# It's NOT 0.000122%!!!!!!!!!!!!!!!!

##### Professional
OK this is from the draws against Djokovic thread, and data is taken from there too.

First off, I am not good at math or statistics, but even I cannot stand all the stupidity in that thread.

First off there are people that countered that it should be looked from other angle, which I am not sure I agree or not, but I will accept this:

"the rankings are circunstancial, what matters is the fact that in all the draws, Federer and Djokovic had pretty much the same probability of being on the same side of the draw, or being on different sides, yet, almost everytime, they are on the same half."

So, it's about what should have been 50/50 and some feel it is not.

So in that thread it says since august 2007, this, itself is a problem as it is picked after looking at data to try to show a more skewed result than it already is, else why don't you use the data since he is on tour and start to play in GS? which is 2005.

Second and a much bigger problem

there were 17 draws, out of the 17, 15 times Djokovic is on Federer's side.

What should be calculated is assuming 50/50 what's the probability of this happening 15 time or more out of 17 draws. I forgot the close form solution and used a numerical method and it a little above 1%, still low but that's not 0.000122%. And keep in mind this is still skews due to hand picked time period after looking at data.

Instead, everyone screams 0.5^13 for hard court and grass. But you cannot do that, if you look at data and take out the part that doesn't suit your conclusion, it will make your result extremely skewed and you can basically draw any conclusion from any data, despite the real data support you or not.

BTW there should be more complex method or take one more step to control for both exception happened on clay court, but simply take out data doesn't suit your conclusion making it entirely invalid.

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#### purge

##### Hall of Fame
you didnt read the first posts right i assume.

the OP in that thread has the opinion that the 2 times fed and djoko didnt meet were at the french where it would be a disadvantage to djokovic as well.
the point was to show how djokovic always got it worse, drawing nadal only on clay and always fed an HC and grass.
that was how the topic started.

im not saying i agree with that conclusion tho

and regarding a certain period of time is perfectly fine. after all you want to prove just how it is in a certain period of time. i dont see whats the problem with that

##### Professional
the OP in that thread has the opinion that the 2 times fed and djoko didnt meet were at the french where it would be a disadvantage to djokovic as well.
the point was to show how djokovic always got it worse, drawing nadal only on clay and always fed an HC and grass.
that was how the topic started.
By using 15/17, it already taken care of this, if you can count against Federer or Nadal as disadvantage on clay, it would be 15/17 either way.

BTW, if you want talk about disadvantage, it would render the entire argument pointless, as in 2011, it's anyone who goes up against Djokovic that has an disadvantage! So let's keep as Federer/Djok

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#### Fate Archer

##### Hall of Fame
Well, if the figure of 15 out of 17 times is correct, that can be solved by binomial distribution I think.

Assuming that there is a 50% probability (p = 0.5) of Federer and Novak being on the same halves of the draw, then that could be calculated by the following formula:

C(n,x) p^x q^n-x ==> C(17,15) * (0.5)^15 * (0.5)^2

I just put these numbers on excel to calculate and it gave me a 0,103759766% chance of said event happening. That ammounts to exactly 15 times out of 17.

If you want to include 16 and 17 by going with 15 times or more, you just have to calculate this same problem for 16 and 17 tries and then sum the resulting probabilities (for 15, 16 and 17), which gives a slightly better 0,117492676% chance of this event happening (at least 15 times out of 17).

It's not a little over 1% as you said, which would still look pretty low to anyone's taste.

Anyone with a better understanding of math or statistics is welcome to correct me if I'm not correctly using the BD to solve this problem or if the reasoning/calculation is incorrect.

#### Raz11

##### Professional
Yeah that's right I think. as other people have pointed out it is better to use the seeding instead to see if there is some form of rigging. If I remember correctly 7 of the last 16 slams has the 1st and 3rd seed meeting in the semi so its not that strange.

#### ledwix

##### Hall of Fame
Um no. The theoretical chance of the seedings being matched up that total number of times is pretty correspondent with the experimental total. HOWEVER, the order in which those seedings lies ALWAYS lies exactly in the path of how Djokovic and Federer change rankings with respect to the top 4. And so you still have to wonder, even if you viewed it purely through seedings and no names, why the sequence corresponded perfectly with the name changes. "Coincidence" is what you call it, but realistically, it's a highly suspicious sequence of events, though you couldn't absolutely prove a conspiracy.

##### Professional
Well, if the figure of 15 out of 17 times is correct, that can be solved by binomial distribution I think.

Assuming that there is a 50% probability (p = 0.5) of Federer and Novak being on the same halves of the draw, then that could be calculated by the following formula:

C(n,x) p^x q^n-x ==> C(17,15) * (0.5)^15 * (0.5)^2

I just put these numbers on excel to calculate and it gave me a 0,103759766% chance of said event happening. That ammounts to exactly 15 times out of 17.

If you want to include 16 and 17 by going with 15 times or more, you just have to calculate this same problem for 16 and 17 tries and then sum the resulting probabilities (for 15, 16 and 17), which gives a slightly better 0,117492676% chance of this event happening (at least 15 times out of 17).

