Chelsea Keep A Lower Profile.

Each team is now 12 games into their Premier League season for 2015/16 and teams are broadly placed where you might expect them to be.

A recent champion winning team, Manchester City top the table, closely followed by neighbours United and Arsenal.

A fallen giant in rebuilding mode, Liverpool lie mid table, but just seven points off fourth and recent struggling teams, Villa and Sunderland languish at the foot of the table along with two of the three promoted teams.

There are some surprises. Leicester appear to merit their lofty position, but the shock of the season so far is of course Chelsea's very public disintegration, both on and off the field.

Tipped by everyone to maintain, if not improve upon their championship winning season of 2014/15 they currently have less than a point a game in 16th.

Luck plays a significant role in deciding the outcomes of a small number of games in a low scoring sport, such as football. Not only in the traditional sense of injuries, red cards and refereeing decisions, but also the natural variation of shot outcomes.

There have been over a 1,000 attempts directed on target so far this Premier League season, ranging from high expectation chances, such as close range shots and penalties to speculative efforts from distance.

The actual points won and lost and goals scored or shots saved are simply one of the millions of possible permutations that may have arisen from these 1,000+ attempts. So we can see if Chelsea has reaped a reward that is consistent with their current plight by simulating not only Chelsea's on target goal attempts so far, but those in each of the 120 matches that have currently taken place.

Any league is intimately entwined and a side's current position, while primarily down to the probabilistic outcome of their own efforts, is also partly dependent upon how many points other teams have won in a particular iteration of the table.

Where's a doctor when you need one!

It seems sensible to compare the range of outcomes that may have befallen Chelsea based on their on target attempts over 12 matches to those that may have transpired for their main rival for last season's title, Manchester City.

While Chelsea chose to largely rely on the squad of players who won the 2014/15 title, presumably partly due to a favourable age profile, with many players either approaching or at their physical and technical peak, City boosted both their squad value and invested in relative youth by the purchase of Sterling and de Bruyne.

From the simulations, Chelsea may claim to have been slightly unfortunate. the 11 points they actually have is around three short of their most likely total of 14 points. But they are well below the deserved rewards that Manchester City could typically expect from their current shot profile.

The comparison between last season's pace setters in the present campaign is equally stark when we look at the range and likelihood of positions each team might currently occupy. The limits of Chelsea's aspirations so far is around 7th, which would merely disguise their precipitous fall, while it would be a surprise if City had fallen outside the top four based on their ability to hit the target and prevent their opponents from doing so at the other end.

Two final plots help to answer the "why" in Chelsea's downfall, although not the underlying reasons. In 2012/13, when Chelsea finished a respectable 3rd, they not only out-shot opponents, they did so from areas that had relatively high goal expectations.

Opponents had more on target goal attempts that had low chances of resulting in a goal (the red peak that dwarfs the blue, Chelsea peak to the left of the plot). And Chelsea's opponents where then swamped by a blue wave of high expectation efforts which carried an implied success expectation of 0.3 or greater.

This season, blue is definitely not the colour. Chelsea has been out-shot in attempts that carry an expectation of between 0.1 and 0.4 and are just keeping up with their opponents thereafter. The profile should it continue is very much that of a lower half of the table team.