After Roberta Vinci, the No. 43 ranked player in the world, defeated No. 1 Serena Williams in the U.S. Open semifinals on Friday, someone asked Vinci if she remembered a bigger upset in women’s tennis. She answered, “No. Just today.”

We took a more quantitative approach and arrived at the same answer. Vinci’s victory was the biggest upset in women’s Open-era tennis history this late in a Grand Slam tournament.

Before the tournament, we used Elo — the ratings system that takes into account players’ match results and quality of opposition and creates power rankings for anything from chess to the NFL — to rate the best women’s tennis players of all time. According to this system, Williams is one of the greatest but not the greatest. (Despite her loss, however, she is still playing well enough to keep building her case.) It’s this system that shows just how historic Vinci’s upset was.

Baseline: A U.S. Open mini-podcast

Carl Bialik and Grantland’s Brian Phillips discuss Roberta Vinci’s upset of Serena Williams and preview the Djokovic-Federer final. For more subscribe to our sports podcast Hot Takedown.

As of Aug. 23, Williams’s Elo rating was 2505 and Vinci’s was 1852 — a difference of 652 points. That gave Vinci about a 3 percent chance of beating Serena. The biggest previous Elo gap for an upset in a Slam quarterfinal, semifinal or final was 574, when Czech player Helena Sukova beat Martina Navratilova in the 1984 Australian Open semifinals. The upset ended a run of six consecutive Slam titles for Navratilova, who never managed to win a calendar-year Grand Slam.

Sukova’s elation was short-lived. Chris Evert beat her to win the title. And that’s not atypical. The winners in these historic upsets have gone just 1-7 when trying to repeat their feats in the next match at the same event.

The real upset is that Vinci made the semifinals at all. These upsets are so rare late in majors because by the quarterfinals or later, both players’ ratings are usually far closer to each others’ than Williams’s and Vinci’s were.

Bigger upsets have happened earlier in majors. Katarina Studenikova’s second-round upset of Monica Seles at Wimbledon in 1996 overcame an Elo gap of 764 points. Williams herself has suffered bigger upsets. Her loss in the third round of Wimbledon in 2005 to Jill Craybas occurred despite a 710-point gap in their Elo ratings.

Men suffer upsets too, despite their best-of-five-set format that gives favorites more chances to come back and assert their superiority. The biggest in a quarterfinal or later was Christophe Roger-Vasselin’s defeat of Jimmy Connors, whose Elo rating was 580 points higher, in the 1983 French Open quarterfinals.

Elo doesn’t capture the stakes of Friday’s upset. Williams’s quest for the Grand Slam made Friday’s result loom larger than most before it. And the upset is even more shocking when you consider that Williams has an extraordinary record late in Grand Slam tournaments. So what happened Friday?

“I thought she played the best tennis in her career,” Williams said in her postmatch press conference about Vinci. ”I think she played literally out of her mind.”