How bad are Charlton in the Cup?

How I done the sums

Like every Charlton fan, particularly after Saturday's embarassment, I assume that Charlton are uniquely awful in the F A Cup. Since the 1999/2000 season, the length in ties of their involvement in the competition has been as follows:

4, 2, 2, 2, 1, 3, 4, 1, 1, 2, 1, 3, 3, 1

To put it another way 5 times out of 14 they've gone out after just one tie.

How bad is this, statistically speaking?

Let's make the simplistic assumption that on average, a team has a 50% chance of winning any cup tie. This isn't true, but it's a starting point.

On that basis, Charlton should have won 7 of their first tie fixtures, but they actually won 9. Hmm, not bad.

If we go on to the second round, and again assume an average 50% chance of winning, there's a 25% cumulative chance of winning both ties. Charlton have won their first two rounds 5 times, which is more than 25%.

The chances of winning the first three rounds - the best Charlton have done in the period - are 12.5%. Charlton have actually managed about 14%.

But, dear reader, can you spot the flaw in my reasoning? The point is that if you are a premier league team, or in the third tier, your chances of winning your first match should be higher than 50%, because there are so many lower level teams in the draw for that round. When you factor that in, it's likely that Charlton have underperformed in the Cup, but not by very much.

A good run in the Cup is a rarity for all but a few top teams, and is statistically unlikely. Charlton's cup performance isn't uniquely awful, and maybe we just need to lower our expectations.