The women’s final erupted with controversy when Ramos first gave Williams a warning for coaching, drawing a vehemently indignant reaction for the 23-time Grand Slam winner, then a point deduction for breaking her racket in frustration. After Williams repeatedly expressed her displeasure with Ramos, including calling him a “thief,” he cited verbal abuse in giving her a penalty that changed the second-set score from 4-3 to 5-3, and Williams, already down a set, quickly fell after that, 6-2, 6-4.

“I’ve seen other men call other umpires several things,” Williams said after the match, which ended with booing during the trophy presentation. “I’m here fighting for women’s rights and for women’s equality and for all kinds of stuff. For me to say ‘thief’ and for him to take a game, it made me feel like it was a sexist remark. He’s never taken a game from a man because they said ‘thief.’ ”

Asked about those comments, Great Britain’s Jamie Murray, who won the mixed doubles title with American Bethanie Mattek-Sands, said, “I think that’s a bit far-fetched.”

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“I think the umpire did what was within his rights,” Murray, a six-time Grand Slam doubles title winner and the older brother of former world No. 1 Andy Murray, told the BBC. “Coaching is common, a lot of people are doing it, some people aren’t getting called for it.

“To get called in a Grand Slam final was perhaps a bit tight, but I think the reaction was pretty overboard.”

The controversial events of the women’s final cast a shadow over Osaka’s triumph, the first for a tennis player representing Japan, and it has continued to be the talk of the tennis world and far beyond. Some of the sport’s most recognizable figures have taken differing positions on who was most to blame, with the likes of Billie Jean King, Chris Evert, Novak Djokovic and Pam Shriver pointing at Ramos, while Martina Navratilova and Mary Carillo, among others, claimed that Williams was more at fault for her behavior.

While some of Ramos’s critics have asserted that he should have acted with more discretion with regard to penalizing Williams, King was more forthright in echoing the charge of sexism. “Did Ramos treat Williams differently than male players have been treated? I think he did,” the 12-time Grand Slam singles titlist, who is also known for her advocacy for women’s rights, wrote in a guest column for The Washington Post.

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At a Davis Cup event in Zadar, Croatia, where U.S. men are set to take on that country — with Ramos serving as chair umpire — players tried to choose their words carefully when asked about the Williams flap. However, several members of the team made it clear that they thought Ramos did not treat Williams unfairly.

“It’s been polarized and in some ways politicized, but we have no doubt that Carlos was just enforcing the rules as he sees them,” captain Jim Courier, who is overseeing a squad that includes Steve Johnson, Mike Bryan, Frances Tiafoe, Sam Querrey and Ryan Harrison, told the Associated Press on Thursday.

“Look, I don’t want this to come out the wrong way,” Johnson said. “But he enforced rules that have been enforced on me over the years.

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“I’ve never been called for coaching, but the racket abuse, the verbal abuse,” Johnson added. “That’s just part of the sport. I think a lot of it maybe got overamplified because it was the finals of the U.S. Open.”

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The AP reported that U.S. Tennis Association President Katrina Adams, who quickly came out in support of Williams and claimed that a gender-based double standard existed in her sport, was overheard apologizing to Ramos at the Davis Cup site. Umpires are generally barred from discussing specifics of matches, and thus Ramos has had little to say about the controversy, other than telling a newspaper in his native Portugal, “It’s a delicate situation, but ‘a la carte’ arbitration does not exist. Do not worry about me!”

On condition of anonymity, though, other umpires have expressed major displeasure with Adams and WTA CEO Steve Simon coming out publicly in favor of Williams. A report Tuesday in The Times of London claimed that some umpires were discussing a possible boycott of Williams’s matches out of dismay over seeing Ramos get “hung out to dry.”

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“The umpiring fraternity is thoroughly disturbed at being abandoned by the WTA,” Richard Ings, a former top-level umpire who is now retired, told ESPN on Tuesday. “They are all fearful that they could be the next Ramos. They feel that no one has their back when they have to make unpopular calls.”

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Another retired umpire, Félix Torralba, downplayed the boycott talk Wednesday, saying to the New York Times, “I would put my hand on fire that it doesn’t come from the professional umpires.” He added, “It might be a comment in a room of people related to officiating, but not from people that work the tour, that are international officials. I would doubt that. I’ve spoken to colleagues. I don’t believe that.”

In Croatia on Thursday, Bryan described Ramos as having “always been a fair, levelheaded guy” who had “made a decision in the heat of the moment” at the U.S. Open.

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“I think we’re all cognizant of the fact that three strikes and you’re going to get a game penalty,” Bryan said.

“It’s hard to say one side or the other without causing a big stir,” Harrison said of the controversy, calling it “a situation where we know Serena is unbelievable, she’s iconic, and we know that Carlos is there because he’s worthy of being there for those matches.”

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“I know Carlos and I know he’s not looking to put himself in a difficult position,” Harrison continued. “I truly believe he was trying to do what he felt like was right at the time, and always in heated situations it’s going to be a very sticky, sticky spot, whenever it’s in a Grand Slam final like that.”

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One potential penalty on which Ramos won’t have to exercise his judgment in Croatia is coaching, because Davis Cup rules allow captains to sit courtside and give players instruction. If an area of consensus has emerged from notable tennis figures commenting on the Williams episode, it’s that coaching is rampant, gets called inconsistently and should simply be allowed in all tournaments.

“If tennis would catch up with the 21st century and allow coaching on every point, the situation on the court [at the U.S. Open] would never have escalated to the level of absurdity that it did,” King wrote for The Post. “Every player, after all, still has to play the match — she has to execute on every point, and she should never be held responsible for the actions of a coach. Coaching happens all the time, at all levels of tennis. So why not just allow it?”

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Until coaching is made legal, though, Murray said that players need to accept the possibility that they might get penalized for it. “I’ve seen a lot of people get called for coaching before, and you might have a grumble and stuff, but you get on with it,” he told the BBC.