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All things being equal, you would mathematically expect an even distribution of Grand Slam titles across the four tournaments. Statistically, you would expect Nadal's tally at the Australian Open, US Open and Wimbledon to be 15, and his tally at Roland Garros to be 5. In fact, it's almost the polar opposite of that, with 13 titles at the French Open, and 7 at the other Grand Slams combined.

Of course, completely even distribution rarely happens in reality, but mathematically as all of the Grand Slams are held with equal regularity, there is no reason not to expect an equal distribution of having won five at each.

Nadal has now won 13 times at Roland Garros, where he would have been expected to win 5 of his 20 titles mathematically, given linear distribution. So he's been 2.6 times more successful than would be expected.

Conversely, Nadal has won 7 titles at the other three Grand Slams, where he would have been expected to win 15 in total given linear distribution. So he's been 2.143 (to three decimal places) less successful than would be expected, or 0.46 recurring as successful as would be expected if expressed as a ratio.

So if we multiply the two 2.6 * 2.143, we get 5.5718, which is the statistical proportion to which Nadal has been better at Roland Garros than at the other Grand Slams combined. In short, he has been over five and a half times better.

While it is not unusual for players to be disproportionately successful on a favourite surface, this is by far the biggest disparity of any Grand Slam winner who won titles at more than one location (by definition, anyone who didn't has an infinite propensity towards the venue where they won).

Federer has been 1.6 times more successful than expected at Wimbledon, and 1.5 times less successful at the other Grand Slams = 2.4 times better.

Djokovic has been 1.88 times more successful than expected at the Australian Open, and 1.416 recurring times less successful at the other Grand Slams = 2.66 times better. If you want to do his hard court ratio then this works out as 1.29 * 1.416 = 1.83 times better.

Sampras was 2 times more successful than expected at Wimbledon, and 1.5 times less successful than would be expected at the other Grand Slams = 3 times better.

Borg was 2.18 times more successful than expected at the French Open, and 1.65 times less successful than would be expected at the other Grand Slams = 3.6 times better.

Connors was 2.5 times more successful than expected at the US Open, and 2 times less successful than would be expected at the other Grand Slams = 5 times better.

Lendl was 1.5 times more successful at the French Open than would be expected, and was 1.2 times less successful than would be expected at the other Grand Slams = 1.8 times better.

Agassi was 2 times more successful at the Australian Open than would be expected, and was 1.5 times less successful than would be expected at the other Grand Slams = 3 times better.

McEnroe was 2.28 times more successful at the US Open than would be expected, and was 1.75 times less successful than would be expected at the other Grand Slams = 3.99 times better.

Wilander was 1.71 times more successful at the French Open than would be expected, and was 1.31 times less successful than would be expected at the other Grand Slams = 2.23 times better.

Edberg was 1.33 times more successful at the French Open than would be expected, and was 1.125 times less successful than would be expected at the other Grand Slams = 1.5 times better.

Becker was 2 times more successful at Wimbledon than would be expected, and was as successful as would be expected at the other Grand Slams = 2 times better.

There are some problems with this result. The importance of Grand Slams has changed over the years, meaning that some of the older players didn't take them all equally seriously. But that should skew their result towards propensity towards a favourite Slam, not away from it.

Another issue is that hard courts make up two of the Slams, so you could argue that diminishes the statistical significance of some results. But even if you go back and calculate it then you will find that it makes no significant difference to the results.

In fact, the player who is closest to Nadal, Jimmy Connors, would be much further away from him in all probability had he not played the Australian Open only twice, in 1974 and 1975. That completely skews his results.

What you can conclude from this is that Nadal is by far the most surface-reliant player in the history of major Grand Slam champions. Equally, you can also say (as was pretty obvious) that he's the best player at a single Grand Slam, on a single surface, ever.
 

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f = (# of titles at fave slam) / (# of titles at all other slams combined) * 3 (3 = number of different slams - 1)

13/7 * 3 = 39/7 = 5,(571428)

No one else bar Connors crosses 3 once you adjust to the reality of a 3-slam era for Borg, Connors and McEnroe (in the latter's prime anyway) as AO wasn't considered a top tournament and attended as such. Borg: 6/5 * 2 = 2,4; Connors: 5/3 * 2 = 3,(3); McEnroe: 4/3 * 2 = 2,(6); although since Mac did attend 2 proper 1983+ AOs in his seven-year prime ('83 and '85), it would be more fair to put 4/3 * (2 2/7) = 64/21 = 3,(047619), so he crosses 3 a little bit.
 

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this confirms
his clay GOAT status and 2nd overall in GOAT race
 

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there's reason why you don't get a Nobel despite being genius on mathematics.
 

