Mathematical Analysis of Women's Tennis Open-Era Challenges Serena's GOAT Status

On the eve of the start of her campaign to secure her 22nd major title, fourth of the year, Serena Williams's claim to the title of Greatest of all Time is being analyzed in an article at Five Thirty Eight titled "Serena Williams And The Difference Between All-Time Great And Greatest Of All Time." The article uses a particular mathematical technique called computing an ELO rating to assign a number (which varies over time) to the relative strength of players in head-to-head competition. The graph of all the major champions (Navratilova, Evert, Graf, Seles, Henin, Venus and Serena) are depicted.

From the graph it can be shown that Serena does not achieve the highest ELO rating of all time.

Elo definitely puts Williams in the top tier of female tennis players, but it tells a slightly more muted story than other measures. In particular: While Williams has been great, and has been doing unprecedented things for a player of her age, the relative weakness of the tier of players beneath her undermines her GOAT claim. 

The possibility that Serena has benefited from “weaker competition” is pretty conventional, and certainly debatable, but Elo gives us a useful way to examine exactly what that possibility means and what it implies.
For the unfamiliar, Elo is a rating method originally developed for chess, but eminently suitable for tennis. It’s very simple: Two players enter a match with Elo ratings based on their prior results. Elo uses their ratings to predict their head-to-head outcome, and then updates those ratings depending on the outcome.² It’s not without limitations: Elo makes every head-to-head prediction based solely on the two players’ ratings, which, in turn, are only affected by previous match results.

However, one aspect of Serena which makes her career unique is her 2nd peak in her ELO rating, which has happened at an unprecedented stage of her career, in her 30s. It also claims that Serena was at her best in 2003 (when she won her first Serena slam).

I understand that these results will disappoint some and encourage others but I appreciate the analysis in that bring at least a measure of quantitative rigor to a discussion which is essentially Qualitiative and subject in nature: Who is the Greatest of all Time? In my mind, the figures STILL indicate hat the answer is Serena Williams.