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The Radical Conventional 09/15/2010 - 12:33 PM

104068554 by Pete Bodo

Mornin'. I'm coming off eight hours sleep for the first time in weeks, so watch out, keyboard! Ha. Seriously, though, a regular night's sleep in the cool, tangy country air is tonic for the soul and mind. And I find it helps me think clearly and maybe get a little further under the skin of things, including the huge achievement of Rafael Nadal.

The problem for me on the night of the U.S. Open men's singles final was having to choose between writing a "gamer" (a story emphasizing the match play and its attendant details) or a "reaction" piece analyzing the big picture meaning of the match, and how Rafa managed to complete a career Grand Slam. I felt appropriately torn. Whichever I chose, I had to ignore some tantalizing issues. But as journalists have been said to be the authors of "the first draft of history," I thought I ought to go with the Big Picture piece. Besides, you all saw the match—you didn't need my eyes to tell you what just happened.

It's a pity, in a way, because I am still trying to figure out how to explain why this final seems likely to lodge in my mind as one of the best tennis matches I've ever seen; it's right up there, as of now, somewhere in the top half-dozen. That's because I've rarely seen so compelling a display of the pure, shotmaking sensibility that Novak Djokovic brought to the court, nor the gale-force power, consistency, and athleticism of Nadal. And while Novak hit the most glorious winners, one of my match notes says I've never seen anyone hit a tennis ball as persuasively as Rafa Nadal.

Roger Federer (don't ever expect me to write about Rafa without Roger's name lurking eight or 11 characters distant) routinely produces magical shots, and he's been as close to an embodiment of quicksilver as anyone who ever played this game. But nobody, including Federer, swings the racket (at least on the forehand side) with the unique combination of raw, explosive power and absolute control as Nadal. Every decent player can do this now and then—time the arrival of a ball and generate adequate racquet-head speed and force to hit the most punishing shot of which he is capable. But nobody can do it as routinely, and make it so intrinsic a part of his game plan, as Nadal.

The sheer brutality of a typical Nadal forehand is a quality that attracts some and repels others. Those who are put off by it might appreciate the gladitorial splendor a bit more if they also acknowledged that to belt a ball with such force requires enormous natural power (is there a better one word description of the essence of life in all its forms than "power"?), applied in a very different way than, say, crushing the skull of a sabertooth tiger with a rock. To hit a tennis shot the way Nadal does repeatedly also demands exquisite timing, body control, and an astonishing degree of discipline and self-assurance—the latter being qualities we generally hold in the highest regard. Each swing of that piledriving forehand basically shouts, "I was born to do this."

Nadal's self-assurance—or should I say, the self-assurance expressed in the shots he hits and the way he hits them—is a radiant, somehow soothing thing to behold. Whatever else you say about it, the only thing you know for sure is that he can't possibly do that thing he's doing any better. It's a fully-realized idea. Don't you wonder how it feels to Nadal himself to hit that shot, a jolt of satisfaction that can only be blunted by the startling frequency with which he must experience it?  Most of us get to experience that feeling now and then, but rarely in an undertaking involving ball and racket, and never with such frequency.

I don't think you can appreciate what Nadal brings to the table without backtracking to his early days on the ATP tour, or without contemplating the sometimes fierce disdain some have for Nadal. Think of it this way: If you look out your window and see your neighbor walking to the bus station on his hands, you're likely to jump up and shout: Kids, come quick, Kowalski is walking to the bus upside down! But see it repeatedly, and by the third week you're likely to just glance up and mutter, Look at that silly Kowalski, those socks don't even match his shoes!

That's how it is with Rafa; he's turned the radical into the conventional. To say he plays "ugly" tennis has evolved from an aesthetic and already somewhat irrelevant observation into an astonishing declaration of ignorance. A bitter fan of one of his rivals can cling to it; any port in storm and all that. But the reality as I see it is that Nadal figured out a new way to accomplish the paramount goal in tennis, or any game: to win.

The more important truth is that Nadal plays "successful" tennis, and that matters. It's why they keep score, and also why we can appreciate beautiful tennis as well. I don't think you would sell many tickets to a tennis match if it were just a demonsration, like dance, even if the star were as gifted and eye-pleasing a player as Federer. And if you still haven't gotten over that that "ugly tennis" hump, just try to appreciate that a player who hits his forehand like David Ferrer—in other words, a wonderful, effective, even pretty forehand—can only aspire to be as good as Ferrer, which is danged good, but nowhere near as good as is Nadal.

I don't know that Nadal will transform tennis, re-making it in something like his own image the way the trinity of Jimmy Connors, Chris Evert and Bjorn Borg did when they showed up at roughly the same time with their two-handed backhands—the repercussions of which are still being felt. That's a big ask, because what Nadal does calls for a potent combination of superior, natural and learned abilities not easily distinguished from each other. Nadal may not transform the way the game is played, but there's no doubt in my mind that Nadal is essentially a transformational character, pointing the way toward a place that perhaps nobody else can reach.


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Posted by Jay 09/16/2010 at 12:58 PM

@manuelsantanafan: Head-to-head comparisons can be misleading. Hingis, although roughly the same age as Venus--slightly older than Serena, joined the tour full-time a few years earlier. The Williames turned pro years before they played full-time--something to do with the Capriati rule about to take effect.

So, Hingis was a seasoned #1 player at 16, and beat the sisters fairly regularly in their early encounters. A few years later, notably, after Serena won her first US Open against Hingis, the tables turned, and the sisters (and others, like Davenport) began to "overpower" (Davenport's term) Hingis regularly. Look at the scores of the late matches between them.

On the other hand, Hingis has always been consistent enough that if any of the big hitters was not "on", she could pull a match out. I saw her play Venus in WTT this summer, and Hingis almost won.

Posted by Aussiemarg,Madame President,Rafa Did Do It For Wayne! 09/16/2010 at 01:00 PM

Slice I agree with your thoughts regarding Rafa.I also take you point on board with that s/final he played at the AO 08 against Tsonga.

I was there live for that match.Tsonga indeed showed what it takes to beat Rafa with ease mind you on a hard court.

Though to Rafa's credit his hard court game since then has improved.I feel he is more aware on the hard court now and his serve has improved out of sight.

Posted by goku24 09/16/2010 at 01:18 PM

Toni Colom, coached Rafa in juniors with his uncle. There are 7 articles, several are translated into English after spanish in the same page.
This year he worked 3 months 4 the LTA,
http://passiontalentgroup.blogspot.com/search/label/Toni%20Nadal
(INSIGHTS IN TONI PHILOSSOPHY.)

