Draw Fixing : A Real World Example (Masters Series 2005-2012)

These two tables provide data from the ATP World Tour Masters 1000 (and it's predecessor ATP Master Series) and look at draws.

1-4,2-3 indicates Seeds #1 and #4 were in the same half, as were seeds #2 and #3.
1-3,2-4 indicates Seeds #1 and #3 were in the same half, as were seeds #2 and #4.

The last two horizontal columns contains the number of 1-4,2-3 and 1-3,2-4 draws for that year. This also looks at the same totals per tournament.

Year/Tournament	Indian Wells	Miami	Monte Carlo	Rome	Hamburg/Madrid (Clay)	Canada	Cincinnati	Madrid/Shanghai (Hard)	Paris	1-4,2-3 Occurrence (Year)	1-3,2-4 Occurrence (Year)
2005	1-4,2-3	1-4,2-3	1-4,2-3	1-4,2-3	1-3,2-4	1-3,2-4	1-4,2-3	1-3,2-4	1-4,2-3	6	3
2006	1-4,2-3	1-4,2-3	1-4,2-3	1-4,2-3	1-4,2-3	1-4,2-3	1-3,2-4	1-4,2-3	1-3,2-4	7	2
2007	1-4,2-3	1-4,2-3	1-4,2-3	1-3,2-4	1-4,2-3	1-4,2-3	1-4,2-3	1-4,2-3	1-3,2-4	7	2
2008	1-4,2-3	1-4,2-3	1-3,2-4	1-3,2-4	1-4,2-3	1-4,2-3	1-4,2-3	1-3,2-4	1-4,2-3	6	3
2009	1-3,2-4	1-4,2-3	1-4,2-3	1-4,2-3	1-3,2-4	1-3,2-4	1-3,2-4	1-3,2-4	1-4,2-3	4	5
2010	1-4,2-3	1-3,2-4	1-4,2-3	1-3,2-4	1-3,2-4	1-4,2-3	1-3,2-4	1-4,2-3	1-3,2-4	4	5
2011	1-4,2-3	1-3,2-4	1-3,2-4	1-3,2-4	1-3,2-4	1-3,2-4	1-3,2-4	1-3,2-4	1-4,2-3	2	7
2012	1-4,2-3	1-3,2-4	1-3,2-4	1-3,2-4	1-3,2-4					1	4
1-4,2-3 (By Tournament)	7	5	5	3	3	4	3	3	4	37
1-3,2-4 (By Tournament)	1	3	3	5	5	3	4	4	3		31

This shows a 37 (1-4,2-3) ~ 54% vs 31 (1-3,2-4) ~ 46% distribution, fairly even.

To avoid controversies regarding match-ups due to changes in ATP rankings, the following table, uses player names, rather than corresponding seedings. The order of tournaments is the same as the first table.

Expected SF	Indian Wells	Miami	Monte Carlo	Rome	Hamburg/Madrid (Clay)	Canada	Cincinnati	Madrid/Shanghai (Hard)	Paris
2005	Federer v Safin, Hewitt v Roddick	Federer v Coria, Roddick v Safin	Federer v Gaudio, Safin v Henman	Roddick v Henman, Safin v Gaudio	Federer v Safin, Roddick v Gaudio	Nadal v Roddick, Hewitt v Agassi	Federer v Safin, Nadal v Hewitt	Nadal v Davydenko, Roddick v Coria	Roddick v Puerta, Coria v Davydenko
2006	Federer v Nalbandian, Nadal v Roddick	Federer v Roddick, Nadal v Nalbandian	Federer v Ljubicic, Nadal v Nalbandian	Federer v Nalbandian, Nadal v Ljubicic	Federer v Davydenko, Nadal v Ljubicic	Federer v Ljubicic, Nadal v Nalbandian	Federer v Ljubicic, Nadal v Nalbandian	Federer v Nalbandian, Nadal v Ljubicic	Federer v Nalbandian, Nadal v Davydenko
2007	Federer v Davydenko, Nadal v Roddick	Federer v Davydenko, Nadal v Roddick	Federer v Davydenko, Nadal v Roddick	Federer v Roddick, Nadal v Davydenko	Federer v Djokovic, Nadal v Davydenko	Federer v Davydenko, Nadal v Djokovic	Federer v Djokovic, Nadal v Roddick	Federer v Davydenko, Nadal v Djokovic	Federer v Djokovic, Nadal v Davydenko
2008	Federer v Davydenko, Nadal v Djokovic	Federer v Davydenko, Nadal v Djokovic	Federer v Djokovic, Nadal v Davydenko	Federer v Djokovic, Nadal v Davydenko	Federer v Davydenko, Nadal v Djokovic	Federer v Davydenko, Nadal v Djokovic	Federer v Davydenko, Nadal v Djokovic	Nadal v Djokovic, Federer v Murray	Nadal v Murray, Federer v Djokovic
2009	Nadal v Djokovic, Federer v Murray	Nadal v Murray, Federer v Djokovic	Nadal v Murray, Federer v Djokovic	Nadal v Murray, Federer v Djokovic	Nadal v Djokovic, Federer v Murray	Federer v Murray, Nadal v Djokovic	Federer v Murray, Nadal v Djokovic	Nadal v Del Potro, Djokovic v Roddick	Federer v Murray, Nadal v Djokovic
2010	Federer v Murray, Nadal v Djokovic	Federer v Murray, Djokovic v Nadal	Djokovic v Cilic, Nadal v Murray	Federer v Nadal, Djokovic v Murray	Federer v Murray, Nadal v Soderling	Nadal v Murray, Djokovic v Federer	Nadal v Federer, Djokovic v Murray	Nadal v Federer, Djokovic v Federer	Federer v Murray, Djokovic v Soderling
2011	Nadal v Soderling, Federer v Djokovic	Nadal v Federer, Djokovic v Soderling	Nadal v Murray, Federer v Ferrer	Nadal v Federer, Djokovic v Murray	Nadal v Federer, Djokovic v Murray	Djokovic v Federer, Nadal v Murray	Djokovic v Federer, Nadal v Murray	Nadal v Ferrer, Murray v Tsonga	Djokovic v Ferrer, Murray v Federer
2012	Djokovic v Murray, Nadal v Federer	Djokovic v Federer, Nadal v Murray	Djokovic v Murray, Nadal v Tsonga	Djokovic v Federer, Nadal v Murray	Djokovic v Federer, Nadal v Tsonga

