Draw Fixing : A Real World Analysis - Part 1 (The 12 vs 12 Question)

First topic message reminder :

The fall out from Draw Fixing: An Official Study on 606v2 has created a deep divide. This followup article does not intend to cause any further . Please respect fellow posters' opinions and pursue a civilised debate.

Draws from 1974-2000 (post Open Era) for all four Slams were used. The data from 2001-2010 was not used to avoid conflicts with the ESPN study as well as look at an independent data set.

The Top 4 of each slam who were seeded 1 through 4 were considered.

The Top 4 are distributed where each half has seeds 1 and 2 at the opposite ends of the draw (64 or 128 players). Seeds 3 and 4 are placed to yield a 1-3, 2-4 or 1-4, 2-3 combination in each half.

1. There was some contention in the earlier article about the distribution of seeds #3 and #4 across the draws 'randomly'.

a. Australian Open (1974-2000) has 12 occurrences of 1-3, 2-4 (44%) combination, and 15 occurrences of 1-4, 2-3 (56%).

(AO had no 1986 Slam, but had two in 1977 (January and December). AO also had 'BYEs' for the Top 4 from 1983-1987).

b. French Open (1974-2000) has 15 occurrences of 1-3, 2-4 (56%) combination, and 12 occurrences of 1-4, 2-3 (44%).

c. Wimbledon (1974-2000) has 14 occurrences of 1-3, 2-4 (52%) combination, and 13 occurrences of 1-4, 2-3 (48%).

d. US Open (1974-2000) has 11 occurrences of 1-3, 2-4 (41%) combination, and 16 occurrences of 1-4, 2-3(59%).

2. Federer vs Djokovic (12vs12) raised a followup question whether similar scenario has happened before. The answer is yes, it has.

a. Connors vs McEnroe (9 projected meetings)

1979 - USO
1980 - FO, W, USO
1981 - FO
1983 - USO
1984 - FO, USO
1985 - W

b. Connors vs Vilas (7 projected meetings)

1975 - W
1976 - USO
1978 - USO
1979 - FO
1982 - FO, USO
1983 - W

c. Edberg v Lendl (9 projected meetings)

1986 - USO
1987 - FO, W
1989 - AO, USO
1990 - W, USO
1991 - AO, FO

d. Edberg v Stich (6 projected meetings)

1991 - USO
1992 - FO, W
1994 - AO, FO
1995 - AO

e. Edberg v Wilander (6 projected meetings)

1987 - USO
1988 - AO, FO, W, USO
1989 - W

The case of Connors is unique because Connors v Vilas is spread over a 8 year span, as an example. If USO wanted Connors all the time, which is understandable, FO and W also wanted a piece of the 'possibly rigging' pie.

Primary sources of data are ATP, ITF and Wikipedia. Spot validation was done using the AO draws from the official website and ITF. Wikipedia has some issues with specific AO draws, which were checked with the official site. I have not yet looked Sampras closely who was very dominant during his tenure.

Please point out any errors. E&OE (as I always indicate). This will be posted on another website that I visit (for full disclosure).

But a problem is the rationale behind purported rigging...it assumes that
a) TDs wanted Fedal finals from 2007 to boost sales,
b) events wouldn't be sellout anyway,
c) Nadal in 2007-2010 feared Nole more than Murray when stats are not conclusive,
d) Nadal Djokovic finals wouldn't become popular,
e) events would be 'happy' or prepared to damage their reputation in the event that draw rigging became leaked...

socal1976 wrote:

reckoner wrote:oh socal, tsk tsk tsk

1. there's only one credible study

2. it's not "your" point

must try harder!

No there are two, a study by Espn done over several years analyzing the top seed matchups in the first two rounds found with an overwhelming percentage chance that the USO men's and women's draw and the French open Draw were not random and where manufactured.

My mistake! Do you have a link for the first?

reckoner wrote:...(one of these being to exclude RG as we suppose it isn't rigged)...

Why is FO not rigged? It that a logical assumption. Either all slams are rigged or none are.

reckoner wrote:... your contention is that this is such a likely scenario that it is reproducible using historical data...

If FO can be dropped as a constraint, why not the ability to extend the time period?

I looked at the ranking changes as input to this. The Connors v McEnroe has quite a few up/down movements. Look at what happens from Sep, 1982 to Aug, 1984.

http://en.wikipedia.org/wiki/List_of_ATP_number_1_ranked_singles_players

As I stated earlier, the consistency and constancy of the Top 4 is a very significant factor in this discussion. The statistical 1-3/2-4 vs 1-4/2-3 is pretty much evenly balanced. I have shown the exceptions to the 1v3 and 2v3 argument that Prostaff85 mentioned.

