Graphic: chances of winning the FA Cup

In the film Amadeus, the young priest sits nervously with the old Salieri as the composer spends his last days in an asylum. “All men,” the priest informs his bitter companion, “are created equal.” A shadow crosses Salieri's face as he recalls the brilliance of Mozart. And with heavy sarcasm he replies: “Oh, are they?”

The arrival of the FA Cup third round has been heralded by an inspired and striking set of advertisements. A milkman, dressed for work, jumps over a Barclays Premier League player. “All men are created equal” the advert proclaims. “Oh, are they?” I reflected bitterly.

You see, brilliant though they are, the ads confuse two things. They confuse equality with randomness. All teams are not created equal and the FA Cup does not make them so. What is, however, true of the cup is that anything can happen because there is randomness in results.

The Fink Tank knows this because Dr Henry Stott, Dr Ian Graham, Dr Mark Latham and I have played the entire FA Cup tournament 100,000 times. When good teams play bad ones, the good ones tend to win. However, this is not a certainty, merely an overwhelming likelihood. When you have a lot of games, those tiny chances of an upset add up. In any one game the chance of a giant killing may be low. In an entire tournament, the chance of an act of giant killing is so large that it would be amazing if it did not happen.

When Barnsley knocked out Chelsea and Liverpool last season this was ridiculously unlikely. But take the chances of every amazing result together and the chance of one astonishing upset is really big.

Perhaps I should give you an example. Taking the goals and shots on goal during the past two years by all the teams left in the FA Cup, the Fink Tank is able to rank them and determine the probability of different outcomes when any two sides meet. We are then able to simulate the tournament 100,000 times. Why do we do this? Because the chances, say, of Arsenal winning the cup are dependent on, say, Manchester United's progress. So you need to look at each team's chances, taking every other side's chances into account.

In the third round we defined a giant killing as the defeat of a club by a team in a lower division. Some of these acts are hardly surprising. Leicester City, of Coca-Cola League One, are favourites against Crystal Palace, of the Championship, for example, while Scunthorpe United, of League One, are favourites to beat Watford, of the Championship.

Altogether, the chance of at least one giant killing in this round is 99.69 per cent. There is a 0.31 per cent chance there will not be one.

For all of this, though, we are of the view that the prices at the bookies overestimate the (in any case pathetic) chances of the long-shot teams winning the cup. And they seriously underestimate the chances of the Cup being won by Manchester United or Chelsea. There is a 78.3 per cent chance of the cup being won by one of the “Big Four”. Beyond this, the chances are evenly spread.

Essentially, if all the big boys go out, any of the Premier League teams have to fancy themselves. Just for reference, Portsmouth have a 1.3 per cent shot of retaining the trophy, which shows you how improbable (but magnificent) last year's triumph was.

For the non-Big Four clubs the draw matters. It does so even more for the Big Four, so anxious are they to avoid one another.