#### zvelf

##### Hall of Fame

So I took the 12 players whom Federer and Djokovic played the most in these periods and gave them each a strength rating. I was originally going to choose 10 players, but 3 players tied for most played against Djokovic (6 times) in 10th position for 2018-2023, and whichever one of them I chose arbitrarily would affect the final data slightly. (Actually, more than 3 players played Djokovic 6 times in 2018-2023, but my tiebreaker rule was who played Djokovic in slams more, and these 3 players still all played Djokovic 3 times in slams over this period. My tiebreaker ended up dropping Dominic Thiem, who played Djokovic 6 times but only twice in slams during this period, and Thiem’s strength weighting was much higher than the ones who made the cut: Kevin Anderson, Hubert Hurkacz, and Jan-Lennard Struff.)

So what’s the most common sense strength rating? Well, I took into account the number of slams won, the number of slam runners-up, the number of slam semifinals reached, the number of total titles won, peak ranking, and win/loss record while looking at these numbers ONLY DURING these periods of play against Federer or Djokovic. If I only looked at slams won and not finalists and semis, that wouldn’t be a very helpful indicator as the Big 3 won almost all the slams during these periods. Who it would help immensely is Djokovic 2011-2016 as that’s when Murray and Wawrinka won 3 slams each. But runner-up should not be weighted the same as a slam, so I weighted it as half as much and reaching semifinals as a quarter as much. Again, if I weighted runners-up and semifinalists even less than this, it would just make Big 4 + Wawrinka’s strength points even stronger.

The one element that needs clarification is the highest ranking score. The way my points for rankings work is if you’re #1 during a given period, you score 100%, #2 is 95%, #3 is 90%, and so on until #20 gets 5%. Every single player evaluated made the top 10 in their respective playing periods except Struff, whose highest ranking between 2017-2023 was #21 and so he got a big fat zero for this aspect of the strength rating.

On top of all of this, everything is graded on a curve based on what was the highest achievement any of these competitors got in these areas. So for example, the highest number of grand slam wins by any Federer or Djokovic opponent in these periods was 6 for 2004-2009 Nadal and 2018-2023 Nadal. So everyone’s grand slam score is a percentage out of 6. Those Nadals would get a score of 1.000. 2011-2016 Murray’s 3 grand slam wins score is 0.500 (3/6). The highest win percentage is 2018-2023 Nadal’s 84.2% so everyone’s win percentage is a percentage out of 84.2%. 2018-2023 Nadal’s score here is 1.000. 2011-2016 Berdych’s 70.1% is worth 0.832 (70.1/84.2). Grading on a curve allows our final strength rating to mean something as we will see in a moment.

All of the different elements are weighted to provide a final score for each player:

slams won x 0.2105 + slam runners-up x 0.1053 + slam semifinals x 0.0526 + titles won x 0.2105 + peak ranking score x 0.2105 + win percentage x 0.2105 with the weighted factors summing to 1.000

So 2004-2009 Nadal’s 0.89 means he is 89% from being the perfect opposing player given his comparison to the peak performance of all the other elements among all opponents of Federer and Djokovic in these periods. 2004-2009 Nadal is 6/6 slams won (1 x 0.2105) + 2/6 slam runners-up (.3333 x 0.1053) + 3/9 slam semifinals (0.3333 x 0.0526) + 36/36 titles won (1 x 0.2105) + #1 peak ranking (1 x 0.2105) + 82.98% win percentage (82.98 / 84.19 x 0.2105) = 0.89

But we’re not done with weighting yet. It matters how much you play somebody. If you play 0.89 Nadal 5% of the time vs. 10% of the time, your strength of competition is a lot different. And I decided to give slam matches double the weight of a non-slam match. Total matches played + total slam matches played = what I’ll call opposition points. So the final strength of the opposition score is a weighted average of a players score x opposition points / total opposition points among the 12 players played. Or another way to explain it is that the final strength of opposition = players score x (total matches played + total slam matches played) / (total matches played + total slam matches played of all 12 opponents).

And we’re still not done because you have to proportion to all matches played within a period. Djokovic played his 12 players 196 times, far more than Federer played his 12, which was 148 times. I proportioned by “opposition points” to make slam matches worth double of a non-slam match.