Quote:
Originally Posted by RoddickAce
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. 20052006 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:
1) 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 22.5 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.
 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.
This clearly does award players that "we normally think of as "an aggressive player."
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.
2) 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?

Some good points here. I think already, in my post to PC1, I addressed the arguments you make in your
#2 section, concerning ratios vs margins. But I'll address your arguments specifically.
1)  you're talking about how highrisk players can get "hot" every once in a while and produce levels of play that more consistent players rarely, if ever, reach. That's an excellent point, and it certainly applies to players like Tsonga, Berdych, Isner.
However, it doesn't apply to Federer. No one, Nadal included, is more consistent than Federer. How many times is Federer upset in the early rounds of a tournament? Not often  and it certainly has happened more frequently to Nadal, particularly in Slams. Federer may be highrisk if you look at his style in a certain way  compared to Nadal, or Djokovic  but his style is very far from hitormiss. And he doesn't have the temperamental psychology that makes some other players perform like a tennis god one day and then crap out the UE's in the next round.
When it comes to someone like Tsonga, no one doubts what you're saying. Tsonga's top AM's may exceed 40% or even 50% when his career is over, and those top figures might beat Nadal's top figures. But for average level of play, Nadal has Tsonga beaten hands down.
And you can see that illustrated very simply just by looking at their title count  and the basic progress of their matches on tour. It's plain that Tsonga has more upanddown days.
I just don't think the Nadal/Federer comparison works the same way. Federer has higher AM's. But it's not because he's a hotandcold player while Nadal is consistent. No one has been more consistent from day to day than Federer.
And you can see that in Federer's AM's. It's not just one or two AM's, like Tosnga produced on hot days, that are superior to Nadal's. Federer has several AM's over 40% (ABMK says he has Nadal at over 40% in one match); and Federer has several more in the high 30s, on my list, before Nadal's highest AM appears.
2)  Here you're talking about how winner/error margins contrast with winner/error ratios. This was the question raised by PC1. He suggested that great, consistent defenders like Nadal might be better represented by ratios. I posted, in reply, several instances where Nadal comes out ahead of his opponent, if margins are used.
In short, Nadal does not win his matches by making 15 winners and 5 ue while his opponent (let's say it's Isner) makes 45 winners and 15 ue. Nadal can't win that match, because he's won only 30 points in total, while Isner has won 50. They might have same 3to1 ratio of winners/ue, but that's entirely inaccurate, given that Isner has probably won that match quickly in straight sets.
Your numbers are similar. You've got Isner already winning 50% of the points through his own aggressive plays. Plus he's taken 2% of the points through Nadal's unforced errors. So Isner has won 52% of the points in the match, at least; he has outplayed Nadal, even if Nadal, as he sometimes does, steals the victory through mental or physical stamina when he has only won 48% of the points in the match.
Now, I'm not just being picky about the numbers you've chosen. I'm talking about which method is superior, as a way to measure quality of play. I'm saying, Isner has a higher Aggressive Margin than Nadal in this example, but that's entirely accurate, since Isner is outplaying Nadal. I'm also saying that, in your example, Nadal has the much higher RATIO of winners to errors: but that's entirely inaccurate as a measure of who is playing better. The ratio makes it seem that Nadal is playing entire levels above Isner, when in fact Rafa has been outplayed in points won and will probably lose the match.
Your numbers don't quite add up to 100%, so I'll change them just a little.
Let's say Isner wins 48% of the points through his aggressive plays. He's also got 2% from Rafa's unforced errors. He's got 50% of the points. Nadal has won 15% of the points aggressively, and 35% from Isner's unforced errors.
Each man is tied in total points won, so we have a fair playing field to decide which method is better.
Isner's winner/error ratio is 48/35, or
1.37. Nadal's ratio is 15/2, or
7.50. Completely inaccurate. Nadal looks like he's killing Isner, when in fact they're neckandneck.
Isner's Aggressive Margin is 48%  35%, or
13%. Nadal's AM is 15%  2%, or
13%. That's a precise representation of the distance between the two men.
I had never noticed it before, but the Aggressive Margin will always tell you accurately which player won the most points. It's tied in mathematically to the breakdown of Total Points Won. I tried it in Excel today, punching in various numbers for Unforced Errors to see if I could get Isner and Nadal to produce the numbers that you gave them. It turns out that you can put in any numbers you want, for the Unforced Errors; it doesn't matter; if Nadal and Isner have won the same number of points, their Aggressive Margins will be equal to one another. If Isner wins 90 points and Nadal 89, Isner's AM will be slightly higher than Nadal's. It has to work out that way mathematically.
Try it out in Excel. You can give Isner 145 unforced errors, and Nadal only 2; or you can give them both 40 unforced errors; the particular figures don't matter. The player's AM's will always reflect the actual margin of victory in Total Points Won.
What the exact AM's will be, of course, is totally dependent on how many UE's the players make. The actual UE figures determine the quality of the AM's.
But the AM's always accurately represent who won the most points, and by how much.
I'm not sure any method can hope to be more fair than that.
Because I have all this data in Excel, I can easily sort by different criteria and compare different methods. I took all my data today and sorted it by ratios, rather than by Aggressive Margins. The ratios end up distorting a lot; but I'll put that it another post.