Draw fixing (hypothesis) at grand slams (2008-2012)

by Chydremion Wed 20 Jun 2012, 7:53 pm

First topic message reminder :

Recently a lot of talk has been done about the possibility of draw fixing at the slams in tennis. It was not only the subject of debate on this site, but also others. The thoughts of the so-called 'conspiracy theorists' were reflected in an interesting study by the Estonian researcher Katarina Pijetlovic in october 2011. Here's the link for who hasn't seen it yet.

http://www.livestream.com/playthegame_dshs/video?clipId=pla_44809e94-aa04-46c7-9f1e-35b212ba9d46

She noticed a strange pattern of Djokovic always landing in Federer's half of the draw at the slams during 2008-2011, with the exception of the French Open (something many posters on this forum had already noticed). Because the French Open showed a healthy pattern she decided to not include it in her study. Her opinion is that the ITF (stimulated by Nike) might fix the draw to increase the chances of getting a Federer-Nadal final. After all those are by far the most popular tennis players in the world. Both sponsored by Nike, who would like a final between the two, as this would mean a lot of advertising.

The omission of the French Open was the main bullet for the opponents of the study to shoot it down and classify it as unstatistical, meaningless, prejudiced. In this article I will try to demonstrate that there was actually no reason to omit the French Open. In my research all slams will be included. Instead of purily looking from a statistical perspective like Katarina Pijetlovic, insight in the dynamics of the recent tennis world will be applied. Our basis assumption is that the ITF and Nike wanted Federer-Nadal finals at the slams. It are the slams that attracts the wider audience. Tennis hadn't always had a wide audience. Many will remember the dark years of the early 2000's, even till 2004, with lot of empty seats at the slams, even in big matches. Tennis wasn't very popular. It was the Federer-Nadal rivalry, hyped into heaven, that really started to attract lots of people. A rivalry that really bursted out in 2006/2007 with consecutive finals the French Open and Wimbledon. There wasn't really much of a problem to get a final back then, with Federer and Nadal at number one and two respectively, so automitically in opposite sides of the draw. There wasn't a single player who could really rival the two. Only at hardcourt slams there was the problem of Nadal not getting to the final, losing to lower players, but this couldn't be helped.

2007 "unfortunately" saw the rise of Novak Djokovic. During the year he got a few wins over Federer and Nadal (all on hardcourts). On clay and at the slams, they still had him very much under control. But he had proven to be the biggest threat so far to their duopoly. The last thing the ITF and Nike wanted, after putting so much effort in promoting Federer and Nadal, was this guy to spoil the party. After all he came from a country that most of the rest of the world looked negatively upon because of what happened there in the 90's, he had a bad haircut, and wore even worse Addidas clothes. They didn't want this guy in the finals instead of the more glamourous looking Federer and Nadal, with the great Nike clothes. What would the fate of tennis be if this guy ever became the top dog.

Djokovic had already made the 2007 US Open final and something had to be done. So from 2008 onwards they started to fix the draw to increase the possibility of a Federer-Nadal final. In the tabel below the slams at which the favourable draw was achieved are marked with a +, when the less favourable draw was achieved there stands a - .

****AO RG W USO

2008 + + + +

2009 + - / +

2010 + + + +

2011 + + + +

2012 - + + ?

This of course needs some explanation. I'll discuss the slams in chronological order.

Period 1: AO08-W09: Djokovic at number three, put in either Federer's or Nadal's half. Federer and Nadal taking number one and two position (not necessarily in this order), automatically in opposite sides of the draw.

AO08: It had been three years ago since Federer last failed to make the final of a hardcourt slams. Nadal still hadn't gone beyond the quarters. It was better to not make life even more difficult for Nadal and to put Djokovic in the opposite (Federer's) half. This was successfully done.
RG08: Nadal was practically unbeatable on clay, so better to put Djokovic in his half, as the Serb would certainly get beaten. Again successful.
W08: At this time Federer was still the king of grass and five time defending champion, while Nadal hadn't won a Wimbledon titel yet. Djokovic in Federer's draw. Successful draw.
USO08: Again Djokovic had to be put in Federer's half, as Nadal still hadn't reached a HC slam final yet, and was beaten twice by Djokovic on HC during 2008. Successful.
AO09: Same stuff as in previous hardcourt slams. Successful draw.
RG09: Best would have been Djokovic in Nadal's half like the year before. This time though the opposite happened, first unsuccessful draw.
W09: Makes no part of the study as Nadal didn't play.

Period 2: USO09: Federer number one, Murray number two. Nadal three, Djokovic four.

US09: The only way to get a Federer-Nadal final was to put Nadal in Murray's half, and Djokovic' in Federer's as a consequence of that. Again the draw was successful.

Period 3: AO10-AO11: Djokovic at number three, put in either Federer's or Nadal's half. Federer and Nadal taking number one and two position (not necessarily in this order), automatically in opposite sides of the draw.

AO10: Nadal had been in very bad form for the last six months, losing to most top ten players he faced in that period. Better to make his work a bit easier and put Djokovic in Federer's half. Djokovic had spanked Nadal recently three times in a row and was too dangerous for the Spaniard. Again success.
RG10: Better to put Djokovic in the draw of the unbeatable (on clay) King of Clay Nadal. Success.
W10: Now this was a hard one. Federer hadn't been playing well since the AO that year, while Nadal had cleaned up the clay season. In which half to put Djokovic? Nadal though for the last year hadn't enjoyed success outside of the clay, and had a very poor showing at Queens in 2010. The Bookies made Federer slight favourite for the title, so Djokovic should be in his half. The draw was succesful.
USO10: Federer had showed great form during the US HC summer, in strong contrast with Nadal, and was the big favourite for the title. Djokovic in Federer's half? Yup, achieved.
AO11: While Nadal had been the strongman of 2010, unfortunately just before AO11 he became ill and got bagled by Lacko and spanked by Davydenko in Doha. So Djokovic had to be in Federer's half. Successfully.

Period 4: RG11-RG12: Federer at number three, put in either Djokovic's or Nadal's half. Djokovic and Nadal taking number one and two position (not necessarily in this order), automatically in opposite sides of the draw.

RG11: The only way to get a Federer-Nadal final was to put Federer in Djokovic' half. Success.
W11: Same story.
USO11: Same story.
AO12: The only way to get a Federer-Nadal final was to put Federer in Djokovic' half. This is the second time though the draw was unsuccesful, as Federer was put in Nadal's half.
RG12: The only way to get a Federer-Nadal final was to put Federer in Djokovic' half. Success.

