, he hadn’t done that in a year. Then on Saturday, he pitched to two batters in a high-leverage, eighth-inning jam, before turning the game over mid-inning to Chapman. It didn’t work, but on paper it should have. Chapman is the Cubs’ best reliever and the at-bat in which Seattle’s Leonys Martin beat Chapman with a go-ahead double had, according to the charts at fangraphs.com, the highest leverage index of any situation in the game.

If that was the 2015 Royals, Wade Davis would have been watching that situation from the bullpen. Maddon doesn’t do it that way, and all the numbers suggest that's smart. But if the real-world results don’t redeem the process, as they didn't on Saturday? Then, for Cubs fans, the numbers will be of little consolation.

“There are all of these different permutations, and I don't know [yet],” Maddon said. “You're right. I don't know."