Originally Posted by pc1
I mean if a player hits 45 winners and has 15 errors, that would be a 3 to 1 ratio. Another player may hit 15 winners and have only 5 errors but has the same 3 to 1 ratio.
If you do plus-minus the first guy is far better at plus 30 than the second guy at plus 10.
I think ratio may be better.
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.