So I crunched the numebrs....and the slam draws look rigged

[Tony48]

I posted this over at MTF:

Fans have voiced complaints about how regularly Federer & Djokovic land on the same half, as well as how often Nadal and Murray land on the same half. And for good reason. I analyzed 3 other eras and not a single one displayed the glaring irregularities that we have come to expect in the Federer-Djokovic-Nadal-Murray era.

So did this happen in the past? I wanted to find out. My method was simple: try and find 3 other eras that were similar in nature to the current "Big 4" era. And those similarities included 1) an era with 4 CONSISTENT players, 2) they had to maintain that consistency simultaneously for at least a few years, and 3) they had to be seeded near the top of the rankings (No. 1 - 5, for example) more often than not.

It was a little difficult trying to pin down a group of 4 players that closely mirrored today's top guys but I found 3:

1. McEnroe-Lendl-Connors-Wilander ERA (1983-1985)
2. Endberg-Becker-Lendl-Agassi ERA (1988-1991)
3. Edberg-Courier-Becker-Sampras ERA (1991-1994)

....and they would be compared to:

4. Federer-Nadal-Djokovic-Murray ERA (2008-present)

Fortunately, there was a lot of behavior in these eras that had characteristics similar to that of today's era, such as top guys that seemed to ALWAYS be seeded 1st and 2nd (a la Federer and Nadal) and guys that came in and crashed the party (a la Djokovic), etc. So theoretically, the draw based on the seeding would behave similarly, right? Right?

Well, here are the stats for the first era:

KEY:
1) number of times it was possible to be paired on the same side of the draw (not being seeded 1st and 2nd, 3rd and 4th, etc.)
2) number of times they were actually paired

McEnroe-Lendl-Connors-Wilander ERA (1983-1985)

MCENROE-LENDL
1) 2 times
2) 1 time (50%)

MCENROE-CONNORS
1) 7 times
2) 4 times (57%), 2 consecutive times

MCENROE-WILANDER
1) 11 times
2) 7 times (63%), 3 consecutive times

LENDL-CONNORS
1) 9 times
2) 4 times (44%), 2 consecutive times

LENDL-WILANDER
1) 11 times
2) 5 times (45%), 3 consecutive times

CONNORS-WILANDER
1) 3 times
2) 0 times

Nothing jumps out. Seems that the 50/50 draw was in full effect here. And it's perfectly reasonable for Connors and Wilander to have not drawn each other out of a mere 3 times of potentially being paired.

Also, there are no ridiculously high numbers when it comes to consecutive times of being paired (we'll revisit this later, lol)

On to the next era:

Endberg-Becker-Lendl-Agassi ERA (1988-1991)

EDBERG-BECKER
1) 6 times
2) 3 times (50%), 0 consecutive times

EDBERG-LENDL
1) 10 times
2) 6 times (60%), 3 consecutive times

EDBERG-AGASSI
1) 7 times
2) 2 times (29%), 2 consecutive times

BECKER-LENDL
1) 6 times
2) 2 times (33%), 0 consecutive times

BECKER-AGASSI
1) 8 times
2) 4 times (50%), 4 consecutive times

LENDL-AGASSI
1) 5 times
2) 4 times (80%), 3 consecutive times

At first glance, because of the high standard set by the first era, the Lendl-Agassi pairing looks suspicious. Their number of potential pairings is relatively low at 5 because Agassi didn't play the Australian Open and Wimbledon at times, as well as Lendl missing some. 4 out of 5 times COULD be seen as high but honestly, a pool of 5 isn't that big.