Posted by Slice-n-Dice 09/16/2010 at 01:36 PM

Aussiemarg, I agree with you that Rafa's hard court game continues to improve. My point was simply to say that the kind of game that can take down an athlete with the wheels, athleticism, power and tenacity of a guy like Rafa exists. it's just rarely exhibited, because it takes an amazing combination of power, precision, touch and, most of all, cajones.

Posted by gauloises (unrepentant FOOP!) 09/16/2010 at 01:43 PM

zenggi -

Sorry, I was away. I'll be at Bercy certainly Monday-Wednesday, and possibly all week if work/funds permit.

Still keeping my fingers crossed that Delpo meets me there. I'd also really, really like to see Nalbandian live, because I've not done that yet. Nole I have seen (watched some of the Rochus match at Wimbledon) but not nearly enough, so I'd love to see him too ...

Are you going? I forget where you're from.

Posted by Goldilocks 09/16/2010 at 01:46 PM

AM, yes, we will have to do just that, lol.

I love me some Rafa. I´m soooooooo happy that Rafa is no longer One Hard Court Slam Wonder. I loved Rafa - the guy who won Australian Open 2009 because he´s improved his hard court game a lot. But I loved loved loved Rafa - the guy who won Us Open 2010 because he´s improved his hard court game leaps and bounds. Yeah, can you tell I´m still over the moon with Rafa´s Career Slam. OK, I´ll stop now.

Anyway, I would also like to thank the non-Rafa fans: Slice n Dice, Dunlop, Andrew, Christopher, Matt Zemek, TMF(I hope I got all your names right, guys), Ladyjulia, Master Ace (please continue to name the Slams in Rafa´s honor because I believe you are his lucky charm) and special mention to AB, for all your wonderful insights. I´ve always enjoyed reading all your posts.

Posted by Goldilocks 09/16/2010 at 02:22 PM

ATP declares "Rafael Nadal will finish as the No. 1 player in the year-end ATP Rankings."

http://www.atpworldtour.com/News/Tennis/2010/09/Other/Nadal-ATP-Wor...

Posted by Goldilocks 09/16/2010 at 02:27 PM

Sorry, this is the correct link:

http://www.atpworldtour.com/News/Tennis/2010/09/Other/Nadal-ATP-World-Tour-Champion.aspx

Posted by Goldilocks 09/16/2010 at 02:42 PM

Triple Pound: I´m with you, now that Rafa has secured the No. 1 player in the year-end ATP Rankings, he does´nt need to play all the tournaments he has entered prior to the WTF. He should rest on his laurels until then. I know it´s unfair to the fans who have purchased the tickets, but something´s gotta give, right? Ahhhh, what to do, what to do?

Calling Carlos Costa, please make the right decisions, ok? Don´t make the same mistake twice, you hear me? LOL.

Posted by claudia celestial girl 09/16/2010 at 03:07 PM

a wonderful 9 seconds for Rafa and Nole fans:

http://www.youtube.com/watch?v=I0CLCCAwKZI

and thanks to goku24 for posting that great link to the Toni Nadal articles!

Posted by Mary Gaand-Maro 09/16/2010 at 03:36 PM

What bloody rot! Just because he won doesn't mean that his ugliness has gone away.

Regardless, I think that to win all the Grand Slams was tougher in the past...frankly, I don't think it's that big of a deal with the all-rounder athletes, technology and surface changes. Just look at the gang that keeps advancing all the time.

Posted by Mart 09/16/2010 at 04:10 PM

For all the adoring Federer fans who want to say their guy is "the best ever", what does it say when Nadal has beaten the "best ever" on ALL surfaces, clay [French Open], grass {Wimbledon] and hardcourt [Australian Open}?

What does it say when Rafa has beaten the "best ever" 14-7 head-to-head, and 6-2 in majors? And he's ONLY 24!!!

I have one word for all of you: DENIAL!

http://www.christconnection.net

Posted by lost in translation 09/16/2010 at 04:33 PM

Mart,

why do you talk about Federer?

You should be happy and celebrate and call Rafa GOAT...

Why all this worry? :-)

Posted by Nam1 09/16/2010 at 04:37 PM

Mary Gaand Maro

This site does not allow bad langauage regardless of what language; please change your moniker, you know that it is a very bad verbal abuse in a cetain language and offensive and demeaning to others on this site whether they understand or not.

Posted by Fay 09/16/2010 at 05:02 PM

Great article although I don't think Nadals tennis is ugly, I have watched him grow into a remarkable player over the years and have seen him live on grass and hard court indoor, for me his most impressive shot is the vintage loopy down the line forehand and his b/h stance crosscourt is incredible, I have never seen anything or anyone like Nadal, he is unique and his worth ethic, mindset and character a apart from the rest. I love to watch Federer play and loved the semi-final against the outstanding Djokovic but in this final Nadal really shined when it counted, his movement is almost cat like on the court, he has so much charisma too, so much passion, how blessed we are to witness 2 greats like Nadal and Federer playing, what an era for tennis. Vamos Rafa always!!!

Posted by Kwaku 09/16/2010 at 05:40 PM

I have an explanation to the Federer-Nadal h2h that many fedfans will be happy to hear. I'll put in some details for the more mathematically-oriented to have them, and also a figure for the less mathematical also to understand qualitatively.

The explanation does not imply that Nadal is better than Federer, and not even that there is a matchup issue. It has to do only with the overlap between their curves of performance as a function of age.

I'll explain it now under extremely simplified hypotheses, but the underlying "what-happens" can be seen very clearly I hope.

Let us consider two players who are exactly as good as each other when their ages are the same. We can call them Federer and Nadal, for instance. This means that we are assuming that 19-year-old Federer is exactly as good as 19-year-old Nadal. We will scale this goodness between 0 and 1.

We also assume that there is are no matchup issues and no random effects, i.e., if a player is 0.7 good and the other is 0.55 good, when they play the 0.7 good will win.

We will assume that both players meet several times every year. How many times turns out to be irrelevant (that is, the h2h turns out to be practically independent of that parameter).

We will neglect the effect of one player not getting to the necessary round to meet the other (like Nadal not getting to the USO final until recently while Federer did reach the FO final, or Federer not reaching any of the three slam finals Nadal has won this year: we can either assume that they always get to meet or that the effect cancels out).

