The theory of 1%

For several top players, a 1% increase in points won means cutting their ranking by half.

I recently came across an article by Craig O’Shannessey on atpworldtour.com which talked about the huge difference a 1% increase in points won can have on a players ranking. The article quotes stats from Dominic Thiem’s 2014 and 2015 seasons, in which he jumped from number 40 to number 20 (effectively halving his ranking) in the world thanks to a 1% bump in his points won.

The margins on points won in tennis is extremely tight (the average match is usually just a 55-45% split), so it is possible that a 1% improvement could have huge positive consequences on a ranking. However, not all points are created equal, so it is also feasible that you could improve your ranking by winning less points, given that you are winning the big ones at big tournaments. However, the data in the article is limited to a single player over a two season span? How does the “Theory of 1%” hold up for more players over many seasons? We dove into the numbers to find out.

Dominic Thiem vs. the Big Four

Let’s start by looking at 17-year span (1998-2015) and comparing Thiem to the Big Four: Federer, Djokovic, Nadal, and Murray. Only Federer has been active at the ATP world tour level throughout this whole period. The graph shows how each player’s percentage of points won in a year was reflected in his year-end ranking. The ranking axis is plotted in logarithmic fashion (factors of 10), meaning that a change near the top of the graph is much larger than near the bottom. Intuitively, it makes sense because do so because the lower the ranking, the more effort it takes to improve (i.e. lower) it.

The graph below shows all players follow a similar trend, winning about 45% of points around the 1000th-ranked level all the way to 55% at the number one spot. Based on our previous analysis, we know that match winners win 55% of points on average. So it makes sense that top-ranked players, who are winning most of their matches, are close to this number overall. The inverse goes for the 1000th-ranked players, who are losing almost all match. Note that the spread in the data is much larger near the top of the rankings (bottom right of the graph), presumably because at this level the effect of winning or losing a few points/matches can have larger effects on ranking points. Winning or losing a grand slam final, for example, can mean a difference of 800 ranking points.

ptsw_vs_yer_fig

The average trend for the 5 players corresponds to reducing (i.e. improving) the year-end ranking by a factor of 2 for each 1% of points won. We’ll call this the rank improvement rate. The higher the number, the steeper the slope of the line, and the more effective the player is at improving his ranking through small changes in his points won percentage. In other words, he is making the best out of fewer points won. Clicking on the graph will also take you to an interactive version of the data, where you can visualize the rank improvement rate for each player individually as well how their rank and points won percentage have evolved over time.

In terms of rank improvement rate for their overall careers, the five players rank as follows:

Player ATP Career Rank Improvement Rate
Rafael Nadal 2002-2015 2.17
Roger Federer 1998-2015 2.09
Andy Murray 2005-2015 2.03
Novak Djokovic 2004-2015 1.93
Dominic Thiem 2011-2015 1.41

Thiem’s rank improvement rate is low primarily because of the 2013 season, where he won almost 53% of points played, yet finished 149 in the rankings. In this season, Thiem posted an overall 4-2 record with just two tournaments played, making the quarters in both. This highlights a particular flaw with this metric: year-end ranking depends heavily on the number of matches played while percent points won does not. Thus in Thiem’s 2013, he simply did not play enough matches to make his point percentage count. This can be true also for players with injury seasons, as Nadal in 2012: a dominant season (56% of points won) cut short by knee injury after Wimbledon. Despite this, Nadal still managed to have the highest average rank improvement rate of all 5 players.

Overall, the theory of 1% seems to be a good rule of thumb: in general, players cut their ranking in half for every 1% of points more they win. It can be a flawed indicator in some cases: in the lower ranks because players simply do not accumulate enough matches to make percentages count and at the very top of the game where individual matches can be of large importance. Nevertheless, we see that despite the different trajectories each of the Big Four has taken to the top of the rankings, their rank improvement rates are all very close to 2. Fundamentally, this suggests that it takes as much improvement to go from #100 to #50 as from #2 to #1. Dominic Thiem has been a bit under that mark over his whole career due to a somewhat unusual season. But in the last two seasons (2014-2015), he has shown a typical rank improvement rate of 2, as O’Shannessy pointed out.

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