It was not a matter Milwaukee manager Ron Roenicke seemed particularly eager to explore.
"I don't think we're so concerned about it," Roenicke said. "You guys are more concerned about the Cardinals than we are. We're concerned about winning ballgames, whoever it's against. It doesn't matter. We have to win games. Whether it's them, whether it's Pittsburgh or whether it's the Cubs, we don't care. We need to win."
After a nine-game winning streak, the Brewers must win Wednesday afternoon to avoid a three-game St. Louis sweep.
Miller, the 23-year-old Cardinals right-hander, allowed a solo home run to Aramis Ramirez plus two harmless singles over six strong innings to win for the first time this season and move to 4-0 with a 1.95 ERA in six career starts against the Brewers. Like Lance Lynn on Monday night, Miller came to Milwaukee struggling, having lost each of his first two 2014 starts with a 6.35 ERA. Like Lynn, Miller limited the Brewers to three hits.
Roenicke chalked it up to "two really good pitchers."
Ramirez agreed, but added, "If we want to win, we've got to beat good pitching. Of course we do have good pitching in the division. St. Louis has some good arms, Pittsburgh, Cincinnati, so if we want to be successful in this division, we have to be able to hit some good pitching."
Miller walked three batters but struck out seven, matching his total in his first two starts combined. In his six starts against the Brewers, he has 36 strikeouts.
"I don't think about that at all," Miller said. " I know there are stats against certain teams and you do better against others, but Milwaukee has a lot of talent. It's not necessarily the team. It's not necessarily anything. It's playing good baseball."
While Miller carved through Milwaukee's lineup, Estrada had to grind. He did not pitch poorly on Tuesday while allowing three runs on five hits, but still fell to 0-5 with a 5.60 ERA in 13 career appearances against the Cardinals, including 0-4 with a 5.52 ERA as a starting pitcher.
"It's frustrating that they keep winning these series against us," Estrada said. "It is a new year. I know obviously they won the series already, but it's early. We're a pretty good team over here. We're very confident in ourselves, and I think things are going to change for us, for sure."
The Cardinals pecked away against the Brewers right-hander this time. In the second inning, Cards catcher Yadier Molina was granted first base on a hit by pitch, moved to third on Jhonny Peralta's double and scored on a groundout by Mark Ellis, who celebrated his promotion from the disabled list with two RBIs.
St. Louis made it 2-0 in the third inning when Matt Carpenter walked and scored on Allen Craig's double, and 3-0 in the fourth inning on Ellis' sacrifice fly. The fourth inning could have been worse for Estrada and the Brewers had they not retired two Cardinals runners between third base and home.
"It was a grind, a mental battle with myself," Estrada said. "It was more trying to get through my delivery. My mechanics were off, and I kept thinking about it."
Ramirez finally put the Brewers on the board half an inning later with a two-out solo home run. It was Ramirez's second homer this season, his team-best 12th RBI and the Brewers' first run since the sixth inning of their Sunday victory over the Pirates.
The Cardinals added to their lead with two home runs of their own in the ninth against Jim Henderson, ending a scoreless streak by Brewers relievers at 18 1/3 innings.
Asked about the Cardinals' recent success against the Brewers, manager Mike Matheny said: "We're holding our breath. This is a good team. We don't take any out, any batter for granted here, because this is a team that has shown the rest of baseball what we know they've got. We just have to keep the kind of focus we have and just control our game. We know this is going to be a good team.
"We keep talking about it, but it's worth talking about. The National League Central is going to be tough, and these guys are going to be right there."