We will assume that both players are exactly the same only that one is 5 years younger than the other.

We will assume that they start playing at around 17 years of age, peak at 22, and continue playing until they are around 32, and that their performance follows a curve with the shape of an asymmetric Gaussian bell. This curve is a Gaussian bell with two different standard deviations (or half width at half maximum = fwhm): one for the left tail, i.e. before the peak at 22 years of age, and another one for the right tail, i.e. after the peak. We will assume that the 17 year old is approximately as good as the 32 year old (the first still learning, the second almost retired).

We can obtain a curve similar to what we need if we make the fwhm of the left tail equal to 7.5 years and the fwhm of the right tail twice as much, i.e. 15 years. Don't worry if you don't get the meaning of this parameters because I have drawn both curves for you:

http://picasaweb.google.es/felipe.jimenez.h/20100106_TW?authkey=Gv1sRgCPSTzcbtytKa6gE#5517615993895269586

The blue curve is Fed's performance as a function of age, and the red one is Nadal's.
Below in blue are Fed's ages and in red are Nadal's ages. They are exactly the same curve with different colors and displaced 5 years horizontally from one another.

Having a professional span between 17 and 32, but peaking at 22, means that the learning curve (left tail) is much steeper than the declining curve (right tail). Which is quite realistic. In this case, the players spend 5 years improving (from 17 to 22) and twice as many declining (from 22 to 32), the ratio between both fwhm being also 2.

Now look at the figure.

On the left there is a gray area. Those are the years when Federer is playing and Nadal has not started.

When Nadal becomes 17, he starts to play and lose to Federer. (Don't tell me that it did not happen like that, because they are ideally mathematical players, not real Federer and real Nadal.) Those matches are represented by blue vertical lines in the figure. There are 16 every year in that figure, but they could be fewer or more.

That happens until he is about 20.3 years of age (and Federer is 25.3). Then, Nadal starts to win whenever he meets Federer, and those matches are represented by the red vertical lines in the figure.

That happens until Federer retires at the age of 32 (and Nadal continues to play; this is represented by another gray area on the right).

Well, if you count the vertical red lines and the blue red lines and divide both numbers, that turns out to be very close to 2 (1.9811 in the figure) no matter how many times these two guys meet every year (as long as that number remains constant).

Coincidentally, 14/7 = 2, which is the h2h ratio.

Of course many simplifying hypotheses have been assumed, and they are not realistic. But this example explains that if two equally good players overlap their careers, the younger one will prolly get a good h2h against the older. Not because he is better, but because he is younger AND (this is the key) the learning curve is steeper than the declining curve.

What say you?

Posted by Kwaku 09/16/2010 at 05:43 PM

half width at half maximum -> full width at half maximum

Posted by Kwaku 09/16/2010 at 05:48 PM

If you can't see the figure, let me know.

Posted by Slice-n-Dice 09/16/2010 at 06:05 PM

Kwaku, that is a very interesting interpretation of a head-to-head matchup based on the comparative learning, peaking and declining years. Nicely done.

Posted by Kombo (GOAT-curious) 09/16/2010 at 06:42 PM

lol @ Mart. You rant zealously, then you post a link to a religious site?! bwahahaha, Hallelujah † indeed, you have no idea how much you have just amused me, no idea.

Posted by Rikyu 09/16/2010 at 06:47 PM

For all the true believers, I suggest reading the following:

http://www.nytimes.com/2009/09/10/sports/tennis/10doping.html?_r=2

http://www.slate.com/id/2221980/pagenum/all/#p2

Also, I would note that the ITF offers "therapeutic use exemptions." So does MLB and look how that turned out:

http://www.slate.com/id/2208429/

Posted by Kombo (GOAT-curious) 09/16/2010 at 06:53 PM

Kwaku - you may have confused some folks with the math and the long explanation. Your key points seem to be:

The learning curve is steeper than the declining curve, the younger player will win more times over the course of a career, much of which is spent in relative decline after a sharp initial rise. Roddick peaked (results-wise) at 19, Hewitt was an early bloomer too. These re two easy examples of players who have since spent the bulk of their careers in relative decline.

Looking forward, it's very likely that if a younger gunner can win his first match against Rafa, he could end up with a very flattering record against him.

Posted by Kwaku 09/16/2010 at 07:23 PM

Kombo,
I'm sure there are better ways to explain what I did (more elegant, more concise, more to the point). But if someone can understand its central idea based solely on your explanation, that person is a genius, lol!

Posted by Kwaku 09/16/2010 at 07:28 PM

S-n-D, I'm happy you liked it.

Posted by TMFunk (formerly the prone-to-error typing TheMightyFunk) 09/16/2010 at 07:54 PM

kwaku,
Interesting theoretical analysis. I can't model it, but how does the h2h change with a change to the age difference? Obviously the "Nadal" curve shifts to the left or right depending on whether we move their ages closer or farther, but I'm curious as to the rate at which that changes the "calculated" h2h and see if we can extrapolate to any other two players whose careers overlapped - Say Federer and Agassi (probably a bad example)...

p.s: This didn't help me as a Federer fan at all btw for obvious reasons! :)

Posted by TMFunk (formerly the prone-to-error typing TheMightyFunk) 09/16/2010 at 08:05 PM

wait - since the two curves are identical to each other except for the phase lag, perhaps the inferred h2h ratio is also always independent of age difference?

Posted by TMFunk (formerly the prone-to-error typing TheMightyFunk) 09/16/2010 at 08:15 PM

And btw - what did they do about the tie when Federer turned 25.3? :) ok, I will stop here...I realise this is a tennis blog...

Posted by ladyjulia 09/16/2010 at 08:24 PM

Kwaku,

That's interesting.

But I can also infer from your model that Nadal, having actually won at the age of 17 (when mathematically he wasn't supposed to) holds the advantage over the older player regardless of the age difference.

What I am trying to say is that "better" is a very qualitative word. However, your model dosen't account for the fact that Nadal holds an inherent advantage over the Fed..whether Fed was 17,25 or 32..its not really going to matter.

I think the model might hold for other great players very well. But this matchup is skewed heavily by Rafa's lefty FH spin...that age becomes a non-issue in my opinion.

Now, if Rafa played with normal spin..then I would agree that their careers would have panned out the way you said, and the H2H would have remained the same 14/7 = 2.

So, in my opinion, it dosen't even boil down to who is the better player between the two. It boils down to who has the advantage between the two. Rafa and Fed could have been exactly the same age, and the H2H would have still be in the proximity of 14-7.

