Using weekly ATP and WTA weekly rankings data from Jeff Sackmann's Github, we analyze the variance of the rankings of players currently in the top 30. We also exclude rankings data outside of the top 100 to minimize the variance impact of when these players first became professional, which is not indicative of their pro performance.
Looking at the WTA rank variance of the current top 30 players, we see that as expected, strong players like Serena Williams and Maria Sharapova who rank consistently at the top (excluding injuries) have low mean rank and low rank variance. For mid-tier players, such as Sam Stosur and Roberta Vinci, the variance on the whole becomes much higher.
Smaller circles, which indicate newer players with fewer weeks in the top 100 under their belts - such as Sloane Stephens and Petra Kvitova - have markedly higher mean and variance than the "power cluster" of consistent, top players. However, there are many mid-tier players with many weeks in the top 100, but still large variance and average rank. For newcomers, their ranking behavior is still yet to be determined - they could join either the consistent top players or the varying mid-tier players.
The graph of the top 30 ATP players show that ranking means are similar across men and women, ranking from 5 to 55. However, the variance is lower for men on the whole. Similar to the WTA results, small circles indicating newcomers generally trend to the right and the top of the graph, meaning higher variance and rank. This is due to the fact that these players undergo a lot of ranking movement when they first go pro, which is not indicating of their long-run ranking behavior.
Again, like in the women's results, men's ranking behavior breaks into two camps: the consistent, top players like Roger Federer and Rafael Nadal, and the mid-tier players who vary more, such as David Ferrer and Philipp Kohlschreiber. One surprise is that Novak Djokovic has such a low average rank but such a high ranking variance - Djokovic has sharp rises in the rankings, and variance penalizes that over small incremental increases.
Finally, looking at the graph of WTA rank variance vs ATP rank variance over the years with regards to the current top 30 players, we see that WTA is significantly higher than ATP variance. This is mostly attributed to periods of extreme variance exhibited by certain players, such as Maria Kirilenko and Jamie Hampton. On the whole, however, looking at the individual variances of the top 30 players, women do have higher rank variance than do men.