It's rare for relievers to earn spots on the All-Star teams unless they are closers with high save totals, which is unfortunate for Griffin Jax because he's been one of the better relief pitchers in the American League this year.

After earning the save in Game 2 of Sunday's doubleheader with Oakland, Jax has a 2.30 ERA in 33 relief appearances. He's struck out more than a third of the batters he's faced (43 of 123) and he's given up only 20 hits and eight runs in 31⅓ innings.

Among relievers with at least 20 innings pitched this season, Jax owns the eighth-highest strikeout rate in the AL, and none of the pitchers ahead of him have a lower walk rate. He owns a 2.09 FIP (fielding independent pitching), which is sixth-lowest among AL relievers.

"He's really turned himself into one of the best relievers in the game," Twins manager Rocco Baldelli said. "He's got a very deep arsenal for a reliever and all those pitches are improving on a regular basis. His stuff is getting better on a regular basis. That's pretty crazy."

Jax pitched well last year, particularly dominant in the postseason, and he's found a way to find another gear. He's throwing his slider a bit harder than he did in the past. He's mixing in a curveball — opposing hitters are 0-for-8 with four strikeouts when it's the last pitch of an at-bat — that he threw sparingly in the past, but he didn't throw it at all last season.

"Everybody makes adjustments," Jax said. "If you're not thinking of ways to get better yourself, then you're far behind."

MVP Willi

Willi Castro made a highlight defensive play Sunday, fielding a ball off the left-field wall and throwing out Tyler Soderstrom attempting to stretch a single into a double. It was a one-hop throw and second baseman Kyle Farmer applied the tag for an out.

It was a play that had added importance when the next batter, J.D. Davis, hit a single to center that would've likely scored a runner from second base in the Twins' 6-2 win during the first game of the doubleheader.

"I thought we had no chance," shortstop Carlos Correa said. "Then he threw a bazooka, and we got him out. Willi is just a great player. If you think about it, he's the real MVP of this team. He plays everywhere. If somebody gets hurt, he replaces them with no problem. If you ask him to play second, he plays great defense at second base. If you ask him to play shortstop, left, center, it doesn't matter. He plays everywhere.

"When you have a guy like that, he makes you so much better as a team. I think we should appreciate him way more than we do already. He's a real great player."

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Castro, the only Twins player who has played in every game this season, has started at least eight games at five separate positions.

"Almost every decision that we have to make on the position player side — I don't even mean [only] roster moves — I mean everything that we do is affected, and the number of options that we have are almost compounded based on the presence of Willi Castro," Baldelli said.

Etc.

• Baldelli was asked why the Twins chose Bailey Ober to start the first game of Sunday's doubleheader with Chris Paddack in the nightcap. "One guy [Ober] has four kids, and he's up at 6 o'clock in the morning every day," Baldelli said.

• Matt Wallner continued his torrid June with two home runs in the St. Paul Saints' 6-3 road win over the Louisville Bats, which included an estimated 481-foot blast to center field in the first inning as the Saints swept the six-game series. Wallner is batting .397 this month with nine homers and 19 RBI in 14 games. Edouard Julien added a leadoff homer on the game's fifth pitch and Yunior Severino hit his third homer of the week.