Posted by TMFunk (formerly the prone-to-error typing TheMightyFunk) 09/16/2010 at 08:33 PM

ladyjulia - well, Kwaku's model has no basis in reality - it is a purely theoretical exercise. The reason it was interesting to me was because the "real" Fedal h2h ratio coincidentally turned out to be almost exactly the same as the artificial ratio generated by this theoretical model! thats why my next reaction was to see if we could play around with the age difference and see if the artificial h2h matched the real h2h of any other two players with a different age difference, but I suspect given the assumptions and parameters of the model, the artificial h2h will always be 1.9 irrespective of age difference. I would like kwaku to confirm that though...

Posted by ladyjulia 09/16/2010 at 08:46 PM

TMFunk,

The curves are Gaussian curves..and the FWHM is approximately the same for both players. If you keep one curve fixed, and displace the other so that the difference is not 5 years, then the overlap between them dosen't remain to that ratio of 2.

For example, keep the red curve the same position...move hte blue by +2-5 yrs...now the blue curve will have more blue vertical lines (I assume this is what kwaku is taking for H2H ratio) and less red lines.

So, by the model, if Fed was in Rafa's generation (instead of Rafa being in Fed's generation), the H2H would have been in his favor (according to the model where their performances are approximated with a bell curve).

I think the H2H would have been worse considering all factors.

So, either we can conclude that their performances are not bell curves, nor have the same FWHM or there are other more dominating factors than age at play.

Posted by ladyjulia 09/16/2010 at 08:48 PM

Kwaku,

Its really interesting though..as TMFunk said, do such models hold for other great players?

Posted by ladyjulia 09/16/2010 at 08:55 PM

Or maybe, the horizontal displacement has to be strictly 5 years. In all other cases, the ratio won't be 2. But everytime, the difference in age is 5, the ratio will be 2? Is that what he is saying?

Let's keep the difference 5, but change the labels. That means if Fed was 17 when Nadal was 22, Fed would eventually end up with a H2H of 14-7.

Ofcourse, we will not know...but strikes me as very,very,very,very unlikely. It would be a fabulous dream, but alas..even if it was a dream, I would know it won't be true to enjoy it.

Posted by TMFunk (formerly the prone-to-error typing TheMightyFunk) 09/16/2010 at 09:15 PM

ladyjulia - you are right, the generated h2h will change if you change the age difference. Obvious from the model that if you make the ages the same the curves would be prefectly superimposed on each other and the generated h2h in that case would be 1 - every single match would be a tie!. So obviously the artificial h2h of 2 isn't constant.
and yes and yes to your 8:55 pm post. Fed and Nadal are simply labels here. You could change to jack and jill and as long as they are five years apart, the ratio would be 2 in this model.

Posted by ladyjulia 09/16/2010 at 09:44 PM

TMfunk,

Yup.

Interesting modeling though. Sports research would have been so much fun!

Posted by DenverB. 09/16/2010 at 09:55 PM

I think Rafa's physique and mentallity are what the next generation will take away from his game. Being a tooth pick is not going to cu t anymore, Rafa is the new prototype. His mentallity on the court is a welcome change to the game, he reminds me of the mma fighter George St. Pierre, always improving, completly focused and willing to fight for every point. The next generation needs to learn this lesson well because the athletes are getting bigger, faster stronger in every sport and tennis has become so physical it is basically a fight with a net in the way.
As far as the beauty thing, Federer's game is like a classic ballert designed for quite halls with effortless power and grace. Nadal's game is like the Spanish flamenco a less formal dance for the streets of madrid a style with rapid foot work and explosions od passionate power.

Posted by Kombo (GOATarded) 09/17/2010 at 01:25 AM

Rafa is not a prototype, he's an anomaly. His style of play is not a model to be immitated, it's hazardous to the point and ill-advised, resulting in perpetual injury fears and regular intravenous blood platelet (sp) infusions. Rafa is not a prototype. And that's okay, neither was Shaq, and he won a heck of a lot.

Posted by Kombo (GOATarded) 09/17/2010 at 01:28 AM

GSP's a really good fighter, unlike it's sometimes very hard to tell what he's doing so well. I also like Fedor and Anderson Silva.

Posted by MM 09/17/2010 at 02:07 AM

Why on earth did Nadal admit to oncourt coaching? After the attention at Wimbledon.... seriously he's not the brightest tool in the shed is he? Or did he think a Spanish interview wouldn't reach the ears of people who care that the rules of the game be followed by the person who is supposed to be an ambassador for the sport. Sheesh.

Posted by Kwaku 09/17/2010 at 02:41 AM

Good morning.
I just woke up. I'll address those issues in a couple of hours, stay with me!

Posted by jesse 09/17/2010 at 03:29 AM

'As far as the beauty thing, Federer's game is like a classic ballert designed for quite halls with effortless power and grace. Nadal's game is like the Spanish flamenco a less formal dance for the streets of madrid a style with rapid foot work and explosions od passionate power.'

GREAT! couldn't agree more!

Posted by jesse 09/17/2010 at 03:34 AM

and, once again, like with so may great innovators that kicked evolution far ahead, the 'specialists' and 'critics' wil keep on being in denial of what nadal's technique is.
they wouldn'y want ot learn something new, unlike

nadal who LOVES to learn.

and as marat said not too long ago, 'if you're good at tennis, you play it. if you're not that good, you comment and write about it.'....
dear marat...

Posted by Kwaku 09/17/2010 at 05:01 AM

Well, under those assumptions, the h2h is independent of the age difference (ad). This might be counter-intuitive because, as TMFunk said, for ad=0 the h2h would be a tie. However, for any age difference different from zero, the h2h ratio will always be exactly 2 in favor of the older player (the 1.9811 is actually also 2 if you calculate things exactly).

The h2h ratio does depend on the relative values of the left fwhm and the right fwhm. Actually, if you calculate it exactly,
h2hr = fwhm_r/fwhm_l
where h2hr is the head-to-head ratio, and fwhm_r and fwhm_l are the full widths at half maximum of the right and left tails respectively.

The one further assumption I've used when making ad vary is that a player won't always start their career at 17 and end at 32, but they will start it when they are 0.3 good (30% as good as in their peak) and finish it when they are 0.3 good again. If you change the 0.3 for 0.4, 0.5 or any other number, the h2hr continues to be exactly the same.

