On a superficial level expected goals is a superfluous statistic, its big brother the actual scoreline succinctly communicates the most crucial information in a neat package of whole numbers. Such statistical intrusions are a common bete noire among pundits of the proper football man variety, who consider the incursion of geeky statisticians into the modern game as an affront to its willfully unscientific macho underpinnings. Why over-complicate the boiling of an egg? Heston Blumenthal may insist that the hen should lay the egg directly into a pot of lightly salted unicorn tears in order to achieve the perfect soft boil, but we know that that's just pretentious codswallop and that unicorns don't exist. But what if they did? Expected goals is essentially a statistical unicorn, it may not really exist, but it can still tell us something.

Expected goals is based on probabilities, on the likelihood of a player scoring from a certain position rather on whether they actually score. So for example, if you are two yards out in front of goal, there is a very high chance, let's say 99/100, that you should score. Now even if you are possessed by Danny Ings and contrive to miss, you can console yourself with the knowledge that the mathematical model has rewarded you with 0.99 expected goals. More difficult chances, let's say a speculative effort from 25 yards, which may rate as a 1/10 chance of scoring, will rank as less probable and be rewarded with a lower expected goals score of 0.10. If the 25 yard screamer is scored by one team but the 2 yard sitter is missed by their opponents, the traditional scoreboard will read 1-0, whereas the expected goals scoreline will be 0.10 - 0.99.

Now that may appear a perverse inversion of the common sense laws of football, but in fact the statistic describes the quality of play more objectively than a traditional scoreline can. When a team is unlucky to lose it will be reflected in the expected goals statistic in a way the simplicity of a scoreboard cannot match. The case of Juventus' seemingly poor start to the 2015/16 season exemplifies the point. While the prima facie evidence of 3 wins from their opening 10 games suggested that The Old Lady was struggling for form, the expected goals statistic told a very different story. Throughout that spell Juventus' expected goal total far exceeded their actual conversion rate. This statistic indicated that while most aspects of their play continued to operate at an elite level their finishing was letting them down. After Juventus addressed this issue they went on to win Serie A.

Effectively, the probability curve has a predictive value, in that it can highlight which teams could be doing better. Moreover, by effectively assessing the quality of play it can help pinpoint departments which need to be improved. If a team isn't scoring at a rate consistent with probability then they would be well advised to remedy the problem either on the training ground or in the transfer market.

Expected Goals has an even less sexy sibling, the ugly duckling that is Expected Goals Against. This value is basically the inverse of Expected Goals and is calculated accordingly. So, if David De Gea miraculously saves the 2 yard sitter it will still count as 0.99 goals against. But if Loris Karius ushers a scuffed 25 yard whisperer (opposite of a screamer?) into his net, it would only count as 0.10 goals against. In this scenario the respective abilities of the goalkeepers would explain the differential between the statistical and real world outcomes. The Expected Goals Against statistic therefore highlights the degree to which individual teams rely on both their goalkeepers and the profligacy of the opposition.

Well, now that we've the long winded preliminaries out of the way, let's look at how this season's Premier League table would look if results were decided solely on the basis Expected Goals calculations. Moreover, the table also depicts the revised points totals (xPoints) for each club, as calculated using Expected Goals, and illustrates the position change (PosDiff) with respect to the actual league table.

---------------------------------------xPoints----PosDiff--------

  1. Manchester City      20.85        <->
  2. Liverpool                   17.34         +1
  3. Chelsea                     15.99          -1
  4. Bournemouth           15.80          +2
  5. Tottenham                15.05         <->
  6. Wolves                       13.98         +1
  7. Manchester Utd        11.83         +1
  8. Leicester City            11.23         +2
  9. Watford                      11.00         +1
  10. Everton                       10.88         +1
  11. Arsenal                       10.67          -7
  12. West Ham                    8.67          +3
  13. Crystal Palace             8.62           +1
  14. Southampton               8.34          +2
  15. Cardiff                            7.84         +5
  16. Brighton                         7.56          -3  
  17. Burnley                           7.20          -4
  18. Fulham                           6.93          -1
  19. Huddersfield                  6.08          -1
  20. Newcastle Utd               5.58          -1

