The numbers that define the levels of performance posted by a team or individual over a period of time will be partly of function of their innate talent, but also partly dependent upon random variation around that true talent. The tendency is for exceptional performances, be it good or bad, to arise over limited time scales because of both talent and non repeatable bouts of randomness. Only by gathering copious amounts of data will true ability shine through the randomness, by which time we will probably have to also control for ageing effects. Our overall assessment of an individual's actual quality, therefore must always allow for the existence of potentially distorting amounts of random variation.
Even when success rates are known with absolute accuracy, random variation will make some coins appear more "talented" than others and in this post I looked at how easy it is to see, and over pay for noise instead of signal. Correcting for noise is possible when looking at player actions which have just two outcomes, a successful one or a failure. Save or shooting percentage are good examples of this. But as we move onto the contribution of randomness in team results, we have to allow for a third significant outcome in football, namely the draw. The most random of the three possible match outcomes.
The simplest way to outline the effects of random variation and team talent on league outcomes is to compare the distributions of points gained in a league over a season, where skill is an undoubted factor against a league decided by pure luck where the talent levels are identical for each team. It isn't quite a coin toss league (because there are three outcomes for each game), but the concept is the same.
I therefore simulated 380 game seasons for a 20 team league, where each team was the equal of the other 19 and home advantage was a fairly typical three or four tenths of a goal. To illustrate, rather than quantify the effect of the actual lop sided division of talent we see in the real Premiership I then compared the characteristics of the 100% Luck league to those of the actual EPL.
The scales have been maintained on each plot, so that the flatter, fatter tailed distribution for real live events can be directly compared to the entirely luck driven, theoretical scenario. To get a clearer picture of the differences involved, the final plot superimposes one plot on the other.
The two distributions have clear differences and the actual points totals achieved in the EPL show many more outstanding seasons being recorded by the big four teams than would have resulted by pure chance. The presence of a fatter tail in reality appears to indicate the clear influence of talent on the season long results recorded in the Premiership.
A feel for the differences can be illustrated if we compare 20 seasons of luck driven Premiership seasons with a similar number of real contests. Only a handful of teams have won the EPL title in reality, with Manchester United dominating, but in the extreme parity version hardly any team hadn't won the title. The most "lucky" titles won were three, compared to United's nine in three fewer attempts (well done QPR). Even Stoke lifted the crown as often as Manchester United (twice) in this egalitarian, altered reality. Equally relegation came almost without favour to all.
Points totals probably hold the most interest. The highest points scoring champions are Chelsea with 95 points compared to just 76 in a luck drive contest and champions overall gain an average of 86 points in reality, 20 points more than dictated in an even fight. At the other extreme, Derby's sterling effort in gaining just 11 points is a full 27 points below the average points total for team's finishing bottom of the "luck"