This further assumption is not very reasonable, but I've used it because a) it comes in handy for the way I've programmed this; b) the model has too many simplifying hypotheses to be used quantitatively (e.g. to see the h2h dependence as a function of age difference).

The aim of the model is only to show that even if two players are exact clones but one is older than the other, the h2h can favor the younger one (and it will probably do it because learning curves tend to be steeper than declining curves). But the operative word is CAN favor: I have not proved it WILL favor because -too many hypotheses.

If anybody wants the matlab code generating the figures (and numbers), ask and you will be given. If you don't have/use matlab but you want me to generate other figures, ask me what values you want for ad, fwhm_r and fwhm_l, and I'll generate the figure and deliver it for you in a few minutes.

I will now go on to read and answer some specific issues raised mainly by ladyjulia and TMFunk.

Posted by Kwaku 09/17/2010 at 05:25 AM

TMFunk,

"how does the h2h change with a change to the age difference?" -> see above, ask if you have further questions.

"see if we can extrapolate to any other two players whose careers overlapped - Say Federer and Agassi" -> as long as their careers overlap, yes. In fact as you know Federer and Nadal are only labels, you can also label those curves as Federer and Agassi. The shapes of the curves in my program are the same, regardless of the real shapes of the Agassi curve (with a larger fwhm_r, i.e., more longevity) or the Federer curve (whose aging I am really curious to witness: that Federer's elegant economical style should make him age well, i.e. still be relatively successful in his early 30's, might be mistaken, and I'm looking forward to seeing it).

"p.s: This didn't help me as a Federer fan at all btw for obvious reasons! :)" Well, for me the reasons are not obvious. If fact I can see no reason at all. This should be good news for a fedfan like you because you have one more thing to answer, besides matchup issues, to those who say that Nadal is better than Federer because the h2h favors him. You can prove that even if they were exactly the same (and therefore no matchup issues), the younger player would prolly get a positive h2h.

Btw, another poster that could be happy about this is manuelsantanafan. He respects the greats of old very much (Pancho González, etc.) One reason not to write off the greats of old is the continuity of competitiveness: Laver was comptetitive with Connors, Connors with Borg, Borg with...., and Sampras with Federer, so maybe Laver is actually as good as Federer (not in terms of achievements ("great"), but in terms of performance ("good")). The fact that the younger player will tend to have a positive h2h against the older one even if they are equally good reinforces that argument.

I must now go, will continue later.

Posted by ladyjulia 09/17/2010 at 06:38 AM

kwaku,

"h2hr = fwhm_r/fwhm_l"

I thought you set the linewidth of the curve don't you? Or else how do you determine what the FWHM should be? I am a little confused now.

I have to go to work now...and won't be able to check whole day today...but I will check back at night what you wrote. Thanks for the interesting discussion.

Posted by Kwaku 09/17/2010 at 07:17 AM

I'll continue only with things not already answered:

TMFunk, "And btw - what did they do about the tie when Federer turned 25.3?"
Irrelevant. It's a point in time. Consider it a tie if you want. Assuming a constant and sufficiently high rate of matches per unit time, the h2hr is equal to the total length of time one player is better than the other (and both in their professional careers) divided by the total length of time the other player is better than the one. Like: (32-25.33)/(25.33-22) = 2 = h2hr (when "Fed" is 22, "Nad" is 17 and starting).

"I will stop here...I realise this is a tennis blog"
Maybe I don't realize :)

ladyjulia, "Nadal, having actually won at the age of 17 (when mathematically he wasn't supposed to) holds the advantage over the older player regardless of the age difference".
First, they are not Nadal and Fed, but idealized identical players with a difference in age. Second, I assumed random effects did not exist or cancelled out, so if a peaking Federer is beaten by a just starting Nadal, we can consider it a random effect (and, in real life, also an effect of the matchup, which is not considered in the model). Federer also beat Rafa in the 2009 WTF, at a time when Rafa was supposed to be peaking and Federer declining: consider that these random effects cancel out. In any case, my model is overly simplified to represent reality accurately, but not so much overly simplified that it cannot show the possibility of a real effect taking place.

"your model dosen't account for the fact that Nadal holds an inherent advantage over the Fed..whether Fed was 17,25 or 32..its not really going to matter".
Exactly, and I said it from the beginning: matchup issues are neglected. It is a big assumption, but legitimate and appropriate if the objective is to show precisely that EVEN IF THERE WERE NO MATCHUP ISSUES, there can still be something going on favoring the younger player's h2h.

"this matchup is skewed heavily by Rafa's lefty FH spin...that age becomes a non-issue in my opinion".
Well, maybe without the age overlapping effect (let's call it like that) the h2h would be 13/8 instead of 14/7 due mainly to the matchup issue (if we consider both players to be roughly equally good, which is again another hypothesis). Or you could assign weights: for instance, the h2h is 14/7 because of the matchup (75%), because of the age overlapping effect (20%) and because Nadal is simply better (5%). What you say does not make age a non-issue, but an issue concurring with other issues (matchup...). (Maybe without both the overlapping and the matchup effects the h2h would be 10/10, i.e. they are equally good players. Who knows.)

"Rafa and Fed could have been exactly the same age, and the H2H would have still be in the proximity of 14-7"
If the overlapping effect exists, and I do think it does, it would be closer to fifty-fifty (maybe 13/8 or 12/9) but I still think that Rafa would come on top because of the matchup issue (assuming they are both roughly equally good players, i.e. against the field --if we take Fed's achievements at Rafa's age they were almost as good as Rafa's, but we cannot assure that Rafa will age as good as Fed has until now).

TMFunk, "The reason it was interesting to me was because the "real" Fedal h2h ratio coincidentally turned out to be almost exactly the same as the artificial ratio generated by this theoretical model!"
I was also surprised. I actually had to do very little tinkering with the parameters before the h2hr = 2 appeared. Later I realized that under my assumptions that was precisely equal to fhhm_r/fhhm_l. Since the age overlapping effect can explain all of the Rafa-Fed real h2h, I assume that the real value of fhhm_r/fhhm_l is smaller than 2, so that the rest until 2 can be explained by the undoubtedly existing matchup issue (assuming they are roughly equally good against the field).

ladyjulia, "The curves are Gaussian curves..and the FWHM is approximately the same for both players"
They are asymmetric Gaussian, and exactly the same (not approximately).

