Mathematical Model for Total Grand Slams if Federer, Nadal or Djokovic Didn't Play Tennis

jonwbecker

New User
I have often wondered how many Grand Slams Federer/Nadal/Djokovic would finish with if the other two didn't play tennis. More often than not it seems like the roadblock to each winning a title is having to play one of the other two. I got to thinking that surely this could be estimated with a mathematical formula and worked through with a simulated models. For example, for Federer, go back through all his Grand Slam tournaments when he lost to Nadal or Djokovic and replace the opponent he played with a hypothetical player X who's chance of beating Federer was let's say the average of a top 10 player non-Nadal/Djokovic player. So if Federer's win percentage against non-Nadal/Djokovic top 10 players was 70%, you could run the model of the match outcome giving Federer a 70% chance of "winning" that match. If this occurred during a quarterfinal or semifinal and Federer "won," you would project out the subsequent matches using the same estimates. Another option would be instead of replacing Nadal/Djokovic with the average chance of a top 10 player beating Federer, you replace Nadal/Djokovic with the actual player that Nadal/Djokovic beat in the real tournament to get to the match-up with Federer (e.g. if Nadal beat Wawrinka to get to play Federer in the next round, replace Nadal with Wawrinka's percent chance of beating Federer). That adds a bit more complexity and work to the model, and I'm not sure if it's worth it.
Also, certainly players' chance of beating other top players changes over time and by court surface, and you could really get in-depth tweaking the model to adjust for that if you wanted. But for simplicity's sake, I prefer the first option of just replacing Nadal/Djokovic with a hypothetical player who is the average of other top 10 players, and see what the model says.
It would be interesting to see how this plays out for each of the big three. My guess is they would each end up with at least 25 major titles. While it is wonderful that tennis fans have gotten to see these three players play their careers at the same time as each other because their duels are so epic and entertaining, it also would have been cool to see what they might have accomplished if the others had not been there. This model might most benefit Federer as he has a losing record to Nadal and Djokovic in Grand Slams. Certainly, Federer could have won more French Opens and Nadal and Djokovic could have won more US and Aussie Opens, and especially more Wimbledons.
I'm too lazy to actually go back through the old draws and work through all of these scenarios myself, but if somebody is inclined to take it on or has an alternative approach for calculating this What-If, I'd be interested in hearing what the results are, and what could be gleaned from it in general.
If you are a college statistics student, this might make for an fun class project you could get credit for!
 
O

OhYes

Guest
Many things would make this scenario bad.
First, overall fatigue of winning Slams that happened to Djokovic, which could lead to injury.
Second, mental fatigue. Sampras thought 14 was enough.
Third, there is no era where only one ATG is allowed to collect Slams. One or two players would eventually come up high and become an obstacle, somekind at least.
Fourth, level of player A would downgrade if he didn't have good enough B or C to compete with. Which would further lead of lower percentage won.

In theory, Fed would have more than 30.
 

Sport

G.O.A.T.
There is no such thing as a mathematical model to calculate that. There is untestable speculation. You can't calculate with certainty how many Majors they would have won without each other, as surprising losses can appear from nowhere.

Mathematical models would have predicted Nadal to defeat Soderlin at RG 2009, yet Nadal lost.

Mathematical models would have predicted Federer to defeat Safin at the AO 2005, yet Federer lost.

Mathematical models would have predicted Djokovic to defeat Nishikori at the USO 2014, yet the Djokovic lost.
 

ledwix

Hall of Fame
It's not going to be a zero-sum game among them. There is something else psychological and motivational going on.

These players have brought out such competition in each other that nobody in their 20s right now has ever won a slam title.

Therefore, I state at this point that they all ended up winning MORE grand slam titles than if the others had never existed, especially Djokovic, who was and still is chasing two other guys.

17 slams would have seemed like an overwhelming record above Sampras when Federer/Nadal reached that amount. But because the others existed, it wasn't so insurmountable, and so they decided to keep going.
 

anarosevoli

Semi-Pro
It's not going to be a zero-sum game among them. There is something else psychological and motivational going on.

These players have brought out such competition in each other that nobody in their 20s right now has ever won a slam title.

Therefore, I state at this point that they all ended up winning MORE grand slam titles than if the others had never existed, especially Djokovic, who was and still is chasing two other guys.

17 slams would have seemed like an overwhelming record above Sampras when Federer/Nadal reached that amount. But because the others existed, it wasn't so insurmountable, and so they decided to keep going.

There are definitely more cannibalism than motivation effects. Who would have taken those 33 to 38 slams in discussion?
They would have had the 17 slams that you mention aready in their mid-twenties, very very unlikely that they would have retired only because they could have thought that they had beaten Sampras.
 

EdSWright

Professional
Many things would make this scenario bad.
First, overall fatigue of winning Slams that happened to Djokovic, which could lead to injury.
Second, mental fatigue. Sampras thought 14 was enough.
Third, there is no era where only one ATG is allowed to collect Slams. One or two players would eventually come up high and become an obstacle, somekind at least.
Fourth, level of player A would downgrade if he didn't have good enough B or C to compete with. Which would further lead of lower percentage won.

In theory, Fed would have more than 30.
Fatigue? That is so 1990s.
 

jonwbecker

New User
There is no such thing as a mathematical model to calculate that. There is untestable speculation. You can't calculate with certainty how many Majors they would have won without each other, as surprising losses can appear from nowhere.

Mathematical models would have predicted Nadal to defeat Soderlin at RG 2009, yet Nadal lost.

Mathematical models would have predicted Federer to defeat Safin at the AO 2005, yet Federer lost.

Mathematical models would have predicted Djokovic to defeat Nishikori at the USO 2014, yet the Djokovic lost.
Yes, surprising losses such as Soderling over Nadal would occur. That's why I said the model would give the Big 3 a certain percentage chance of winning those fictional matches, such as 70% or whatever their odds are of winning against non-Big 3 top players.

I think the Big 3 are highly self-motivated and would have remained focused and dominated even without the other 2 pushing them.

And yes, I understand they are still playing and winning Slams! Just having fun speculation on what their final major totals would be without the others. Right now all 3 seem to be on pace to finish around 20-21 (although I'm sure that comment could spark debate), whereas in a fictionalized world without the others each might have finished with at least 25 and perhaps more.
 
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