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Are you a fan of 1970s men’s tennis and esoteric statistical investigations? If so, you’re going to love Netflix’s new documentary about Guillermo Vilas, and his long-running quest to be retroactively crowned a world No. 1 player. And if you care about the triumphs and heartbreaks of great athletes, you might love it even more.

As you can probably tell from my opening question above, Settling the Score, which was released on Tuesday, runs on two very different narrative tracks. The first, and by far the most colorful, traces Vilas’ career, and the transformations that defined it.

When we first encounter young Guillermo in Buenos Aires in the late 1960s, he’s a clean-cut 16-year-old jock. He sports a side part, wears conservative, all-white tennis clothes, swings a wooden racquet, and wonders if his well-heeled parents are right, that he’ll never make a decent living playing tennis. From there, we watch as Vilas’ hair grows longer and he evolves into a thoughtful young pro in the early ’70s, one who writes poetry, plays in a jazz-rock band, and injects some counterculture style into his clubby sport.

Finally, we see Vilas, at the urging his imperious coach Ion Tiriac, leave all of his other interests behind and turn himself into a muscle-bound tennis machine, one who wins 145 matches, 16 tournaments and two majors over the course of his Herculean 1977 season. His 46-match win streak from that year is still the men’s Open era record. And yet Vilas is denied the No. 1 ranking. Somehow, despite striking out at the Grand Slams, Jimmy Connors finishes at the top that year.

“I was winning and winning and could never take the next step to No. 1,” Vilas told me in 2017. “The answer was always the same: ‘Still second.’ I felt helpless. The system did not help me at all.”

In those days, a player’s ranking was determined by averaging all of his results. This meant that the more Vilas played, the less each of his individual wins mattered. Going by today’s best-of-18-result system, where majors are weighted more heavily, Vilas would have finished No. 1.

"Settling the Score" captures Guillermo Vilas, the No. 1 that wasn't

"Settling the Score" captures Guillermo Vilas, the No. 1 that wasn't

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Vilas, during his historically dominant 1977 season. (Getty Images)

The movie’s second narrative track concerns the quest, by Argentine tennis journalist Eduardo Puppo, to rectify that injustice. In 2007, Puppo read that the WTA had amended its rankings from 1976, and in doing so had lifted Evonne Goolagong Cawley to the No. 1 spot for two weeks. It was a short reign, but a big deal for Goolagong Cawley. Puppo thought he could do the same for Vilas, who had been derisively branded “The Eternal Second” by the Argentine press. Vowing to prove that his countryman had been No. 1 for at least some point, Puppo took a 12-year dive down a rankings rabbit hole. He dug through the ATP’s records, tried to recalculate the rankings from 1973 to ’78, and quit in despair at least twice.

“He put Vilas’s ATP ranking at the top of his priorities,” Puppo’s wife tells says, with a half-incredulous smile.

But it was his wife who helped Puppo find the answer he was looking for. Seeing that he was at a dead end, she encouraged him to seek assistance from the online tennis-fanatic community. Puppo eventually connected with a Romanian mathematician named Marian Ciulpan. Stunningly, Ciulpan discovered the information Puppo had been seeking: That Vilas would have been ranked No. 1 over seven weeks in late 1975 and early 1976, except that the ATP didn’t publish rankings during those weeks. This wasn’t unusual; in those pre-digital days, putting out a rankings list was a time-consuming process, and the ATP only did it 13 times in 1975. Now, of course, the tour publishes them weekly; if that had been the case 45 years ago, Vilas would have been No. 1. Puppo and Vilas have petitioned the ATP to change the historical record, but have so far been rebuffed.

“We just can’t adopt this version of rankings as official history,” then-ATP CEO Chris Kermode told Chris Clarey of The New York Times in 2015. “Otherwise you would have everyone coming in and saying the same thing. Where do you stop?”

