Mick Hartley

So now there are four English teams through to the Champions League quarter-finals. I’ll admit that I’m not very strong on probablities, but as a kind of geeky exercise in brain power – I should be able to work this out – I was trying to calculate the chances of four English semi-finalists – which would of course require that each English team is drawn against non-English opposition.

In Friday’s draw, the first team out of the hat will have seven possible opponents. After the first pairing, the next team out will have five possible opponents. Then the next team will have three possibilities, leaving two at the end. That makes 7 x 5 x 3, equals 105 different combinations – obviously ignoring stuff like which team is at home first in each of the ties. 105 – is that plausible? Have I done that right?

Anyway, next step: how many of those 105 meet the criterion of producing four English vs. four non-English ties. First out of the hat – say it’s English – has four non-English possibilities. If that works out, next out of the hat has three non-English possibilities. Then two. So….4 x 3 x 2 equals 24. Out of 105 possible draws, 24 would give us the desired four English vs. non-English. Which is about 23%. More doubts creep in at this stage. Have I made some unwarranted assumption somewhere? – for instance when I assume the first out of the hat is English? I don’t see why, but my poor record on probability calculations does make me wonder.

Whatever – 23% seems intuitively plausible. Of course it’s a whole other question as to the chances of all four English teams then winning. The likeliest outcome would be for whichever poor sods drew Barcelona to miss out, with the other three having better than even chances.

What about the worst possible outcome in the draw: two all-English quarter finals? First English team drawn has three possible English opponents. But then for each of those three combinations there are three different possibilities of how the other teams combine – making 3 x 3 equals nine. Which is 8.6%.

Which would mean the other alternative – one all-English tie, two English vs. non-English ties, and one all non-English, is by far the likeliest possibility, at about 68%. If I’ve done the maths right – a big if.

Fascinating, eh?