MILWAUKEE >> A month since Farhan Zaidi declared the Giants’ rotation the best in baseball, those dreams have fizzled out along with their playoff hopes.

In the ideal scenario, Logan Webb and Blake Snell would have given them a two-headed monster at the top, Robbie Ray would look more like the 2021 Cy Young winner than a grizzled veteran coming off major surgery, and their pair of promising rookies would continue to build on strong first impressions.

On their most pivotal trip of the season, with their playoff hopes hanging in the balance, no San Francisco starter even threw a pitch in the sixth inning or later.

Hayden Birdsong walked off the mound Thursday afternoon with an out left in the fourth inning, and by the time the frame was over the Giants were in a six-run hole. They were shut out, 6-0, dropping two of three to the Brewers and finishing 2-4 on the road trip that started with another series loss in Seattle.

The right-hander born about four hours south of here, in Mattoon, Illinois, who celebrates his 23rd birthday Friday, was the lynchpin to the Giants’ pitching plans down the stretch. Understanding that he and Kyle Harrison would both surpass previous career-highs in innings, the Giants determined that Birdsong had pitched well enough to earn a full-time rotation spot and traded away a more known quantity in Alex Cobb to clear the decks.

Birdsong has taken the ball five times since the trade deadline, and the Giants are 0-5 in those games. The latest loss sent them seven games back of the Braves for the final wild card with 27 games to play, dealing another blow to their playoff chances that stood at 1.7% entering the day, according to FanGraphs.

Going 3-0 with a 2.45 ERA in five innings four times in his first six big-league starts, Birdsong hasn’t made it out of the fifth once in his past five starts. The six runs Thursday raised his ERA since the trade deadline to 9.16.