Fix!

101 Great Goals asks: Was the FA Cup draw fixed?
Certainly, it's nice for the FA that there's a chance of a Manyoo-Money Launderers final. But this could have happened by chance.
What's more suspicious is Chelsea's progress in the Cup, in two ways:
1. They've had four home ties. The chances of this happening by chance are 0.5 to the power 4 = 6.2% (1 in 16).
2. Their first three ties were against lower-league opposition. In the third round, they got Macclesfield from League 2, when there were only 12 teams of 63  from League 2 or lower in the draw. In the fourth round, they got Forest from League One, when only 8 of 31 other teams in the draw were League One or lower. And in the fifth round, they got Norwich, when there were only 6 of 15 teams from the Championship or lower.
Though the probabilities of such easy ties coming out of a fair draw were reasonable in each round, they multiply to yield a low probability over the three rounds: (12/63) x (8/31) x (6/15) = 1.96%.
The chances of three home ties against such lower opposition are just 0.2%  - 1.96% x 12.5% - or 1 in 500.
This is very low for a random process, so it  should ring alarm bells.
Or should it?
First, the FA Cup draw consists of loads of chance events. Some combinations of these will look unlikely. But because there are so many unlikely combinations, some are likely to turn up. If you test enough hypotheses,  some will look statistically significant. Had things turned out differently, I could be raising suspicions about Manyoo's or S***s' draws.
There's a parallel here with the Drake equation (not, alas, named after Ted, the former Chelsea manager). It says that the probability of life on any given planet are minuscule, but because there are so many planets, life elsewhere is almost inevitable.
Second, we shouldn't judge processes merely by outcomes. The fact is that to rig the draw would require buying the silence of lots of people, such as the ex-players drawing the balls, which is unlikely.
There's a message here about economic inequality. Even fair processes can occasionally yield outcomes that look suspiciously unfair.

Comments

[Bryan Appleyard]

Well quite, but that's not all there is to the Drake Equation. Drake wasn't saying there was life on other planets, only that, in order to establish the probability, certain things needed to be known. In the case of the FA Cup the great unknown is: will Mourinho still be at Chelsea for the final.

[dave heasman]

And Ted Drake didn't "just" manage Chelsea. He scored 7 goals for Arsenal in one match. I'd like to have seen that, preferably last week.

[jameshigham]

Takes some wading through but you appear to be on to something here.