"Simpson Paradox" and Federer

DarthFed

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Yes, he doesn't really spell it out as well as he could but that is the "paradox". It is where the winner of the match won less points than the loser of the match. I think part of his point is that it shows that it was very difficult to beat him, such that it took something wacky like his opponent winning less points than him yet sneaking out the match. The whole swinging for the fences part is pointless IMO.
 

GameSetAndMath

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Moxie629 said:
DarthFed said:
Moxie629 said:
DarthFed said:
GameSetAndMath said:
Although not required by the scoring mechanism, most of the time the player with
more points wins the match also. Let us call a win a lucky win if it is an example of
Simpson's paradox (although it need not necessarily be lucky).

One way to interpret the results of the article is that if a match involving Fed
is won by someone in a lucky manner, it is more often won by Fed's opponent than Fed.
In other words, Fed is more often unlucky than lucky.

It would be interesting if the author can release the complete list of such
matches involving Fed. I wonder whether 5-set loss to Djokovic (where
Djoker took a wild swing in return on an important point) at USO falls in
this category.

Djokovic had more points than Roger in the 2011 semi, not sure about 2010 though I'd think Djokovic would have more points since he won 2 lopsided sets in that one.

You and Tennis Miller are right that it does not include matches where the winner won a few more points than the loser (obviously a tight match). So it is incomplete, yet 4-24 is rather overwhelming. It just means in those matches on average Roger did not do well in big moments. Taking a match like 2009 AO that was obviously the case. I wonder if 2009 USO is also one of those 24 losses. Not sure what else to read into that stat. In no way does it make him look good unless I'm completely blind.

I think you ARE completely blind, in your pessimism. Don't compare him to the likes of Djokovic or Nadal in such a stat. That's clearly not where he picked up the most of them. It's against under-card players going for broke. The stat's not supposed to make him look bad, it's supposed to make him look good. I completely disagree that it says that Roger didn't do well in the big moments. Exactly the opposite, I'd say: it means he DID play the big moments well. That's why he could let garbage points go by. Because he'd still get over on the opponent, when it mattered.

First of all we don't know what matches make up this stat. The author of the article is taking a guess as to the reason the record is so poor in that situation but for all we know a lot of these matches were vs. top 10. In fact, that is most likely the case because he was rarely in close contests with lower ranked players until very recently.

Losing 24 times where he won more points than his opponent vs. winning 4 times where he won less points somehow shows that he played well in the tight moments in those 28 matches? I'm confused :nono

To be honest, perhaps I'm confused, too. I thought the article stated the opposite. Too many double-negatives, perhaps. But if I'm wrong, why is the author trying to make this as an argument for Roger's greatness? That wouldn't make sense.

I knew you were confused (from post #13 in this thread) even before this post.
But, decided to let it go.
 

GameSetAndMath

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DarthFed said:
Yes, he doesn't really spell it out as well as he could but that is the "paradox". It is where the winner of the match won less points than the loser of the match. I think part of his point is that it shows that it was very difficult to beat him, such that it took something wacky like his opponent winning less points than him yet sneaking out the match. The whole swinging for the fences part is pointless IMO.

You are correct in your elaboration of "paradox" (although it should be obvious to most
people).

However, I think the underlined statement is wrong. There can be many matches in
which the opponent won Fed convincingly (i.e., by winning more points than Fed
and winning the match) and those matches are not considered in this study at all.
So, the author is not trying to say opponent needs to do something wacky to win
against Fed.
 

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It's been said that there are lies, damn lies, and then worst of all, statistics . I'm not big on stats necessarily or always meaning much, although sometimes in context they do. For example, if Nadal holds serve more often than anyone, does this mean he has the best serve? Becker beat Edberg 25 out of 35 times, so Becker was undisputedly better?

In this paradox example, I don't think the stats tell us anything about anyone mentioned in the article, not just Federer. You'd need many more examples out of 1000+ matches to even begin to try to draw conclusions.

So basically, all that I think can really be said about this "Simpson's Paradox" is "Doh!".

Cheers

TM
 

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I completely agree with the article and disagree with most of the posters here. I have noticed the same trend with Roger since the beginning of his career.

This is a positive not negative thing, and has nothing to do with how he performs in the clutch (indeed various indicators of his performance in tight points are amongst the highest on the ATP tour, for instance tie break records).

It does on the contrary have to do with statistical variance. In other words, an inferior player who adopts a risky game plan (example, an Ivo Karlovic who ignores all return games and only holds serve to try to force a tiebreak where he goes for outright winners on all returns) will lose far more playing that strategy against standard ATP tour players, except when he is up against the elite players where that 5-10% locked in winning percentage is actually better than what his normal matchup would entail.

So of course you forget the many games where he is completely blown out by Roger, but only focus on the one time where he managed to win 3 tiebreaks in a row.