Perhaps most persuasively, Kermode “cited the fact that if the rankings had been different, then tournament seedings would have been different, meaning players would have faced different opponents.”

"Settling the Score" captures Guillermo Vilas, the No. 1 that wasn't

"Settling the Score" captures Guillermo Vilas, the No. 1 that wasn't

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Borg and his good friend Vilas, at the 1978 French Open. (Getty Images)

This might be the point in the review where you would expect a critic to write a sentence like this: “While Vilas is the most famous character in the story, it’s Puppo who turns out to be the most fascinating.” That isn’t the case here, at least for me. It’s Vilas who still fascinates in Settling the Score. Maybe it’s the fact that, compared to his more famous contemporaries—Connors, Bjorn Borg, John McEnroe—the Argentine wasn’t covered as thoroughly, especially in the U.S. There’s a lot to learn about Vilas, and while at first glance his desire to be elevated to No. 1 might seem frivolous or even pointless, the movie shows us why it means so much to him.

Settling the Score is cleverly structured in a couple of ways. First, it sets up his two rivals for the No. 1 ranking in 1977, Connors and Borg, as opposing characters in his life.

Connors is his first “enemy,” as Vilas describes him. When they meet at the Orange Bowl as juniors in the late ’60s, Jimbo is the favorite to win the tournament. But Vilas thinks he looks small and “weak,” and that his newfangled T-2000 racquet is just a way to compensate for that weakness. When Vilas beats Connors, it helps convince the Argentine that he can hold his own with anyone, from anywhere. There had never been a South American men’s tennis star to that point, and until his Orange Bowl success, Vilas hadn’t dared to imagine that he could be the first.

Borg, by contrast, is cast as Vilas’ early friend. On court, the two long-haired baseliners practice for hours together and help each other with their technique; off-court, as Borg says, they hang out and eat a lot of “jogurt.” One of the highlights of this movie for me was seeing extended clips of their 1975 final at Roland Garros. As usual, when it came to the big matches, Borg had Vilas’ number—a fact that Settling the Score glosses over. The movie doesn’t mention, for example, that one reason Vilas was so dominant in 1977 is that Borg chose to play World Team Tennis that year; Vilas never had to face his nemesis during his 46-match win streak.

"Settling the Score" captures Guillermo Vilas, the No. 1 that wasn't

"Settling the Score" captures Guillermo Vilas, the No. 1 that wasn't

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The Argentine and his Romanian taskmaster coach, Ion Tiriac, in 1982. (Getty Images)

But Settling the Score is less about Vilas’ rivalries with other players than it is about the battle between the two sides of his own personality. Willie was part poet and part grinder, but only one of those two sides would take him to the top of the rankings. So, with Tiriac as his taskmaster, Vilas jettisoned everything in his life that didn’t help him win tennis matches. Tiriac drove him through lacerating, six-hour practice sessions, and made himself into his mentor, manager, father figure and confidante. Opponents joked that Vilas needed to look over to Tiriac to make sure it was OK to shake hands when a match was over.

Their work paid off in one of the greatest single-season campaigns in tennis history, but success came with a price. We can see it during the Masters event in New York at end of that long season. Rather than watch the final between Borg and Connors, Vilas traveled upstate to visit Woodstock, where he wandered around, trying to recapture some of the ’60s spirit that he had no time for as a player. We can see the price Vilas paid even more clearly when he invites his father, Jose Roque Vilas, to travel with him to the Australian Open in 1979. Vilas wins the title, but his father tells him that devoting everything to tennis isn’t the right way to live. He vows never to watch Vilas play again, and according to Vilas, he stuck to his word.

The movie ends with Puppo visiting Vilas in Monte Carlo. Their quest has ended in failure, and part of Vilas seems broken by it. Over the last 15 years, as the Big 3 have put a stranglehold on the No. 1 ranking, the value of that being a member of that exclusive club has only increased. Vilas was a player who gave up everything to be No. 1, and succeeded. But he’s not allowed to say it.