Conclusion:

In 17 slams 15 times the favourable draw was achieved. Only twice the unfavourable. Each time the statistical chance to get a certain draw was 50% each for the favourable and the unfavourable. So you would expect a more even division between favourable and unfavourable draws, something like 8/9 or 7/10 or even 6/11. 2/15 looks very suspect. Probably the ITF decided to do twice the unfavourable draw. 17 times the favourable ones would even make the die-hard naysayers grow suspicious. Maybe not accidently the unfavourable AO12 draw was only a few months after Katarina Pijetlovic had proposed her study, when suspicion grew.

Now remains the question of how did they actually fix the draw? It's impossible to find hard proof for this. The number three and four seeds are picked by hand by the defending champion. No video material of this can be found on the internet, which is not the case for lots of other occasions involving tennis. I remember though seeing video material of the draw picking during the news report on TV. I remember for this year's AO seeing Djokovic pick one piece of paper out of (wherever they put it in) to decide which player goes in a certain half of the draw. Now is the question, do they really pick a second time? There are only two players, number 3 and 4 to be handpicked. As soon if one is picked, they know in which half the other has to be. There is no need to pick the second player, and my guess is they don't do it. This though gives the chance to put twice the same number (3 or 4) on the two pieces of paper, without anyone noticing. This way they can choose which player to put in which half of the draw. This corruption can happen without the necessity of the defending champion being part of the fraud.

by Jeremy_Kyle Fri 22 Jun 2012, 12:15 am

Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Also , we already debated the issue in depht, and we found out that Fed and Djoko met on the same side for 6 times in a row, implying a very slim probability of 1.5% of this fact to happen.

Please help yourself......

https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

by **laverfan** Fri 22 Jun 2012, 1:52 am

Jeremy_Kyle wrote:
Adam D wrote:I would like to remind everyone that draw fixing has never been proved and until it is, all accusations of it are pure speculation.

As a founder of this site, I have a care of duty to remind you not to post libelous statements that could result in legal action against the site.

So to clarify, you may offer up potential reasoning as to why you may suspect draw rigging has taken place but any comments delivered as fact, will be removed.

The only fact is that it has never been proven in a court of law.

Therefore, please respect the hard work that the founders. admin and moderators have put in to this site by not posting statements that could get the site shut down.

You all have a care of duty in this matter - if you suspect a post of being libelous, please report it.

Funny how you guys think you are so important ....bring me a case of a forum that was brought to justice for a thing like that and I'll say you are right....also you seem not to worry at all you stole a logo from the beebs and a good deal of its users which looks even more worrisome to me

Laws of different countries may be different, but here are two that are worth reading.

http://abcnews.go.com/Business/jury-awards-13-million-texas-defamation-suit-anonymous/story?id=16194071#.T-O8mCtYuE4

http://online.wsj.com/article/SB124287328648142113.html

http://techcrunch.com/2011/05/20/twitter-sued-for-breaking-uk-super-injunction-oh-yes/

Do a google search if you are so inclined to read further.

by **laverfan** Fri 22 Jun 2012, 2:12 am

Jeremy_Kyle wrote:
https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

From the same article that is referenced...

socal1976 wrote:Wrong, julius, the draw isn't random and evidence has been provided to show that, frankly very overwhelming evidence. If the draw is manufactured for the first 2 rounds what evidence do we have that they don't tamper with semi draws to suit their purposes. Evidence has already shown they mess with the first two rounds, do they all of a sudden find religion when it comes to the semi draws?

Extrapolation of the ESPN study to a different public event, televised and seen by millions. chin

Why are the draws between each slam considered related events, just because the same Top 4 appear in it consistently, perhaps? Wink

I have provided several example of long-running Tennis rivalries who have seen similar draws (albeit not identical).

Let me extrapolate - Was 9/11 a conspiracy because US was involved in the Iran-Contra affair (Olly North, remember him - http://en.wikipedia.org/wiki/Iran%E2%80%93Contra_affair )? Run

by Guest Fri 22 Jun 2012, 2:19 am

There are lies, damn lies, and warm balls ...

by Tom_____ Fri 22 Jun 2012, 2:20 am

Jeremy_Kyle wrote:
Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Also , we already debated the issue in depht, and we found out that Fed and Djoko met on the same side for 6 times in a row, implying a very slim probability of 1.5% of this fact to happen.

Please help yourself......

https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

Oh dear me. By replying in that manner you have just shown how little you understand statistics. The calcs show we can be 95% confident that the streak of draws we have experienced still fit into a fair 50/50 distribution. You can quote singular probabilities for individual events, however my calc is all encompassing I'm afraid. It indicates such a run is possible and could even be expected in a fair system.

by **laverfan** Fri 22 Jun 2012, 2:31 am

Jeremy_Kyle wrote:Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Can I suggest that you can do a similar calculation regarding distributions, and show where "Tom___" is incorrect?

From a US 12th grade Standard Deviation page...

Specifically, if a set of data is normally (randomly, for our purposes) distributed about its mean, then about 2/3 of the data values will lie within 1 standard deviation of the mean value, and about 95/100 of the data values will lie within 2 standard deviations of the mean value.

http://www.batesville.k12.in.us/physics/apphynet/Measurement/standard_deviation.htm

by **laverfan** Fri 22 Jun 2012, 2:34 am

Nore Staat wrote:There are lies, damn lies, and warm balls ...

by Chydremion Fri 22 Jun 2012, 9:51 am

Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

1) Getting Federer-Djokovic was not always the favourable draw. Often it was, but not always. The point of the draw fixing is not getting Federer-Djokovic, but getting the most favourable draw. Your analysis means nothing. Read my article again.

2) With your statistics you went back to 2005, which is totally irrelevant to this debate, as Djokovic was not a factor then. I'm sure your (statistically still acceptable) result of 66,7% would be far higher (and far less statistically acceptable) if you kept to the period of this debate, 2008-2012.

by User 774433 Fri 22 Jun 2012, 10:15 am

Oh dear.
Fed and djoko in same side of draw in Wimby.

Run

by **JuliusHMarx** Fri 22 Jun 2012, 10:17 am

Chydremion wrote:1) Getting Federer-Djokovic was not always the favourable draw. Often it was, but not always. The point of the draw fixing is not getting Federer-Djokovic, but getting the most favourable draw. Your analysis means nothing. Read my article again.

2) With your statistics you went back to 2005, which is totally irrelevant to this debate, as Djokovic was not a factor then. I'm sure your (statistically still acceptable) result of 66,7% would be far higher (and far less statistically acceptable) if you kept to the period of this debate, 2008-2012.

1. The favourable draw is highly subjective. For eaxmple, in the AO2009, Djoko got the favourable draw against Fed, who had had beaten in the previous AO, rather than Nadal who had recently beaten Djoko at the Olympics.