The table reveals both Arsenal and Cardiff as standout statistical outliers. The mathematical model demotes The Gunners a mammoth 7 positions, while promoting Cardiff from basement dwellers to the penthouse dwelling heights of 15th. The numbers suggest that Cardiff are likely the victims of their own attacking profligacy and propensity for defensive mishaps, while the inverse could be true for Arsenal. In short, Arsenal's quality is compensating for deficiencies in their overall performance, while, on the other hand, Cardiff lack the requisite quality to capitalise on their play. Burnley and Brighton are also outperforming their statistical alter egos by a notable margin, while West Ham's league position lags slightly behind their performance curve.

The second table will illustrate the difference between actual points totals and statistically derived totals. For example, Man City currently sit on 20 points in the official standings, but their estimated points total is 20.85; the table therefore records a reading of -0.85. Chelsea meanwhile, also have 20 points, but their statistical total is only 15.99, meaning that here the table records a reading of +4.01.

  1. Manchester City   -0.85
  2. Chelsea                  +4.01
  3. Liverpool                +2.66
  4. Arsenal                   +7.33
  5. Tottenham              +2.95
  6. Bournemouth         +0.20
  7. Wolves                     +1.02
  8. Manchester Utd      +1.17
  9. Watford                    +2.60
  10. Leicester City          +0.77
  11. Everton                     +1.12
  12. Burnley                     +0.80
  13. Brighton                    +0.44
  14. Crystal Palace          -1.62
  15. West Ham                 -1.67
  16. Southampton            -3.34   
  17. Fulham                       -1.93
  18. Huddersfield              -3.08
  19. Newcastle United      -3.58
  20. Cardiff                         -5.84

The most interesting trend in this version of the table is the extent to which the top teams, Man City excepted, outperform themselves. From 2nd to 13th, the total points accrued in reality is greater that their respective statistical equivalents. Conversely, for teams at the lower end of the table their statistical output fails to generate the points total it mathematically merits. Again this table suggests the influence of a talent coefficient skewing points totals in favour of elite squads. This hypothesis suggests that Manchester City's squad, which is commonly considered the most talented, is coasting a little. Since their nearest competitors all appear to be benefiting from a points boost at what appear to be the upper limits of any putative talent coefficient, Arsenal especially, a business as usual model would suggest that Man City should extend their cushion at the top eventually.

The following table will assess attacking proficiency and defensive solidity. It will do so by comparing the actual number of goals scored and conceded by each team and comparing the divergence between those totals and the totals derived from the Expected Goals metric. To do so we will introduce a new measure, an expected goals differential, which will relate both to goals scored and conceded. This new statistical measure is calculated in the following manner;

Manchester City have scored 21 goals in reality, but their expected goals total is 22.49: the difference of -1.49 will be recorded in the table's xGd (expected goals differential) column. The formula is;

Actual Goals scored - Expected Goals Scored = xGd

Meanwhile, they have to date conceded 3 goals, which is less than the 4 the model predicts, and this outcome is recorded as -1.00 on the table's xGAd (expected goals against differential) column. The formula in this instance is;

Actual Goals Conceded - Expected Goals Conceded = xGAd

A team performing at the height of their ability would register a positive total in the xGd column and a negative result in the xGAd column. This translates to scoring more and conceding less than would be statistically expected. Of course, the inverse, a negative total in the xGd column, and a positive result in the xGAd column, would be indicative of a team which, in statistical terms, is under-performing across the board. For comparative purposes the table also references the numbers of actual goals scored (G) and conceded (GA).