"If you keep one curve fixed, and displace the other so that the difference is not 5 years, then the overlap between them dosen't remain to that ratio of 2"
Well, coincidentally it does, as explained above, under the assumptions also explained. Looks like a coincidence, but it's a consequence of choosing fhhm_r/fhhm_l = 2.

"For example, keep the red curve the same position...move hte blue by +2-5 yrs...now the blue curve will have more blue vertical lines "
Nope. I can show you the figure if you're interested.

"if Fed was in Rafa's generation (instead of Rafa being in Fed's generation), the H2H would have been in his favor"
What?? You prolly mean if Fed were younger. Then yes.

"we can conclude that their performances are not bell curves, nor have the same FWHM or there are other more dominating factors than age at play"
Are you talking about reality? Then of course: they are not bell curves (have many ups and down each according to form, injuries, etc.), the don't have the same FWHM (if any), they are just different etc. etc. But my simplifying assumptions are not only legitimate, but also good and basically necessary, if the objective is to prove that EVEN IF THERE WERE NO OTHER DIFFERENCES (matchups, different players, etc.), just the age overlapping can explain the asymmetric h2h. For identical players (twins) with just an age difference.

"do such models hold for other great players?"
The model is not for Fed and Nad. These are only labels. So the answer is yes. But the answer is no because the model assumes things that are not real. Like identical players. It only proves that if the players were identical, the age difference all by itself could account for an asymmetric h2h in favor of the younger one (unless the declining curve was steeper than the learning curve, which is obviously not true in real life).

"Let's keep the difference 5, but change the labels. That means if Fed was 17 when Nadal was 22, Fed would eventually end up with a H2H of 14-7"
Of course! They are labels. Change them, change the colors, and you have the symmetric figures and numbers. But it does not mean that if we freeze real Fed in a deep freezer for 10 years he will beat a 5-year older Rafa.

"It would be a fabulous dream, but alas..even if it was a dream, I would know it won't be true to enjoy it."
Enjoy the dream! My take is that, NOW IN REAL LIFE, the matchup issue is a strong one, so if Federer were 5 years younger than Nadal his h2h might be even worse. Federer would be 17 trying to beat a peaking Nadal of 22 and even with a matchup issue, so at the beginning he would just have no chance. And when Fed peaks Nadal would be declining, but with a small slope (not steeply), so the matchup could compensate for that. Then there is the issue of any of the two not getting to the needed round to meet the other. So who knows anyway. But I'm sure that if Federer was 5 years younger than Nadal, his h2h would still be bad against him, not so far from 14/7, and maybe even slightly worse (or slightly better).

TMFunk, "the generated h2h will change if you change the age difference. Obvious from the model that if you make the ages the same the curves would be prefectly superimposed on each other and the generated h2h in that case would be 1"
As I said, nope. It's a discontinuous function being -2 for a negative age difference, 0 for twins, and +2 for a positive age difference. That is, if fhhm_r/fhhm_l = 2 and the rest of the assumptions hold.

Posted by Kwaku 09/17/2010 at 07:33 AM

ladyjulia, "I thought you set the linewidth of the curve don't you? Or else how do you determine what the FWHM should be?"

I don't understand what you mean by "the linewidth of the curve". If it is the length of time between the moment a player starts to play and the moment he retires, then I explained it above.

As for the left and right FWHM values, they were tinkered by me a little at the beginning in order to get a player starting at 17, peaking at 22, and playing until 32, with the same level of performance at 17 as at 32. When I did that and run the program, I was surprised to see that the h2hr turned out to be 2. Soon I realized that the h2hr turns out to be exactly equal to fwhm_r/fwhm_l under this very simplified model. So h2hr = fwhm_r/fwhm_l is something that can be proved (under those assumptions), not something I decided. Not part of the problem statement, but part of its solution.

In real life the peak is prolly closer to 24 than 22, so my theoretical fwhm_r/fwhm_l should be smaller than 2, and therefore also the h2hr. Besides performance at 32 is prolly different from performance at 17, and both of them better than around 30% of peak performance. And every curve has ups and downs due to form, injuries, etc. But this does not matter much, and indeed it should be neglected in order to prove what I wanted to prove.

Posted by Kwaku 09/17/2010 at 07:56 AM

I uploaded the corresponding figure for a 2-year difference, like ladyjulia suggested.
It is the last "photo" here:
http://picasaweb.google.es/felipe.jimenez.h/20100106_TW?authkey=Gv1sRgCPSTzcbtytKa6gE#
Please tell me if you cannot access it.

Posted by TheMightyFunk 09/17/2010 at 09:47 AM

kwaku - I haven't erad all your responses in detail and probably won't be able to until later in the afternoon, but promise I will and get back to you if I have any questions. One comment did catch my eye though that I feel compelled to respond to:

"p.s: This didn't help me as a Federer fan at all btw for obvious reasons! :)" Well, for me the reasons are not obvious. If fact I can see no reason at all. This should be good news for a fedfan like you because you have one more thing to answer, besides matchup issues, to those who say that Nadal is better than Federer because the h2h favors him. You can prove that even if they were exactly the same (and therefore no matchup issues), the younger player would prolly get a positive h2h."

- All that is fine, but the reason it doesn't help me as a Fed fan is the starting premise of the model that the two are equal - As a Fed fan, I believe Federer is better, no (and H2H be da-nd!)? You come up with a model that explains why Federer is better in spite of the H2H and then we will talk. :) btw - this last comment and the original are tongue-in-cheek comments, not intended to start a GOAT debate :)

Posted by TheMightyFunk 09/17/2010 at 09:50 AM

and wow, so the generated h2h is always 2? That was my initial guess and then I ended up changing my view based on the "twins" result.

Posted by Slice-n-Dice 09/17/2010 at 10:43 AM

One of the more interesting facts about the rivalry between Federer and Nadal is that Nadal won their very first meeting as professionals--a straight set win in the third round of the 2004 Miami Masters event, when Nadal was 17 years old and ranked no. 34 in the world. Federer, 22 years old at that stage in his career, had won his first two majors and was ranked no. 1.

Posted by Slice-n-Dice 09/17/2010 at 10:57 AM

Kwaku and others,

As was said, the model is just that... a model, which means it follows certain "laws" and assumptions. The primary law it follows is that a professional player will begin his career in a learning phase (and hence, will not achieve over time their best results against the field), enters a peak phase (which is a moment in time, but which in reality might actually endure for a few years), and finally enters a declining phase (during which the player's performance falls. The primary assumptions are two-fold: (1) a player's learning phase follows a steeper path than his/her declining phase's path -- in other words, the learning phase doesn't last as long as the declining phase, and therefore their performance relative to the field improves at a greater rate than their relative decline; and (2) these "paths" are identical for two or more players who are deemed to be equal in skill.