2. Cherry-picking the draws that suit the theory and ignoring the rest. Is that sound statistical procedure?

by Chydremion Fri 22 Jun 2012, 10:20 am

JuliusHMarx wrote:
Chydremion wrote:1) Getting Federer-Djokovic was not always the favourable draw. Often it was, but not always. The point of the draw fixing is not getting Federer-Djokovic, but getting the most favourable draw. Your analysis means nothing. Read my article again.

2) With your statistics you went back to 2005, which is totally irrelevant to this debate, as Djokovic was not a factor then. I'm sure your (statistically still acceptable) result of 66,7% would be far higher (and far less statistically acceptable) if you kept to the period of this debate, 2008-2012.

1. The favourable draw is highly subjective. For eaxmple, in the AO2009, Djoko got the favourable draw against Fed, who had had beaten in the previous AO, rather than Nadal who had recently beaten Djoko at the Olympics.

2. Cherry-picking the draws that suit the theory and ignoring the rest. Is that sound statistical procedure?

1. Federer had got Djokovic back twice by then, beaten him pretty comfortably. By the way few people seemed to accept Djokovic victory at AO 08 as 'real', remember the mono (excuse?) Fed had? When the real Fed turned up he was beating Djokovic so far.

2. I'm not cherry-picking. I just chose the period in which the draw-fixing would have been necessary. It really wasn't in 2006-2007. If I was cherry-picking I wouldn't have included 2012, because the AO didn't support my hypothesis (well partly but..).

by Jeremy_Kyle Fri 22 Jun 2012, 10:32 am

Tom_____ wrote:
Jeremy_Kyle wrote:
Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Also , we already debated the issue in depht, and we found out that Fed and Djoko met on the same side for 6 times in a row, implying a very slim probability of 1.5% of this fact to happen.

Please help yourself......

https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

Oh dear me. By replying in that manner you have just shown how little you understand statistics. The calcs show we can be 95% confident that the streak of draws we have experienced still fit into a fair 50/50 distribution. You can quote singular probabilities for individual events, however my calc is all encompassing I'm afraid. It indicates such a run is possible and could even be expected in a fair system.

What's the point of discussing this, if you clearly don't know what are you talking about.

You say that your calculation is based on considering all the population, adding that the results are right because there is a 95% confidence level (??). Now, the confidence level is referring to the probabability that the results shown in a sample reflect the reality of the population. Which I'm sure you'll agree with me is utter nonsense as you are considering the population and not a sample.

You also pointed out that a STDDEV of 2.74 is a "natural variance": I personally never heard before of such a thing as natural variances in statistics.

The only useful information I can gather from your data is that there is less than 5% probability of the above occurrence to happen, which is not great.

by Chydremion Fri 22 Jun 2012, 10:36 am

It Must Be Love wrote:Oh dear.
Fed and djoko in same side of draw in Wimby.

Time to update my table! Makes it 2/16 (unfavourable/favourable). 50% chance lol!

by **JuliusHMarx** Fri 22 Jun 2012, 10:41 am

Unfavourable to get Fed, with his 2 recent 1/4 finals at Wimby, rather than Murray with his 2 recent semi-finals?
If the last 2 years are anything to go by, Djoko will get the guy who beats Fed - very favourable for Djoko.

by Chydremion Fri 22 Jun 2012, 10:45 am

JuliusHMarx wrote:Unfavourable to get Fed, with his 2 recent 1/4 finals at Wimby, rather than Murray with his 2 recent semi-finals?
If the last 2 years are anything to go by, Djoko will get the guy who beats Fed - very favourable for Djoko.

I was referring to my article, about the favourable draw to get a Federer-Nadal final. I don't mean the draw is favourable for Djokovic.
But I guess you knew that, but are just acting difficultly.

by CaledonianCraig Fri 22 Jun 2012, 10:51 am

JuliusHMarx wrote:Unfavourable to get Fed, with his 2 recent 1/4 finals at Wimby, rather than Murray with his 2 recent semi-finals?
If the last 2 years are anything to go by, Djoko will get the guy who beats Fed - very favourable for Djoko.

I would agree with that. And I sneekily feel Djokovic is content enough with the draw so what is the problem? Fed has not won a slam for two years whilst Nadal is still in slam-winning mode.

by **JuliusHMarx** Fri 22 Jun 2012, 10:52 am

Chydremion wrote:
JuliusHMarx wrote:Unfavourable to get Fed, with his 2 recent 1/4 finals at Wimby, rather than Murray with his 2 recent semi-finals?
If the last 2 years are anything to go by, Djoko will get the guy who beats Fed - very favourable for Djoko.

I was referring to my article, about the favourable draw to get a Federer-Nadal final. I don't mean the draw is favourable for Djokovic.
But I guess you knew that, but are just acting difficultly.

Actually, no I didn't - I guess I thought it was the same as socal's idea that it was allegedly rigged against Djoko, rather than allegedly rigged for a Fedal final. Fed has made 1 slam final in the last 2 years - I don't think anyone really expects a Fedal final regardless of the draw.

by lydian Fri 22 Jun 2012, 11:21 am

Exactly JHM...Nadal would probably prefer to get Federer than Murray these days at slams....infact when I say "these days" you could take that back to 2008 given Federer hasnt beaten Nadal in a slam since 2007. The premise for this rigging stuff is pure rubbish and has been debunked on a number of levels in terms of opponent difficulty, slam revenues and seed placement.

by sirfredperry Fri 22 Jun 2012, 11:39 am

Conspiracy or not, it does seem REMARKABLE that Fed constantly gets Djoko and Murray has to contend with getting past Nadal. But will Fed and Djoko actually meet? Don't think they've ever played each other on grass. Is that right?

by lydian Fri 22 Jun 2012, 11:55 am

Thats right SFP, they havent played on grass.
If this draw rigging was true then the slams would have some nerve to continue the run dont you think...
Yes its an anomaly but getting Federer in the draw isnt the big deal it once was. Its more how you see it from Fed's point of view...would he prefer to face Djokovic or Nadal? Answer...neither!
Given Fed hasnt got past QF since 2009 its pure conjecture anyway.

by **JuliusHMarx** Fri 22 Jun 2012, 12:05 pm

Yeah, the idea that keeping Fed and Nadal apart could give a Fedal final would be extremely hopeful.
If anyone was rigging it, they would put them in the same half, with a much greater chance of a Fedal semi-final, followed by a Rafa/Djoko final. Surely that would be the best way to maximise viewers (unless people think a Rafa/Djoko final is not a big draw?)
It would also keep Murray, the home favourite, away from Nadal, who he has lost to in the last 2 semis.

by Guest Fri 22 Jun 2012, 12:07 pm

I heard that Wimbledon were experimenting with the new cold balls technology this year.

by Tom_____ Fri 22 Jun 2012, 12:26 pm

Jeremy_Kyle wrote:
Tom_____ wrote:
Jeremy_Kyle wrote:
Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Also , we already debated the issue in depht, and we found out that Fed and Djoko met on the same side for 6 times in a row, implying a very slim probability of 1.5% of this fact to happen.