--------------------------------------G-------------xGd----------GA---------xGAd-------------

  1. Manchester City      21           -1.49            3             -1.00
  2. Chelsea                     18           +2.28          5              -3.59
  3. Liverpool                   15           -1.66           3              -2.90
  4. Arsenal                      19           +8.99         10            -0.95
  5. Tottenham                15           +0.21          7              -2.66
  6. Bournemouth           16            -0.08          12            +2.75
  7. Wolves                         9            -2.06           6             -0.15
  8. Manchester Utd       13            +0.17         14            +3.02
  9. Watford                     11            +0.45         12            +0.99
  10. Leicester City           14            +4.86         12            +3.42
  11. Everton                      13            +3.48         12            +2.24
  12. Burnley                      10             +2.31        12            -2.11
  13. Brighton                      9             -0.49          13            -1.71
  14. Crystal Palace           5              -2.02            9            -2.56
  15. West Ham                  8              -0.73          13            -0.32
  16. Southampton             6             -4.61          14            -0.02
  17. Fulham                        9             -0.41           21           +3.00
  18. Huddersfield               4             -0.75          17            +3.74
  19. Newcastle Utd            6             +0.02         13            +0.14
  20. Cardiff                          4             -3.44          17            +3.32        

By analysing the interaction between GA and xGAd we can infer that Defensive solidity is of predictive value at both extremes of the table. While the xGAd figures for Fulham, Cardiff, and Huddersfield are replicated higher up the table, by Manchester Utd and Leicester for example, the fact remains that even if those figures improved to baseline probability levels, they would fail to fully compensate for their profligacy in attack. The room for improvement suggested by Cardiff's xGd and xGAd totals, may in fact point to the limited quality of their individual players, which is hardly surprising given the limited investment in the squad over the summer.

Unlike their nearest rivals, Newcastle are operating at about par in terms of xGd and xGAd, their lowly league position may be attributable to an unforgiving fixture list rather than repeatedly sub-par performances.

Southampton, hovering just above the relegation zone; are handicapped by the impotence of their attack, the most wasteful in the league, which in turn makes them overly reliant on defensive solidity. Any reduction in their xGAd figure, which is based on the already shaky defensive foundations of having conceded 14 goals, could see the Saints slip even further down the table.

At the sunny side of the table, the old adage that defences win titles is supported by the statistics. The top 5 sides all concede less than is statistically probable, and among them only Arsenal concede at a rate higher than one a game. Again we can infer a talent coefficient; better defenders make less mistakes while the best goalkeepers can bail them out if they do.

Interestingly, only 4 clubs outperform their statistical selves across both the xGd and xGAd measures; Chelsea, Arsenal, Tottenham and Burnley. Therefore, the results suggest that these sides are performing closer to their full potentials than any of their Premier League peers, or put more simply, that they are in the best form. Since you would expect any putative talent coefficient to favour Chelsea, Arsenal, and Tottenham to a greater degree than Burnley, the figures suggest that The Clarets are the most efficient team, with respect to their potential, in the Premier League at present. While that may be, it disguises the fact that any reversion toward the mean in their performance levels would precipitate a dramatic plunge down the standings; let us not forget that they sit fourth from bottom on the revised Expected Goals version of the table.

Arsenal's league high xGd of +8.99 marks a significant deviation from the norm and must be considered unsustainable over the duration of the season. This is particularly true given the unreliability of their defence which has already conceded 10 times over the opening spell games. Their relatively healthy xGAd figure of -0.95 suggests that their defensive frailties are largely systemic. It is likely that The Gunners form will regress back toward the mean at some stage and it is during that period when a clearer picture of their progress, if any, under Unai Emery will emerge.

Although, Man City sit top, and Liverpool trail only on goal-difference, both sides are yet to fully find their goal scoring rhythms, registering xGd scores of -1.49 and -1.66 respectively. Liverpool's improvement in defence, and particularly their investment in an upgraded goalkeeper is paying dividends, their xGAd rating of -2.90 is the second highest in the league, and at the moment ensures that they remain competitive at the very sharp end of affairs. In comparison to their fellow table-toppers, Chelsea are operating closer to their peak levels, with less room for improvement, a fact which suggests that a concerted title bid may just be beyond them this season. It may be a similar story for Tottenham, who will require Harry Kane to rediscover his golden touch, in order to bolster their comparatively feeble xGd rating of +0.21 closer to the levels of their direct competitors.