Indeed when you look at the great losses in Rogers career, they are almost universally performed by players who are having career games. You see, its wrong to say oh yes well he lost a close game, that proves he is not clutch. WHen you should be saying, oh wow, Roger actually made that a close match, where most players would have been blown out playing a guy on a hotstreak.
 

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Incidentally part of the trend is also explainable by return statistics. Namely the fact that Federer in his prime would win about as many points in the return game as the best returners in the game (eg the Nadals and Djokovics, the Davydenko/Nalbandian/Ferrer) but convert far fewer break point opportunities.

THat latter point is important, b/c converting break points is often not about being clutch, but rather about technique. In this case, it happens that one of Roger's career weaknesses (back hand return on the ad side) is amongst the most exploitable on tour.
 

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For what it's worth, Brad Gilbert and Chris Fowler are about to discuss this article on ESPN.
 

GameSetAndMath

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Moxie629 said:
For what it's worth, Brad Gilbert and Chris Fowler are about to discuss this article on ESPN.

Well, they talked about it. But, did not really add any new insights.
 

DarthFed

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Gilbert kind of echoed the same thoughts as the article. It'd be tough to say without them showing what matches are included in the 4-24 record. It is easy to see that a match where the winner gets it by a score of 7-6, 2-6, 7-6 is likely one for the "paradox". And in that score you have to say the winner is clutch and by default the loser wasn't. For Roger the only one I know offhand is the AO 09 final. Needless to say he was horrid in the big moments there, even before the 5th set. But that is only one of the 28...
 

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Another one is the canada masters 2007 against Djokovic, although that was won by Novak with only two points less.
 

DarthFed

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Denisovich said:
Another one is the canada masters 2007 against Djokovic, although that was won by Novak with only two points less.

Good call, that was similar to the hypothetical one I noted, I think Novak won 2 tiebreaks and saved 4-5 set points in the 1st with Roger serving for it.
 

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Also, Rome 2006 against Nadal (179 -176).

That one plus the AO final are the only ones against Nadal actually.
 

DarthFed

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Lost 2 match points and 2 tiebreaks in that one as well. Similar pattern as to what I figured...

Also I was wondering if you'd found the list already or are checking out stats of matches you think are part of the stat. I wonder if 05 AO semi with Safin is on that list.
 

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Just checked and that is part of it, Fed won 201 points to 194.
 

Denis

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Found another one:

2010 Paris Bercy (semifinal) against Monfils 125 -121. 3 tie-breaks.
 

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DarthFed said:
Lost 2 match points and 2 tiebreaks in that one as well. Similar pattern as to what I figured...

Also I was wondering if you'd found the list already or are checking out stats of matches you think are part of the stat. I wonder if 05 AO semi with Safin is on that list.

No, Im just wikipedia-ing and using the atp site simultaneously.
 

DarthFed

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Denisovich said:
Found another one:

2010 Paris Bercy (semifinal) against Monfils 125 -121. 3 tie-breaks.

Funny I was just checking that one out but couldn't find the stats. Roger blew 5 match points that match. Again...similar pattern. Very tight matches with some very unclutch play.

Now the trick would be thinking up the 4 that he won where he had less points than the loser.
 

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Its more difficult the other way around because you can't check as easily which matches he won as the ones he lost. But I went through the finals (not very thoroughly, only the ones that seemed tight) and none of those fitted the pattern.

Found one!

2000 Basel against Hewitt. Hewitt won one point more but lost the match :D
 

DarthFed

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Denisovich said:
Its more difficult the other way around because you can't check as easily which matches he won as the ones he lost. But I went through the finals (not very thoroughly, only the ones that seemed tight) and none of those fitted the pattern.

Found one!

2000 Basel against Hewitt. Hewitt won one point more but lost the match :D

My memory is more sharp when it comes to failure than success (both for me and the teams/players I root for).

2008 Basel vs. Hewitt was not on my radar at all. 2006 YEC vs. Roddick probably doesn't fit in this paradox but that was a match where Roger saved 1 or 2 match points in the 2nd set and ended up winning the match.
 

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DarthFed said:
Denisovich said:
Its more difficult the other way around because you can't check as easily which matches he won as the ones he lost. But I went through the finals (not very thoroughly, only the ones that seemed tight) and none of those fitted the pattern.

Found one!

2000 Basel against Hewitt. Hewitt won one point more but lost the match :D

My memory is more sharp when it comes to failure than success (both for me and the teams/players I root for).

2008 Basel vs. Hewitt was not on my radar at all. 2006 YEC vs. Roddick probably doesn't fit in this paradox but that was a match where Roger saved 1 or 2 match points in the 2nd set and ended up winning the match.

You would to have to be family to Federer to remember that one. In 2000 Federer was ranked 29 or so and had yet to make a QF at a slam. ;)