Please help yourself......

https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

Oh dear me. By replying in that manner you have just shown how little you understand statistics. The calcs show we can be 95% confident that the streak of draws we have experienced still fit into a fair 50/50 distribution. You can quote singular probabilities for individual events, however my calc is all encompassing I'm afraid. It indicates such a run is possible and could even be expected in a fair system.

What's the point of discussing this, if you clearly don't know what are you talking about.

You say that your calculation is based on considering all the population, adding that the results are right because there is a 95% confidence level (??). Now, the confidence level is referring to the probabability that the results shown in a sample reflect the reality of the population. Which I'm sure you'll agree with me is utter nonsense as you are considering the population and not a sample.

You also pointed out that a STDDEV of 2.74 is a "natural variance": I personally never heard before of such a thing as natural variances in statistics.

The only useful information I can gather from your data is that there is less than 5% probability of the above occurrence to happen, which is not great.

I really think you are embarrassing yourself here. Firstly i never mentioned natural variance. Its a calculated expected variance of at set of events with a 50/50 probability. the STDDEV of 2.74 is the average deviation you could expect from the mean of 15 times Djoko would be played Fed in a draw form a set of 30 events. This means if you did the 30 draws over and over again, you would find that on average you would see 15 +/-2.74 (i.e 12.26-17.74) Fed-djoko draws. Obviously whilst sometimes you will get exactly 15 Fed-Djoko draws, other times you will get a results outside 12.26-17.74. Like only 5 Fed-Djoko draws (10 away form the mean), or even 0 Fed-Djoko draws (15 from the mean). In these cases if you only have 1 set of 30 draws to analyse you can use the normal probability distribution to work out the probability that the strange looking results still falls in a normal distribution expected with a 50/50 probability. In our observed case we have 20 Fed-Djoko draws (5 away from the mean, which is 1.8 standard deviations). This is fine as only if were were over 2 standard deviations (5% test) of the mean would you start to think that the assumed theoretical probability of 50/50 might be incorrect. As it is, statistically we can say that it is most probable that the draws are not bias and the 50/50 chance is a correct assumption. However even if we were outside 2 standard deviations of the mean, then there is a strong argument we should be analysing to 3 standard deviations (1% test) given that the probability tested is very middle ground at 50/50. I.e i'm being kind by only doing a 5% test. - hence my earlier comments that we would need 100s if not 1000s of draws to be conducted to be able to talk seriously about bias, rather than just a streak witnessed within a fair system.

by **JuliusHMarx** Fri 22 Jun 2012, 12:34 pm

Ah yes, I remember now - 2nd and 3rd standard deviation tests. We had to learn stats in order to evaluate the results of our psychology experiments during my degree course. So long ago!
Anyway, even if something fell outside the 2nd standard deviation I think we used to have to conclude something along the lines of 'it warrants further study to try and replicate' or 'it strongly suggests' rather than 'it proves something'.
Does that sound about right Tom?

by Tom_____ Fri 22 Jun 2012, 12:36 pm

Chydremion wrote:
Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

1) Getting Federer-Djokovic was not always the favourable draw. Often it was, but not always. The point of the draw fixing is not getting Federer-Djokovic, but getting the most favourable draw. Your analysis means nothing. Read my article again.

2) With your statistics you went back to 2005, which is totally irrelevant to this debate, as Djokovic was not a factor then. I'm sure your (statistically still acceptable) result of 66,7% would be far higher (and far less statistically acceptable) if you kept to the period of this debate, 2008-2012.

1)If getting the favourable draw is what you want to analyse, then you have to first define what a favourable draw is in an absolute manner. The way to do this would be to take each draw in turn and define whether it is favourable to a particular player - we would have to fix who that player was and select events where the probability remained constant. You also have to consider that in 2008, who do you say is a factor out of Djoko and Murray for instance given that both scored slam victories over their respective 1 and 2 in that year - the opening post of this thread is quite frankly laughable because the reasoning for a rigged draw alters frequently. For instance the logic used of Djoko getting to the 2007 USO final is then used as and argument for him to be considered a threat, but the following year Murray made the final by beating Nadal and we get we have the following logic applied:

"US09: The only way to get a Federer-Nadal final was to put Nadal in Murray's half, and Djokovic' in Federer's as a consequence of that. Again the draw was successful."

Using logic if you wanted Nadal to get to the USO final you may consider a bad idea to put him in the same half as a Murray who beat him the previous year at the USO. Post 2008 you could then say Murray is also a threat, using the Djoko 2007 logic, yet this is not followed through in the OP and the logic is changed to suit the notion of bias - this is flawed logic.

The problem i can see here is there is a tendancy to bring subjectivity into this by looking in hindsight, when its statistically incorrect to do so. You could equally write another post that came up with reasons why the whole the draw system was rigged against another particular player, or for a different commercial reason, that warps and changes over time. Its poppycok because in reality you have to fix variables and analyse them separately to build up a picture of reality. The overall consensus was that Djoko and Fed have appeared in one half of the draw more often than they should - statistically this can be shown that the draws we have seen still lie within a normal distribution of 50/50 events.

2) statistically its incorrect to consider only 2008 onwards. I would have thought this would be obvious to people, but i'll try to explain again. The reason you cannot start at an arbitrary date is because you would then not be considering what went before it, as quite naturally a streak one way or the other may balance over time you would be focusing only on one period of the test. For example, if you stood tossing a coin all day and decided that during the period where you threw 8 heads in a row the coin had suddenly become biased, whilst ignoring the fact that during the whole day you had a roughly equal number of Heads and Tails throw. If the draws were indeed fair you have to analyse every draw available where the probability of 50/50 existed, otherwise you may skew results unfairly - this is literally what you are doing by asking for only 2008-on to be considered only. You are ignoring the corrective factor provided by pre-2008 draws.

by Jeremy_Kyle Fri 22 Jun 2012, 12:36 pm

Tom_____ wrote:
Jeremy_Kyle wrote:
Tom_____ wrote:
Jeremy_Kyle wrote:
Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Also , we already debated the issue in depht, and we found out that Fed and Djoko met on the same side for 6 times in a row, implying a very slim probability of 1.5% of this fact to happen.

Please help yourself......

https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

Oh dear me. By replying in that manner you have just shown how little you understand statistics. The calcs show we can be 95% confident that the streak of draws we have experienced still fit into a fair 50/50 distribution. You can quote singular probabilities for individual events, however my calc is all encompassing I'm afraid. It indicates such a run is possible and could even be expected in a fair system.

What's the point of discussing this, if you clearly don't know what are you talking about.