By multiplying 'unrelated' events probability, the probability is being lowered. Each slam has a draw independent of the others.

I am looking at some other interesting Tennis 'coincidences' which have even lower probability. For example, the 1973 W is such an aberration to normal patterns that it has no logical explanations.

Excellent post by prostaff one 1/4000 just about says it all. That is more than just some coincidence especially when we se evidence piling in from statisticians who are looking at the draws.

Reckoner... this is what Socal is referring to. http://tinyurl.com/3e6ra4d

He also did an article on it.

But why would 3 majors risk draw rigging...if it came out it would cripple the credibility of the whole game...and their sales (the so called reason for rigging in first place) would plummet the following year.

In fact Laverfan let the record show that I was the first person who raised this issue and many people on this website kept denying that there was any evidence and kept calling me a conspiracy theorist. Well I feel vindicated.

Yes but social why would they take such a calamitous and obvious risk when suspicion would arise after 12/12? It doesn't add up for all 3 majors to be in collusion to do it.

socal this was noticed as it was happening - but hey take the credit if it means so much to ya!

lydian - because they wanted a nice final to show the gibbering masses

laverfan - you haven't really answered my last question. I get that you don't agree with the premise, but I'm sorry to say you aren't convincing me with the historical data you are producing as it is not close enough to what we are discussing.

I am quite happy to admit the possibility that the draws are not rigged, are you able to admit that people have good reason to be skeptical?

I can see why people are skeptical but I still think the risk far outweighs the benefit...it would be one of the biggest sporting scandals of all time and damage tennis to the very core.

I dunno - most people flat out do not care about such details... come on Tim!

What are you talking about reckoner I have been vocally on the record on this specific issues right here on this site. Now this is the second group of mathmeticians who are looking at this thing and calling foul. Actually 3rd group because Espn had their numbers sent to another statistician and peer reviewed.

And lydian, I ll tell you why they would mess with the system. They are capitalists who expending tens of millions in investment on wimbeldon or the USO their average ratings over five years in large ways impacts their TV contract. In order to get bigger TV contract they need Fedal finals and matchups. Also lydian those with the financial stake are not really monitored in anyway, there is little oversight and money involved.

socal1976 wrote:What are you talking about reckoner I have been vocally on the record on this specific issues right here on this site. Now this is the second group of mathmeticians who are looking at this thing and calling foul. Actually 3rd group because Espn had their numbers sent to another statistician and peer reviewed.

And lydian, I ll tell you why they would mess with the system. They are capitalists who expending tens of millions in investment on wimbeldon or the USO their average ratings over five years in large ways impacts their TV contract. In order to get bigger TV contract they need Fedal finals and matchups. Also lydian those with the financial stake are not really monitored in anyway, there is little oversight and money involved.

I'm saying that some of us may just have noticed that Federer and Djokovic kept on getting drawn in the same half before you posted a word. Tell me, did you invent the wheel too?

Hang on the ESPN study IS the one possibly credible study I was talking about, what's the other one then? Not that half baked Estonian one I hope lol.

Well estonians can do math and run statistical models lets not take a condscending Kiplingesque view of the world. Yes, but I was the first one to bring a source with two sets of credible statisticians looking at it. Of course we all noticed how bizarre it was and I mentioned it for years.

socal1976 wrote:Well estonians can do math and run statistical models lets not take a condscending Kiplingesque view of the world. Yes, but I was the first one to bring a source with two sets of credible statisticians looking at it. Of course we all noticed how bizarre it was and I mentioned it for years.

It should be obvious I'm not being condescending about the study being Estonian, just the quality of their study. Aren't you a lawyer?

Yes i am

Well the Estonian study's a bit flawed, don't you agree?

it would be nice if the people who continually denounced me as a conspiracy theorist and crack pot finally acknowledge they were wrong, but that is unlikely to happen on this site. Whenever I would mention the issue a certain section would vociferously attack it as conspiracy theorist nonsense. Now there are two seperate statistical analyses done by real statisticians that question the randomness of the draws. Frankly I told you so and a bag of chips.

