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Old 01-06-2013, 03:53 PM   #24
Join Date: Jul 2008
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Originally Posted by krosero View Post
In a nutshell, I think the Aggressive Margin is better than ratios, and I'll try to explain why as succinctly as I can.

Just like you, I have always suspected that ratios might be better, just from thinking about the problem the way you just laid it out. But when I actually look at the stats I've collected, I find that plus-minus differentials do not put Nadal at a disadvantage. To the contrary, in matches in which he plays far more aggressive players and the match is a close one (we have to assume it's close, to keep things fair), Nadal tends to have better plus-minus differentials than the more aggressive players.

The best example I know is when he beat Verdasco at the 2009 AO. The match was extremely close (Nadal won 193 points, Verdasco 192), so it's a good example of two players who were more or less equal in level of play. Verdasco hit nearly twice as many winners as Nadal did (95 to 52). So it's a perfect example of Nadal facing a much more aggressive player.

But the plus-minus methods do not put him at a disadvantage. Nadal's official winner/error differential was +27, compared to only +19 for Verdasco. So that method treats him fairly: in fact it exaggerates his quality of play, because he didn't win the match by such a large margin. The Aggressive Margin represents the match most accurately: Nadal's AM was 23.9%, Verdasco's 23.6%.

The same occurs in the final that year, between Nadal and Federer (another extremely close match decided by a 1-point edge). Federer usually hits more winners than Nadal. In this match Federer had 71 winners, to Nadal's 50. But Nadal is the one with a better winner/error differential: Federer is at only +7, while Nadal is at +9.

In other words, when Nadal wins matches, it's because he's keeping his unforced errors down extraordinarily low. That's why he can win the winner/error differential contest.

Intuitively, I would have thought that Nadal, like you wrote above, has 15 winners and 5 ue, while his opponent, playing at an equal level, has 45 winners and 15 unforced errors. But the guy with those low numbers will not win that match: he's won 15 points with winners, and 15 points with his opponent's errors. He's got a total of 30 points. Nadal's opponent, on the other hand, has 45 winners + 5 ue from Nadal: a total of 50 points. Nadal's opponent will almost surely beat him, if the ratios advance like this.

What actually happens when different styles clash is that, all things being equal, Nadal will have 15 winners and 15 unforced errors, while Isner will have 50 winners and 50 unforced errors. Either man can win that match.

If the match is of less quality, then Nadal will have 15 winners and 25 errors (-10), while Isner will have 50 winners and 60 errors (-10).

I have many more examples of how Nadal actually looks very good when simple plus-minus methods are used. In the 2006 Wimbledon final, which Nadal lost to Federer in four sets, Nadal had a better winner/error differential than Federer did (+16 compared to +11). That's because something different is going on with the missing category of FORCED errors: but you see what I mean. Plus/minus differentials are often very good for Nadal.

When Nadal lost to Soderling in four sets at RG, again he had a better differential than the man he lost to: +5 compared to +2. And that's an extreme example of clashing styles: Soderling hit almost twice as many winners as Nadal did (61 to 33). Yet Nadal comes out with the better differential.

The Aggressive Margin, again, represents the match accurately: Soderling has 20.7%, Nadal 15.1%.

And in that 2006 Wimbledon final, the AM again is the more accurate method: Federer has 30.5%, Nadal 22.4%.

Soderling, when he upset Federer at RG in 2010, outstripped Roger in winners (49-40). But once again the guy with fewer winners somehow ended up with the better winner/error differential: Soderling's was only +7, while Federer's was +13. Federer kept his UEs down very low (though that was not enough to win him the match).

I do know of one example where a plus/minus method puts Nadal at a disadvantage. When he beat Berdych in their Wimbledon final in 2010 (a straight set match), his winner/error differential was only +8, while Berdych was +10.

So in that case, Nadal's level of play is not represented correctly. But the Aggressive Margin method gets it right: Nadal has 32.2%, Berdych 23.4%.

