Manchester City.Bad Luck at the Wrong Time?

Just as the pre Christmas coronation of Manchester City as the pre eminent force in the EPL was premature,the rush to latterly write them off as even possible contenders was equally hasty.Unbeaten and unbowed in the league until mid December,their decline from those heady early days had seen them fall eight points behind their cross city rivals,United.However,a Red defeat at relegation haunted Wigan coupled with a Blue steamrollering of WBA has put the ball back in play and given City the chance to take the title race down to the final Sunday.

It's only natural to want to ascribe reasons for every event and the amount of football data that is now available makes it tempting to attempt to pin point the exact moment when Manchester City being caught and passed by United became an inevitability.Individual players suddenly become much less efficient at performing task at which they had previously excelled,water tight defences start to leak goals and goals dry up at the other end of the pitch.These type of events undoubtedly occur through out a season,but are they a sign of inherent weakness within sides,a failure of management or just the vagaries of random chance distributing the product of a skill based talent in a seemingly unnatural order.

The concept of randomness playing any part in a skill based activity such as football is often difficult to accept.The skilled component is usually easy to identify with.Barcelona are obviously better than Manchester United who in turn are better than Stoke and while superior skill will give one team a better chance to win a contest it won't guarantee victory because random events sometimes get in the way,especially where results are decided by relatively rare events,like goals.

Manchester City's March slump has cost them favouritism in the title race,but is it any different to the run of winless games every top team suffers or to Liverpool's run of home FA Cup ties in a truly random draw or Swansea's fall from "nascent Barca" to "struggling first season EPL side" in the space of a month.Thirty minutes before last year's real FA Cup semi final draw,Stoke didn't draw Bolton in the rehearsal.So many footballing events are partially driven by random chance.

One important skill based attribute that has a discernible random element is the rate at which teams score the game's opening goal.The better side in a match up is more likely to open the scoring and as has been documented once a team hits the front they become very likely to take the majority of the points.It's both convenient and sensible to express the pre game difference in ability between teams in terms of goals.For example if it was possible to persuade two teams to play innumerable games against each other then the average scoreline over those many games would be an effective illustration of the difference in class between the sides.Typically an average home side would score 1.5 goals and allow 1.0 goals to an average away team and we can use these figures to predict which team is most likely to score the game's first goal,when it would most likely occur and what course the game will take after the score.However,the chance that a team will score first in a game is an expression of the longterm outcome and over shorter timescales that probability may not be realised.So let's see how Manchester City have fared in the 1st goal stakes in the 2011-12 season.

How Man City and their Opponents Scored their Opening Goals in 2011-12.

Opponent.	Time of 1st Man C goal	Expected Time of 1st MC Goal.	Time of 1st Opponent Goal	Expected Time of 1st Opp Goal.
Swansea	57	38	90	72
@ Bolton	26	48	39	60
@ Spurs	34	54	68	56
Wigan	13	36	90	78
@ Fulham	18	44	55	64
Everton	68	43	90	64
@ Blackburn	56	44	90	64
Aston Villa	28	40	65	70
@ Man Utd	22	60	81	49
Wolves	52	36	75	78
@ QPR	43	40	28	69
Newcastle	41	38	89	71
@ Liverpool	31	54	33	55
Norwich	32	36	81	78
@ Chelsea	2	58	34	52
Arsenal	53	46	90	62
Stoke	29	37	90	76
@ WBA	90	44	90	64
@ Sunderland	90	44	90	64
Liverpool	10	48	90	61
@ Wigan	22	40	90	68
Spurs	56	48	60	61
@ Everton	90	49	60	60
Fulham	10	38	90	71
@ Aston Villa	63	44	90	62
Blackburn	30	36	90	78
Bolton	23	35	90	79
@ Swansea	90	44	83	62
Chelsea	78	48	60	61
@ Stoke	76	44	59	62
Sunderland	43	37	31	76
@ Arsenal	90	58	87	52
Average.	46	44	73	66

The above table charts the time the first goal scored by Manchester City and their opponents in each game so far this season.At the moment we are just looking at the first goal scored by each team in the game and not necessarily the opening goal of the match,for example City scored after 43' at QPR,but Rangers had already opened the game scoring after 23'.The predicted goal times are derived from my overall team rating for Man City based on their performances over their 30 previous matches,so increasingly games from this season are included in the calculation.For reference I have had City as rated marginally behind their rivals United for the entire season.

The sample of games comprises 32 ,so we should expect the expected values to be reasonably close to City's actual returns.The average time at which City opened their account so far was the 46' and the average expected time derived from their team rating was 44'.In around half of the games they scored before the predicted time and half of the time the goal came later.So Man City's scoring is entirely consistent with a team of their quality.Defensively they excelled.The average time of the defence's first concession was 73 minutes (where goalless games are capped at 90') compared to an expected 66'.