You say that your calculation is based on considering all the population, adding that the results are right because there is a 95% confidence level (??). Now, the confidence level is referring to the probabability that the results shown in a sample reflect the reality of the population. Which I'm sure you'll agree with me is utter nonsense as you are considering the population and not a sample.

You also pointed out that a STDDEV of 2.74 is a "natural variance": I personally never heard before of such a thing as natural variances in statistics.

The only useful information I can gather from your data is that there is less than 5% probability of the above occurrence to happen, which is not great.

I really think you are embarrassing yourself here. Firstly i never mentioned natural variance. Its a calculated expected variance of at set of events with a 50/50 probability. .

Who has written this?

"Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically."

Also you mentioned a "confidence level of 95%" ignoring what it means.

Again, I'll close this discussion here as you just demonstrate once more not knowing well what are you talking about.

by Tom_____ Fri 22 Jun 2012, 12:49 pm

JuliusHMarx wrote:Ah yes, I remember now - 2nd and 3rd standard deviation tests. We had to learn stats in order to evaluate the results of our psychology experiments during my degree course. So long ago!
Anyway, even if something fell outside the 2nd standard deviation I think we used to have to conclude something along the lines of 'it warrants further study to try and replicate' or 'it strongly suggests' rather than 'it proves something'.
Does that sound about right Tom?

Yes thats right JM. Unfortunately players do not play the sport long enough for further study to find anything of significance, hence subjectivity will no doubt rumble on on this subject. Maybe we could all wait another 15 years and see if a similar pattern of draws is produced for the next Fed-Nadal type rivalry - or alternatively go back in time to Ags/Pete or Lendl/Becker/Edberg etc etc.

by **laverfan** Fri 22 Jun 2012, 12:52 pm

Jeremy_Kyle wrote:Again, I'll close this discussion here as you just demonstrate once more not knowing well what are you talking about.

Natural or calculated variance, does it make a difference? chin

This is splitting quarks, IMO.

by ChequeredJersey Fri 22 Jun 2012, 12:53 pm

When looking at this draw, the previous draws cannot be taken into account. Once the previous draws have occurred they have no bearing on the probability of this one- it's still a 50-50 call whether Djok and Fed would play in the semis or not. If you Start a new hypothesis for the next 10 Majors then you could evidence your theory but retrospective studies are notoriously unrevealing.

If we take your figure of 1.5% chance that the "favourable" (which I disagree with, I think outside of major finals, Nadal-Djoko and Fed-Murray is more likely to lead to a Fedal final anyway) and try to look at it all it says it that this unlikely outcome (but 1.5% in the scheme of thing and without any real prediction isn't that unlikely. It's well within acceptable realms for coincidence, unless you're doing a scientific paper and want to be really sure of what you are saying) has occurred, nothing more. The question is, is it more unlikely that it has occurred due to coincidence or due to underlying corruption in tennis, including people thinking they can get away with it and it actually being worth getting away with. I don't know enough to make a guess at the odds of the latter, but as it stands and without any calculation of the probability of the option you are suggesting, I'd say there was minimal or less evidence for draw-fixing

by **laverfan** Fri 22 Jun 2012, 1:00 pm

Perhaps we should now debate about the conspiracy to make Mahut-Isner play a marathon in R2 @W.

Or the DelPotro-Nadal conspiracy @W. Please suggest a new one for the next slam. Djokovic-Federer is passe now. Run

by Tom_____ Fri 22 Jun 2012, 1:16 pm

Jeremy_Kyle wrote:
Tom_____ wrote:
Jeremy_Kyle wrote:
Tom_____ wrote:
Jeremy_Kyle wrote:
Tom_____ wrote:
Tom_____ wrote:I might look at this tomorrow and show some calcs. However what i will say is that the probability of Djoko and Fed appearing in the same half is 50% except for if/when the two have ever been no.1 and no.2 in the world. This is very similar to a coin flip. It takes over 100 throws and really a few 1000 to really prove a coin is biased or not as the probability tested is 50% (very middle ground). Given that at best we have about 20 slams to test for bias, the chance that there is no bias is high, even if we witness a streak of draws one way or the other. There simply hasn't been enough draws for a mathematically high probability of rigging to exist.

Ok everyone, i've completed a significance test on using a binomial distribution and and approximated normal distribution using the 30 slams since Djokovic has been active:

Now for a start we have to think about what to acutally test for bias. Simply saying Federer and Nadal are placed to reach the final a bit rediculous when the two were 1 and 2 seeds for so long - theres simply not been a long enough time when that has not been the case to even bother with the calc. The true complaint here appears to be that Djoko and Fed are in the same half more often than a random slam draw would place them. Therefore Djoko is the one to assess

Going back thorugh time to the start of Djokovic's slam career - all draws he technically had a 50% chance of being in Feds half:

Wimbers:
2011 Fed-Djoko
2010 Fed- Djoko
2009 Fed- Djoko
2008 Fed-Djoko
2007 Nadal- Djoko
2006 Fed-Djoko
2005 Roddick-Djoko

FO
2012 Fed-Djoko
2011 Fed- Djoko
2010 Nadal - Djoko
2009 Fed- Djoko
2008 Nadal - Djoko
2007 Nadal - Djoko
2006 Nadal - Djoko
2005 Roddick-Djoko

USO
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed-Djoko
2007 Nadal-Djoko
2006 Nadal-Djoko
2005 Fed-Djoko

AUS
2012 Murray-Djoko
2011 Fed-Djoko
2010 Fed-Djoko
2009 Fed-Djoko
2008 Fed- Djoko
2007 Fed-Djoko
2006 Fed-Djoko
2005 Fed-Djoko

Total times Djoko has been in Feds half: 20 = x
Total Times Djoko has not been in Feds half: 10
Total draws 'n'=30

Assumed probability of them dropping in the same half is 0.5 (50%)

Actual recorded occurrence = 0.6667 (66.7% or 2/3rds)

Occurrence of Fed-Djoko = n.P = 30 x 0.5 = 15 = (Ux) the expected mean
expected Variance = n.P(1-P) = 15 x 0.5 = 7.50

Standard dev = Var^0.5 = 2.74

Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically.

Sorry to say, but pretty dumb staff all in all, you googled how to make the calculations but forgot to learn how to interpret them. Actually a standard dev of 2.74 ( and I trust you blindly on this) would already spark some concerns.

Also , we already debated the issue in depht, and we found out that Fed and Djoko met on the same side for 6 times in a row, implying a very slim probability of 1.5% of this fact to happen.

Please help yourself......

https://www.606v2.com/t12476-socal-s-conspiracy-corner-phd-statistician-proves-the-draws-aren-t-random

Oh dear me. By replying in that manner you have just shown how little you understand statistics. The calcs show we can be 95% confident that the streak of draws we have experienced still fit into a fair 50/50 distribution. You can quote singular probabilities for individual events, however my calc is all encompassing I'm afraid. It indicates such a run is possible and could even be expected in a fair system.

