# Peak level of play (Federer, Nadal, Djokovic & Co.)

Discussion in 'Former Pro Player Talk' started by krosero, Jan 5, 2013.

1. ### kikiBanned

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Not to be preposterous...but what does this thread do on this section? should be in the GP´s.

2. ### SpicyCurry1990Hall of Fame

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Hey krosero, great work! After reading through the methodology I agree that this metric is very good for analyzing the separations in playing levels between two players in a match and showcasing who will win, far better than win/ue ratio.

My question though is this, how can you apply this to compare "levels" from different matches?

For example:
Nadal hits 16 winners/isner forced errors to 1 unforced errors
Isner hits 0 winners/nadal forced errors to 32 unforced errors

Nadal's aggressive margin is 15/49 = 30.5%
Isner's aggressive margin is -32/49 = -65%

Clearly this shows us Nadal dominated this match

But lets say Nadal plays Isner again next week
Isner hits 48 winners/nadal forced errors to 24 unforced errors

Isner's aggressive margin is 24/72 = 33%
Nadal's aggressive margin is 0/72 = 0%

Clearly Isner dominated this match

However when you compare the two matches you see a situation where:

Nadal had a 16:1 ratio of winners/forced errors to unforced errors and lost just 1 point in the match be rated at 30.5%!
vs
Isner only had a 2:1 ratio of winners/forced errors to unforced errors and lost 24 points in the match be rated 33%!

Clearly this does penalize a defensive style because Nadal could play at super high levels defensively and get every ball back in play and either hit winners or only draw errors all match from Isner, and have that performance be rated as worse dropping just 1 point, than a match where Isner dictates the match but sprays a good deal of errors playing offensively. Does this make sense?

Another bias in cross comparison that arises is this is also clearly biased vs defensively levels in general. Example Djokovic vs Nadal at AO 12 had amazing defensive levels. Many shots that could have been "winners" in other matches vs other people were retrieved and put back into play often multiple times in the same point! However, if that point ultimately ended with an unforced error (due to a player going for too big of a shot to finally hit through the great defender) does that mean the quality of that rally is lost? No, but that is how it would come out as in the aggressive margin stat because its indistinguishable from a routine cross court forehand being hit out.

Next of course, this is biased against the level of opponent. Just because Federer has a 40% margin vs Roddick does not mean its a higher level than Djokovic getting 35% vs Nadal because Nadal is a higher quality player.

Finally, this is also biased against slow surfaces, you need to normalize all slams against your average computed value across all matches at that slam to get true levels, because lets say the AM average is 12% at Wimb, 7% at the USO, and 5% at the AO, and 2% at the FO. A performance of 22% at the FO should be rated better than one at 30% at Wimby.

1)great idea to see levels within a match

2)Does not translate to level comparison across matches unless amended by other stats in conjunction, such as total points won being averaged with the Aggressive Margin or something. (Which is what this stat was created to do right, compare levels across matches? We already get a sense of levels within matches just from the score line)

3)This is not biased vs defensive players within a match, but is biased for defensive players across matches

4)This is biased for fast surfaces

5)This does not account for levels of opponents

Last edited: Jul 24, 2014
3. ### NatFTalk Tennis Guru

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I think it was established earlier on in the thread that a high AM against an opponent also with a high AM is more impressive than a high AM against an opponent who's AM is low.

4. ### SpicyCurry1990Hall of Fame

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Not necessarily though any situation is possible. The whole metric relies on rewarding offensive tennis over defensive in cross match comparison.

Equally possible results:

Having a low AM vs an opponent having a low AM - either both players played terrible offense and made a lot of bad mistakes or both players played great defense and many would be winners were put back into play.

Having a high AM vs an opponent having a high AM - either both players played terrible defense and a lot of rallies that should have continued ended with weak stroke winners or both players played great offensively and hit a lot of great winning shots.

Having a high AM vs an opponent having a low AM - either you played a great match offensively and terrible match defensively vs an opponent playing a terrible match in both regards or you played a great match offensively and defensively vs an opponent playing a good match in one or even both regards.

