By Bruce Levine–

CHICAGO (CBS) — The New York Yankees added a third dominant reliever to their already potent bullpen Monday when they acquired the hard-throwing Aroldis Chapman from the Reds. In adding Chapman, New York is set to try and replicate what the world champion Kansas City Royals did with their power-packed bullpen over the past two seasons.

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Locally, how this could impact the Chicago Cubs’ future bullpen may be interesting to watch develop.

Even with a projected rotation that should give their bullpen more of a break next season after the signing of right-hander John Lackey, the Cubs are still hell bent on deepening the relief corps for 2016. They have added five bullpen arms to the 40-man roster since the end of the postseason, and the front office also re-signed pitchers Trevor Cahill and Clayton Richard, two important additions during the 2015 campaign.

So how could the Cubs’ bullpen be further strengthened? Enter Andrew Miller.

As the Yankees’ closer last season, Miller converted 36 of 38 save opportunities after signing a four-year, $36-million contract in December 2014. He also had a 2.04 ERA and 0.86 WHIP while striking out 100 batters in 61 2/3 innings.

Miller will now be projected as the team’s left-handed setup man, with Chapman taking over the closer’s role. With Dellin Betances setting up from the right side, the Yankees now have the three pitchers with the highest strikeout rates in 2015 (minimum of 40 innings pitched).

Currently, New York’s bullpen WAR is projected at a major league high 6.6 for next season, according to fangraphs.com.

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For now, the Yankees say they aren’t trading the 30-year-old Miller. Take that for what you think it’s worth, as Miller was being talked about as a trading chip long before the Chapman deal was completed.

The Cubs have right-hander Hector Rondon as their closer but are still open to adding a big bullpen arm during the season, as manager Joe Maddon often aggressively utilizes his relievers.

“There is always wear and tear in the pen,” Cubs president of baseball operations Theo Epstein said on 670 The Score on Dec. 19. “Joe has a good record managing the pen during the season and keeping them healthy. We want not one long reliever but a number of bullpen guys that potentially could go multiple innings. We aren’t looking for mop-up guys but people who can be effective every time out.”

The Yankees are short on starting pitching. In a potential deal, they’d likely ask for a quality young rotation pitcher or a power bat in return for a bullpen stud. The Cubs may not have the pitching to match up, but aging Yankees sluggers such as Alex Rodriguez, Carlos Beltran and Mark Teixeira are going into the final stages of their careers. A big bat from the Cubs such as Jorge Soler or Javier Baez may interest Yankees general manager Brian Cashman as spring training and the season progresses.

Miller missed three weeks with a left flexor forearm strain, beginning on June 11, but he still made 60 appearances. Miller finished the season with a strong September, going 8-of-9 in save chances and striking out 30 in 15 innings. That strong finish should help clubs look at the forearm injury in a more positive way when projecting Miller’s arm strength and health moving forward.

The White Sox were one of several teams bidding on Miller in late 2014. After the Miller bidding shifted from three to four years, the White Sox signed former Yankee closer David Robertson to a four-year, $46-million contract.

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Bruce Levine covers the Cubs and White Sox for 670 The Score and CBSChicago.com. Follow him on Twitter @MLBBruceLevine.