What's the point of discussing this, if you clearly don't know what are you talking about.

You say that your calculation is based on considering all the population, adding that the results are right because there is a 95% confidence level (??). Now, the confidence level is referring to the probabability that the results shown in a sample reflect the reality of the population. Which I'm sure you'll agree with me is utter nonsense as you are considering the population and not a sample.

You also pointed out that a STDDEV of 2.74 is a "natural variance": I personally never heard before of such a thing as natural variances in statistics.

The only useful information I can gather from your data is that there is less than 5% probability of the above occurrence to happen, which is not great.

I really think you are embarrassing yourself here. Firstly i never mentioned natural variance. Its a calculated expected variance of at set of events with a 50/50 probability. .

Who has written this?

"Using binomial tables the results show a 95% confidence that the draws seen so far fall within the natural variance expected for 30 events with a 50/50 chance. The approximated normal distribution agrees with this results. I.e the draws are not biased, statistically."

Also you mentioned a "confidence level of 95%" ignoring what it means.

Again, I'll close this discussion here as you just demonstrate once more not knowing well what are you talking about.

Thankyou you have just shown that i have not stated that the Standard deviation is a natural variance, as i said i did not mention natural variance in my sentence stating the ST DEV of 2.74 in direct response to your sentence quoted below.

Jeremy_Kyle wrote:You also pointed out that a STDDEV of 2.74 is a "natural variance": I personally never heard before of such a thing as natural variances in statistics.

I then went on to explain what the expected variance is to try to help you understand. In hindsight in the quote you post above i could have put 'Natural process variation' instead of 'natural variance', however what i wanted to put was something like 'results fall within 2 or 3 standard deviations of the mean, hence no bias', but i thought that might be a little bit too technical for you. Natural variance is a reasonable term to use if you are familiar with the subject.

a random internet phrase easily found:
"Natural process variation, sometimes just called process variation, is the statistical description of natural fluctuations in process outputs.....The variation within the upper and lower control limits (UCL and LCL) is considered the natural variation of the process"

- in this case limits were set at +/-2 standard deviations, a P range of 0.025-0.975.

"The most important goal of understanding the principle of natural process variation is to consider the natural variance in the output before we make any changes to the process. "

All you have ultimately shown here is that you don't grasp this subject at all and you're not willing to.

Just FYI - the confidence level of 95% means you can be 95% confident what you are seeing is not bias. It doesn't mean bias is impossible, simply very improbable.

by Jeremy_Kyle Fri 22 Jun 2012, 1:22 pm

http://stattrek.com/statistics/dictionary.aspx?definition=confidence_level

by **laverfan** Fri 22 Jun 2012, 1:29 pm

JK and Tom___

Instead of a semantics argument, can both of you agree on a common definition and proceed further than this impasse, for the sake of taking this debate forward.

by Jeremy_Kyle Fri 22 Jun 2012, 1:40 pm

Even ignoring all the inaccuracies I seriously doubt the calculation itself is correct. Eventually I will check it over the w/e if you are interested.......

by Josiah Maiestas Fri 22 Jun 2012, 1:42 pm

Chequered, see youre one of those who chooses to ignore that Djokovic gets Federer and Nadal gets Murray in 16 of 18 slam draws, yeah you can support the validity of the draw, just don't forget the odds of this run are significantly unlikely. Why not do a lottery type draw, where the viewers can get up close without need for conspiracy? In my eyes they gave Federer to Nadal in Australia as they hadn't met the last few times over there, and they didn't want Murray or Djoker to ruin it. Since that final ended up taking 6 hours and bored most people, they don't want that repeated so they expect Federer to beat Djokovic in the semi's.

by **laverfan** Fri 22 Jun 2012, 1:47 pm

Also, despite all these conspiracy theories, W (and AELTC) have yet again, rigged a Federer-Djokovic semifinal. What sheer arrogance! Laugh

Broadcasters must be expecting a larger revenue now. Wink

Jeremy_Kyle wrote:Even ignoring all the inaccuracies I seriously doubt the calculation itself is correct. Eventually I will check it over the w/e if you are interested.......

Much obliged, if you can, pretty please. Draw fixing (hypothesis) at grand slams (2008-2012) - Page 3 Loki8

by Guest Fri 22 Jun 2012, 1:47 pm

ChequeredJersey wrote:... Once the previous draws have occurred they have no bearing on the probability of this one- it's still a 50-50 call whether ... retrospective studies are notoriously unrevealing. ...

Although I too am suspicious of retrospective studies, I still have confidence that the sun will rise tomorrow Yikes

by **laverfan** Fri 22 Jun 2012, 1:49 pm

Nore Staat wrote:
ChequeredJersey wrote:... Once the previous draws have occurred they have no bearing on the probability of this one- it's still a 50-50 call whether ... retrospective studies are notoriously unrevealing. ...
Although I too am suspicious of retrospective studies, I still have confidence that the sun will rise tomorrow

Did you check the weather forecast? Run

by ChequeredJersey Fri 22 Jun 2012, 1:58 pm

I agree that a lottery type draw would be much better and can see no reason why they shouldn't do so. I am not ignoring the fact that these matchups have occurred 16/18 slams, I am refuting that this is strong evidence as of itself. I am confident that you could look retrospectively at other potential matchups in draws in tennis now and in previous years and in every other sport and find similar patterns which I feel are most likely coincidental. Finding patterns where there is only coincidence is a universal human fallacy.

However what would be interesting would be to place a bet, if possible, on the next 8 GS draws

by Josiah Maiestas Fri 22 Jun 2012, 2:17 pm

Anyway, if you want to win it you have to beat them all. (Unless youre name is Nadal and you don't have to play any serious matches until the semi's). Smile

by Chydremion Fri 22 Jun 2012, 3:46 pm

Tom_____ wrote:
Chydremion wrote:1) Getting Federer-Djokovic was not always the favourable draw. Often it was, but not always. The point of the draw fixing is not getting Federer-Djokovic, but getting the most favourable draw. Your analysis means nothing. Read my article again.

2) With your statistics you went back to 2005, which is totally irrelevant to this debate, as Djokovic was not a factor then. I'm sure your (statistically still acceptable) result of 66,7% would be far higher (and far less statistically acceptable) if you kept to the period of this debate, 2008-2012.

1)If getting the favourable draw is what you want to analyse, then you have to first define what a favourable draw is in an absolute manner. The way to do this would be to take each draw in turn and define whether it is favourable to a particular player - we would have to fix who that player was and select events where the probability remained constant. You also have to consider that in 2008, who do you say is a factor out of Djoko and Murray for instance given that both scored slam victories over their respective 1 and 2 in that year - the opening post of this thread is quite frankly laughable because the reasoning for a rigged draw alters frequently. For instance the logic used of Djoko getting to the 2007 USO final is then used as and argument for him to be considered a threat, but the following year Murray made the final by beating Nadal and we get we have the following logic applied:

"US09: The only way to get a Federer-Nadal final was to put Nadal in Murray's half, and Djokovic' in Federer's as a consequence of that. Again the draw was successful."