As to the estonian study I don't know if it is flawed or not because math is not my area of expertise. But since it is the second study raising questions and the first study I did research the background of the people involved and the study by Espn was peer reviewed that lends the second supporting study more credence. The people who did the initial study and the third party that reviewed the statistical work were both highly respected. Now we see this estonian study looking at a different aspect and getting a similar conclusion. I haven't seen anything that cast doubt on their methods or anlaysis but since the ESpn study is out there and credible why would I automatically assume this second one is not credible.

socal1976 wrote:As to the estonian study I don't know if it is flawed or not because math is not my area of expertise. But since it is the second study raising questions and the first study I did research the background of the people involved and the study by Espn was peer reviewed that lends the second supporting study more credence. The people who did the initial study and the third party that reviewed the statistical work were both highly respected. Now we see this estonian study looking at a different aspect and getting a similar conclusion. I haven't seen anything that cast doubt on their methods or anlaysis but since the ESpn study is out there and credible why would I automatically assume this second one is not credible.

Ah well this was all discussed on a very similar thread, their methodology was a bit dodgy.

We need to separate the two study instances.

1. ESPN study focussed ONLY on USO from 2001-2011 to show the strength of the R1 opponents for the top seeds at USO was not as expected.

2. The Estonian Study (University of Talinn) focussed on the Federer vs Djokovic 12 vs 12 scenario, calling it in question.

These two studies have nothing to do with each other. The R1 ESPN study focussed on USO only. They did not raise any questions about the general draws.

The 'conspiracy' theorists have tied these two together.

The Estonian study has the big FO hole in it. Also, statistically, the 1-3,2-4 vs 1-4-2-3 (without using the names of associated players with each number) is evenly distributed.

This article focussed on 12vs12, not the ESPN study. I have provided examples of a consistent Top 4, in two different eras, Connors v McEnroe and Edberg v Lendl with 9 projected meetings.

Reckoner has stated that I am using a 'larger' time window to prove my hypothesis. I took 1974-2000 (27 x 4 slams) without any bias, unlike the 12vs12 hypothesis.

If there is a future consistent Top 4, this will likely happen again, as the statistal probability is already there.

Apart from Lydian's 'risk of tainting the sport' for ages to come (look at US MLB and the Steroids scandal which had George Mitchell - the Irish Peace Negotiator - was asked to be involved in), if the 12vs12 was actually rigged, how would the 'fixers' cover their tracks. No one would answer such a question.

To take a Cricket analogy, the whole match-fixing scandal which involved Hansie Cronje from South Africa (among others) is a much more prominent scandal which had player involvement. Football has it's fair share of similar instances.

The argument of 1/4096 is not debatable, according to Prostaff5. It would be non-issue if we had a new Top 4 every year with the same exact draw distribution.

I understand the skepticism expressed by posters, because large financial incentives are involved, that such actions are possible, and hence the whole establishment is rotten.

This has been equated to the Dubya War, which is politics, not sport.

Laverfan, the espn study didn't not simply focus on the USO, they USO men's and women's draw figure prominently because with a very high percentage of likelihood they determined that the USO draws in the first two rounds were not random. And they also found lesser problems but still very significant issues with the woman's draw at RG the last few years as well. At the other slams they found less convincing evidence in regards to the the narrow issue of the first two round draws for the top seeds.

The conspiracy theorists have not tied anything together laverfan, if you show that on some level the draws are not random and manufactured then both of these studies raise questions as to the randomness of the draw process as a whole. If they play with the first two rounds why would they not tweak the draw at the semi final level?

laverfan,

While I admire the effort you put into this (just trying to check a small portion of your data was painful), I do not think your examples are even all that relevant. I checked your Connors vs McEnroe example:

laverfan wrote:a. Connors vs McEnroe (9 projected meetings)

1979 - USO
1980 - FO, W, USO
1981 - FO
1983 - USO
1984 - FO, USO
1985 - W

So I looked at the period from 1979 USO - 1985 W and searched for all those slams where one of them was seeded 1 or 2, and the other 3 or 4, so that they would have a 50/50 chance of being drawn in the same half. This yielded 13 slams. Then I looked at how they were actually drawn:

1979 USO - same half
1980 FO - same half
1980 W - same half
1980 USO - same half
1981 FO - same half
1981 W - opposite halves
1981 USO - opposite halves
1983 USO - same half
1984 FO - same half
1984 W - opposite halves
1984 USO - same half
1985 FO - opposite halves
1985 W - same half

So, out of 13 cases, they were drawn 9 times in the same half, and 4 times in the opposite halves. Not quite balanced, but not particularly extraordinary.

All you did was throw our the 4 cases where they were in the opposite half and - surprise surprise - you were left with a "series" of 9 meetings.