Based on the table containing player names, some samples are (based on seedings, Federer v Djokovic and Djokovic v Federer is considered equivalent for the expected SF).

Djokovic v Federer - 17 occurrences
Djokovic v Nadal - 15 occurrences

Nadal v Murray - 11 occurrences
Djokovic v Murray - 6 occurrences
Federer v Murray - 11 occurrences

Federer v Davydenko - 11 occurrences
Federer v Roddick - 2 occurrences
Federer v Ljubicic - 3 occurrences
Federer v Nadal - 7 occurrences

Let me know if I should go further back beyond 2005. 2005 is an arbitrary cutoff, but does include the current top 4.

Apart from Indian Wells showing a 7-1 proclivity towards 1-4,2-3 matchup, despite the 37-31 balance overall, is probably worthy of further analysis.

E&OE

This data is based on Wikipedia, which may be prone to errors. A couple of tournaments, where Federer and Nadal withdrew due to fatigue, I have used the printed versions from the ATP web site to validate the actual draw on Wikipedia. Data from 2005 Indian Wells - Madrid 2012.

So there's no fixing.

Thanks, useful.

Don't worry about Indian Wells, there's nothing too surprising about one tournament producing a 7-1 result either way. Indeed the probability of that configuration is 16*(0.5)^8 = 1.5% (assuming we're indifferent as to which option only comes up once). That sounds remote, but how many events are there? Given there's 10 there's a 15%* of that happening on one of them, not exactly a shocker.

* yes, I did take 1 -(Pr(not happening)^10). I didn't just multiply 1.5% by 10.

Yet there will be some window licker on this forum that will try his hardest to discredit the findings as he doesn't understand that the concept that draws are made by seeds and not by name.

Stunnng work though LF.

Great work LF...this again shows no evidence of draw rigging whatsoever (as I suspected this analysis would show). Great to see the confirmation.

Given that Masters events have an even greater need than slams to boost revenue (they just dont have the same cache - pardon the pun), if you expected to see rigging it would be in those events where the top 4 are also usually prevalent. I'm sure the therorists will have their excuses though!

Would like to hear from SoCal and others and see if this changes their viewpoint.

laverfan wrote:Would like to hear from SoCal and others and see if this changes their viewpoint.

laverfan wrote:Would like to hear from SoCal and others and see if this changes their viewpoint.

Such a nice research but ended in a funny note with that comment

How long did it take for you to compile this stats? this is no easy task , either your a statistician or scientist or u should one of those avengers super hero on stats research.

Lets get back to meaningful discussion by standing on the side of the Socal , how on earth Johny Bravo and Mammoth Mahut drawn on Wimbledon 1st round draw twice in a row?

Last but not least why on earth the Joker gets the toughest draw every time with Federer in it why not just Gasquet?

Oh yes, the people who don't believe in draw fixing think they are smart by examining the masters series. Hello, what? Master serie? 99% of world population probably doesnt know what that is. It's at the slams where the big money is made, and where draw fixing is necessary. Master series are only followed by avid tennis fans, or even addicts, who will watch regardless of who is playing the final.

Chydremion wrote:Oh yes, the people who don't believe in draw fixing think they are smart by examining the masters series. Hello, what? Master serie? 99% of world population probably doesnt know what that is. It's at the slams where the big money is made, and where draw fixing is necessary. Master series are only followed by avid tennis fans, or even addicts, who will watch regardless of who is playing the final.