Using logic if you wanted Nadal to get to the USO final you may consider a bad idea to put him in the same half as a Murray who beat him the previous year at the USO. Post 2008 you could then say Murray is also a threat, using the Djoko 2007 logic, yet this is not followed through in the OP and the logic is changed to suit the notion of bias - this is flawed logic.

The problem i can see here is there is a tendancy to bring subjectivity into this by looking in hindsight, when its statistically incorrect to do so. You could equally write another post that came up with reasons why the whole the draw system was rigged against another particular player, or for a different commercial reason, that warps and changes over time. Its poppycok because in reality you have to fix variables and analyse them separately to build up a picture of reality. The overall consensus was that Djoko and Fed have appeared in one half of the draw more often than they should - statistically this can be shown that the draws we have seen still lie within a normal distribution of 50/50 events.

2) statistically its incorrect to consider only 2008 onwards. I would have thought this would be obvious to people, but i'll try to explain again. The reason you cannot start at an arbitrary date is because you would then not be considering what went before it, as quite naturally a streak one way or the other may balance over time you would be focusing only on one period of the test. For example, if you stood tossing a coin all day and decided that during the period where you threw 8 heads in a row the coin had suddenly become biased, whilst ignoring the fact that during the whole day you had a roughly equal number of Heads and Tails throw. If the draws were indeed fair you have to analyse every draw available where the probability of 50/50 existed, otherwise you may skew results unfairly - this is literally what you are doing by asking for only 2008-on to be considered only. You are ignoring the corrective factor provided by pre-2008 draws.

1) Yes Murray might have been a threat at the US Open 2009, but that is irrelevant. If you read my article better you'll understand the only way for a Federer-Nadal final was to put him in Murray's half. Even if Murray was the terminator, they would still have had to place him in Murray's half.

2) It's a bit hard to see a conspiracy without hindsight. You wanted me to predict it beforehand or what?

3) Why start in 2005 when Djokovic was no factor at all? 2008 makes much more sense. Maybe this isn't enough for the statictics, the good thing for draw-riggers is that the sample will never be big enough to have proof, but anyway 2008 is a logical starting point, much more than your 2005.

by Chydremion Fri 22 Jun 2012, 3:50 pm

JuliusHMarx wrote:Yeah, the idea that keeping Fed and Nadal apart could give a Fedal final would be extremely hopeful.
If anyone was rigging it, they would put them in the same half, with a much greater chance of a Fedal semi-final, followed by a Rafa/Djoko final. Surely that would be the best way to maximise viewers (unless people think a Rafa/Djoko final is not a big draw?)
It would also keep Murray, the home favourite, away from Nadal, who he has lost to in the last 2 semis.

Well people accuse me of hindsight but if this isn't hindsight I don't know. Until 2011 Federer and Nadal were the two best players in the world and supposed to dominate 2011. Even when Djokovic went on his run it was by many considered a fluke that would end soon. How many people said normal service would be resumed in 2012? Yes, now a Fedal final looks unlikely but certainly a year ago more finals between the two were expected than have occured.

by Tom_____ Fri 22 Jun 2012, 4:00 pm

laverfan wrote:Also, despite all these conspiracy theories, W (and AELTC) have yet again, rigged a Federer-Djokovic semifinal. What sheer arrogance!

Broadcasters must be expecting a larger revenue now.

Jeremy_Kyle wrote:Even ignoring all the inaccuracies I seriously doubt the calculation itself is correct. Eventually I will check it over the w/e if you are interested.......

Much obliged, if you can, pretty please.

You'll find the calc is correct - as there's not much to do really. For binomial approximately to normal distribution; n = no. events 30, p = probability = 0.5; mean (u) = n.p = 15, variance = n.p(n-1) = 7.5; ST DEV = square root of variance = 2.74. Result (X) in this case = 20 fed-djoko draws

z = (X-u)/ST DEV = 1.82. (this is how many standard deviations the result is away from the mean)

As this is less than 2, we are within 95% of all expected results for a normal distribution with a probability of 0.5 and pass the globally adopted 5% significance test. However in this instance, as i have said a 1% test is preferred as the 0.5 probability is very middle ground, hence 3 standard deviations would be allowed before you had to worry about the 0.5 theoretical probability being incorrect.

by Chydremion Fri 22 Jun 2012, 4:22 pm

I hope that sometime this year Federer will get to number 2 with Nadal at three. Would be interesting if Nadal would get in Djokovic' half to make a Fedal final possible and so reinforce my hypothesis.

by Tom_____ Fri 22 Jun 2012, 4:31 pm

Chydremion wrote:
Tom_____ wrote:
Chydremion wrote:1) Getting Federer-Djokovic was not always the favourable draw. Often it was, but not always. The point of the draw fixing is not getting Federer-Djokovic, but getting the most favourable draw. Your analysis means nothing. Read my article again.

2) With your statistics you went back to 2005, which is totally irrelevant to this debate, as Djokovic was not a factor then. I'm sure your (statistically still acceptable) result of 66,7% would be far higher (and far less statistically acceptable) if you kept to the period of this debate, 2008-2012.

1)If getting the favourable draw is what you want to analyse, then you have to first define what a favourable draw is in an absolute manner. The way to do this would be to take each draw in turn and define whether it is favourable to a particular player - we would have to fix who that player was and select events where the probability remained constant. You also have to consider that in 2008, who do you say is a factor out of Djoko and Murray for instance given that both scored slam victories over their respective 1 and 2 in that year - the opening post of this thread is quite frankly laughable because the reasoning for a rigged draw alters frequently. For instance the logic used of Djoko getting to the 2007 USO final is then used as and argument for him to be considered a threat, but the following year Murray made the final by beating Nadal and we get we have the following logic applied:

"US09: The only way to get a Federer-Nadal final was to put Nadal in Murray's half, and Djokovic' in Federer's as a consequence of that. Again the draw was successful."

Using logic if you wanted Nadal to get to the USO final you may consider a bad idea to put him in the same half as a Murray who beat him the previous year at the USO. Post 2008 you could then say Murray is also a threat, using the Djoko 2007 logic, yet this is not followed through in the OP and the logic is changed to suit the notion of bias - this is flawed logic.