5. ### kandamrgamHall of Fame

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Good work Krosero, cant appreciate enough. Few points:

1. The subjectivity in determining what's a forced error and what's unforced is big deal here. To make the subjective part clear, think about it like this: if a player commits a FE its a decent error, while if he commits a UE then its a poor error from his side. Now apply the same distinction to winners. If a player hits a difficult winner (turning defense to offense) shouldn't we call it a good winner? And similarly a put-away winner as mediocre winner? Differentiating a poor error from a decent error is as subjective as differentiating good winner and mediocre winner.

a. Players like Nadal and Djoker would turn most decent FE into UE since their defense is good to reach the ball, hence it skews the result against their opponents.

b. To make matters worse, Wimbledon officials have an extremely lenient view on UE. That makes Wimbledon AMs so different.

If we get the distinction right, good. But it's not going to work that way. Sometimes I think, ok even though we don't have numbers on easy winners and good winners which would have been an asset, why should we disregard what we have, ie, FE and UE? Something is better than nothing right? Other times the whole subjectivity (as in case of Wimbledon matches) leads me to believe the exercise is pointless. I'm in two minds.

2. No metric is going to tell us the quality of the match. There is no substitute for watching. Stats only tell us how the point ended, not how it was won (or rather how the point was constructed). But this is one step closer, better than Winner-UE differential.

I will list a few drawbacks of AM (most of which others have already stated, especially Spicy Curry), but by no means I mean I'm attacking it. Just so that if it helps.. AM is a good step forward.

3. As others have said AM doesn't really help to gauge quality of modern tennis's grueling nature. It rather tells us how good the match was according to the classical definition of better tennis, ie it tells how well the players played aggressively. If we were all to agree that tennis is better won by playing aggressively and not forcing the opponent to play an error, then yes AM is a good measure. First, it's anti-clay. Clay is not won firing winners. Second, that's not the way tennis in general is moving forward very very unfortunately.

That takes me to the important point. AM is a good metric for matches before say, 1985. Previous eras agree with the logic of AM. The more physical the tennis gets the more AM is invalid. We can restrict it for the past?

4. I see that Federer's AMs have improved over the years since his peak years (04-07). Does that mean he is playing better today? Or did I get this wrong?

5. Match where AM is outright wrong

2010 London
Federer - 25.4%

2011 London
Federer - 48.2%

This suggests 2011 Nadal played better, that too against a much better Federer (as far as AM is concerned, not really speaking). Which is very wrong. Nadal played way way better in 2010. Though the Winner-UE differential states otherwise.

6. AM penalizing clay and defensive games

2011 Rome
Djokovic - 11.5%

One of the best matches on clay in recent times. Dont judge by AM, Nadal was really really high level and the match too. Yet CAM (combined AM) is 17%!!

7. Few matches were my AM doesn't go well with my subjective perception.

UO:

2013 - Nadal 22%, Djokovic 13%
2010 - Nadal 23%, Djokovic 16%
2011 - Djokovic 22%, Nadal 13%

AM suggests 2010 was the best, but my subjective memory tells me 2011 and 2013 were better. Cant argue here.

2007 WC
Federer - 33.1%

2008 WC
Federer - 30.3%

Again AM suggests 2007 was better. Personally I think 2008 had better shot making, rallies etc, overall a higher quality match.

8. Matches where AM doesn't reveal "levels" (point 2. basically)

The following two matches are very interesting. They are different yet similar.

2012 AO
Djokovic - 14.4%

This match was not the greatest in terms of shot making but it was the most brutal and for that one reason it was of very very high quality. The match didn't even happen on clay. Yet the CAM is just 25%!!

2005 AO
Safin - 19%
Federer - 20.8%

This was a very attacking match. And overall very high quality. Yet AM is not that really high because of the UEs that resulted out of the aggressive game. I dont think anybody will argue WC 2007 Final was better than AO 2005 Semi.

The interesting aspect of both the matches is that, in 2012 both the players were defending very very well until errors were extracted from opponent (and since its a long match there were a good share of winners as well), but in the 2005 match both players were outright attacking and for this reason UEs went up as well. So two contrasting styles, yet both were high quality matches resulting in somewhat similar UE and Winners count. So not only AM doesn't tell us the quality here, it also doesn't tell us what kind of game is played. One had UEs because of defense, the other because of aggression.