Next:

Edberg-Courier-Becker-Sampras ERA

EDBERG-COURIER
1) 6 times
2) 3 times (50%), 2 consecutive times

EDBERG-BECKER
1) 5 times
2) 2 times (40%), 0 consecutive times

EDBERG-SAMPRAS
1) 10 times
2) 6 times (60%), 2 consecutive times

COURIER-BECKER
1) 9 times
2) 5 times (56%), 2 consecutive times

COURLER-SAMPRAS
1) 9 times
2) 6 times (67%), 4 consecutive times

BECKER-SAMPRAS
1) 8 times
2) 2 times (25%), 0 consecutive times

Not much to see here. The Becker-Sampras pairing might be a little low given its potential pairing of 8, but since the OTHER pairings are pretty equal, it's probably safe to assume that this is just one of those statistical anomalies (assuming you think 25% even merits attention at all).

Now here's where the fun begins:

Federer-Nadal-Djokovic-Murray ERA (2008-present)

FEDERER-NADAL
1) 3 times
2) 0 times

FEDERER-DJOKOVIC
1) 15 times
2) 13 times (87%), 7 consecutive times

FEDERER-MURRAY
1) 12 times
2) 1 time (8%)

NADAL DJOKOVIC
1) 11 times
2) 2 times (18%), 0 consecutive times

NADAL-MURRAY
1) 14 times
2) 13 times (93%), 8 consecutive times *PRESENT STREAK*

DJOKOVIC-MURRAY
1) 9 times
2) 1 time (11%)

Where do you even begin with something so ridiculous and unprecedented? Either the percentage is under 20% or over 85%...in every single pairing! (if you exclude Federer-Nadal).

And 8 consecutive, on-going pairings between Nadal and Murray? The highest in the other era was 4 and Nadal-Murray has doubled that and likely to continue.*** And if it weren't for the 2010 French Open, Djokovic and Federer would be on a current streak of 12!

And if these numbers are any indication, expect to NEVER see a Federer-Nadal semi-final in a slam (as long as they stay relevant).

Given all this data and how they bare NO resemblance to past draws, I think it's fair to suggest that the slam draws these days are rigged.

Also, if anyone wants to see all of the seeding data (or just look at it to make any corrections), you can download it here: http://www.mediafire.com/?x1j2ngft97j3l4c

EDIT:

***that portion contains an error. I'll fix it later today....getting ready for work

[Kaz00]

Mmmhmm interesting!!

[r2473]

I was at a roulette table one time and black had come up 8 times in a row. Some fool next to me put $300 on red. Guess what, black came up again.

[DjokovicForTheWin]

HHHHHHHHTTTTTTTT

HTHTHTHTHTHTHTHT

Both are equally likely tardsssssssssssssssss.

[tacou]

mildly interesting...i think it is more relevant how many times 1 played 3 vs 1 played 4

[LuckyR]

The dice have no memory. Take a statistics class...

[Tony48]

Originally Posted by LuckyR

The dice have no memory. Take a statistics class...

That's really cheap, IMO.

No offense but how irregular does a draw have to be before common sense kicks in? Blaming obscenely irregular occurrences on "low probability" is a free pass for someone to cheat.

It's statistically probable for someone to win the lottery 100 times in a row. If that happened, would you honestly say that it happened with no interference?

My main point is that PAST draws are about as even can be. Then comes along the incentive of having Nadal and Federer (the most popular tennis players in history) play constant finals and you have irregularities in the draw. Sometimes I think statistics need to take a backseat to instinct.

[veroniquem]

I totally agree, the numbers look ridiculous. Fed-Murray: 1 out of 12? And Nadal-Murray: 13 out of 14? How people can think this is just a matter of chance is beyond me.
If draws were riggged in soccer (and they were), I can't see why not in tennis.

[Baxter]

I always knew this, I just never knew they pretending it was random.

[Tony48]

And it's not even about the Nadal-Murray thing. It's more about how ever single match-up in the previous eras had incredibly balanced pairings when compared to today's era. Those eras reflect the 50/50 nature of a random draw and yet today's era couldn't be further from it (even with a larger sample size).

[ViscaB]

Again the sample is too small to draw any conclusions...

[Tony48]

Originally Posted by ViscaB

Again the sample is too small to draw any conclusions...

