Football

As both my readers will know, I am a keen supporter of Norwich City FC, known to its fans as the Canaries, on account of their bright yellow strip. I can haz season ticket

and on any Saturday afternoon when the Canaries are playing at home, I am almost always there cheering them on.

Now, enamoured as I am of the Beautiful Game, I have started to wonder what it is that makes it so different, so appealing. The players themselves are not especially appealing. And notwithstanding inasmuch as which the recent elevation of Mr Stephen Fry, National Treasure, to the Board of Norwich City FC, the standard of invective from the spectators has hardly improved, despite my repeated bellowing from the River End that the referee is a Purblind Polypheme, the Antithesis of Argus, and so on and so forth in like fashion, and expressing my displeasure that so many home games seem to be a replay of Oedipus At Colonus, with the referee playing the part of the blind and tragic hero.

But I digress.

The reason, I deem, that football is so exciting is that the results are so unpredictable. Teams that might seem evenly matched on paper can come away from games with wide discrepancies of scores; it is possible for amateur underdogs to hold fully professional Premiership teams to account; and also for teams in generally good form to go down unexpectedly to an otherwise lacklustre opposition. Why? Because goals are so few. Because scoring them is so difficult. Because seemingly tiny decisions, by a player, or an official, can turn an assured win into a crushing defeat. Because a ball, kicked a smidgeon too soon, or too late, can smash into the net or careen off the crossbar, changing the course of a game, or a season, like the proverbial butterfly in Tokyo causing a wet weekend in Vancouver, to coin a phrase. That’s why we supporters can go from elation to despair to elation in the space of minutes, even seconds – even if the final result is a goalless draw (an outcome that baffles fans of games in which points are more freely given).

The number of goals scored in football matches can be modelled by the Poisson distribution, in other words what Wikipedia tells me is the ‘law of small numbers’ which

is the probability distribution of the number of occurrences of an event that happens rarely but has very many opportunities to happen

which seems to describe football perfectly. Teams have many opportunities to score goals, but rarely do so. In a now famous editorial in Your Favourite Weekly Professional Science Magazine Beginning With N, entitled ‘We Wuz Robbed’ (Nature 211, 670: 13 Aug 1966), John Maddox found much to criticize in the then-recently held World Cup competition (at which England triumphed). Maddox found that the numbers of goals scored in matches followed a Poisson distribution in which the expected number of goals was not significantly different from the mean of the observed scores. What does this mean? Essentially, that all the 32 teams in the final stages of the World Cup were, pretty much, evenly matched – on the basis of skill, no team stood a better chance of lifting the trophy than any other. ‘If it is assumed that the goal scoring potentiality of the two teams is equally well described by the Poisson distribution already specified,’ Maddox wrote:

the chance that the result will be a draw is a mere 0.27. In other words, if two teams are equally matched, the chance that the result will be an active injustice to one of them will be 0.73. By the same token, a team which is slightly less skilled than its opponent can nevertheless expect a one in three chance of winning the deciding match.

Maddox’s sense of unfairness was conditioned by his view that any proper competition should decide which of the teams is actually the best, rather than the luckiest. To this end, he advocated a number of changes to the rules, such that matches shouldn’t be restricted to ninety minutes, but should go on until the superiority of one of the teams is ‘properly established’ by a score of (say) three standard deviations over that of the losing side, or until both teams agreed on a draw. To avoid trying the patience of the spectators in games requiring the scoring of dozens, if not hundreds of goals, alterations would have to be made so that goals would be easier to score. Maddox came up with two suggestions:

Such a change could easily be brought about, possibly by widening the goalposts or by abolishing goalkeepers.

While I am deciding whether I agree with these provisions or not, in that they might make watching football a whole lot less emotionally charged, and therefore much less fun, notwithstanding the welcome avoidance of the travesty that is the penalty shoot-out, I must perforce ruminate on the current situation at Carrow Road.

It is long since the Canaries were in the Premiership (the old Division One). Two seasons ago they crashed out of the Championship (Division Two) but spent just one season in League One (Division Three) before being promoted once again to the Championship, where they are now. They’ve had a good season, so far, staying in the top third of the Championship, with a decent shot at being promoted back to the Premiership next season. The last two home games, however, have been dismal. They only managed a draw against struggling, injury-prone Doncaster Rovers. Another draw, against bottom-of-the-league Preston North End, while a more exciting game of football, was likewise a disappointment.

Their performance at away fixtures has been more heartening, and they are playing away tonight, at Leicester City, a team revitalized by the stewardship of erstwhile England Manager Sven Goran Eriksson. My prediction? Well, in view of Norwich’s recent performance at away matches, I’d expect a win.

But a canny manager would always say that you’re only as good as your last match, that this is a game of 22 players – and that in view of the hard logic of the Poisson distribution, no matter how finely one judges the relative performances of teams in earlier encounters, the current game will be end-to-end stuff and could go either way. Teams are much more evenly matched than their relative rankings in the league table would suggest. The fortunes of any team can turn on a hair. Perhaps that’s why football managers are paid so much. And why footballers – and fans – are so superstitious.

UPDATE: Norwich has just beaten Leicester 3-2. On The Ball City!