9. Misleading AM because of aces.

2010 WC
Isner - 39.4%
Mahut - 41.9%

In the end it was a serve fest. Since ace is a winner, you know the end result. The highest CAM I have seen for a match - 81%!! Nobody is going to tell this was better than 2012 AO final.

10. Lastly, Can we call it Aggression Margin rather than Aggressive Margin? The margin itself isn't is aggressive, it's the margin of aggression. Aggressive Margin reminds me of Aggressive Pricing, Marketing etc where pricing/marketing etc can be either aggressive, defensive etc.

6. ### kandamrgamHall of Fame

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I would like to see AM calculated differently.

1. Will discount aces.

2. Will introduce a new factor, "r", which is the rally length. The greater the length of rallies, lesser the effect of UE should be on AM. This will help us in assessing matches like AO '12 Final. Like, "r" will be greater for RG than say for example WC matches. It can be roughly measured as "(duration of match) / (total points)".

3. I will also calculate AM based on their entire errors without the distinction FE and UE. Let me call it EM (Error Margin - nothing much, just a stupid name). This helps in comparing dissimilar matches which doesn't have UE calculation anomalies.

Equation:
Code:
```[B]AMa = (Wa - Aa + FEb - UEa/r)/TP[/B]
```
But,
Code:
`Pa = Wa + FEb + UEb`
Hence,
Code:
`[B]AMa = ((Pa - Aa) - (UEb + UEa/r))/TP[/B]`
Where
Code:
```TP = Total Points in the entire match
A = Aces
FE = Forced Errors
UE = Unforced Errors
W = Winners
P = Points won
r = Rally Length```

Similarly for EM

Equation,
Code:
`[B]EMa = (Wa - Aa - Ea/r)/TP[/B]`
But,
Code:
`Pb = Wb + Ea`
Hence,
Code:
`[B]EMa = ((Wa - Aa) - (Pb - Wb)/r)/TP[/B]`
Where
Code:
```TP = Total Points in the entire match
A = Aces
E = Errors (forced + unforced)
W = Winners
P = Points won
r = Rally Length```

AMs and EMs of few matches:

r = 4 (I remember the stat shown on TV during the 2011 match during the 2nd set that the average rally length on Federer's serve is 4 and on Nadal's serve is 8. Seemed too much to me then, quite unreal. Think 4 is reasonable)

2010 London
Federer - 32.7%, 10.6%

2011 London
Federer - 48.2%, 18.8%

2011 Rome, r = 6
Djokovic - 32.1%, 14.1%

r = 5

2010 UO
Djokovic - 28.9%, 8.9%

2011 UO
Djokovic - 34.3%, 11.2%

2013 UO
Djokovic - 29.3%, 9.5% (oddly, favours Nole for his attacking game)

r = 4

2007 WC
Federer - 33.6%, 4.3% (goes to show Roger didn't play well if we exclude his aces)

2008 WC
Federer - 33.7%, 6.8%

2012 AO, r = 6 (this is true, I remember the stat. At one stage average length was eight)
Djokovic - 27.5%, 7%

2005 AO, r = 4
Safin - 26.3%, 4.2%
Federer - 26.4%, 4.5%

2010 WC, r = 3
Isner - 31.5%, 4.8%
Mahut - 34.1%, 6.5%

Not very perfect, but I think does a better job. r factor is reasonably chosen according to the match. EMs not surprisingly helps in cross-comparing dissimilar matches better.

7. ### kroseroLegend

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Great stuff, guys, all intelligent, interesting comments. Right now I'm mid-stream in some other projects so I can't reply in more detail, but when I find time to get into deep statistical analysis again I'll say more. Feel welcome in the meantime to keep making posts; I'll get to them in time.

8. ### Boom-BoomHall of Fame

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Interesting feat. Do we have stats on other matches without UE?

9. ### kroseroLegend

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No not as far as I know.

10. ### NatFTalk Tennis Guru

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Why should we exclude aces? Surely the serve is an important factor in level of play. It's fine to try and evaluate level of play off the ground but for overall levels it seems silly and biased (IMO) to not include aces. If player A and player B have equal numbers according to your formula but B served significantly better. Surely you'd have to agree B was the better player.

I'd be interested in these numbers with r and aces included.

