Goal Difference and League Points.

One of the most analysed seasons by a side in recent years is the 2011/12 campaign by Newcastle, where Alan Pardew's side narrowly missed out on Champions League football, despite a goal difference of just +5, but with an accumulated points total of 65. It was an improvement from 2010/11, when they had finished below mid table and with a negative goal difference.

Their 2011/12 season begged two questions. Firstly, had the quality of the squad improved sufficiently to merit the seven place jump in finishing position and secondly, could a side that had outscored their opponents per game by the slimmest of margins, expect to amass so many points?

Improved team quality can be answered in hindsight. Tim Krul established himself as the first choice keeper in 2011/12 and new arrivals, both attracted and continue to attract transfer interest from the likes of Chelsea and Arsenal. So the improved results was probably no false dawn, they were a better side than they had previously been. But of more interest from an analytical viewpoint was the use they put to six fewer goals they conceded compared to 2010/11.

The rate at which sides score and concede goals over a season is a clear and obvious indicator of how successful they will be and this can be demonstrated by the strong correlation between goal difference and end of season points accrued. Inevitably, some teams will be lie above the line of best fit and some below. Although a side may have a large influence on their scoring rates they are unlikely to be able to call on goals or clean sheets at will. Therefore, the partly random way in which goals in each team's matches arrive may randomly influence the rate at which a team wins or draws games.

During the 38 game Premiership era, nine teams have finished with a goal difference of five as Newcastle did in 2011/12 and the average points gained by all nine teams was 56. Very close to the line of best fit. However, the range of points totals experienced by these sides spanned 19 points, from Newcastle's high of 65 to a low of 46 by Spurs. So Newcastle's lucky season is apparently counterbalanced by Spurs' unlucky distribution in 2007/08.

Similarly, nine sides has also finished with a goal difference of minus five, again the average points gained is close to the line of best fit at 46 and the range between best and worst points totals is 14 again nearly a third of the average. So it isn't uncommon for teams with identical goal differences to record relatively large differences in final points at the extremes.

Newcastle have taken part in seventeen 38 games seasons in the Premiership and their points total has over and under perform against their actual goal difference almost equally. They have over performed in eight seasons and been below par in nine. So there is no reason to suppose that they have a tradition of squeezing out the most from their goal stats, although playing staff and managers will of course change.

We can further look at how Newcastle's distribution of wins and losses in 2011/12 differ from the typical range of winning margins we might expect from a side that has a finishing goal difference of 5. Or more particularly, to account for goal environment, scored at an average rate of 1.47 goals per game and conceded at 1.34 as Newcastle did.

From the plot, Newcastle managed almost twice the number of two goal victories compared to the average expectation for a team that posts a goal difference of 5 over the season. To maintain that goal difference, they must be involved in more high scoring defeats than usual and the goal trading is illustrated in the larger than expected number of heavy defeats/smaller than expected narrow defeats and lack of wins by four or more goals.

Ideally a side would wish to concede all of their seasons goals in a handful of heavy defeats, leaving the goals they did score to gather points at an efficient rate. The "extra" points Newcastle achieved by producing a watered down version of this ideal left them on the edge of qualifying for Europe's premier league and knockout competition.

However, the less heady historical experience of teams which outscored their opponents by a similar margin, also suggested that random variation was more prevalent than intent. Squad turnover and the power law that dictates the length of managerial tenure in the Premiership gives us limited samples to test if a Pardew led Newcastle can over perform the usual relationship between points and goal difference.

Manchester United's 2012/13 title winning season was a similarly impressive outlier. A goal difference of +43 on average amasses just under 80 points, whereas Sir Alex signed of with 89 and a similar plot for their frequency of expected margin of victory or defeat graphically highlights where United claimed their "extra" batch of points.

Fewer draws, fewer large margin wins and losses, saw the surplus goals tumble down into creating almost twice as many single goal margin of victories than a side with such a goal difference would on average accumulate.

Unlike Newcastle, we do have a long history of stable management at United, although player churn does remain, so this this caveat in mind, we can see if there is a history of continual over achievement against goal difference at Old Trafford. A sign that there may possibly be causative actions working alongside random variation.

In twelve of the 18 twenty team Premiership seasons, United have gained more points than you would expected from the linear relationship that appears to exist between goal difference and league points, including nine of the last eleven seasons. This makes United the most frequent over performing team of the last 18 seasons, lying around two standard deviations away from the average percentage of over performing seasons of all teams with at least 10 years worth of matches.

Newcastle were widely predicted to regress after their exceptional 2001/12 season, and under the added burden of Europa League football, they duly obliged, in terms of points gained, at least. When measured against goal difference, their 41 points from a record of 45 goals scored and 68 conceded was four more than an average side could expect. So far this year, they are three points ahead of their goal difference expectation.

Newcastle may have failed to consistently perform at the level they appeared to show in 2011/12, but they have still have enjoyed the luck of the draw in terms of where and when goals have arrived in their matches.

In similar vein, United's luck has continually been predicted to turn, although their over-performance stretches back into the '90's and it may have taken the not inconsiderable change of manager and predictable injury concerns to key players to depress their overall performance. Although, as with Newcastle, their points total so far is just ahead of par for a team of their goal difference.

In many sports, score differential mirrors league position based on the results of individual matches very closely. Over achievement, such as Newcastle and United have experienced over varying timescales may well be largely down to expected variation seen in large enough sample size of numerous teams. But in a contest where a side's performance can be a tactical combination of what they are capable of doing and what circumstance dictate they need to do in the latter stages of individual matches, to perhaps turn one point into three, there may be a small amount of wriggle room to hand some credit to the coach.