CHICAGO -- It’s one thing to earn the moniker “The Korean Babe Ruth.” It’s quite another to leave the Pacific Rim, sign in the major leagues and spend a month putting up Bambino-like numbers. It’s yet another thing to cope with the aftermath of sudden fame at baseball’s highest level.

Eric Thames has come through all of it just fine, with a little help from his long-ball-hitting friends, and that has made the Milwaukee Brewers one of baseball’s most interesting teams.

When we last checked in with Thames, he was on a historic run on his way to an 11-homer April in which he posted a 1.276 OPS. The Korean Babe Ruth allusions became widespread because Thames became a fixture on television, radio and podcasts, and he was the subject of numerous articles. Plus, the Brewers were off to a good start, so it made for a nice, little April story.

“It was definitely an honor to be wanted by all the shows and personalities,” Thames said. “But it got tiring. It got to a point where, you know, I’m really big into my routine and doing the same things. It was kind of like the first time in my life I got tired of talking.”

Thames cooled off, in no small part because he started getting fewer pitches to hit. Then, not long after Thames’ opportunities to drive the ball began to dry up, his star teammate, Ryan Braun, went on the shelf with a calf strain. Panic in the streets of Milwaukee! The regression monster is loose!

What do you think happened? The Brewers got even better. By the time Braun returned from the disabled list for Sunday’s game against the Cubs after a nine-game absence, the Brewers had won seven of the games he missed and moved into first place in the NL Central. The short-handed lineup ranked third in the majors during that span by averaging six runs per game.

That average was maintained Sunday, when the Brewers scored five late runs in a 13-6 loss to Chicago. Thames had to leave the game early when his calf tightened up as he legged out a groundout. It has become an ongoing problem for him, and every time it crops up, the Brewers proceed with caution. It’s a hard pill for the psyche of a player as routine-driven as Thames to swallow. Indeed, after the game, he stewed in front of his locker. The smattering of media waiting on him eventually dispersed, not wanting to poke the grumbling bear. Hey, the guy cares.

“I’ve been very impressed with how a number of our players have adjusted in-season, and certainly Eric is among them,” Brewers GM David Stearns said. “Pitchers throughout the industry have clearly taken notice of what he did early in the season, and they’ve unquestionably adjusted their approach. Eric has stayed very patient. I think that speaks to his dedication to the team as a whole.”

The amazing thing about the Brewers’ start is that they have rarely had all of their key pieces rolling at the same time. But the depth on this team is formidable. To wit: While Braun was out, Thames’ power game slumped. He managed just a pair of singles during Braun’s absence, and he missed time with strep throat. Teams were staying away from him, testing the patience he worked so hard to hone during his time in Korea. In May, only 42.1 percent of the pitches Thames has seen have been strikes. Only eight qualifying big leaguers have seen fewer. But the Brewers have continued scoring and winning.

“We always want to focus on the guys with the biggest numbers,” Brewers manager Craig Counsell said. “On this team right now, there are a lot of guys who we want to just be the best version of themselves. That’s what has led to a lot of our offensive production. A lot of guys are contributing. It doesn’t have to be Eric every day or Ryan every day. Guys have taken their turns being that guy -- driving the bus, as we like to say. It’s been a lot of different guys, and to me, that’s how you consistently score runs in this league.”

Given that Thames’ mantra is “don’t chase,” and he isn't getting strikes, that leaves but one alternative, and he has accepted it. In other words, he has taken his walks and trusted his teammates to do their work. Those two lone singles Thames posted during Braun’s absence? During that time frame, he put up a .429 on-base percentage.

For the season, his .432 on-base mark ranks eighth in baseball. Yet it has been a challenge, as it is when you know you can hit a major league fastball 450 feet. While Thames’ chase rate during May is better than league average (22 percent), it is up 5.7 percent from April. He knows that in this Milwaukee lineup, he doesn’t need to do that. But it would be nice to get some pitches to drive.