The problem i can see here is there is a tendancy to bring subjectivity into this by looking in hindsight, when its statistically incorrect to do so. You could equally write another post that came up with reasons why the whole the draw system was rigged against another particular player, or for a different commercial reason, that warps and changes over time. Its poppycok because in reality you have to fix variables and analyse them separately to build up a picture of reality. The overall consensus was that Djoko and Fed have appeared in one half of the draw more often than they should - statistically this can be shown that the draws we have seen still lie within a normal distribution of 50/50 events.

2) statistically its incorrect to consider only 2008 onwards. I would have thought this would be obvious to people, but i'll try to explain again. The reason you cannot start at an arbitrary date is because you would then not be considering what went before it, as quite naturally a streak one way or the other may balance over time you would be focusing only on one period of the test. For example, if you stood tossing a coin all day and decided that during the period where you threw 8 heads in a row the coin had suddenly become biased, whilst ignoring the fact that during the whole day you had a roughly equal number of Heads and Tails throw. If the draws were indeed fair you have to analyse every draw available where the probability of 50/50 existed, otherwise you may skew results unfairly - this is literally what you are doing by asking for only 2008-on to be considered only. You are ignoring the corrective factor provided by pre-2008 draws.

1) Yes Murray might have been a threat at the US Open 2009, but that is irrelevant. If you read my article better you'll understand the only way for a Federer-Nadal final was to put him in Murray's half. Even if Murray was the terminator, they would still have had to place him in Murray's half.

2) It's a bit hard to see a conspiracy without hindsight. You wanted me to predict it beforehand or what?

3) Why start in 2005 when Djokovic was no factor at all? 2008 makes much more sense. Maybe this isn't enough for the statictics, the good thing for draw-riggers is that the sample will never be big enough to have proof, but anyway 2008 is a logical starting point, much more than your 2005.

1) Disagree on relevance, particularly as you say that USO 2009 they put Murray in Nadals half to help Nadal reach the final, when Murray beat him in the USO 2008. You would logically argue Nadal would be hindered no matter who he faced in 2009. At the time Murray had won the previous 2 HC meetings. Djokovic and Nadal had shared the last 2 HC meetings stretching back to 2008. At the 2009 USO, Nadal had Tsonga in his half (who took him out on HC AUS open 2008), Murray (Who took him out USO 2008), Berdych, Monfils & Ferrer (Who beat Nadal at USO 2007). I can't see how anyone could argue Nadals draw was set up for him to reach a Fed final that year if you start picking apart individual draws on their own merit.

2) Fine to spot a hindsight conspiracy, but not fine to change the reasoning with hindsight to support the conspiracy on subsequent events.

3) 2005 was when Djoko started playing slams. Its not 'my 2005', its when you have to statistically start analysing. All these results have to be considered when assessing the subsequent draw for fairness, as the streak of Djoko-Fed draws we are seeing has a corrective factor from the pre 2008 that statistically can not be ignored for the test to remain fair. Otherwise you are trying to cherry pick a sample, which voids any mathematical test. As i alluded to earlier its like tossing a coin 100 times and then using the 8 heads in a row that you happened to finish with to say the coin was biased. You must take into account all available results that form part of a set of data. You cannot discount some results based on the reason that you hope to prove (i.e discount <2008, because 'you think' bias was present after 2008), as this creates a feedback loop which skews results.

by **JuliusHMarx** Fri 22 Jun 2012, 4:39 pm

Nadal hasn't beaten Djoko off clay for a year and a half. If Djoko was in Nadal's half, you'd have to say Djoko would be clear favourite to get to the final. Of course, Djoko's the favourite to beat Fed as well.
Anyone who wants a Fedal match has to hope they're in the same half - it's the only real chance of them meeting.

by socal1976 Fri 22 Jun 2012, 4:48 pm

Adam D wrote:I would like to remind everyone that draw fixing has never been proved and until it is, all accusations of it are pure speculation.

As a founder of this site, I have a care of duty to remind you not to post libelous statements that could result in legal action against the site.

So to clarify, you may offer up potential reasoning as to why you may suspect draw rigging has taken place but any comments delivered as fact, will be removed.

The only fact is that it has never been proven in a court of law.

Therefore, please respect the hard work that the founders. admin and moderators have put in to this site by not posting statements that could get the site shut down.

You all have a care of duty in this matter - if you suspect a post of being libelous, please report it.

The statement that dear impartial moderator dictator julius deleted was in no way a violation these rules. It was all opinion statements and anything stated as fact is true and I use conditional opinion based language and even use words to denote that this is my opinion. I did not state it was proven or true that draw rigging has taken place. Yet as usual I am picked out by julius for draw rigging comments when most of my post and it was very long was just complimenting the OP for arguments he already made. I am lawyer for chrissake I know better than any of you, Julius included what is an actionable fact based conclusion and what is speculation and opinion. And I challenge that my last post in no way violated these rules. And even if one or two sentences were violative it was a one page post that took my time why delete the whole thng? In short Julius is a crap and biased moderator, I can see where this thing is going and if he isn't removed I probably will be lessening and lessening my contribution and just not even showing up. Sad, because I came to this tennis site when their was 6 posters and have produced thousands of posts for this site but if even the old established posters are singled out for censorship and a person who knows nothing about the law determines only his comments controversial and erases them, well that is a little more than I will be willing to take.

by **JuliusHMarx** Fri 22 Jun 2012, 4:58 pm

Hey everybody - I'm crap! Laugh

by socal1976 Fri 22 Jun 2012, 4:59 pm

lydian wrote:Dont be hasty socal...if you're posting things about "fixing" that are accusatory of draw committees then the site has to be clearly careful. If posters are defending the draws not being fixed then thats different. No need to throw the baby out with the bath water.

Wrong my statements did not state that it was a fact that draw rigging took place and it was obvious. I said I had doubts about the oversight of the process and that it was producting odd numbers. What can cause a lawsuit out of what I wrote? I know better than Julius and probably even the adminstrator's what an actionable fact conclusion is and what unactionable opinion or suspicion is. Besides my post was long and most of it was complimenting the OP for arguments he already made and I commented on. It is a shame that I am being forced out and censored based on the legal opinions of a untrained individual who sees nothing wrong with the original comments but if I write a post complimenting and mostly citing the OP"s already published column my entire 200 word post gets deleted.

Basically crap and biased moderation if you ask me. This is why this site will always limit itself. Moderators come on who over edit and eventually drive good posters away. I have seen it happen over and over again on this site.

by socal1976 Fri 22 Jun 2012, 5:01 pm

JuliusHMarx wrote:Hey everybody - I'm crap!

I didn't say you were crap there you go misquoting me, I said your moderation stinks and is crap and in my opinion it. Here is a legal lesson julius I can not be sued for libel for saying your moderation is crap or biased. My statement isn't a fact statement it is MY OPINION. I won't get sued for libel unless I can prove you are made of feces. My opinion is you are a bad and divisive moderator which equals crap as a moderator.

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