Lower down the league, Manchester United's well publicised travails in defence are highlighted by an xGAd rating of +3.02. This figure is all the more stark given the benign fixture list they have enjoyed thus far. Having largely faced teams from outside the league's elite, it is more probable that their poor xGAd score is attributable to errors of their own making than the quality of the opposition. Equally worrying for Mourinho, is their xGd score of +0.17, which suggests an inability to fully capitalise on the defensive frailties of weaker opposition.

The statistics depict Everton and Leicester as the least balanced sides. Both score at a higher rate than the model would predict; Everton's xGd is +3.48, while Leicester's sits even higher at +4.86. These scores rank them among the most clinical sides in the EPL, but then they need to be. Everton's xGAd is +2.24, while Leicester's is +3.42. Given their respective defensive vulnerabilities any drop off in attacking efficiency could leave both sides nervously looking over their shoulders later in the season.

Now let's look back to last season's final Expected Goals table, to see if it offered any predictive value for this season. Alongside league position, the following table will also illustrate how each team's points total related to their statistically modelled total (PtDiff) and in turn how this influenced their final position in the league (PosDiff). For example, Arsenal's final points total was -2.90 behind that predicted by the probability curve a fact which is illustrated in the PtDiff column. Overall, the model placed The Gunners in 5th position which was one place higher than their 6th place finish, which is depicted in the PosDiff column.

--------------------------------------PtDiff-----PosDiff---------

  1. Manchester City       +8.91      <->
  2. Liverpool                    -4.38       +2
  3. Tottenham                +0.98       <->
  4. Chelsea                     +1.54        +1
  5. Arsenal                      -2.90         +1
  6. Manchester Utd      +18.67       -4
  7. Crystal Palace          -14.03       +4
  8. Leicester City           -8.83          +1
  9. Southampton           -12.22       +8
  10. Everton                      +2.00        -2
  11. Watford                      -5.69         +3
  12. Newcastle                 -2.24          -2
  13. West Brom                -11.96       +7
  14. Burnley                       +13.00      -7
  15. Brighton                     -0.85          <->
  16. West Ham                 +2.74        -2
  17. Bournemouth            +6.36        -4
  18. Huddersfield             +0.16         -2
  19. Stoke                           -3.17        <->
  20. Swansea                    +0.69         -2      

The most glaring revelation is the extent to which Manchester Utd over-performed last season, outpacing their statistical selves by a whopping 18.67 points. In this light their form this season can be interpreted as a regression to baseline performance, rather than an absolute implosion. Burnley snaffled an extra 13 points, presumably by using some sort of Dyche-ian diversion tactics. While, Manchester City's 100 point season was realised on the back of consistently outperforming the probability curve. At the other end of the spectrum Crystal Palace, Southampton, and, the ultimately relegated, West Brom all under-performed to a significant degree.

In order to delve deeper into this deeper we need now to look at the next table which will plot actual goals scored scored (G) with reference to Expected Goals differential (xGd) and actual goals conceded (GA) against Expected Goals Against differential (xGAd).

-------------------------------------------G----------xGd---------GA---------xGAd-----

  1. Manchester City       108        +14.57        27            +2.49
  2. Manchester Utd          68        +8.96          28            -15.54
  3. Tottenham                   74        +5.09          36            +0.14
  4. Liverpool                      84        +6.51          38            +2.25
  5. Chelsea                        62        +2.84          38            +3.97
  6. Arsenal                         74        +1.73          51           +2.25
  7. Burnley                         36        +3.23          39            -13.16
  8. Everton                         44        +0.29          58            +2.50
  9. Leicester                      56        +5.71          60            +10.69
  10. Newcastle                    39        -5.63           47            -5.47
  11. Crystal Palace             45        -11.75         55            +1.46
  12. Bournemouth              45         +5.01         61            -3.93
  13. West Ham                    48         +11.20      68            +9.65
  14. Watford                        44         -1.85          64            +10.02
  15. Brighton                       34         -3.21          54             +0.92
  16. Huddersfield               28         -4.13          58             +4.78
  17. Southampton              37         -4.88          56             +9.44
  18. Swansea                      28         -1.71          56             +5.83
  19. Stoke                            35         -1.75           68            +2.46
  20. West Brom                  31          -4.18          56             +7.01

There is a clear dividing line drawn bisecting the Premier League with respect to xGd. All the teams in the top 9 scored at a rate above that of probability, whereas conversely all the teams from 14th down scored at a rate inferior to that suggested by probability. The picture with respect to xGAd is more uniform, the majority of teams conceded more than the statistical model predicted. Last season at least, attacks ruled the roost.

