Sean Doolittle notched his 11th save in 11 chances with the Nationals on Sunday. (Jake Roth/USA Today)

SAN DIEGO — The Nationals headed to Houston Sunday evening for the Battle of the Ballpark of the Palm Beaches having taken three of four games from the Padres because of their pitching staff and, more specifically, their bullpen. Manager Dusty Baker asserted it after Washington’s 4-1 win at Petco Park Sunday. So did Daniel Murphy.

“The bullpen [was] unbelievable,” Murphy said. “It was absolutely unbelievable.”

A month and five days ago, before Washington began its midseason bullpen renovation with the acquisition of Sean Doolittle and Ryan Madson, imagining a world in which the bullpen carried the club was impossible. The relief corps was dreadful, the weak link on an otherwise championship-caliber ballclub. At the time of the trade, its 5.27 ERA was the worst in baseball. Opponents were batting .274, also the worst in baseball. A 1.46 WHIP was tied for the second-worst.

The bullpen’s failures irked the clubhouse. It often squandered strong starts. To overcome this and build a commanding lead in the National League East, the offense was scoring more runs than any other in club history. Things reached the point where Baker bluntly stated — more than once — that the bullpen needed an upgrade through trades.

Since then, also lifted by the deadline-day addition of Brandon Kintzler, the Nationals’ group of relievers does not resemble that unit. It is now one of the best in baseball.

Let’s start with the Padres series. Including Matt Grace’s spot start in Max Scherzer’s place, the Nationals bullpen logged 15 1/3 innings in the four games, allowing two runs on five hits. It wasn’t just the new acquisitions. While Madson was placed on the disabled list Thursday with a sprained right finger, Kintzler and Doolittle, who’s converted each of his 11 save chances as a National, combined to pitch four of the 15 2/3 innings. The bulk of the work came from the holdovers. And that didn’t include Enny Romero, who’s also on the disabled list.

Now let’s zoom out. Since July 18, the day Madson and Doolittle debuted, the Nationals’ bullpen has compiled a 3.34 ERA, good for eighth in baseball. Opponents are batting .200, which ranks third. It’s striking out 9.8 batters per nine innings, ranking sixth. It has a 1.09 WHIP, which is fourth. It’s 3.19 FIP sits in second.

Overall, the Nationals’ pitching staff, which includes one of baseball’s best starting rotations throughout the season, ranks third in the majors with a 3.53 ERA since July 18. At the time of the trade, its 4.09 ERA ranked ninth. The improved performance has compensated for Washington’s severe drop-off in run production, an expected happening when four starters, including Bryce Harper, are on the disabled list. Since July 18, the Nationals are averaging 4.1 runs per game. They’ve been shut out three times and reached double-digits twice. It took the Nationals until the 87th game of the season to get shut out. They scored 10 or more runs in 14 games before then.

In the 30 games since Madson and Doolittle arrived, the Nationals have won 11 games when scoring fewer than five runs. They did that 16 times in 92 games before the trade. Also since the trade, they are 6-3 in one-run games. They were 13-12 before.

“The main thing is that we pitch well,” Baker said. “And if you pitch well, then you don’t need as much offense. You’ve seen lately we haven’t had the same kind of offense that we usually have. But we’re finding ways to win games. It starts with the pitching. We’ve got good pitching every day. These guys are just trying to find a way to win.”

Ultimately, it only matters if the bullpen performs in the postseason. By then, the Nationals should have Madson and Romero healthy. Maybe even Koda Glover. And that unit, teamed up with the starting rotation and a lineup at full strength, makes the Nationals legitimate World Series contenders.

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