Are these draws rigged or am I being paranoid? probably stupid question about maths

[Barnabas]

In tennis, since 2007, the best 4 players in the world have been Rafael Nadal, Roger Federer, Andy Murray and Novak Djokovic.

The number 1 and number 2 players are always placed on the opposite sides of the draw as to allow them to meet in the final.

Number 3 and 4 are placed randomly, and can end up in any half.

in the last 13 slams Murray has been placed in Nadal's half and Djokovic's in Federer's half. It has even has happened in the last 2 Slams with Federer being number 3 and no longer top 2.

Are they rigging the supposedly draws? Or are the 13 times in a row this has happened just an imaginary pattern like people who select random on their mp3 player and feel that the mp3 player plays some songs more often than others?

When does a chance becomes small enough as to make somethiing suspicious?

[Dauphin]

French Open 2010?

[Traianvs]

The question is rather: who the hell cares?

[BlackCat]

The question is rather: who the hell cares?

Well, you apparently cared - if you didn't, you wouldn't have posted in this thread

[Flubber]

Number 3 and 4 are placed randomly, and can end up in any half.

?

Are you sure this is the case. When I helped at a tennis tourney (kids level stuff) we seeded eight and the rules were that seeds 1,4,5 and 8 were in one half and 2,3,6,7 in other and in fact they were placed so 1 would meet 8 before the winner of that would meet the winner of 4 and 5 etc etc.

I am not saying you are wrong for the pros-- I haven't checked but if they were following this fairly standard type of seeding and the rankings were fairly static for a while, you could have a situation where tourneys looked much the same with respect to top end placement repeatedly.

I just don't think that 3 and 4 are placed randomly

[MikeH]

It's a bit unlikely... but not that suspicious.

And 3rd and 4th are picked randomly into top or bottom half, but those players have swapped ranking places over that time. So the same pairing can be 1 vs 4 and then the next year 1 vs 3...

[MikeH]

For most of this time this has been a 50/50 coin toss, so the probability is only 1 in 8192, which isn't at at all unrealistic.

[Kuciwalker]

The important thing is that this 1 in 8192 compares favorably with the number of phenomena you might have observed and thought "hmmm, this is strange".

To clarify, the idea is that you are constantly exposed to random patterns. Some of these will be very improbably streaks. If you observe 8192 patterns then you wouldn't be surprised to see one that has a 1 in 8192 probability.

[MikeH]

Exactly.

Humans are keen to attribute some hidden meaning to things that are actually not all that unusual, and we tend to like to think there must be some reason behind things that are perfectly likely.

[Flubber]

In tennis, since 2007, the best 4 players in the world have been Rafael Nadal, Roger Federer, Andy Murray and Novak Djokovic.

The number 1 and number 2 players are always placed on the opposite sides of the draw as to allow them to meet in the final.

Number 3 and 4 are placed randomly, and can end up in any half.

in the last 13 slams Murray has been placed in Nadal's half and Djokovic's in Federer's half. It has even has happened in the last 2 Slams with Federer being number 3 and no longer top 2.

Are they rigging the supposedly draws? Or are the 13 times in a row this has happened just an imaginary pattern like people who select random on their mp3 player and feel that the mp3 player plays some songs more often than others?

When does a chance becomes small enough as to make somethiing suspicious?

Hmmm I looked up the ATP rules and it is inaccurate to say that seeds 3 and 4 are placed "randomly". Using a 64 player competition, they will be placed in position 17 and 48 with the first drawn of the two players going into slot 17. So it is impossible for a top 4 seed to meet another top 4 seed before the semis.

But to the meat of your question. This does render the result you have observed to be somewhat unlikely but in each individual event you might have 62 other players each with a 50/50 chance of being in the same half as the number one seed. With such numbers of players I would think streaks are common. In fact it would be UNCOMMON if there were not a player or players with streaks of say 7 times straight on the same side of the draw as some other given player. I wonder what the probability would be that no player would have a streak of 13 in a row on the same side of the draw as some other player?

Obviously the circumstance of the 3 and 4 seed is more noticeable . MY question on any "fix" theory are the following

1, who benefits?
2. Is not the draw done on an event by event basis and thus would involve numerous different people every time?
3. THis is obviously something that gets noticed at the top end so would not this be a particularly clumsy sort of "fix"

[MikeH]

Yeah, they are placed in 17 or 48, but it's random which of those two slots they go into. Hence random which of the top two they face.

[Dauphin]

In the French open 2010, Murray was on the other side of the draw. The streak didn't happen as barnabus described.

[MikeH]

ha. I almost checked the data... but couldn't be bothered.

[Barnabas]

it almost happened 13 out of 14 times :P

Thanks for the answers

[Dauphin]

I think the French Open in 2008 or 2009 also had Murray on the other side as Nadal faced Djokovic in a semi. So not quite. But the points made above still hold.