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For years, the Yankees and pitching coach Matt Blake have gained a reputation for taking relievers that have been mediocre — or worse — with other organizations and turning those afterthoughts into useful — or better — bullpen pieces in The Bronx.

There was Clay Holmes, who went from wallowing with Pittsburgh to Yankees closer, and other lesser-known arms like lefties Wandy Peralta and Lucas Luetge, as well as right-hander Ian Hamilton.

Even Fernando Cruz, whose stuff has always been recognized, is having more success with the Yankees than he did in his years in Cincinnati following his arrival in the trade that sent Jose Trevino to the Reds this past offseason.

All of them came to the Yankees with unimpressive résumés and quickly became better with the Yankees.

So why, with as good a track record as any in the majors over the past several seasons, has it gone so poorly for Devin Williams?

And how have Blake and Co. gone about trying to fix it?

“It was shocking to everybody,” Blake said of Williams’ early season struggles, when he was battered around for 10 earned runs, a dozen hits and seven walks in just eight innings in his first 10 appearances.

“Everybody was trying to figure out what was going on here and what are we missing?” Blake said. “He’s not getting the swing-and-miss and the strikes we were hoping for. We had all those questions and had to get it fixed on the fly.”

Williams is back in the closer role — at least temporarily, with Luke Weaver on the IL with a hamstring strain — but the former Brewer is beginning to resemble the pitcher he was in Milwaukee.

After putting up a whiff rate of just 26.8 percent on his changeup and 25.6 percent with his four-seamer in March and April, Williams was at 39.6 percent with his change and 47.1 percent with his four-seamer in May.

Those numbers are more in line with those he had with the Brewers last season, with a 48.8 percent on the changeup and 32.7 percent with the fastball.

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“I think he’s gotten comfortable in the environment,’’ Blake said. “He had the challenge of not pitching well and having it magnified in New York.”

On the pitching side, Blake said Williams was “maybe a little too overreliant on the changeup early on and his fastball command wasn’t great, which limited what he was doing.”

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Since then, Blake said Williams has been both “more unpredictable and more aggressive in the zone to control counts better so can get that expansion and chase in counts he wants.”

The results, while not vintage Williams, have improved.

His strikeout rate since May 7 has jumped from 11.4 per nine innings to 12.8 and his walks have dropped from 4.5 per nine innings to 1.5.

And in his past 13 appearances, he’s walked two and struck out 17 and his WHIP is 0.830.

“The best thing we did was being able to pull him out of the [closer] role without sacrificing our relationship with him and say, ‘We fully believe you will have success in this role, but let’s take a break and find some different spots to get you in to get you rolling,’ ” Blake said. “That freed us up to get him back on track and hopefully we can build on that.”

Williams still hasn’t gotten all the way back, and questions about whether he will be the closer the Yankees sought when they traded Nestor Cortes and Caleb Durbin for him persist.

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But Blake is more confident now.

“He’s in a good place and the rhythm of his attack plan to batters has gotten stronger,’’ Blake said. “He feels good about his process and we feel good about putting him in those spots again. He’s gonna have some hiccups along the way, but there’s much more stability to get through those now.”