Heavy Topspin

As I write this, Serena Williams is two matches away from winning her 24th grand slam. She’s been stuck on 23 since early 2017, which must be frustrating, since the all-time record is 24. Serena already holds the open-era record (for titles since 1968), one ahead of Steffi Graf’s 22. But Margaret Court is the leader across all eras, with 24 major championships between 1960 and 1973.

Williams is, of course, one of the greatest players of all time. Maybe the greatest. Court is also in the conversation, along with other luminaries such as Graf, Martina Navratilova, and Chris Evert. Cross-era comparisons in tennis are extremely difficult, because nearly everything about the game has changed. Serena’s technique, training, equipment, and tour schedule–not to mention wealth and celebrity status!–would all be extremely foreign to a 1960s or 70s superstar such as Court.

The challenge of cross-era comparisons hasn’t stopped fans from expressing opinions about where Williams should stand on the all-time leaderboard. Regardless of whose trophy cabinet numbers 23 or 24, Serena supporters tend to rely on three main arguments:

1. The level of competition is way higher now than it was back then.
2. Court won the Australian Open 11 times, back when it was the weakest of the four majors.
3. Court is an obnoxious blowhard whose opinions are unacceptable.

Number one is probably true, but if we’re going to attempt cross-era comparisons, I think the only valid way to do so is to treat all eras as equal. We’ll never know how Williams would have fared with a wooden racket, or how Court’s body would’ve responded to today’s more physical game. You can make a logical case that today’s players are simply better than those of a couple generations ago, who were better than the ones before them, and so on. But the very idea of a “greatest of all time” implies something different than the “greatest of all time measured by today’s standards,” so we’re going to treat all eras as equal.

Number three is also popular, but my database isn’t able to shine much light on that line of argument.

That leaves number two, the relative weakness of the Australian Open.

Aussie ease

Court won the Australian Open 11 times, more than any other woman has claimed a single major title. In itself, that’s not a negative. Nobody counts it against Rafael Nadal that he’s won the French Open 12 times. But in the amateur era–and for some years after tennis went fully professional–the Australian Open wasn’t a mandatory stop for the best players in the world. It was a long trip, and it hadn’t yet gained the prestige that it holds today.

Thus, it’s fair to conclude that Court’s 1963 Wimbledon title was a more noteworthy accomplishment than her trophy 1963 Australian Championships. Most of us would agree that we should discount those Australian Opens. But by how much?

Difficulty-adjusted slam titles

In the past, I’ve compared men’s greatest-of-all-time candidates by major titles, adjusted for the level of competition. In the modern game, the field is almost exactly the same from one major to the next, but the draw can make one tournament considerably more difficult to win than another. The same technique allows us to compare draw difficulty and field quality for tournaments from the 1970s when both varied. For instance, the difficulty of Court’s path to the 1973 US Open title rated as average, in line with many of Williams’s title paths. But her 1973 Australian crown was only two-thirds as difficult–one of the easiest paths to a major title in the open era.

It’s no accident that I’m using Court’s last few major titles as examples. By analyzing performances from the 1970s, we’re pushing up against the edge of the weakness of historical tennis data. It’s well-nigh impossible to estimate the exact difficulty level of most of Court’s titles, because so little data is available from the amateur era. Instead, we’ll need to approximate using the limited information we have.

My difficulty adjustments rely on Elo ratings, which I have calculated as far back as 1972. (We have fairly complete results back to 1970 or so, but it takes a bit of time to amass a decent sample of match results for each player and for ratings to stabilize.) Let’s look at the relative difficulty of the four grand slams in the first five possible years, 1972-76:

Major            Difficulty  
Australian Open        0.60  
French Open            0.54  
Wimbledon              0.99  
US Open                0.85

The average major title, 1972-present, rates 1.0, with more difficult paths earning higher numbers. The fields weren’t as deep in the 1970s as they are now, so the typical path to a slam title then was lower than 1.0. In this first five-year period, we see that Wimbledon was in line with the historical average, the US Open was a bit easier, and the other two quarters of the grand slam were considerably less challenging. If we follow my suggestion above, to treat all eras as equal–except for the weakness of the Australian draws–we need to normalize these difficulties so that the other three slams average 1.0:

Major            Difficulty  
Australian Open        0.76  
French Open            0.68
Wimbledon              1.25  
US Open                1.07

Extrapolating backwards

We don’t know much about the field quality of the Australian majors in Court’s prime. For lack of a better option, then, we’ll use the 1972-76 average, since that’s as close as we can get. These probably overstate the quality of the Australian draws relative to the other slams, but if we’re inching toward calling Serena the all-time leader at Court’s expense, we should make conservative assumptions, to give us more confidence in our end result.

Here’s what happens to Court’s career totals if we apply the normalized adjustments:

Major            Difficulty  Slams  Adj Slams  
Australian Open        0.76     11        8.3  
French Open            0.68      5        3.4  
Wimbledon              1.25      3        3.7  
US Open                1.07      5        5.4  
Total                           24       20.8

The same process–adjusting each slam for difficulty, and normalizing for era–makes milder tweaks to Williams’s and Graf’s totals. Serena ends up with 23.3, and Graf with 21.9. Neither is enough to give us reason to change how we view those players’ accomplishments. And both are better than Court’s modified tally.

The small herd of GOATs

Remember that this is not an era adjustment. To the contrary, this calculation is based on the simplifying assumption that all eras are equal, except for the fact that for many years, some of the best players didn’t travel to Australia, making that major easier to win than the others.

These numbers also–obviously!–don’t tell us that Court wasn’t one of the best ever. Even if she had skipped her home slam, she still would’ve retired with 13 majors, plus a pile of doubles grand slam trophies and a long list of other career accomplishments. If Australia were less geographically remote, she probably wouldn’t have won those eleven titles–but she may well have won eight.

For all of Court’s accomplishments, she loses her top spot on the sport’s most hallowed list once we account for the weakness of the early Australian Open draws. At the very least, she falls behind Williams and Graf. Remember that my adjustments are conservative ones, so if we collect more data and discover that we should more aggressively discount her 1960’s Australian titles, her resulting total might leave her closer to 18, tied with Evert and Navratilova.

Serena may never equal or beat Court’s 24 titles. But even if she retires with 23, the modern level of competition–which showed up at every major, every year–means that she already deserves her place atop the leaderboard.