Well a proper sample size (such as 50) isn't going to happen because Federer isn't going to be playing nine years from now. That's why I used data from the past, which would give SOME indication as to how draws typically behave. And now, that it's a proven fact that Nadal-Federer finals get higher ratings than any other tennis match, the draws behave abnormally.

I'm going to make another hypothesis. Before Djokovic became relevant, I bet that the chance of him being on the same side as Nadal or Federer was a lot more balanced.

[DarthFed]

Lol people really don't find anything suspicious about this? Interesting read OP.

[Tony48]

This is BEFORE Djokovic became relevant (and before the present Federer-Nadal rivalry:

Federer-Nadal-Djokovic-Murray pre-ERA (2005-2007)

FEDERER-NADAL
1) 3 times
2) 1 time (33%)

FEDERER-DJOKOVIC
1) 12 times
2) 5 times (42%), 2 consecutive times

FEDERER-MURRAY
1) 8 times
2) 5 time (63%), 2 consecutive times

NADAL DJOKOVIC
1) 11 times
2) 6 times (55%), 3 consecutive times

NADAL-MURRAY
1) 7 times
2) 3 times (43%), 0 consecutive times

DJOKOVIC-MURRAY
1) 8 times
2) 3 time (38%), 3 consecutive times

Just like I hypothesized, the pairing data was a LOT more balanced back when Djokovic and Murray were nobodies.

[Bud]

Originally Posted by veroniquem

I totally agree, the numbers look ridiculous. Fed-Murray: 1 out of 12? And Nadal-Murray: 13 out of 14? How people can think this is just a matter of chance is beyond me.
If draws were riggged in soccer (and they were), I can't see why not in tennis.

No way these pairings are random, IMO.

[Bud]

Originally Posted by Tony48

This is BEFORE Djokovic became relevant (and before the present Federer-Nadal rivalry:

Federer-Nadal-Djokovic-Murray pre-ERA (2005-2007)

FEDERER-NADAL
1) 3 times
2) 1 time (33%)

FEDERER-DJOKOVIC
1) 12 times
2) 5 times (42%), 2 consecutive times

FEDERER-MURRAY
1) 8 times
2) 5 time (63%), 2 consecutive times

NADAL DJOKOVIC
1) 11 times
2) 6 times (55%), 3 consecutive times

NADAL-MURRAY
1) 7 times
2) 3 times (43%), 0 consecutive times

DJOKOVIC-MURRAY
1) 8 times
2) 3 time (38%), 3 consecutive times

Just like I hypothesized, the pairing data was a LOT more balanced back when Djokovic and Murray were nobodies.

Yep, these are numbers that look more probable

It doesn't take a brain surgeon to see that the numbers presented in your OP are dramatically skewed

[Bud]

Originally Posted by hunter121

The dice have no memory.

Flip a coin 14 times. When you get heads or tails 13 times then come back and post.

[DjokovicForTheWin]

Wow, how can people still be arguing about this? The rankings, i.e. the player name attached to a particular seed # is independent of the draw selections.

Consider hypothetical 4 events:
1) 1/4, 2/3
2) 1/3, 2,4
3) 1/3, 2/4
4) 1/4, 2,3

Notice the 50% distribution above of the seedings. The draw is done with the seed #'s, not the names. The names attached are whatever they may be depending on the current rankings.

Now consider the rankings in those 4 events:
Tourney 1, Nadal is #1, Fed #2, Djoker #3, potential Fedal
Tourney 2, Djoker take over #1, Nadal #2, Fed #3, potential Fedal
Tourney 3, Djoker still #1, Nadal #2, Fed #3, potential Fedal
Tourney 4, Let's say Fed falls to #4 now, Djoker #1, Nadal #2, potential Fedal

In all cases you get a potential Fedal final. 4 times in a ROW (seems impossible right??)!! But the draw was still random with ~50% probability (2 and 2) law being obeyed (in real life it was 8 and 6 as shown in previous posts). The draw knows nothing of how the rankings will change due to players getting better and worse. They are independent.

