ARLINGTON – Some good things happened for the White Sox during a 6-5 loss to the Rangers Saturday night at Globe Life Park, dropping them to 36-38 and preventing the South Siders from getting to .500.

Tim Anderson homered, doubled and singled and matched a career high with four RBIs. Josh Osich, after losing a pregame cow milking contest to the Rangers’ Shawn Kelley, threw 2 1/3 scoreless innings of relief. And the White Sox defense threw out two Rangers at home, one at third and doubled another off first.

• Box score

And now for the less-than-perfect news.

Odrisamer Despaigne made his third start for the White Sox, and after a second straight rough outing, it very well could be his last trip to the mound for the organization. This start was especially tough with the White Sox grabbing a 4-0 lead with two outs in the first inning off Texas starter Lance Lynn.

By the time a 39-minute first inning had come to a close, the Rangers had fought back within 4-3 and, at the very least, taken momentum from the visitors.

“It hurts, but you do what you can,” White Sox manager Rick Renteria said. “He’s our guy there. I think that all things being equal, you try to work through it.”

“I just gave up a four-run lead and that’s unacceptable,” said Despaigne through interpreter Billy Russo. “I felt good at the beginning, but I didn’t have the best sequence. I didn’t mix up my pitches. I am falling behind in the count constantly. That’s something at this level you can’t do as a pitcher, because you know the hitters are going to take advantage.”

Nomar Mazara launched a 430-foot home run to right in the first -- his first of two off of Despaigne -- and Logan Forsythe doubled home another in the opening frame. Despaigne was helped out of the jam when Asdrubal Cabrera was nailed at home on a perfect relay throw from right fielder Charlie Tilson to second baseman Yolmer Sánchez to catcher Zack Collins.

Tilson and Sanchez also threw out Willie Calhoun trying to stretch a double into a triple with one out in the third, and Sanchez later doubled off Forsythe at first on Jeff Mathis’ line drive in the fourth. When the Rangers scored two in the sixth to take the lead, Mathis was thrown out at home on Leury Garcia’s Major League leading ninth outfield assist.

Those two runs were scored off reliever Evan Marshall, who entered with a 5-4 lead and a 0.00 ERA over 18 games and 17 1/3 innings. The Rangers put up the first earned runs against the right-hander this season.

“You would like to say it’s just one of those days, but honestly, it’s just a command thing,” Marshall said. “I’ve been pretty good with the ball, but four pitch walk, 3-0 to the next guy. That’s seven straight. I haven’t done that in a long time.

“Just a little bit off. It’s one of those things where a couple of close pitches go another way, and I’m in a different count and things go differently. You tip your cap. They were on me tonight. It’s a good streak for me to start this year. Like to start a new one tomorrow.”

Despaigne has not found nearly the same level of success as Marshall, albeit in a much more limited situation. He has a 9.45 ERA over three starts, with 24 hits and seven walks allowed in 13 1/3 innings.

Dylan Cease, the No. 18 prospect overall according to MLB Pipeline, could move from Triple-A Charlotte to the White Sox rotation as soon as the first week of July. But even without Cease and Carlos Rodon undergoing season-ending Tommy John surgery, as well as Dylan Covey and Manny Banuelos dealing with injures, the White Sox could be looking for another starting option.

“As far as we are concerned, Despaigne is here until he’s not,” Renteria said. “He will continue to get his opportunities until we all find either a different option, or we decide we need an option. Right now, we’ll still send him out here and try to allow him to do his job.”