### UEFA's Cold Balls

There's an excellent rumour going around that the Champions League draw was fixed. Just google "Champions league draw fixed" like I did and you'll get the flavour. What appears to be beyond dispute is that at 10.28am yesterday someone posted this on a Liverpool Echo football forum :

"Rumour going around draw has been leaked….. this is no doubt rubbish but if Rumour is true it’s LFC - arsenal and Chelsea - fenerbache and manure v roma. No bookies will take bets on the draw either……. "

The bookies bit is a red herring because none of them take bets on Cup draws ever. As much as I'd like to cry foul, I suspect this is just coincidence, exacerbated by our old friend hindsight bias. How many posts like these have been made over the last 10 years, to be forgotten within a day because they were wrong ?

As a nerd though I am interested in the actual odds against one person guessing this correctly in one go. Not least because I once Emailed Football 365 after a suspicious Euro Championships playoff draw in which the four higher ranked teams were all drawn against the four lower ranked teams, with the higher playing away first. One of F365's football writers quoted my odds from the Email, only for a slew of follow-up Emails to arrive the next day pointing out that I had botched the calculation.

When I googled as above, I picked up various answers of 63-1, 119-1, 191-1 and "less than 1%". The later being a more sensible line to take (although not as sensible as avoiding the odds question entirely). I reckon those are all wrong and it's quite simple. One ball is drawn. The second must match the first as predicted, probability = 1/7. Then the third ball, which could be anyone. Fourth must match the prediction, 1/5. Fifth, again could be anyone, sixth must match, 1/3, last two fall into place. So I make it 1/(7*5*3) or 104-1. Any more offers accepted in the comments :-)

"Rumour going around draw has been leaked….. this is no doubt rubbish but if Rumour is true it’s LFC - arsenal and Chelsea - fenerbache and manure v roma. No bookies will take bets on the draw either……. "

The bookies bit is a red herring because none of them take bets on Cup draws ever. As much as I'd like to cry foul, I suspect this is just coincidence, exacerbated by our old friend hindsight bias. How many posts like these have been made over the last 10 years, to be forgotten within a day because they were wrong ?

As a nerd though I am interested in the actual odds against one person guessing this correctly in one go. Not least because I once Emailed Football 365 after a suspicious Euro Championships playoff draw in which the four higher ranked teams were all drawn against the four lower ranked teams, with the higher playing away first. One of F365's football writers quoted my odds from the Email, only for a slew of follow-up Emails to arrive the next day pointing out that I had botched the calculation.

When I googled as above, I picked up various answers of 63-1, 119-1, 191-1 and "less than 1%". The later being a more sensible line to take (although not as sensible as avoiding the odds question entirely). I reckon those are all wrong and it's quite simple. One ball is drawn. The second must match the first as predicted, probability = 1/7. Then the third ball, which could be anyone. Fourth must match the prediction, 1/5. Fifth, again could be anyone, sixth must match, 1/3, last two fall into place. So I make it 1/(7*5*3) or 104-1. Any more offers accepted in the comments :-)

## 2 Comments:

At 8:47 PM, Anonymous said…

Your calculation right, as far as I know.

Of course if they picked the draw in the right *order* it's around 40000-1, which is longer even than Schalke's odds of winning the thing.

At 11:31 AM, peterbirks said…

Your calculation is correct. For four teams there are 3 possible combinations of pairs. For teams there are 15 combinations. For 8 teams there are 105 combinations. Note that your 3-5-7 sequence is in play here. So, extrapolating, for 10 teams there would be 945 combinations (105*9); for 12 there would be 10,395 (945*11); for 14 there would be 135,135 and for 16 (the fifth round of the Homebase FA Cup, or whatever it's called these days) it would be 2,027,025, although I haven't checked those numbers.

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