Friday, July 29, 2011

Football and Luck

Those of you who don't like soccer or numbers can look away now. This really don't concern you.

Last season I played the Premiership fixture list using a coin toss. I used a simple system. Heads was a goal; tails wasn't. I tossed a coin for each team until I got tails, then I stopped. Form and home advantage were ignored. So a fixture would have a result:

Villa: heads, heads, heads, tails = 3
Birmingham: tails = 0


Arsenal: heads, heads, tails = 2
Chelsea: heads, tails = 1

I know it's sad and you think I have too much time on my hands but I get time off and am alone a lot.

What I wanted to find out was the range of points totals produced simply by luck.

The outcome? Well I'm glad you're still with me and interested. It's fascinating isn't it? To win my league required 67 points. The four champions league places were achieved with 67, 65, 61 and 61. The three relegated teams got 31, 37 and 41.

In effect this gives us the monkey mark.

So now we look at the real league table for 2010/11. We discover that the top four, Man Utd, Chelsea, Man City and Arsenal all achieved more than 67 points. They were above average and outperformed the toss of a coin. We probably knew that. Our top four teams were a cut above all the rest.

The three relegated teams all got more than 31 but less than the safety mark of 42 in the, excuse me, tossers league. They were below average and would probably have done better if they had resolved their games on a coin toss.

Everyone else was very average and luck probably played a part in the order teams 5 -17 finished.

In case you are interested Wigan won my league and Man Utd, West Ham and Wolves were relegated. I tired hard not to put any bias into my tossing apart from exercising a deep hatred of Wolves. West Brom finished second. Needing to win their last game to clinch the league they lost 1-0 at home to Man City.

There were far more draws, especially 0-0 draws in my system. It follows, since tails-tails will happen, on average, every fourth time.


Jonathan Potts said...

This is actually very close to the sort of thing I do professionally - except I look at animal movements rather than football (and using maths rather than actually sitting tossing coins repeatedly). E.g. how far does the movement of a particular animal deviate from a random walk (turning angles and length of straight-line movements determined at random)? Maybe you missed your calling as an interdisciplinary statistical physicist, Steve?

St said...

Jon, the older I get the more callings I realise I missed. I have to try and avoid getting interested in new things these days or I get hooked. Statistics has, as you know as a regular reader, always been one of my things.

Chris Pettifer said...

Sounds like there was scandal during your football season with lots of thrown games.

RuthJ said...

OK, I took a bet with myself that all three comments on this post would be by blokes, but I am stymied by Chris's gender-neutral name. So I'm betting he's a he.

Maybe that is a sexist viewpoint, or maybe it is just realistic. Either way I have spoilt the statistic with this post.