The Rangers limped into the All-Star break on an eight-game losing streak, with a 38-57 record, last in the American League West. But Beltre entered the break leading the AL with a .337 batting average, 13 home runs and 51 RBIs, and Darvish is 8-5 with a 2.97 ERA in 142 strikeouts in 17 starts.
They approach the solution differently. Here are their words:
How they're holding up amid the team-wide collapse
Beltre: "I try. You have to look yourself in the mirror and see what you can do to help the ballclub. It doesn't matter what happened yesterday if you're losing 20 in a row. The next game is the one you're going to win and believe you're going to win. That might not be the case, but you cannot sit down and feel sorry for yourself and just crawl back and believe the season is over.
"I always have that in me, that I'm always trying to do what I can to win ballgames. It's not about me. It's about the team. I'm not going to help the team just trying to sit there and feel sorry for myself."
Darvish: "I don't know. That's the short answer. I cannot pinpoint what went wrong, when it went wrong, how it went wrong. But the team is still fighting. We're struggling but we're still fighting. It's really hard to motivate myself, especially with the team in the situation that we're in. People are not focused sometimes when we're in the situation. But as a professional baseball player, I just have to do whatever I have to do.
"I don't think I have, 100 percent. I'm always trying. But if you look at the numbers, it's not there. But I like to reflect on what I did in the first half, improve and take it to the second half of the season."
Their respective roles with teammates differ, with Beltre being an everyday player and Darvish working once every five games.
Beltre: "Instead of having three or four young guys, you have probably 15. You have to be a little more on things that they're doing to make sure they're doing things right. Obviously when you're losing things pop out more. In those cases you have to make sure not to make excuses why we're losing. We try to make sure everybody's doing things right."
Darvish: "I don't tell my teammates anything. They're professional baseball players, as well. They have to figure it out. In the midst of that, I just have to focus on what I'm capable of doing.
"I'd like to go deeper in innings. Every game I pitch, I'd like to go deeper and give more chance for the team so we can win."
On the All-Star Game itself, Beltre is 1-for-5 in three appearances. As for Darvish, well, he's been invited twice before.
Beltre: "No doubt it's been tough the last seven weeks or so. We haven't been playing the way we wanted to. It's been not fun to watch, not fun to be part of it. We know that we don't have the team we assumed to have out of Spring Training but we still have good enough players to compete. That is not reflected in our record. These four days will be for everybody on our team to sit back, relax and refresh and try to start over, not think about how we've been struggling."
Darvish: "It'll be interesting. Let's say I go to two more All-Star Games and not pitch. It'll be a record."
Thomas Harding is a reporter for MLB.com. Read his blog, Hardball in the Rockies, and follow him on Twitter @harding_at_mlb. This story was not subject to the approval of Major League Baseball or its clubs.