In my introduction to this series, I talked about Prestige Score and provided a graphic illustration of the Big Four network and a graph of the overall prestige score distribution for players based on Prof. Radicchi’s website. However, while working out an example of the Prestige Score for Charles Allen, it struck me that it is very easy to calculate this distribution for the Big Four only. The overall equation, which you can found on Tennis Note #25, simplifies to four simultaneous linear equations and four unknowns (the prestige score for each player). Solving the system for each year, results in the Prestige Score distribution illustrated below:

This is for only the network of the big 4. Prestige Score totals to 1 (100%) and is based on h2h between players. In case you are wondering, one of the big reasons why Rafa is so high — he has the least total losses to members of the Big Four (42). You can also see Novak rise over the years — especially when he over took Roger Federer (2011). Federer’s record against the Big Four is the worst (57). This graphic would change if I disregarded Murray.

There are a few points I would like to make:

This does not treat each year independently. This is based on cumulative records between players. I started with 2006 because all the players had at least one loss against one of the members by then. This simplifies the equation. In some sense, we like to state that the Big Four did not rise until 2008 (which can be seen in the overall Prestige Score graphic). This graph is current up until March 20, 2016. I will try to update it over time for those who discover this note at a later date. One thing to really take into consideration — in order for the Big Four to play each other 205 times (if I did my math correctly), they mostly faced each other in later rounds due to their higher ranking and how seeding works in draws. There are several charts on Wikipedia that illustrate their dominance in terms of tournaments.

There are a few observations I make immediately:

Rafael Nadal has always had a superior record to the other members of the Big Four. He has the least losses to the other three members. However, these records have evened out with Novak Djokovic. Thus, you see his Prestige Score, which was lopsided for so long, slowly decrease over time. Although it is easy to point out major years like 2008 and 2010 as well as his steady increase from 2011 until 2014 when he starts to fall. Novak Djokovic had a brilliant 2011 season. So brilliant, that it kickstarted his Prestige Score. He had only 2 losses to the Big 4 and won 12 times against them (6 against Nadal alone). His records continued to get better and then 2015 hit and Djokovic collected even more. His record was 15–4 against the other members. I have no doubt that if Djokovic continues his dominance, he will eventually overtake Nadal. Roger Federer is widely regarded as the GOAT by so many people but it is interesting to look at where he stands among those considered his adversaries. In the early years, the Big Four was really the Big Two aka Roger and Rafa, in which they had a somewhat even record (and before you ask, from 2004–07, they played 7 clay, 5 hard, and 2 grass court matches). However, with more matches over time, you find more stability in the Prestige Score unless you do something as drastic as Djokovic (see point 2). The major takeaway — Federer has maintained form and has in fact improved a bit in his 30s. Andy Murray was on a rise in his early years but the reason he continues to maintain the lowest Prestige score is simple: his record against the other members is 26–52. To put this in context: Roger Federer is 47–57, Rafael Nadal is 62–42, and Novak Djokovic is 70–54. The only way to rise is to beat the other three continuously and change his record.

The difference in Prestige Score from the previous year shows progression between the players as the network continues to grow. Do not be fooled in the early years — huge prestige score difference may also just mean larger number of matches played.

Now overall Prestige Score does not tell the complete story. The following visual illustrates the difference in Prestige Score from the previous year. Here you can really see which years truly made a difference for players. Specifically, 2011 sticks out for Novak Djokovic as an impact year compared to 2010 while, 2012–2015 has been a steady increase. If you are wondering about the dip in 2016, remember the year just started so it is honestly meaningless to over analyze.

I could deconstruct this into little pieces but I would rather hear your thoughts and observations from the analysis by commenting below!