“Oh my gosh,” Thames said, when asked if he is indeed getting fewer fat pitches. “It’s tough, you know. This is the big leagues. You’re not going to get cookies every time. What made me a good hitter in April was that when I got the good pitch, I didn’t miss it. Now the guys are just pouring stuff on the black, you know, close enough to the strike zone that it could be a strike. That’s just the way it is. There will be other times when it will go the other way, when I will get more pitches to hit.”

The Brewers’ record is supported by their run differential and could be even better, if not for some shaky ninth-inning results that happened before Milwaukee shifted its closer role from Neftali Feliz to Corey Knebel. Now it gets really interesting for Stearns, who faces the same round of questions that confront every decision-maker for teams on the verge of shifting into win-now mode.

“I don’t know that our organization can ever look at exclusively a short-term strategy,” Stearns said. “And that applies to this year, next year, five years from now. We’re an organization that has set a path and a goal to compete consistently. In order to do that, we have to continue to balance the near-term needs of the major league team with the long-term strengths of the organization. That is our focus now and will be our focus going forward.”

The Brewers feature the third-youngest group of position players in the majors. That’s despite the fact that Stearns’ thrifty shopping on the free-agent market landed him two post-30 contributors whom, entering the season, no one paid any attention to. One is Thames, and the other is 31-year-old journeyman Eric Sogard. If Thames was the April sensation, May has belonged to Sogard.

Sogard, who looks more like a middle school math teacher than a ballplayer, had not played in the majors since 2015. However, Stearns called him up when Braun went on the shelf. Sogard proceeded to homer off New York’s Matt Harvey in his first Milwaukee appearance and has been doing his best Roy Hobbs impression ever since, hitting .500/.621./.909 in his first eight games. Just like Stearns drew it up, right? Well, kind of, because almost any time a developing team seems to make an unexpected leap forward, there are surprise contributions from role players.

“Everyone that we’ve asked to play a role on this team has done a really nice job,” Stearns said. “[Sogard] is a great example of a player who worked himself back from injury, put in a lot of work, got an opportunity and has been a really important part of this team since he got here.”

How real are these Brewers? Consider this: The Brewers own a plus-27 run differential after Sunday’s game, bettered in the National League by only Washington, Arizona and Los Angeles. Milwaukee’s odds of making the postseason, according to the simulations at fivethirtyeight.com, have improved from 13 percent to 36 percent. It still feels tenuous, but it also feels kind of real.

Still, don’t expect a repeat of 2008, when the Brewers traded four players, one of which turned out to be top-notch outfielder Michael Brantley, to the Indians for a half-season of CC Sabathia. Sabathia was dynamite for Milwaukee, going 11-2 with a 1.65 ERA in helping the Brewers into the postseason. Then he signed with the Yankees. This time around, the Brewers are looking to straddle the line between maximizing the opportunities of this season and prioritizing the long-term objective of annual contention.

“I don’t know that what we’ve done to this point has impacted our overall strategy,” Stearns said. “That’s true whether it occurs this year or any year. What it does is it continues to inform us about our players at the major league level and the steps they’re taking.”

Another thought with a team potentially shifting into win-now mode is this: Why should they be so eager to shake up a mix of players that is already working really well?

“I think that is a big part of the calculus,” Stearns said. “We have confidence in the players we have. We have confidence that these guys are going to continue to get better. I think you can look at some of our players and see meaningful strides that the players have taken in just the first month of the season. If that continues, our team is going to continue to improve.”

Meanwhile, Thames is sticking to his routine, whether or not the national shows come calling. He’s still in the early stages of getting acquainted with Milwaukee, a perfect locale for a player with a frequently expressed appreciation for good beer. In fact, on Monday, Thames, along with Knebel and teammate Oliver Drake, are teaming up with a national brewery based in Milwaukee to mix up a new beer that will be served for a limited time at Miller Park. You could say that, in more ways than one, something special is brewing in Brewtown.

“Our team is feeling so much emotion right now,” Thames said. “We can feel it. It’s not like, ‘Wow, we’re in first place now.’ We know that we’re a good team now. It’s a good thing to be a part of that. Even my family said watching the games that we look like a team that is jelling. Everybody is having fun. We’re picking each other up. We know we’re good, and we go out there and let our play speak for itself.”