What is your point? If your point is that the Federer-Djokovic "study" did a similar thing by throwing out FO, then that is valid. But there remains a significant difference. In the Federer-Djokovic case, they were drawn together 14 out 16 times (I do not like throwing out FO and quoting 12/12, but 14/16 is valid and it is still fairly unlikely to happen), which is far more extreme than 9 out of 13 times.

What exactly is the point you are trying to make?

laverfan wrote:

reckoner wrote:I suspect if you tried to find an exact like for like comparison from historical data it'd be very difficult?

I actually have a very well-known example. Laver v Rosewall 79-63 h2h. It pales Federer vs Djokovic completely.

I do not think this relates to Federer-Djokovic at all.

Federer-Djokovic is interesting not because they were drawn in the same half 14 times but because they were drawn 14 times out of 16 possible. If they had been drawn 14 times out of 28 possible or indeed 30 times out of 60 possible, it would be entirely uninteresting.

It is not the total number of times they are in the same half that counts, it is the lopsided nature of those draws. You do not see anything like that in Laver-Rosewall.

socal1976 wrote:it would be nice if the people who continually denounced me as a conspiracy theorist and crack pot finally acknowledge they were wrong, but that is unlikely to happen on this site. Whenever I would mention the issue a certain section would vociferously attack it as conspiracy theorist nonsense. Now there are two seperate statistical analyses done by real statisticians that question the randomness of the draws. Frankly I told you so and a bag of chips.

There are no studies that question the randomness of the draw whatsoever regarding the pairings of the top 4 seeds (where the seeds are numbers rather than names). The ESPN study did not even mention it or examine the method of the draw process for the pairings of the top 4, which is an entirely different method than for the initial process for the lower/non-seeds i.e. early rounds.
It would be incorrect (from a statistical and scientific point of view) to draw conclusions about one event from any studies that look at different events.

summerblues wrote:While I admire the effort you put into this (just trying to check a small portion of your data was painful)...

I am glad someone appreciates the effort...

summerblues wrote:What exactly is the point you are trying to make?

I removed the 4 opposite-half scenarios to make the 12vs12 and the 9 meetings comparable. If you assume 14/16 (87.5%). Then it is 9/13 (69.2%) in the Connors v McEnroe case.

Statistically 9 (CvM) or 12 (DvF) are not any different in the same half, are they?

summerblues wrote:...and it is still fairly unlikely to happen...

But you do not seem to discount the possibility, that statistically, it will happen.

summerblues wrote:...If they had been drawn 14 times out of 28 possible or indeed 30 times out of 60 possible, it would be entirely uninteresting.

You are willing to accept a 70-30 in the CvM case, but now want a 50-50 split in the DvF case. Is that fair?

socal1976 wrote:...they determined that the USO draws in the first two rounds were not random.

Remember it is only R1. There is no control over who gets to R2. Just ask Hewitt at W 2003.

socal1976 wrote:...if you show that on some level the draws are not random and manufactured then both of these studies raise questions as to the randomness of the draw process as a whole. If they play with the first two rounds why would they not tweak the draw at the semi final level?

This is the usual 'taint' theory. If they are not random, then it is easy to blame one or the other. I also find it interesting that if RG was found tainted on the Womens side, it was considered clean on the Mens side by the Estonian researchers. Should I not apply the same 'taint' theory and call both RG and USO tainted universally?

Mathematics of convenience in the Estonian case.

How about we include the FO and try and find 14/16 possible meetings in slams then? Much looser criteria, should be easier I'd imagine?

Fair comment reckoner.

On the other side how about we find a similarly stable top 4 for 4 year period through the Open Era...and occurences of when two rivals like Djokovic and Federer who were solidly in top4 but rarely seeded 1and2 or 3and4?

reckoner wrote:How about we include the FO and try and find 14/16 possible meetings in slams then? Much looser criteria, should be easier I'd imagine?

You are not happy with my 9/13 CvM?

69.2 < 87.5!

and 7 yrs vs 4...

Let me do some research. 50% < 69.2% < 87.5%.