I love denial.

invisiblecoolers wrote:How long did it take for you to compile this stats? :shocked:

6-8 hours over the weekend.

chydremion wrote:It's at the slams where the big money is made, and where draw fixing is necessary.

The ESPN study looks only R1/R2.

The University of Talinn study looks at slams, but discards the data at FO, because it does not suit their hypothesis. What other tournaments would you like to be examined?

One important fact to point out, in case you might have missed it, is, apart from the slams, it is only at the Masters series where all top seeds turn up, otherwise they can play different tournaments in the ATP 500/250 chain and never meet each other.

In other words, ATP 500/250 do not have Top 4 participation as the ATP 1000s do (apart from withdrawals).

invisiblecoolers wrote:Lets get back to meaningful discussion by standing on the side of the Socal , how on earth Johny Bravo and Mammoth Mahut drawn on Wimbledon 1st round draw twice in a row?

From 1970-2011, there are seven or eight instances of two players meeting in consecutive Wimbledons. My research so far has revealed the following.

2011 W Isner v Mahut
2010 W Isner v Mahut

2008 W Ginepri v Gonzalez
2007 W Ginepri v Gonzalez

Near misses....

1977 W Connors v Lewis
1980 W Connors v Lewis

2007 W Almagro v Tursunov
2005 W Almagro v Tursunov

2008 W Melzer v Ljubicic
2005 W Melzer v Ljubicic


BTW, researching this has turned it out to be a much more painful exercise compared to the Masters Series research. It is a work-in-progress right now. I had wanted to complete it, before I published partial results, but you forced my hand.

@LF your works and research are amazing as usual

But for the fun sake I gonna stand on Socal's side and say this come Wimbledon the draw will be like this

Nole- Fed and Rafa- Murray .

Wimby authorities certainly don't want their fav. child Murray to face Djoko and would certainly love to have a blockbuster Fed-Rafa on cards atleast, so the draws would be rigged

I am betting that Fognini will be drawn with Nole in the first round!

legendkillarV2 wrote:I am betting that Fognini will be drawn with Nole in the first round!

, thats left for FO LK not for Wimbledon.

invisiblecoolers wrote:

legendkillarV2 wrote:I am betting that Fognini will be drawn with Nole in the first round!

, thats left for FO LK not for Wimbledon.

the picture is set.

Djokovic defeats Fognini in a first 5 set thriller.

Djokovic makes the final.

Loses it to Nadal over a 10 day final.

We blame Fognini for the first round for Djokovic losing!

fairytale stuff.

@ lk

legendkillarV2 wrote:

Chydremion wrote:Oh yes, the people who don't believe in draw fixing think they are smart by examining the masters series. Hello, what? Master serie? 99% of world population probably doesnt know what that is. It's at the slams where the big money is made, and where draw fixing is necessary. Master series are only followed by avid tennis fans, or even addicts, who will watch regardless of who is playing the final.

I love denial.

And I love great arguments like yours.

Chydremion wrote:And I love great arguments like yours.

Would you care to discuss the information I provided?

laverfan wrote:

Chydremion wrote:And I love great arguments like yours.

Would you care to discuss the information I provided?

Your asking for too much LF

laverfan wrote:

Chydremion wrote:And I love great arguments like yours.

Would you care to discuss the information I provided?

The subject of your article (master series) is irrelevant to the message you try to bring. I suppose all your stats are right but the only thing we can conclude is that there's probably no draw fixing in master series. So what?

Chydremion wrote:

laverfan wrote:

Chydremion wrote:And I love great arguments like yours.

Would you care to discuss the information I provided?

The subject of your article (master series) is irrelevant to the message you try to bring. I suppose all your stats are right but the only thing we can conclude is that there's probably no draw fixing in master series. So what?

Are you going to bring your findings to the cause of Slam draw rigging?

Chydremion wrote:The subject of your article (master series) is irrelevant to the message you try to bring.

I analysed the Tour Masters 1000 and the predecessor Master Series, surprised that you do not see relevance.

Chydremion wrote: I suppose all your stats are right but the only thing we can conclude is that there's probably no draw fixing in master series. So what?

What else would you like to analyse? Slams have been analysed and the flaw in the Talinn study already pointed out (exclusion of FO for Mens).

There is quite a bit of discussion here.

https://www.606v2.com/t28203-draw-fixing-a-real-world-analysis-part-1-the-12-vs-12-question

Also, I can do an analysis similar to this one for slams from 2005-2012. Would that be a worthwhile discussion?

legendkillarV2 wrote:

Chydremion wrote:

laverfan wrote:

Chydremion wrote:And I love great arguments like yours.

Would you care to discuss the information I provided?

The subject of your article (master series) is irrelevant to the message you try to bring. I suppose all your stats are right but the only thing we can conclude is that there's probably no draw fixing in master series. So what?

Are you going to bring your findings to the cause of Slam draw rigging?

I will, as soon as I find the time to write a probably extensive article about it. Too much work at the moment though.