Monday 21 May 2012

Probability, Cup Hoodoos and Variance

The most prevalent of insights about statistics are lies, damned lies, and cliche. Among the more ubiquitous examples of the latter is the claim that you can use statistics to prove anything.

The problem here is that statistics don’t prove anything beyond that which they explicitly state. The demand of the human mind to look for patterns and meanings where none exist is what gives rise to the spurious worth with which statistics are valued.

An example: Pats have conceded less goals this season to date than at this point last year. The simplistic interpretation is that St Pats now have a better defence. There are however many other variables, and other questions which need to be answered before you make that assertion. Has the defence been playing against inferior strikers? Is goalscoring generally down across the league? Have the Shed End Invincibles intimidated referees so much at Richmond Park that they are reluctant to give decisions which may result in goalscoring chances against St Pats? None of these theories can be empirically proven, they are playthings of a subjective mind and the fuel for discussion among those with sufficient interest. 

The crux is that stats are not to be interpreted. They should not be used to ‘prove’ anything. They are to be accepted as ‘what is’.

So, the stats DON’T say Pats aren’t good at winning the FAI Cup. People say it.

What the stats DO say is that Pats last won the Cup in 1961, and have failed in 51 subsequent attempts. (Pedantic point number 1: Before you cry dunce at my mathematical ineptitude you should note that the League of Ireland season and the earthly calendar did not remain in perfect sync across that period).

Of course, it would be hard to argue down the hoodoo with any Pats fan who had set off on Cup Final morning with a song his heart and a feeling in his gut that this would be their year on any one of the half a dozen days since 1961 when the red and white ribbons were chucked in the bin while the Saints went marching off with runners-up medals. (Pedantic point number 2: Red and white ribbons would in fact have been used on the Cup when Pats were defeated by Derry in 2006 and also Shelbourne in 1996).

Pats’ cup record has been a reliable stick for opposition fans to beat them with. Rubbing salt in the wound is the fact that Sporting Fingal were formed, won the cup at their second attempt and disbanded all within a few years while Pats fans looked on shaking their heads at their ongoing inability to regain the trophy. 

Realistically, such records entirely are for the edification of media and fans. The record is ultimately a quirk of variance. It makes an easy reference point for the media when previewing or reviewing any FAI Cup game involving Pats. For the players, the management and the owners - I expect - club history matters very little. Most would be media savvy enough never to say such a thing in public, but you must ask yourself “What is a football club?”

It is difficult to reconcile that the Chelsea FC that I remember as a kid are now European champions. I think of Kerry Dixon, Pat Nevin, David Speedie and Gordon Durie, a decent side from the European Ban days who had their gems picked by other clubs and soon found themselves in the old Division 2. So too is it difficult to reconcile the struggling Manchester City teams - Mick McCarthy and Perry Suckling - with the star-studded Premier League champions. Surely these football clubs - though having the same names as decades before - are completely different entities?

The football club is different things to different people. For footballers and managers it is a vehicle for their ambitions, an opportunity to succeed, a stepping stone to further their career. Fundamentally their motivation is selfish. For owners, it is either an investment to turn a profit, or a rich man’s plaything, or rarely perhaps something more philanthropic. All the above are transient however, the only permanent fixture - in varying numbers - are the fans, the patrons, the supporters. They make the whole thing viable. The fans are the club. But they can’t pick the team, set the tactics, kick a ball, sell a player, implement a youth structure or impact the results one iota. We’ve all seen defeats where it looked like the fans hurt more than the players. (Pedantic point number 3: When the fans own the club this dynamic changes somewhat. Still investors are needed and day to day decisions are made by boards appointed by the fans rather than the fans themselves explicitly)

The League of Ireland transfer carousel is so absurdly active that the squads are almost reset each season. Year on year continuity of personnel is rare. Many players with FAI Cup winners medals have passed through Richmond Park over the decades, many have left St Pats and gone on to win their FAI Cup medals elsewhere. So too have managers left the club to win elsewhere the cup they could not bring back to Inchicore. 

Cup winning teams have a looser correlation with quality than league winners. It’s broadly accepted that the best team wins the league, but to win a knockout competition, “class” is less important. Few would argue that Greece were the greatest football team in Europe in 2004, nor were Denmark in 1992. What you need aside from a competent group of footballers is a few breaks, and a little bit of luck to come your way. The wind of variance in your sails is of more value than any world class striker.

Using a few convenient though sturdy enough approximations, let’s say Pats have been among the top 9 teams in terms of class every year since they last won the cup. Let’s also say that there is on average a 10% chance of each one of the top 9 clubs winning the cup, and we’ll disperse the remaining 10% among the rest of the field (bottom dwellers in top flight, the second tier and non-league).

If we accept that Pats - on average - have had a 10% chance of winning the cup, well they should have won the cup something in the region of 5 times since 1961. Shels, Bohs and Dundalk have done exactly that, Derry have four wins, as have Sligo Rovers. The ‘’other’’ Rovers’ numbers won’t make anyone here feel better, so we’ll move on, but I think the point is made - a prominent League of Ireland club should be looking at winning the cup on average once a decade.

If something has a 10% chance but only occurs one time in 52 trials or less than 2% of the time as with Pats cup wins - is something amiss?

Not at all. What we have is variance. This is the effect of how real outcomes deviate from expected outcomes. This is broadly why the European economy is heading to hell in a handcart. People made the wrong bets and were overexposed to unexpected outcomes - things that ‘’weren’t supposed to happen’’.

People get carried away by trends and make sweeping conclusions from small samples:

There was period where the Epsom Derby winner had ‘double’ third and fourth letters with surprising frequency:

1995 LaMMtara
1996 ShAAmit
1997 BeNNy The Dip

in 1998, GuLLand carried the hopes of many trendspotters over the finishing line.....some 10 places behind the wiNNer. A foolproof system for picking Derby winners? No, just variance.

The curse of the Superbowl coin toss is a telling case. Up to last year’s game the NFC side had won the coin toss 14 years in a row. Yes the 50/50 coin toss had been in the favour of one side on 14 successive occasions. This pattern has probability in the region of 1 in 16,000 of happening. A dud coin? No, just variance.

These outliers of probability have to exist, something must be on the edge, or else there is no edge. It’s just a little soul destroying when your football club is blighted with them. What is more reassuring however is that all these outliers of probability will eventually gravitate closer to their true expectancy as the number of trials increases. (Pedantic point number 4: this doesn’t mean that the probability changes, just that pattern of improbable outcomes is unlikely to continue).

So if the players are good enough, and the management savvy enough, and we acknowledge that the fans can’t influence things one way or another, then the hoodoo is debunked and Pats surely have as good a chance of winning the 2012 FAI Cup as any team that’s riding high in the league and facing non-league opposition in the first round.

So too, of course, is there a chance of being the “Pats-ies in a giantkilling act”. A sub-editors dream, but let’s not go there.

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