Originally Posted by Flash O'Groove
After thinking about it for a few days, I think their is some issue with this reasoning. The AM is the measure of the ability of a player to execute successfully an aggressive pattern of winning points. From our spectator's point of view, we will often equate an high AM with high quality of play, because winners are more spectacular . Thus, we will consider a match where one player as high AM as a pleasant match, and more so if both players have an high AM. Thus, quality means more, is this case, spectacular than "high competitive level of play".
Actually the AM's cannot tell you which matches were most entertaining -- if we think of entertaining matches as having a lot of winners.
There are two ways to get a high AM. You could increase your winners; that would be a more entertaining match. Or you could get a high AM by decreasing your unforced errors. In the latter case, maybe the number of winners you made was not unusually high and what was really great about your level of play was how few errors you made. That sort of match would not qualify as entertaining -- not if we're looking for winner-heavy matches.
Maybe you read my post above to Urban, about the 1987-88 USO finals between Wilander and Lendl. Most people, myself included, would consider the '88 final to be more exciting. There is more net play and Lendl is hitting a lot of passes and other aggressive winners. The rate of winners -- meaning how frequently they occurred in the match -- was faster than in the '87 match. But the rate of errors was also faster than it was in '87.
The '87 final featured endless rallies, and some people said it was like watching paint dry. I actually think the match was better quality than the '88 final, because Lendl's UE's were so low. (He went from 58ue in '87 to 85ueE in '88.) But that made the match less exciting.
And you can guess what I'm going to say next: the less exciting match had the higher AM's.
Originally Posted by Flash O'Groove
For exemple, I disagree with your statement that the level of play of Murray in the Olympic final is as high as Fed's level during the Wimbledon final. We know that he was able to execute an aggressive pattern of winnings points as successfully as Roger did, and we know than from a spectator standpoints, his performance was as enjoyable. But that doesn't necessarily means that he played better, as the AM is related to the level of his opponent. In this case, the AM of Federer for the Olympic final suggest that he played worse: he couldn't execute successfully an aggressive pattern of play, and he probably didn't defend as well, thus enabling Murray to considerably rise his own AM, even if himself played worse too! The inverse is possible too: Murray was so good in the Olympic final that Federer's AM dropped. I know for seeing these matches that Federer's level did drop off (he was clearly mentally tired after is SF against Del Potro), but the statistics themselves don't really tell the competitive level of play of both players. They say that the Wimbledon final was a better match from a spectator points of view.
The part I bolded is where I have disagreements.
Federer did not play well in the Olympic final, agreed. He made a lot more UE's than in the Wimbledon final, yes, so far so good.
But if your opponent's UE's rise, your own AM will fall. You can work it out in Excel or with a calculator: punch in higher numbers for Federer's UE. Murray's AM will fall.
Or just think about it this way: when your opponent's UEs increase, you're getting more of the points for free. More of the points in the match are being handed to you on a platter (I'm exaggerating to make the point) -- that is, you did not have to make any aggressive plays on those points. The number of points that you have to win through your own aggressive plays to win the match has suddenly decreased.
Let's take the Olympic final and increase Federer's UEs.
Federer won 68 points and made 31 UE's - AM of 12.1%
Murray won 97 points and made 17 UE's - AM of 29.7%
Those were the real numbers. Murray won 97 points in the match, making aggressive plays for 66 of the points. And he won 31 additional points that Federer handed to him.
Now let's change Federer's UE to 41:
Federer won 68 points and made 41 UE's - AM of 6.1%.
Murray won 97 points and made 17 UE's - AM of 23.6%.
Now Murray only has to make aggressive plays on 56 points; 41 points are now being handed to him.
Let's say Murray tanks, and hands Federer all of the points in the match. Federer wins 6-0, 6-0, 6-0. Eighteen straight games, 72 straight points -- all of them won by Federer on Murray's unforced errors. Federer didn't have to lift a finger to win anything.
Murray's AM in that scenario would be negative: -100%. Federer's AM would be exactly 0.0%.
I think you've put your finger on some good issues, but I don't think it's valid to say that Murray's AM was high in the Olympic final because Federer's was low. If your opponent is handing you the match, you're getting free points rather than making aggressive plays, so your own AM has to go down too.