How Manchester City Performed after the Game's 1st Goal.

Opponent.	First Goal Time.	Man City EP after 1st Goal	Actual Points.
Swansea	57	2.82	3
@ Bolton	26	2.45	3
@ Spurs	34	2.25	3
Wigan	13	2.92	3
@ Fulham	18	2.63	1
Everton	68	2.70	3
@ Blackburn	56	2.66	3
Aston Villa	28	2.80	3
@ Man Utd	22	1.82	3
Wolves	52	2.90	3
@ QPR	43	1.44	3
Newcastle	41	2.81	3
@ Liverpool	31	2.21	1
Norwich	32	2.91	3
@ Chelsea	2	1.93	0
Arsenal	53	2.60	3
Stoke	29	2.88	3
@ WBA		2.11	1
@ Sunderland	90	0.17	0
Liverpool	10	2.50	3
@ Wigan	22	2.77	3
Spurs	56	2.57	3
@ Everton	60	0.59	0
Fulham	10	2.84	3
@ Aston Villa	63	2.65	3
Blackburn	30	2.91	3
Bolton	23	2.93	3
@ Swansea	83	0.33	0
Chelsea	60	0.62	3
@ Stoke	59	0.74	1
Sunderland	31	1.68	1
@ Arsenal	87	0.17	0
Total.		68.3	71

If we now move onto the more influential first match goal in the table above.(Opening goals scored by City's opponents are in red).Visually they have appeared to perform to remarkable levels.However,they are the second best team in the division and the pair are by some distance clear of third placed Arsenal,so they should expect to score first much more often than concede.I've further calculated the number of points a City team consistent with my estimation of their ability would expect to amass after the game's 1st goal and once again their actual total of 71 points is reasonably consistent with a predicted 68 points.The most notably feature of this aspect of City's season is the rapid accumulation of more recent games where they have found themselves playing from behind compared to pre Christmas.

On opening day The Etihad welcomed Swansea and such was City's likely superiority over their Welsh rivals that they had in excess of an 80% chance of scoring the opening goal should the game have one.Figures stayed at similar levels for the majority of City's home games and remained above 50% for all but their visits to teams from the top three or four.Cumulatively,the Blues should have scored the opening goal in 22 of their games upto their defeat at Arsenal on Sunday and their actual total is just one off at 23.So their 1st goals scoring rate is not exceptional for a team of their quality.The uneven distribution,with more 1st goals conceded in March,appears unusual,but such irregular patterns are actually typical of processes that have random components.Fake random patterns are always easy to identify because unusual events are evenly distributed in the sample,so a person's perception of what appears unusual is often at odds with nature's actual randomness.

Summary of Manchester City's First Goal Exploits.2011-12.

Manchester City 2011-12 Season.	Predicted	Actual
No.of 1st Goals Scored by ManC.	22	23
Expected Points after 1st Goal.	68.5	71
No.of 1st Goals Scored until mid Dec.	12	15
No. of 1st Goals Scored after mid Dec.	11	8
Expected and Actual Points after 1st Goal until mid Dec.	40	41
Expected and Actual Points after 1st Goal after mid Dec.	26	30

Assigning a reason for Manchester City's apparent decline is understandable.However,Balotelli was as bizarrely entertaining in November when he was holding indoor fireworks parties (and getting sent off) as he was in March when he was gate crashing press conferences (and getting sent off).Mancini was as graceless when failing to beat Stoke at the Britannia in March as he always is and a squad of City's depth should be less tired than most other less well resourced teams come the season finale.So there's little obvious reason for a Spring collapse.A more likely explanation is that if you can maintain your talent output,you will still most likely get your doses of luck in lumps.

The need to provide a reason for events often obscures the role that chance can play.

Indeed if we risk reducing sample sizes even further by splitting the season we see that City gained the considerable advantage of opening the scoring 15 times compared to a predicted 12 pre mid December and 8 times compared to a predicted 11 post mid December.So in the grander scheme they were slightly lucky early and less so late,although neither set of figures are likely to be significantly different from each other.Another indicator that City post "slump" were no different to City pre "slump" is that when they did (randomly) concede the 1st goal more often recently,they managed to claim four more points from those losing positions than the Expected Points model suggested they should.

A Premiership season is but 38 games long and while that is long enough for one of the best teams to always win the league,it isn't always long enough for talent to always overwhelm randomness.Aston Villa aren't draw specialists,they just happen to have drawn alot of games in a relatively small timescale and if they draw at Manchester United on Sunday and City win at Norwich on Grand National Day,there's a chance that the story of City's collapse won't even get written.

Update.Since City's defeat to Arsenal,they have opened the scoring in all of their subsequent games,scoring 13 times,conceding just twice.They have taken 12 points from 12 and are now favourites to take the Premier League title with just two games remaining.

For more on City's season see Chris Anderson here  and Danny Pugsley here.