Obviously, none of these things is "true" in the absolute, empirical sense. But as a model for analyzing how an older player might fair against a yonger rival of nearly equal skill, it is very useful.

Posted by Kwaku 09/17/2010 at 12:10 PM

S-n-D, "as a model for analyzing how an older player might fair against a yonger rival of nearly equal skill, it is very useful."
Thank you, that's its purpose :)

Posted by Slice-n-Dice 09/17/2010 at 12:22 PM

I totally get it, Kwaku. Thanks for sharing.

Posted by Kwaku 09/17/2010 at 12:42 PM

TMFunk,

So you want a theory that proves that if you have two players, the one with the losing h2h is always the better one? Or even that the older player is always the better one, regardless of the h2h? Lolol! I'm sure that would please many Fed fans like you ;) but I'm pretty sure such a theory is impossible to justify reasonably. Being older does not make you better, and having a losing h2h with someone does not make you better either, no matter what theories you invent! At least I have proved that it doesn't necessarily make you worse, which is something you should be happy about :D

And you're even asking it from a Rafan who actually thinks that after the end of their careers Rafa will have proved that he is better than Fed! Don't get me started, lest I develop a theory that can prove that Rafa is better than Fed even before their careers have ended, lol! Like this I would not have to wait ;-)

Now seriously:
"the starting premise of the model that the two are equal".

Nope. There is no premise at all that Fed and Nadal are equal (I am starting to think I should have used different labels for the two identical players). The premise is that we have two players that are equal, but they are not Fed and Raf. Now, if two identical players (save age) can have a 2:1 h2h just because of age overlap, that does help Federer. Here is a reasoning whereby you can actually use the theory to "help Fed":

** I'll prove that it is possible that Fed CAN BE (not necessarily is) BETTER THAN (not equal to) Nadal and still have a losing h2h with him, even under the assumption that there are no matchup issues, i.e. they will both fare against the field like they fare against each other. (This is very important because the usual explanation always involves matchup issues, and now you don't need that.)

We start with a universe in which Fed and Nadal are equally good and have a 3:1 h2h in favor of Nadal based solely on the age overlap effect. That is possible if the fwhm_r/fwhm_l ratio is 3 instead of 1.

And now consider universes similar to this one in which Fed is incrementally better and Nadal stays the same. A small variation in how good Fed is should not produce a huge variation in their h2h. Therefore, by carefully making Federer incrementally better, you should be able to stop at the point (universe) in which their h2h is exactly 2:1, like in this universe, with Federer being better, not just equal to Nadal. **

Posted by Kwaku 09/17/2010 at 12:52 PM

S-n-D,
Do you know that you were the one very first poster I talked with when I arrived at TW several years ago? It was about whether lefties have an unfair advantage that ad points are served left-to-right, and whether serving first to the ad court would change that. Do you remember?
(But please let's not talk about that again, I have enough with this now, lol! You think they have and advantage, and I think there is symmetry, so lets agree to disagree for the time being.) (Actually I think they have a slight disadvantage, not advantage, but we can talk about that some other time.)

Posted by Kwaku 09/17/2010 at 12:56 PM

if the fwhm_r/fwhm_l ratio is 3 instead of 1 -> if the fwhm_r/fwhm_l ratio is 3 instead of 2

Posted by TMFunk 09/17/2010 at 12:58 PM

"the starting premise of the model that the two are equal".

Nope. There is no premise at all that Fed and Nadal are equal (I am starting to think I should have used different labels for the two identical players). The premise is that we have two players that are equal, but they are not Fed and Raf."

c'mon kwaku - Now you are just playing with words. :) I completely get the model, and I know you can change the names to Jack and Jill and it would be the same as long as the premise is that the Jack and Jill are equal in skill. But you drew me and possibly others to your post here on the other thread with the teaser that it explains the Federer/Nadal h2h and that Fed fans would like it. So to now say with innocent face that "The premise is that we have two players that are equal, but they are not Fed and Rafa" is a bit contradictory to your original lead-in to your model, don't you think? Nah, I can't let you slip by like that. :)

All I am saying is that as a Fed fan if I'm supposed to be happy with the starting premise that Fed and Rafa are equal in skill, well, thanks but no deal! :) btw, I'm just having fun and yanking your chain here...:)

Posted by Kwaku 09/17/2010 at 12:59 PM

"Slice-n-Dice 09/17/2010 at 10:43 AM
One of the more interesting facts about the rivalry between Federer and Nadal is that Nadal won their very first meeting as professionals--a straight set win in the third round of the 2004 Miami Masters event, when Nadal was 17 years old and ranked no. 34 in the world. Federer, 22 years old at that stage in his career, had won his first two majors and was ranked no. 1."

Yes, it's indeed very interesting, and a sign of the times to come, lol!
Here is a vid:
http://www.youtube.com/watch?v=CvAGAdLArKY

Posted by Kwaku 09/17/2010 at 01:04 PM

TMFunk,
I am dead serious that the theory can help Fed.
And I was 100% honest: what I wrote at the other thread was not a teaser that promises something I have not delivered (as far as I see things, and quite sure at that). I may be mistaken in something, but I am still totally convinced that Fed fans should be happy to know about this. Because it gives an additional explanation for the h2h, other than the well-known matchup one, that does not involve Fed being worse.

Posted by Kwaku 09/17/2010 at 01:07 PM

"So to now say with innocent face that "The premise is that we have two players that are equal, but they are not Fed and Rafa" is a bit contradictory..."

Well, and I have actually given you a literal reasoning by which that can be done. It is between the two asterisks ** ... ** at 12:42.

Posted by TMFunk 09/17/2010 at 01:22 PM

kwaku - I think you are missing my attempt at humour, and that's my fault. I agree with you 100% that your model provides a theoretical explanation for how an age difference can skew the h2h of two equally skilled players in favour of the younger player. No argument there. never was.

What I was trying to make a funny post about was that the only explanation that will make me "happy" as a Fed fan is one that demonstrates why Federer has a bad H2H with Nadal in spite of being the more skilled player. It was just a joke aimed I guess at fed fans (like myself) who think Federer is the best thing since sliced bread and get all worked up and defensive whenever the H2H comes up as an explanation for why he is not better than Nadal (not like myself - I can laugh pretty easily at that). Don't think I was successful in my endeavor :)

Posted by TeamNadal 09/17/2010 at 01:24 PM

wow, if "its and buts were candy and nuts" we'd all have a wonderful Christmas....