The most glaring outlier, once again is Manchester Utd, who it turns out, in statistical terms, are just an expensively assembled Burnley. Both sides' xGAd is significantly ahead of both the Premier League norm and what would statistically be expected. Too far most probably. The statistics indicate how reliant both these sides were on their goalkeepers. Quite simply it is unlikely that Utd would have finished in the Champions League places, let alone second, were it not for David De Gea. So far this season, Utd's xGAd has not just dis-improved slightly, it is among the worst in the league. Mourinho, it turns out, knows a thing or two about defending, he knew they weren't good enough. Furthermore, that Utd enjoyed the league's second highest xGd figure, yet scored a comparatively meagre 68 goals further evidences Mourinho's safety first approach. Therefore, last season, despite a conservative gameplan, Utd struggled to prevent goal scoring opportunities against them. If you subtract innumerable DeGea miracles from that equation, you you are left with a predictable outcome, one which is expressed in the mathematical function of this season's league table.

As would be expected from the most talented team in the league, Man City outscored the probability curve by a decisive margin. This attests to what Pep's side is capable of at its best and places this season's slight under-performance in the ominous context of there's much more to come. Less expected perhaps was the clinical nature of West Ham's forward line, which emerged as the second most clinical across the season. This appears to have been The Hammers saving grace last season, while their defence was collectively as well as individually vulnerable, as attested to by a GA figure of 68 and and xGAd of 9.65, their attacking style wasn't what you'd describe as swashbuckling. A reversion to the mean with respect to goal scoring would have seen them flirting with relegation with even greater coquettish abandon than transpired - which we should all be thankful of since no one wants to think of David Moyes in stockings.

At the other extreme, Christian Benteke's scoring amnesia translates into Crystal Palace, recording the lowest xGd rating across the season, a trend which has not been rectified during the summer. Such is their over-reliance on Wilfried Zaha that it would be no surprise to see him, not so much being wrapped in cotton-wool as cryogenically frozen between matches. Elsewhere, Newcastle's profligacy, marked by an xGd of -5.63, and conservative gameplan, was enabled by their resoluteness in defense. Rafa Benitez's defensive nous could have propelled his ex-club Liverpool further up the table. Although the Merseysider's defensive performance was far from apocalyptic, last season's GA total of 38, which translates rather neatly to one per game, falls short of the defensive parsimony needed to launch a truly concerted title bid. Last Season's xGAd was broadly equivalent to those of their rivals, Manchester Utd excepted, and suggests that the comparative shortfall with respect to Man City was largely organisational. This season's xGAd rating suggests that Liverpool's overhaul of their defence during recent transfer windows is beginning to pay off. One team who have seemingly done little to address their defensive shortcomings are Leicester. Last season's GA of 60 and xGAd of +10.69, could well be emulated this season, with the equivalent figures after only 8 games already standing at 12 and +3.42.

So, to conclude, it appears that the Expected Goals statistic suggests that Manchester City should retain their title, that Liverpool are best equipped to challenge, and that 3rd and 4th will be between Chelsea and Tottenham. For Manchester Utd, it turns out that last season was something of a David De Gea inspired miracle, and that this season's league position is more representative of their true standing as a team. Arsenal, are currently riding the crest of a wave, but will likely fall away, probably, in keeping with festive tradition, over the Christmas period.

At the other end of things, it looks particularly bleak for Cardiff, who lack the quality to convert their opportunities into points. Fulham and Huddersfield also look set to struggle, while Southampton will need to find a goalscorer from somewhere in order to rest somewhat easily. All in all that was a pretty long article just to conclude with the blindingly obvious. Jeff, you know what? I'm with Merse and Thommo on this one!