Friday, 18 April 2014

Luck Can Make An Average Team Appear Special.

It is very easy to be drawn to extreme performances, either good or bad when looking at the analytical side of football. Exceptional performance stands out, is always highlighted in the media and talked about by the fans. It's difficult not to get carried along.

Liverpool's title charge and the consummate ease by which Crystal Palace cruised to 40 points, of course is partly down to the expertise of their respective managers, fans and players, but it is also likely that random fortune also pushed their sides higher, as well.

The temptation, though is to look for the cause to the effect and ascribe 100% of the former to the latter. But the praise is rarely fully deserved and the criticism is often unduly harsh when expected success fails to arrive promptly.

One way to avoid the almost irresistible rush to narrative, is to start with a singularly anonymous team, one that, for a season,at least is steeped in mediocrity. 52 points with a barely positive goal difference has been the average seasonal performance of a Premiership team over the last decade and the Spurs team of 2004/05 exceeded no one's expectations by recording this benchmark.

The side Martin Jol inherited mid term from Jacques Santini finished 19 points clear of the drop, 43 points from the summit, reached the 6th round of the FA Cup before losing to Newcastle and the 5th stage of the league cup before bowing out to Liverpool, despite taking the first kick in the penalty shootout. They failed to defeat any of the then Big 3 of Arsenal, Chelsea or Manchester United and their 52 points were exactly in line with expectations from their pre-match odds over the 38 games.

So the 52 points gained by Spurs in 2004/05 probably reflected the most likely outcome for a team of their ability playing in that season's Premiership. It is a comforting occasion when theory and reality combine to give the illusion of control without the appearance of outlying products of talent and a lop sided portion of random chance.

The range of possible outcomes from a group of games is most easily demonstrated by simulating seasonal outcomes using strength of schedule adjusted match odds. The usual method projects the range of league points that might be posted by a side of say Spurs talent once the vagaries of random chance are given full rein by continual repetition. However, it is a simple process to break down a team's match probabilities into individual slices that quantify the chances of winning or losing by a particular margin.

So alongside the usual range of points projections, we can add another commonly used statistic, namely goal difference.

How Likely Winning or Losing Margin Varies with the Chance of Winning the Game Outright.

Chance of Winning the Game. 65% 46%
Winning By a Margin of 1 25% 24%
Winning By a Margin of 2 20% 14%
Winning By a Margin of 3 12% 6%
Winning By a Margin of 4 5% 2%
Losing By a Margin of 1 10% 17%
Losing By a Margin of 2 3% 7%
Losing By a Margin of 3 0.8% 2%
Losing By a Margin of 4 0.1% 0.5%

Spurs' cumulative points expectation from the individual match odds for all 38 league games in 2004/05 was that they would get 52 points and typically that would result in a goal difference of small, single figures.

However, just as it is possible, but highly unlikely that an average side could either win or lose all 38 matches, a single iteration may see a side of Spurs' 2004/05 talent deviate from their expected average and in doing so produce atypically higher or lower goal differences.

The most likely goal difference is indeed centred around zero, but there is also a reasonable chance that our league average side might record multiple years when their goal difference drops well into negative double digits or rises to similar positive heights.

If we take the 2004/05 season as a benchmark, Spurs' range of possible goal differences only begins to peter out as they record values matched by Manchester United, who finished 3rd at one extreme and Norwich who were relegated at the other.

Even with thousands of repetitions, sample sizes start to fall as we look at the spread of actual points recorded by the same goal difference. But the spread of points gained with the same goal difference, in this case -2, is similarly wide, if slightly less well defined, falling into the low 40's and as high as the early 60's. If we again look at the 2004/05 season, Everton recorded a goal difference of -1, but won 61 points.

If average Spurs, mk 200405 can produce an impressive array of goal differences from the same talent base and an equally diverse range of league points from seasons with identical goal differences, the random walk should also be apparent within individual seasons.

Below are two final plots that trace individual seasons taken from just a couple of dozen simulations using our generic, average team and patterns and trends, that could be easily mistaken for real changes within the team are readily apparent. Even though they have been generated from the same game odds, used in an identical order.

The first graph could easily be depicted as a promising start that stalled after around a dozen matches and then got progressively worse as the side stumbled over the survival finishing line, before the season ends on a low point and four consecutive losses.

While the second plot, again drawn from the same match probabilities, show an almost polar opposite. A poor start is gradually arrested and followed by an impressive second half of the season, containing a 12 game winning streak and likely  UEFA Champions League qualification, probably in the first qualifying round.

Two very different outcomes to essentially the same talent laden season, made possible by the random distribution of rewards in a short 38 game period.

Fortunately, even when we try to chose a mundane, everyday side to illustrate how the same talent base can produce very different results, an event often intervenes to proved a potential narrative where none really exists.

Santini left to be replaced by his assistant, Jol after 12 matches. Jol's first match in charge was a 4-5 loss at home to rivals, Arsenal. And each of these graphs provides convenient inflexion points at or around 12 matches and it would be incredibly hard to resist attaching the cause of a managerial departure to the effects seen in either plot.

Even if we knew that both were merely produced as one possible reality out of many with the help of a spreadsheet.

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