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What a stupid thread - I stopped reading after the first sentence. Why would you expect an even distribution across the 4 slams when they are played on 3 different surfaces?

Only people who have never played tennis on different surfaces make such stupid posts. I have a friend who always grinds me down when we play on American green clay, but I always blow him off the court when we play on indoor hard.
 

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Discussion Starter #9
What a stupid thread - I stopped reading after the first sentence. Why would you expect an even distribution across the 4 slams when they are played on 3 different surfaces?
Well, I already explained this. They are held with the same regularity, so mathematically you would expect even distribution across the four. As I said, this rarely happens in reality, and indeed none of the players listed has a perfect distribution of results; they are all skewed towards one Grand Slam or another. And, of course, this brief calculation doesn't take into account how many times each player played each of the Grand Slams, but it gives some indication.

However, only one player comes anywhere near Nadal in terms of propensity towards his favoured Slam, and that player didn't play the Australian Open for the last 15 years of his career; if he had then he would doubtless be nowhere near Nadal.

I also explained in the OP that the fact that two of the Grand Slams are on hard courts does influence the results:

...hard courts make up two of the Slams, so you could argue that diminishes the statistical significance of some results. But even if you go back and calculate it then you will find that it makes no significant difference to the results.

In fact, the player who is closest to Nadal, Jimmy Connors, would be much further away from him in all probability had he not played the Australian Open only twice, in 1974 and 1975. That completely skews his results.
The fact that the Slams are on different surfaces is irrelevant to the mathematical significance, in fact that is precisely what the OP is testing! The propensity towards better results at a preferred Grand Slam. Mathematically, Nadal's results are way more skewed towards winning at his preferred Grand Slam, the French Open on clay, than any other comparable player.

This is the foundation for why I personally believe that while Nadal is definitively the best player on clay, he can never be considered definitively the best player overall because his entire career is founded on clay results. Undoubtedly, he is a great player overall, but without his French Open results, he's nowhere near the best player.

What Nadal fans would probably then argue is that this applies equally to Federer, Djokovic, or Sampras. But actually it doesn't. It just doesn't apply to any other player to anything approaching the same degree. People might not wish to hear that. People might not understand it. But it's simply a mathematical fact.
 

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he is unreally good in FO, better than anybody else in any tournament in history, so...
 

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What a stupid thread - I stopped reading after the first sentence. Why would you expect an even distribution across the 4 slams when they are played on 3 different surfaces?

Only people who have never played tennis on different surfaces make such stupid posts. I have a friend who always grinds me down when we play on American green clay, but I always blow him off the court when we play on indoor hard.
most people on this board don´t have a clue about tennis and have never played it.

this part:
*All things being equal, you would mathematically expect an even distribution of Grand Slam titles across the four tournaments *

big LOL
 
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Good exercise developing what is known in the distribution of Nadal slams.

As already said, you have to take Connors, Borg and Mc Enroe out of the AO equation.

Integrated only from Lendl, Wilander, Edberg, Becker etc., with another variable however.

On grass until 1987, on hard from 1988.
This is important for Lendl in particular, winner "only" of 2 AO on hard (89-90), at the end of his career peak.

Now, the type of surface, the materials and the current game tone all that down a bit in the long run.

Lendl with the material and on the grass now, would also win Wimbledon.
 

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I stop reading at the first sentence.

"All things being equal, you would mathematically expect an even distribution of Grand Slam titles across the four tournaments"

What does "all things being equal" mean? All four tournaments played on same surface? If not the case, then this assumption is completely wrong. No need to read more.
 

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Discussion Starter #16
most people on this board don´t have a clue about tennis and have never played it.

*All things being equal, you would mathematically expect an even distribution of Grand Slam titles across the four tournaments *
Firstly, I've played tennis with professional tennis players, I was top 15 in my age group in the country when I was younger. I don't play tennis any more because I wasn't good enough to be professional, but I have played at a higher level than 99% of people on here, rest assured. This doesn't matter at all because it's of zero relevance to the thread, or the mathematics involved. In fact, someone who knew absolutely nothing about tennis and more about maths than me could have done it quite easily.

Secondly, I've already answered your comment here.

The whole point of the calculation is to test to what degree players show a propensity towards their preferred Slam. Of course, I am aware that players have a bias towards certain surfaces / tournaments, I acknowledged that in the OP, and that is, in fact, the whole point of the calculations in the first place! Mathematically, you would expect an even distribution of Grand Slam titles across the four tournaments. That's not something that can be challenged or disagreed with; it's simply a mathematical fact.

The data in the OP cannot be disagreed with or argued with. It's just factual. You can debate its significance. You can disagree with my conclusions. You might well not understand it. But you can't claim that it's not the case, because it is mathematically the case.
 

