Originally Posted by krosero
To have a high Aggressive Margin does not mean that you have to be what we normally think of as "an aggressive player." A guy who makes relatively few winners and few errors, like Nadal, can have just as high an Aggressive Margin as a guy who makes a ton of winners and errors. What matters is whether you can win points but not pay too high a cost in errors. Whoever does better at that balancing act has the higher Aggressive Margin and is almost always the winner of the match.
I think your analysis is quite interesting, but I disagree with the bolded statement. It also depends on what you define as peak. Are we referring to a period of time? ie. 2005-2006 for Federer. Or are we referring to peak levels in certain matches? If you are referring to peak level in certain matches, then that is fine, but players like Berdych, Tsonga and Del Potro will have very high margins for certain matches. If we are drawing a conclusion from the sample about a period of time, then there are some points to consider (see the reasons below).
To clarify, I don't think there is anything wrong with biasing towards more aggressive players since you are effectively trying to measure how aggressive a player relative to his/her errors.
Reasons for bias towards aggressive players:
Aggressive players play high risk high reward tennis, over the wide spread of matches played throughout one's career, they are more likely to have wins with a high margin of aggressively won points over unforced errors, than their defensive counterparts. This can cause skewed results. For example, let's say Isner and Nadal play 150 matches against the field during the defined "peak period" (150 matches is roughly 2-2.5 years).
- Isner -Being a risky player, Isner always has a high winner/forced error, high unforced ratio. Over his 150 matches, his aggressive margin is 10%, because of his high unforced error count. However, he gets on fire 10 of the 150 (6.67%) matches he played, and has a high margin of 50% for his top 10 scores, supposedly representing his peak period.
This clearly does award players that "we normally think of as "an aggressive player."
- Nadal -Being a defensive player, Nadal has a lower winner, lower unforced ratio. Over his 150 matches, his aggressive margin is 25%. Because of his steady play, this 25% held true for each of his 200 matches. Thus, his top 10 matches also average 25%, which is 1/2 of what Isner achieved in his top 10 matches.
To reduce this bias, perhaps one can define a peak period, say all matches in 2005 and 2006, and then select a random sample of matches to calculate the aggressive margin, rather than selecting the top aggressive margins over a large amount of years.
Also, using a direct calculation of % points won aggressively subtracting the % points lost due to unforced errors will be advantageous for the aggressive player.
ie: In a match, Isner won 50% of points aggressively, but lost 30% of points due to unforced errors. The aggressive margin is 20%. The RATIO is 50/30 = 1.67 times more aggressively won points than errors.
Nadal won 15% of points aggressively, but lost 2% of points due to unforced errors. The aggressive margin is 13%. The RATIO is 7.5 times more aggressively won points than errors.
Which statistic is actually more impressive in terms of "balancing aggressive shots and errors" as you said you were trying to find out from the stats?