*sprays* the room

Posted by Kwaku 09/17/2010 at 01:27 PM

TMFunk,

This was my post at the other thread:

"[OT Warning]:
In the previous thread I have just posted an explanation to the Nadal-Federer h2h that two kinds of people will be happy to read: a) Federer fans; b) people who enjoy mathematics."

Sorry to have created false expectations. I now see it could lead to expect a FULL explanation of the h2h (!!), instead of a PARTIAL one, so I should prolly have said "about" instead of "to", so that it read like this:

"[OT Warning]:
In the previous thread I have just posted an explanation ABOUT the Nadal-Federer h2h that two kinds of people will be happy to read: a) Federer fans; b) people who enjoy mathematics."

In any case, let me stress the bottom line:

* The theory CAN INDEED BE USED TO HELP FED. It is an additional reason, never explained until now (as far as I know), of why Federer can be better than Nadal and still have a losing h2h with him. The matchup reason has been used a lot. But having an additional reason that is totally independent from the matchup one certainly helps Fed.

* I am still totally sure that I WOULD LOVE TO KNOW ABOUT IT IF I WAS A FED FAN.

Finally. Even if "about" would have been more precise than "to", it was not a disingenuous mistake, but a genuine one (and quite subtle btw). I have not been disingenuous nor talked with an innocent face, but come out with something I sincerely think valuable and able to "help Fed" (and also manuelsantanafan, as stated above).

Posted by Kwaku 09/17/2010 at 01:29 PM

Sorry then, TMFunk, it is true I did not get the humor in it.

Posted by Kwaku 09/17/2010 at 01:33 PM

"...funny post about was that the only explanation that will make me "happy" as a Fed fan is one that demonstrates why Federer has a bad H2H with Nadal in spite of being the more skilled player"

But I almost delivered precisely that, even if you asked it in humor! I delivered an explanation that

"demonstrates why Federer has a bad H2H with Nadal in spite of POSSIBLY being the more skilled player"

So I proved it is POSSIBLE, and even without the matchup issue. Not bad, imo ;)

Posted by TMFunk 09/17/2010 at 01:34 PM

kwaku - I apologize if I've offended you. As I said, I was just having fun and yanking your chain a bit with my "innocent face" comment - No intent to accuse of being disingenuous AT ALL. Like I said - just an attempt at humour that had completely unintended consequences. I need to take some "joke development and management" classes...

And again, thank you for your model. Sincerely, it is very helpful as a means to model the effect of age difference on equally skilled players.

Posted by Kwaku 09/17/2010 at 01:41 PM

No problem at all, TMFunk. When I said "Sorry then, TMFunk, it is true I did not get the humor in it.", I was erasing any comment relative to "innocent face". Unfortunately there is no [Delete] button here.

It turns out that precisely today AB talked about disingenuous posters and I was not sure if he was referring to me, so I was oversensitive (see my 06:37 at http://tennisworld.typepad.com/tennisworld/2010/09/the-longest-journey/comments/page/11/#comments). It turns out he was not referring to me (see his 01:48).

Yes, I was oversensitive, so sorry. And I also have to learn to pay more attention the emoticons of funny faces, because they were actually there in your post now that I reread it.

Posted by TMFunk 09/17/2010 at 01:41 PM

And btw, no, you did not create any false expectations. Again, had no intention of implying that at all. I quite enjoyed your model and the subsequent conversations around it!

Posted by TMFunk 09/17/2010 at 01:44 PM

No worries kwaku. This is always a risk with the written word - You sometimes cannot judge the emotion or intent without the supporting body language, tone of delivery etc that is so important in verbal or in-person communication. I need to remember that before posting!

Posted by Slice-n-Dice 09/17/2010 at 02:48 PM

Ah, Kwaku, you remember, too! Yes, that is one we'll have to agree to disagree on, and hold our tongues 'til another day! LOL

Posted by Kwaku 09/17/2010 at 03:29 PM

SnD, I thought you might have forgotten it was me bc I was Kofi back then ;)

Posted by mel 09/17/2010 at 07:47 PM

TO TEAM NADAL: YOU HAD ME IN STITCHES. THAT WAS BRILLIANT. I HOPE THE TROLLS GOT ELIMINATED ALREADY!
VAMOS!

Posted by Mim 09/17/2010 at 10:33 PM

Rafael Nadal is amazing. He's an absolute legend and a complete joy to watch. I never tire of it! I want more!


VAMOS RAFA! Congratulations on yet another record-making, astonishing feat. You deserve it!

Posted by Michelle 09/17/2010 at 10:38 PM

Rafael Nadal is extremely hardworking. But he is also supremely talented. Like Mr.Bodo pointed out, it's almost impossible to see where one begins and the other ends.

I consider it all one thing: GENIUS.

His mindset, his work ethic, his athleticism, his creativity, his heart, his spirit, his forehand, his backhand, his net play, his footwork, his speed, his compassion towards his opponents, his love and appreiciation of his fans, his humility and modesty..all of it! He's simply a genius. I am grateful and thankful to have him. I am blessed to be his fan.

Posted by Kwaku 09/22/2010 at 08:25 AM

I have modified the model a little (improving it, I hope).

Upsets happen, so the player with the better performance at any given moment does not always win. An upset is more likely when the performances of both players are similar, and more rare when they are very different.

In order to account for that, instead of introducing random effects as a function of performance differences, I have simply calculated the quotient between the red and the blue areas. That is equivalent to considering the difference in performances every time they meet, assuming they meet at a constantly high rate. It means that if both players meet and their difference in performance is great, that contributes more to the h2hr than if their difference in performance is small.

This also solves a difficulty with the previous model, namely, that the h2hr was a discontinuous function of ad. With the new model, the function is smooth, as is plotted in the last "picture" of the folder. Let me remind you its link:

http://picasaweb.google.com/felipe.jimenez.h/20100106_TW?authkey=Gv1sRgCPSTzcbtytKa6gE#

(please somebody tell me if you can access it).

Posted by Account Deleted 09/22/2010 at 11:57 AM

http://i56.tinypic.com/iz9lr5.jpg

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Posted by Kwaku 09/23/2010 at 04:50 AM

Moderator 12:06 AM please.

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