11. ### Aggasirules5Banned

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Great stuff. While you are at it, also discount moonballs to the backhand.

12. ### NatFTalk Tennis Guru

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Is there any particular site that has rally length recorded?

13. ### itoaxelBanned

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Interesting how far apart each of those years are in aggressive % when all 3 were competitive matches.

14. ### abmkG.O.A.T.

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Federer vs Murray Wimbledon 2015 semi-final :

107 points won for federer, 11 UEs
91 points won for murray, 17 UEs

total UE count = 28
total points = 198

fed's AM = (107-28)/198 = 39.9%
murray's AM = (91-28/198) = 31.8%

granted wimbledon scorers are generous with their UE counts .......still ...that's some damn fine numbers !

15. ### NatFTalk Tennis Guru

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Sort of what I thought, incredible stats and an impressive level of play - probably his best serving performance. But not his best match ever by any stretch. His performance against Roddick in 2003 is still his best Wimbledon performance IMO.

16. ### kroseroLegend

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Quite possible. AM's for that match were:

Federer - 44.3%
Roddick - 31.7%

Roddick's AM was similar to Murray's, but Federer's was a little higher against Roddick.

Seems very reasonable to me; and going by that logic Federer's performance in '03 was a little higher than yesterday's, at least statistically. I put in that caveat because comparing AM's across such a long time span can be problematic; and there are also match-ups issues, in any comparison, of course.

One point I agree with in the recent discussion is that aces can inflate AM's. Federer's been serving so great recently, that you have to wonder whether his ace counts are inflating his AM's to any degree (possibly the case with his 50 aces in the '09 final).

But in this comparison it's not a factor. Against Roddick in '03 Federer hit 17 aces in 84 service points. Against Murray yesterday it was 20 aces in 91 points. Practically a wash.

What I'd love to know is Federer's unreturned rate for these matches. Surprised I couldn't find that rate for the Roddick match, I assumed that had been charted and posted somewhere. And yesterday's performance has gone down already as one of Federer's career service performances so it would be interesting to see how well it lives up to that description in unreturned % which is really the best stat to look at.

(It's certainly far better than looking at aces alone -- and only aces, of course, would be reflected in AM's).

Very similar matches these wins over Roddick and Murray, now that we mention them. Both straight-setters, similar length, Federer with 11 UE's yesterday, and 12 against Roddick (a full dozen years ago!)

17. ### kroseroLegend

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The r factor is interesting, and it addresses a central problem with UE, namely: a loose error after 2 or 3 shots is not the same as an "unforced " error made after a grueling 40-ball exchange.

The problem is, aces can't be discounted, not by any stretch. The only reason to take out serves entirely like that would be to isolate the rest of the players' games, ie, to compare their groundies/volleys. But the total match performance has to include aces. That's true for many reasons but in this context I would just want to say that aces are the best answer to the grueling-rally problem: if you're facing someone who's a better groundstroker than you, or better at rallying in general, just don't have the rally! Don't get into one. End the point before it's begun. Best, most efficient way to win a tennis point.

I do agree with you that aces can inflate AM's. No doubt about it. But removing the aces is not a solution, for the reasons I mentioned above and, ultimately, because heavy ace-serving is just one of many tennis dynamics, not all of which are perfectly captured by any single statistical model. I'm not sure any model could do justice equally well to every type of match. Some models will reflect/highlight certain aspects better than others. That's just the nature of statistics, I think.

The model you have above is interesting in that introduces rally length as a factor, but something is off, too, because you've got Nadal above Federer in the 2007 Wimbledon final. That would only be justifiable as a comparison of a limited aspect of the match; for example, maybe your model shows that Nadal's game was superior to Federer's apart from service, which I agree with -- but it doesn't reflect the total result, or the final result, however you want to put it.

18. ### abmkG.O.A.T.

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AMs for the USO men's semis :

djokovic vs cilic in the US Open semi :

djokovic : 27.4%
cilic : -9.01%

federer vs wawrinka in the US Open semi :

federer : 29.67%
stan : 9.67%

19. ### abmkG.O.A.T.

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djokovic's and opponent's AMs in the wimbledon finals he's won :

2011 :
djokovic : 38.42%