PITTSBURGH -- There were two common narratives regarding the Chicago Cubs' potential improvement on offense in spring training: If Jason Heyward returned to some kind of productive form and Kyle Schwarber was healthy for a full season, the Cubs could put up some monstrous numbers.

So far, so good, as they dropped a 14-spot on the Pittsburgh Pirates on Monday night, which gives them a whopping 53 runs scored over the past six games. They've won five of them.

"I expect to hit every first inning," regular No. 5 batter Addison Russell said after the 14-3 win. "We have guys that grind out at-bats from their first at-bat until their last at-bat. Guys will get on somehow, some way. And guys with big knocks along the way."

Russell earned his first career four-hit day, but not by smashing the ball all over the park. He took what the pitcher gave him, going to right field and simply staying within himself.

This kind of maturity is actually another way the Cubs can be even better on offense than their championship squad, which scored the second-most runs in the National League last season. Remember, they were just babies over the past two playoff seasons. Now they're young veterans who understand what an opposing pitcher is trying to do to them.

Addison Russell had four hits Monday to key an offensive onslaught by the Cubs. Charles LeClaire/USA TODAY Sports

"It's been my approach the whole year," Russell said. "I'm really not looking for a specific pitch. I'm really not trying to do too much. Just put it in play and see where it goes. It's been working out. It's a pretty easy approach. Just sticking with it."

Don’t forget about the "guys with big knocks," who Russell referenced. The Cubs have had a few of those lately as well, none more surprising or possibly more rewarding for the team than the hits that formerly maligned outfielder Heyward has delivered. He smashed a first-pitch fastball from Pirates starter Chad Kuhl into the right-center-field bleachers to extend a 1-0 advantage to 4-0, a clear signal that the rout was on.

"That was a really good line drive," Heyward stated. "He made a good pitch, but I was ready for one in the zone."

Kuhl's head was spinning by the time he left the game. He gave up nine runs in less than two innings, helping push the Cubs' season average to 5.42 runs per game, tops in the National League.

"It's another year together," Heyward said. "If I'm producing and Schwarber can settle in for a year, a lot of good things can come of it."

Back in spring, manager Joe Maddon hinted at an offense that could average over five runs a game for the entire season. When you consider weather patterns are less likely to help hitters in April, the Cubs might still have plenty of room for growth. After all, Kris Bryant hasn't really gotten going and neither has Schwarber nor Ben Zobrist. Javier Baez is the lone Cub really struggling right now, so we can expect improvement there as well. Even if Heyward (.294) or Miguel Montero (.379) hit a rough patch, the Cubs are so deep they probably won't miss a beat.

"It's always foot on the gas," Monday's winner Brett Anderson said. "There's no letdown."

"It has to be demoralizing for the opposing starters," he continued.

It feels like the Cubs are just getting started. They'll have their down moments -- every offense does -- but perhaps Maddon was too conservative. Five runs a game translates to 810 runs, just two more than the Cubs scored last season. They're on pace for much more right now and a slight increase could net them 900 runs. The last NL team to score that many was the 2003 Atlanta Braves.

It's way too early to know if that's possible for the Cubs, so they'll just enjoy the moment instead.