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Well, I already explained this. They are held with the same regularity, so mathematically you would expect even distribution across the four. As I said, this rarely happens in reality, and indeed none of the players listed has a perfect distribution of results; they are all skewed towards one Grand Slam or another. And, of course, this brief calculation doesn't take into account how many times each player played each of the Grand Slams, but it gives some indication.

However, only one player comes anywhere near Nadal in terms of propensity towards his favoured Slam, and that player didn't play the Australian Open for the last 15 years of his career; if he had then he would doubtless be nowhere near Nadal.

I also explained in the OP that the fact that two of the Grand Slams are on hard courts does influence the results:

The fact that the Slams are on different surfaces is irrelevant to the mathematical significance, in fact that is precisely what the OP is testing! The propensity towards better results at a preferred Grand Slam. Mathematically, Nadal's results are way more skewed towards winning at his preferred Grand Slam, the French Open on clay, than any other comparable player.

This is the foundation for why I personally believe that while Nadal is definitively the best player on clay, he can never be considered definitively the best player overall because his entire career is founded on clay results. Undoubtedly, he is a great player overall, but without his French Open results, he's nowhere near the best player.

What Nadal fans would probably then argue is that this applies equally to Federer, Djokovic, or Sampras. But actually it doesn't. It just doesn't apply to any other player to anything approaching the same degree. People might not wish to hear that. People might not understand it. But it's simply a mathematical fact.
I normally don't like to get involved in Goat debates, but since you meticulously used advanced mathematics to make primitive-minded inference in order to showcase someone in relatively poorer light than your preferred player, let me use medieval analogy to allow you to make factual inference.

Let's suppose that there were two medieval Kings A and B with their own kingdoms and harems. King A is brutish and rugged while the bards sing about how the grace and poise of King B puts even swans and peacocks to shame. King A fiercely guards his kingdom, not allowing King B to even take a look at his harem. On the other hand, King B not only fails to guard his kingdom from King A and another King C from time to time, but himself opens his harem to King C now and then. Now, which of the two is a greater king?

If you are telling me that a player with a disproportionate number of slams on his favoured surface is inferior to another who chokes away match points on his favoured surface, I can only say that you need help.
 

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I stop reading at the first sentence.

"All things being equal, you would mathematically expect an even distribution of Grand Slam titles across the four tournaments"

What does "all things being equal" mean? All four tournaments played on same surface? If not the case, then this assumption is completely wrong. No need to read more.
I had the same reaction and stopped reading at the exact same point as you (I.e after the first sentence)
 

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Discussion Starter #19
f = (# of titles at fave slam) / (# of titles at all other slams combined) * 3 (3 = number of different slams - 1)

13/7 * 3 = 39/7 = 5,(571428)

No one else bar Connors crosses 3 once you adjust to the reality of a 3-slam era for Borg, Connors and McEnroe (in the latter's prime anyway) as AO wasn't considered a top tournament and attended as such. Borg: 6/5 * 2 = 2,4; Connors: 5/3 * 2 = 3,(3); McEnroe: 4/3 * 2 = 2,(6); although since Mac did attend 2 proper 1983+ AOs in his seven-year prime ('83 and '85), it would be more fair to put 4/3 * (2 2/7) = 64/21 = 3,(047619), so he crosses 3 a little bit.
Thank you for the input. I could have done something like this, and it's not a perfect exercise, but even if you conduct the exercise in a way that skews the results of the players that you mentioned, Nadal's results are still by far the most skewed towards a particular surface and Slam. I knew this anyway, its obvious, but the OP proves that this is the case mathematically, and no-one can ever legitimately claim that it applies to other players, because it doesn't.
 

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Discussion Starter #20
I normally don't like to get involved in Goat debates, but since you meticulously used advanced mathematics to make primitive-minded inference in order to showcase someone in relatively poorer light than your preferred player
I don't think I used advanced mathematics, I think I used fairly basic maths. I don't think it's a primitive inference, I think it explicitly demonstrates something that is irrefutable. And I don't wish to cast Nadal is a poorer light, I just genuinely believe that he's the best ever on clay, but we can't say that he's definitively the best because he's so reliant on his clay results, as demonstrated by the OP. But there are many other statistics that we could also cite, and they all point to the same thing; Nadal is the best on clay by miles, he isn't the best on any other surface, in any other conditions, so he's not definitively the best.

That's just my personal view, but if you make that comment then Nadal fans will assert that other players are equally reliant on their favourite Slam / surface, etc. We now know definitively that this argument is simply incorrect. However, it's an unbelievable achievement to reach 13 French Open titles, Nadal has had an amazing career, I don't wish to detract from that. But I can't accept that he's definitively the best overall. For me, it doesn't stand up to statistical scrutiny. That's just my view, you can disagree with that, but you can't disagree with the facts.
 
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