ST. LOUIS -- The St. Louis Cardinals' offseason search went from calculus-problem difficult to second-grade math the minute a trade that had nothing to do with them happened about a thousand miles away.

It wasn’t so much that the Cardinals had fixated on Adam Eaton as the only solution to the problem they had set out to solve: How to patch their leaky defense and squeeze a little action into their listless baserunning. What changed their thinking was what it took the Washington Nationals to land Eaton -- three bona fide pitching prospects, a haul of talent the Cardinals didn’t have and, if they did, couldn’t afford to move.

The names of the young pitchers traded to the Chicago White Sox in the Eaton trade -- Lucas Giolito, Reynaldo Lopez and Dane Dunning -- scared the Cardinals into the realization that they didn’t have the prospects to overpay in talent. That meant they were simply going to have to overpay. They’d have to shell out a painful number of dollars and a No. 19 overall draft pick (which many teams treat like several million dollars nowadays).

Once the Cardinals realized what it was going to take to keep from being left with their hat in their hand, they threw their hat in the ring quickly and boldly. They had a deal in place with Dexter Fowler barely more than 24 hours after the Eaton deal got finalized. They have called a Friday morning press conference to announce what many people already know, that Fowler will switch allegiances in the heartland’s best rivalry, presuming that nothing worrisome pops up on the physical he’s scheduled to get early Friday.

So Fowler is no longer a Cub -- he’s a Cardinal. Instead of being asked to break a 108-year championship drought, he’ll be asked to break a five-year championship drought. What’s similar is that, if both teams’ thinking was sound, he could be the final piece in both cases.

There had been so much smoke around Fowler and the Cardinals, it was obvious there had to be a flame or two smoldering somewhere. The rumors were so persistent by Tuesday that, at the winter meetings in National Harbor, Maryland, I asked Cardinals manager Mike Matheny flat-out what he thought of Fowler’s skills and how he thought they would fit on his team.

Matheny’s eyes lit up.

Yours would have, too, if you were asked about Fowler after you had managed a team that was the 17th-best fielding team in the majors and the second-worst at baserunning, per FanGraphs.

Matheny compared Fowler’s approach at the plate to that of his best player, Matt Carpenter. Not a bad comp. Matheny used the same adjective -- “exciting” -- that GM John Mozeliak had used several times the night before in describing who they were looking for. So Fowler will bat leadoff and Carpenter will be the Cardinals’ No. 3 hitter, with second-year shortstop Aledmys Diaz wedged in between and Stephen Piscotty batting cleanup to round out the top of a lineup that drips with execution and experience.

“The more players that you can have like that, I think the better off you're going to be,” Matheny said.

Fowler, 30, may not be the center fielder Eaton is, but Fowler has better instincts than incumbent Randal Grichuk and should play center field a couple of years for the Cardinals before they have to move him to a corner. By then, perhaps Grichuk will be ready for the CF challenge, or perhaps one of the Cardinals’ prospects will be ready.

In 2016, Fowler snapped a string of five consecutive seasons with negative defensive runs saved. Back in July, ESPN analyst Doug Glanville delved into how improved positioning helped fix Fowler’s defense.

The more exciting way to look at it for Cardinals fans is that Grichuk will now be playing left field, and he figures to instantly become a Gold Glove contender there. He’s more athletic than practically anybody else who plays left field in the National League. Even if he struggles at times with the move, he’ll be a massive upgrade over Matt Holliday or Brandon Moss, the sluggers who manned the position in 2016.

The other crucial gain for the Cardinals is that top prospect Alex Reyes gets to keep pitching for them. Any trade was going to cost them Reyes, their 100 mph-hurling young pitcher, or an uncomfortably large chunk of talent from their minor league pipeline.

Mozeliak had all but ruled out a trade on that consideration alone Wednesday night. So he pivoted. He closed the spreadsheet that showed him all the minor league players he would have to give up and opened the one that displayed the team’s balance sheet.

“You’re typically going to have to step out of your comfort level to get something done,” he had said.