If the rankings did not change at all, with Nadal #1 and Fed #3, and you had 8 consecutive Fedal, then there'd be something to talk about.

[LanceStern]

Do the number crunching with #1 vs #3 and #1 vs #4. And #2 vs #3 and #2 vs #4

Then come back. It's as fair as it should be

EDIT: Already been done:

Originally Posted by colonelforbin

Here's another way to look at it, based on seeding. When they make the draw they are basically pulling seed numbers out of a hat, whoever's name is attached to that seed is irrelevant. This means the situation should be assessed by which seeds drew one another in the last 14 slams.

2011
USO: #1/#3 - #2/#4
WB: #1/#4 - #2/#3
RG: #1/#4 - #2/#3
AO: #1/#4 - #2/#3
2010:
US: #1/#4 - #2/#3
WB: #1/#3 - #2/#4
RG: #1/#4 - #2/#3
AO: #1/#3 - #2/#4
2009:
US: #1/#4 - #2/#3
WB: #1/#3 - #2/#4
RG: #1/#3 - #2/#4
AO: #1/#4 - #2/#3
2008:
US: #1/#4 - #2/#3
WB: #1/#3 - #2/#4

Instances of #1/#4 - #2/#3: 8
Instances of #1/#3 - #2/#4: 6

The proper way yo approach the situation is that there is a 50% chance that the #1 seed will draw the #4 seed and the #2 seed will draw the #3 seed, and vice versa. And from this perspective the outcome is not that far off at all.

Originally Posted by winstonplum

This is the third draw in a row where Nadal and Novak were on opposite sides of the draw and got Murray and Fed on their respective sides of the draw. The odds of this happening were 12.5%. Low but not crazy. Starting with the '11 AO, Nadal and Fed were 1 and 2, so this completely changes the variables and thus the probability. Going backwards, this one and two set also had three consectutive slams with Nadal getting Murray and Fed getting Novak. But at the '10 FO, Nadal would have gotten Novak, but Novak lost to Melzner in the quarters. At the '10 AO, Fed was one and Nadal was two, but Murray was five, again totally changing the variables and thus the probability. Remember Delpo was four there. At the '09 USO, Fed was one, but Murray was two. All of the variables keep changing, so it's completely inaccurate to say that the ITF keeps flipping a coin and Fed keep going to Novak and Murray keeps going to Rafa. Now if the current 1 through 4 seeds hold until Melbourne next January the chance and Fed going to Novak again are 6.125%; again very low, but not totally hook, line and sinker conspiracy time.

[Tony48]

When they make the draw they are basically pulling seed numbers out of a hat, whoever's name is attached to that seed is irrelevant.

Well that's the basis of my theory....the name is IS relevant when it comes to this era. Of course it's going to be balanced when you only take the seed number into account....because the names are constantly changing and being attached to different seed numbers

Hypothetical:

1 Federer 3 Djokovic
2 Federer 3 Djokovic
1 Federer 4 Djokovic
1 Federer 3 Djokovic
1 Djokovic 4 Federer
1 Djokovic 3 Federer
3 Federer 2 Djokovic
2 Federer 4 Djokovic
1 Djokovic 4 Djokovic
3 Federer 1 Djokovic
1 Federer 3 Djokovic
1 Federer 4 Djokovic
2 Djokovic 4 Djokovic
2 Federer 3 Djokovic
2 Federer 4 Djokovic
2 Federer 4 Djokovic
1 Djokovic 3 Federer
2 Djokovic 3 Federer
1 Federer 3 Djokovic
1 Federer 4 Djokovic
2 Djokovic 3 Federer


In this scenario, Federer and Djokovic have met (or on the same side of the draw) 21 straight times, 100% of the time.

But if you only look at the seeds:

1 can meet 3 or 4
-meeting 3: 7 times (58%)
-meeting 4: 5 times (42%)

2 can meet 3 or 4
-meeting 3: 5 times (55%)
-meeting 4: 4 times (445)

and so forth.

Only looking at the numbers is naive and short-sighted.