It's not a little over 1% as you said, which would still look pretty low to anyone's taste.

Anyone with a better understanding of math or statistics is welcome to correct me if I'm not correctly using the BD to solve this problem or if the reasoning/calculation is incorrect.

Yes, it's a little over 0.1%, and binomial distribution is the correct way, now that I remember it. BTW I run it 100,000 times but somehow thought I only run it 10,000 times, hence the mistake on my part, LOL

##### Bionic Poster
So basically the draws are rigged yes?

#### Fate Archer

##### Hall of Fame
So basically the draws are rigged yes?
And the funny part is that, if I'm not mistaken, the only 2 times Federer and Novak didn't meet in the semis were at the French Open, where as we all know, Nadal is pretty much the favorite to win all the matches up to and including the final.

If the draws are rigged or not, at this point it's all a question of believing (or not). Just like UFO's, 9/11, moon landing hoaxes or what have you... no matter how much circumstantial evidence there is, believing is all that matters.

#### TopFH

##### Hall of Fame
And the funny part is that, if I'm not mistaken, the only 2 times Federer and Novak didn't meet in the semis were at the French Open, where as we all know, Nadal is pretty much the favorite to win all the matches up to and including the final.

If the draws are rigged or not, at this point it's all a question of believing (or not). Just like UFO's, 9/11, moon landing hoaxes or what have you... no matter how much circumstantial evidence there is, believing is all that matters.
Djokovic would be the favorite now IMO.

#### Achilles82

##### Professional
First off, I am not good at math or statistics, but even I cannot stand all the stupidity in that thread.
Ok, I am good.

So in that thread it says since august 2007, this, itself is a problem as it is picked after looking at data to try to show a more skewed result than it already is, else why don't you use the data since he is on tour and start to play in GS? which is 2005.
Because in august 2007, Novak played first time in grand slam as world no3. Before that he wasn't even considered a serious threat

Second and a much bigger problem

there were 17 draws, out of the 17, 15 times Djokovic is on Federer's side.
Theory is that Djokovic was fixed to be on Federer's side of draw, because it's considered that Djokovic has big chance to win against Nadal, and therefore you risk not to have Federer - Nadal final.

Now, do you think Djokovic is favorite against Nadal at French open?. The answer is NO!

Djokovic is not favorite against Nadal on clay, and therefore YOU DON'T HAVE TO FIX THAT TOURNAMENT!

Instead, everyone screams 0.5^13 for hard court and grass. But you cannot do that
Of course you can. You look at the tournaments who needed to be fixed. There is no reason or motive to fix Novak not to play Nadal in French Open, because Nadal is clear favorite.

But on every other grand slam, Djokovic is the favorite against Nadal, and EVERY TIME he was on Federer's side of the draw.

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##### Professional
Ok, I am good.
My ass, you clearly know even less than me, which would be close to zero.

##### Professional
Of course you can. You look at the tournaments who needed to be fixed. There is no reason or motive to fix Novak not to play Nadal in French Open, because Nadal is clear favorite.

But on every other grand slam, Djokovic is the favorite against Nadal, and EVERY TIME he was on Federer's side of the draw.

Of course you can. You look at the tournaments who needed to be fixed. There is no reason or motive to fix Novak not to play Nadal in French Open, because Nadal is clear favorite.

Here is what shows you know even less stats than me.

EVEN if I consider above to be TRUE.

It's still 15/17, because out of 4 FO, twice he was NOT on nadal's side.

So you still can't do 0.5^13.

See? Even if we use your assumption, you still get it wrong, so pathetic.

#### Achilles82

##### Professional
It's still 15/17, because out of 4 FO, twice he was NOT on nadal's side.

So you still can't do 0.5^13.

See?
No I don't.

None of 4 french opens are counted in those 13 tournaments. French Open is not the issue. French open is regular (as far as Djokovic is concerned). Because it would be pointless to fix it, get it?

13 grand slams that I'm counting are only hard court and grass court. It's 13 out of 13.

I mean seriously, you don't see anything suspicious here? You don't find it odd that Novak was on Nadal's side of a draw, ONLY at French Open? On every other grand slam, for more then 4 years, he was on Federer's side of a draw? You don't see anything weird about that?

##### Professional
No I don't.

None of 4 french opens are counted in those 13 tournaments. French Open is not the issue. French open is regular (as far as Djokovic is concerned). Because it would be pointless to fix it, get it?

13 grand slams that I'm counting are only hard court and grass court. It's 13 out of 13.

I mean seriously, you don't see anything suspicious here? You don't find it odd that Novak was on Nadal's side of a draw, ONLY at French Open? On every other grand slam, for more then 4 years, he was on Federer's side of a draw? You don't see anything weird about that?

... I am speechless.

If you took out the regular, of course the result is super skewed...

I am NOT saying the chance isn't low, but it's a little over 0.117492676%, thanks to Fate Archer who worked it out the right way. Unlikely yes, but it's not a crazy low number such as 0.5^13.

I am not saying it is or not some conspiracy, as the result could support both way, and everyone is entitled to believe what they believe. However, fact is fact, don't bind it to suite your goal please.

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