Here is an example (from the Women's side - I do not expect the ATP/WTA argument. )

Graf v Sabatini (in Slams only)

1987 French Open Clay SF Graf 6–4, 4–6, 7–5
1987 Wimbledon Grass QF Graf 4–6, 6–1, 6–1
1988 French Open (2) Clay SF Graf 6–3, 7–6(3)
1988 US Open Hard F Graf 6–3, 3–6, 6–1
1989 Australian Open Hard SF Graf 6–3, 6–0
1989 US Open (2) Hard SF Graf 3–6, 6–4, 6–2
1990 US Open (3) Hard F Sabatini 6–2, 7–6(4)
1991 Wimbledon (2) Grass F Graf 6–4, 3–6, 8–6
1992 Wimbledon (3) Grass SF Graf 6–3, 6–3
1993 US Open (4) Hard QF Graf 6–2, 5–7, 6–1
1995 French Open (4) Clay QF Graf 6–1, 6–0
1995 US Open (5) Hard SF Graf 6–4, 7–6(5)

Grand Slam matches: Graf, 11–1
Grand Slam finals: Graf, 2–1

So 9 matches in the same half, 3 matches in the opposite half. That is 9/12 = 75% (closer to 87.5 ).

http://en.wikipedia.org/wiki/Graf%E2%80%93Sabatini_rivalry

Research continues.

PS: Instead of cutting and pasting it back here - just a link for this one - http://en.wikipedia.org/wiki/Evert%E2%80%93Mandlikova_rivalry

Grand Slam matches: Evert 10-3
Grand Slam finals: Evert 3-0
Grand Slam semifinals: Tied 3-3

So 10 out of 13 is 76.9% in a 6 year time span (1980-1986).

I am certain if I go back further towards pre Open Era, I will find a Mens and Womens equivalent. Time for the trusty Bud Collins.

that's over 8 years tho...

reckoner wrote:that's over 8 years tho...

I was editing, as you were posting. Please take a look at my edits.

well that is closer for sure... but hey laverfan, I feel bad about you doing all this research, please enjoy the sunshine or something!

reckoner wrote:well that is closer for sure... but hey laverfan, I feel bad about you doing all this research, please enjoy the sunshine or something!

Duly noted, . At least you are willing to discuss. Others may just be watching and reading.

Good crunching work LF...clearly Djokovic-Federer 4 year period is the stand-out but there are other examples as you are showing which come closer and show these runs have the chance of happening. I also think the chance for the Djo-Fed run is exacerbated by the top 4 hardly changing and as I say 1v2 and 3v4 not happening much as a ranking for Fed and Djo.

And on the other hand I just dont believe that 3 major TDs would collude in rigging draws...and they all happen to start doing it the same year too? Sorry its just too weird - and risky!

well as I say, while I think there's room for skepticism I am not convinced that all the draws are rigged. while it's a low probablitlity run of events neither study shows anything statistically conclusive and in the end it comes down to how you feel about it.

finding a historically similar case can be kind of a fun intellectual pursuit for those who like tennis stats so I hope that's the case in this instance!

I am willing to accept if there is a scandal. But apart from such 'flawed' theories, I would have seen it over the years. I can see the pro-circuit pre Open Era possibility, for whetting the public appetite, for generating money.

I can see Socal's 'money' argument as being valid, but the evidence is not there.

reckoner wrote:

finding a historically similar case can be kind of a fun intellectual pursuit for those who like tennis stats so I hope that's the case in this instance!

That is fun, you are correct.

Nice summary LF...its about evidence and what we have wasnt conclusive...or rather didnt prove the "theory" due to a few flaws.

Speaking of stats....LF, an interesting exercise is work on updates to court speeds across the main ATP events...but its hard work to get the facts. The ATP/ITF themselves dont do any work in this area - speed index they use is useless and not studied across all courts. The best metric is to examine numbers of %breaks (from service games) per event...theory being the faster the surface the harder it is to break, the lower the %. It worked extremely well in 2008-09 but havent seen stats for 10-11...would be interesting to see if the variance that there used to be is closing...to support the convergent surface homogeniety argument. A 2nd method is to examine no. of tiebreaks out of sets played...but tends to be a less reliable indicator.

laverfan wrote:you are correct.

Does that mean I get "a bag of chips" like socal?

reckoner wrote:

laverfan wrote:you are correct.

Does that mean I get "a bag of chips" like socal?

This is the best I can do.

we totally need an emoticon for "bag of chips"... but many thanks for the tasty beverage - it's Friday after all!

Edberg/Wilander meetings were fixed by the Riksdag.

NOTE TO ADMIN: More emoticons please...!

If people want to add want they'd like we can build a list...

1. Bag of chips
2. Broken record
3. Stats king
4. Yikes (more scared than the 'Shocked' one)

lydian wrote:NOTE TO ADMIN: More emoticons please...!

If people want to add want they'd like we can build a list...

1. Bag of chips
2. Broken record
3. Stats king
4. Yikes (more scared than the 'Shocked' one)

are these any good? would you believe these won't load on my browser... gah.