Warning: Anyone who has already had enough of the probability theory behind this in the above posts is advised to skip to the next post now! 

Just to expand on what Indiana said, the odds against do depend a lot on how you describe the 'coincidence' in question, which is why it is always a bit dodgy to do it after the event, though of course that's when it tends to generate the most interest for obvious reasons!

If we say "what is the probability that two given players who meet in R1 one week will be scheduled to meet each other twice in R1 and another time before the QFs in the next three tournaments they both play in, when one of them is seeded every time and the other one isn't seeded at all" (the "scheduled" bit sneakily avoids the need to estimate how likely they are to win their R1 matches when they don't play each other in R1!), then the answer is as follows:

(1/24) x (1/24) x (1/24) + 3 x (1/24) x (1/24) x (1/12)

The first term covers the case when all meetings are in R1 (we shouldn't exclude a possibility that would look like even more of a coincidence than what actually happened) and the second covers the case where one of the potential meetings is in R2, which would require the unseeded player to be drawn in the unseeded v unseeded match next to the seed's match in the draw, with the 3 x being needed because there are three different ways this can happen, i.e. the R2 meeting can be in week 2, week 3 or week 4.

That is about a 1 in 1975 chance, which is very low. However, there were 491 Futures last year (see http://www.itftennis.com/shared/medialibrary/pdf/original/IO_47105_original.PDF) with 16 R1 pairings in each one, so if you tracked each pairing over the next three tournaments they both played in, you might expect something like this to happen 'by coincidence' a handful of times per year. i.e. it's very rare, but not so rare as to suggest that the draws have been fixed.

But surely the odds of Gabb drawing evo in the first round must be 31 to 1,because Gabb could draw anyone because hes not seeded.

HossTheBoss wrote:

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But surely the odds of Gabb drawing evo in the first round must be 31 to 1,because Gabb could draw anyone because hes not seeded.

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If he's not seeded, he can't get drawn in any of the 8 slots the seeds go in, so he's got a 2 in 3 chance of being in a R1 match that doesn't have a seed in it and a 1 in 3 chance of drawing a seed, hence a 1 in 24 chance of drawing a specific seed.

 

HossTheBoss wrote:

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But surely the odds of Gabb drawing evo in the first round must be 31 to 1,because Gabb could draw anyone because hes not seeded.

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No, it is still 23 to 1 looked at that way round.  The chances are reduced by the fact that the seeds must be separated.

Imagine a 32 man drawsheet with the 8 seeds in place.  There are then 24 spots left to place the other non-seeded competitors.  Each can go into any of these 24 spots and there is a 1 in 24 chance that they will be placed with a particular seed.

There is basically a 1 in 3 chance of drawing a seed with a 1 in 24 chance of drawing a particular seed, and a 2 in 3 chance of drawing a fellow non-seed with a 2 in 69 chance of drawing a particular one of the other 23 non seeds.

edit :  ah, I got diverted and meanwhile Steven answered too.  Well, at least we agree   

-- Edited by indiana on Tuesday 21st of September 2010 09:50:41 AM

Early results wins for Milton cox coco Pritchard Evo a set up and 3-0 up

seagull wrote:

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Could it be the same 4 S/F's 3 weeks in a row?

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Well, it would complete the full set of possible semi final combinations for the four of them 

 

I'm sure those of you who like to play on the stereotype will enjoy speculating about what this tweet from Dan Cox means:  "Wrexham...what a place"