Ryan Madson and Sean Doolittle joined the Nationals Tuesday. (Billy Hurst/Associated Press)

ANAHEIM, Calif. — A couple days before Ryan Madson and Sean Doolitte got word they had been traded to the Nationals, a rumor spread across the Oakland Athletics clubhouse. Starter Sonny Gray had been scratched from his start (he wasn’t). He was headed out in some deal or another (he wasn’t). So when Madson and Doolittle heard their names come up in trade rumors Saturday, they brushed them off.

Even when A’s Manager Bob Melvin called Doolittle into his office, the lefty didn’t think much of it. Then he saw other members of the A’s front office there, too.

“Then I knew,” Doolittle, who was drafted by the A’s in 2007 and has been with them ever since, said. “It was kind of a flood of emotions there for a little bit, but I feel like I got my feet back under me, and I’m super excited to be here.”

Both Doolittle and Madson bustled through their first day with the Nationals, from sessions with reporters to meet-and-greets with teammates to conversations with Manager Dusty Baker and Pitching Coach Mike Maddux. Their lockers are stationed next to one another in the visitors’ clubhouse, Doolittle’s with a No. 62 jersey and Madson with a No. 44. They spent a great deal of time sitting there together and chatting together in the outfield during batting practice, the long-awaited cavalry trying to get settled in a new stable.

“I’m going to say it gives him more comfort,” Madson said with a smile. “Cause he’s been with Oakland, just one team. I’ll say it’s probably more comfortable for him coming with me. But I’m going to lean on him, too.”

The Nationals will lean on both of them. Their desperation for relief help has been well-documented, written and discussed and etched in the minds of the baseball community since before the season began. Now, that help has arrived, but it is human and in the form of two men who were playing meaningless games a week ago and are now being heralded as saviors.

“You can say: ‘Oh, we need to do this.’ It’s not that. That will lead you down the wrong path,” Madson said, “… it is a road that you can go down and put that extra pressure and stress on yourself. But this game comes with enough [of that], so it’s good to just focus on what you do well and what makes you good.”

What makes Doolittle good is a plus-fastball he throws nearly 90 percent of the time and combines with a slider to devastate left-handers. What makes Madson good is a reinvented sinker, reliable change-up and rejuvenated curve, all of which have helped him compile a 2.06 ERA at age 36. Both of them have closing experience, and both will immediately slot into late-inning roles for this bullpen, though exactly which role remains unclear. Since the deal, Baker has been adamant that he will not name either man a closer right now, and he reiterated that Tuesday.

“We really have to watch Doolittle’s workload I was told,” Baker, who called Melvin for reports on his new relievers, said, “… we won’t be just setup man/closer situation as much as you’d like it to be. It’ll be sort of workload combination with what we have now.”

Doolittle has battled shoulder trouble in his career, and he lost significant time in the first half to the injury. He said Tuesday that he is ready to do whatever the Nationals ask of him — consecutive days, etc. — though Baker seems determined to limit his usage and be careful using Madson on back-to-back days, too.

“It was a probably a lot easier for Melvin to use them as he wanted to in Oakland because they weren’t in very many games,” Baker said, “so easier to use them in games when it was meaningful.”

The Nationals can also be cautious. Though their games are meaningful in the traditional baseball sense of the word, their National League East lead is large enough that they should not have to push either man beyond a safe limit, thereby preserving them for when the games become more meaningful in October. After two days in strange limbo, Madson and Doolittle now have two months to settle in before then.

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