I also asked the Professor how this system would compare with ELO ratings and he states:

The main difference is that the ELO system is not based on the construction of a network. I expect however that ELO and Prestige Score provide highly correlated rankings.

Lastly, Prof. Radicchi stressed:

Players still in activity are penalized in a global ranking. The same is also true for players who started to play before the beginning of the ATP era (e.g., Rod Laver). In this sense, the use of Prestige Score is more fair when based on single years.

In other words, we will not know where our current era lies in comparison to previous eras. The Prof. Radicchi will rerun this analysis after this golden era of tennis ends. In the mean time, because Prof. Radicchi has provided the Top 100 prestige scores for each year since 1968, I decided to make this visual interactive story via Tableau. For your convenience, I will highlight a few points through animated GIFs and let you explore on your own!

Prestige Scores from 1968-Present (May 2015)

The first panel of the interactive let’s you visualize all the prestige scores v. prestige rank for each year. You can limit your field of view for a particular rank and year. You can also search for an individual player or group of players.

This first panel illustrates all the prestige scores. One thing I noticed is how the curve changed in the lower ranks relative to one another. The second panel takes the difference in prestige scores between one rank and the next rank. This illustrates the spread of competition. Typically, there is higher spread in the top ranks and it essentially decreases, as expected — the top players dominate a lot more and the rest are fighting for a spot. Let’s zoom in on the top players!

We can take the difference in prestige scores between one rank and the next, in order to determine how close one player is to the next. For instance, in May 2015, Djokovic is 1.12% higher in prestige score than Federer. Federer is 1.36% higher than Murray. So on, so forth. What is interesting is the early days: Nadal and Federer literally dominated so the huge peak was at rank 2 — meaning that the top two players were close but the rest of the competition is far away.

Top 25 Prestige Scores of All Time

You can almost see the ebb and flow of top players through the years. You will have to go the Tableau viz to see the entire timeline for the big 4.

After looking at how the spreads change over the years, I identified the top 25 prestige scores of all time and displayed the corresponding players in panel 3 so you can visualize their prestige rank and score in a timeline fashion.The list included players who may not have won slam titles, but have had a wonderful careers. One player that popped out was Hewitt in 2013. Hewitt ended the year with an ATP rank of 60 but with the but because he had five top 10 wins, his prestige score and rank was much higher.

Prestige Scores and Ages

Who was the most dominate player for each age?

ELO identified certain top tennis players of all time. I took this list and compared their prestige score with an estimated age. You can sort by ages and look at who had the highest score for their age. Nadal’s dominance through his early 20s is the absolute best while Djokovic dominates in his late 20s. Federer and Connors dominate later years. Time will tell how this visual will change in the later stages of the big 4’s career.

Changes in Cumulative Match Win % and Prestige Score

Cumulative match win percentage is typically used to illustrate the growth of players over time. However, if you take the difference between the year of interest and the next year, then you can see if there was growth relative to the past. In the image above, this is illustrated through the size of the box while the prestige score is in a similar color scheme.

The last question I asked Prof. Radicchi is for all those who found this entire analysis fascinating: What type of classes does someone need to take in order to learn something like networks?

I am myself teaching a course name “Performance Analytics” whose purpose is to introduce undergraduate students to mathematical and statistical methods used in the analysis of data from professional sports. Unfortunately, there are not many colleges that offers classes on network science. The number of graduate programs in complex systems and networks is, however, growing so I expect it will become easier to find specialistic courses in the near future everywhere. Traditional courses where graph (network) theory is partially covered are in math, statistics, and computer and social sciences.

Luckily for you I took an actual class entitled Networks in my freshman year and provided a link to an early draft of their textbook at the very bottom [from my professor’s website]. There are too many stories to tell from all of these charts. Once the year ends, I will update the interactive. I would love to hear your interpretations and observations so please feel free to leave a response with your findings by clicking the response tab below and do not forget to check out Tennis Prestige and the original paper!