The odd thing about that example is that we all think of Berdych as having a more aggressive style than Nadal. But Nadal actually hit more winners than Berdych in that match (29-27). And Nadal made more unforced errors than Berdych (21-17). Totally surprising, but that's why Berdych's differentials turned out better than Nadal's.

I thought Nadal really went for his shots in that match. He did it in a controlled way, as always, but he went for them.

It seems that simple winner/error differentials can actually favor the guy who is more patient (or consistent, or cautious), because that guy can keep his unforced errors down extraordinarily low and can therefore come out with a favorable winner/error differential.

The Aggressive Margin method does not have these drawbacks, partly because it considers all the points in a match (forced errors as well as unforced errors).

Thanks for this particular question, PC1, it has helped me to learn a lot more about this method; and it's fun talking about these matches. Like I said, I thought about this ratio problem exactly as you did -- until I checked the differentials I'd gathered over the years.
You've done the studies so I believe you.

Originally Posted by krosero View Post
Another great example of clashing styles: 1988 USO final between Wilander and Lendl. Wilander had approximately 35 winners and 35 errors. Lendl was at about 85 winners and 85 unforced errors. The match went down to the wire, 6-4 in the fifth.

I'm taking those stats from memory, but yes, each player's winners and errors were almost exactly equal. Only the totals between the players differed, and by a lot: you can't get a greater contrast in styles than those two men.

Wilander, despite being nowhere near as aggressive as Lendl, is represented accurately in the Aggressive Margins. He had 13.8%, Lendl 12.2%.

If you add those 7 to Becker's 15 df's, his total UE would be 22. Sampras had 7 UE of every kind (all 7 were DF's), per official sources including NBC.

So, if Becker has 22 UE's, Sampras' AM is 44.3%, Becker's 32.1%.

If you give Becker more than 22, Sampras' AM would go down.

If Becker goes down below 22, Sampras' AM would rise. Becker has at least 15 UE's (his df's), so Sampras' ceiling in this match would be 47.2%.

I would be wary of comparing AM's across eras if we go back as far as Laver. (Even comparing against the Sampras era could be problematic). But sure, it's worth doing.


The AM takes into account every point in the match, so quick answer is yes. The AM is calculated by taking the total number of points that a player won, and subtracting the points that he won through his opponent's unforced errors. The result, mathematically, must be the points that he won aggressively (his Aggressive Points), either through clean winners/aces or by forcing his opponent into errors.

The last step is to take those Aggressive Points and compare them to the same player's Unforced Errors. The final result is the Aggressive Margin.

I can't imagine how this method would be more accurate if service winners are excluded. It MIGHT become more accurate, in that case, if you're looking for levels of play apart from service. But I have doubts about that, because the serve is connected to everything. Not every point in tennis has a forehand, but every point has a serve.

Moose and I have seen matches in which winner/error differentials -- because they only use unforced errors -- give a distorted picture of the match. The loser will come away with a higher winner/error differential, for example. But the loser, in these examples, definitely lost more than 50% of all the points played (we know because we counted). That's how you know that the victor must have pulled ahead in the missing category of forced errors.

And when there is a large difference in the quality of two players' serves -- or a large difference in the quality of their returns -- one player will get a lot more free points by forcing errors on the return. Those errors are not aces, and not outright unreturnable serves, so they don't show up in the typical winner/error stats. But those errors often make the difference.

So I'm not sure what you're trying to isolate by taking out the serve. You might isolate something, but total level of play definitely has to include everything.
Interesting how in the 1988 US Open Lendl was deemed to be more aggressive but I understand that's a part of his more powerful stroking style. We often (not me by the way)relate aggressive play to rushes to the net. If I recall Wilander rushed the net far more often. Another question does occur to me, net rushes often forces passing shots errors, can we statistically take this into account?

Last edited by pc1; 01-06-2013 at 04:42 PM.
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