Do Referees Subconsciously Influence Matches?

The Expected Points Model I use in this blog is a very potent weapon in analysis performance based questions in soccer.All things being equal the cumulative total pre game EP over a reasonably large number of games for individual teams almost always tallies up to be very close to the actual points a team achieves.If there is a major discrepancy between the actual and predicted points totals there is usually a readily discernible reason why.For example if we were to by pure chance select a series of games where the team was destined to have a player dismissed,the cumulative pre game EP for that team would be well above the actual points gained.However,the cause,namely the red cards would be readily apparent.

It is therefore possible to use an Expected Points approach to evaluate any influence a certain referee may
have had on the outcome of a batch of games.However,before I go any further I want to emphasis that because a referee shows up as an outlier in any analysis involving match decisions,it no way implies that there may be deliberate bias involved.People can respond subconsciously in different ways to very similar situations and if the majority react in a different way to you that difference can become apparent.It may present a problem in terms of consistency of decisions,but it doesn't automatically mean that there is deliberate bias at work.

Secondly,random events can converge to make a set of games appear unusual and the result of a common denominator such as the referee,when in fact they have just come about by random chance.I'll deal with these issues in a later post,but for now here's how games controlled by the major EPL ref's from the last seven seasons have panned out.

Recent and major decisions tend to be over emphasised in people's memories,so it's hardly surprising that every set of fans think that every official is out to get their team regardless of venue and regardless of their team's standing in the match in question.But it is an enduring opinion that refs favour either the home teams or the better teams in a game.This is reinforced because in general home sides and favourites will do more attacking,receive more free kicks and penalties and although this can be construed as favouritism from officialdom,it is really just down the better team getting it's just deserts.

These natural advantages enjoyed by home teams is already accounted for in the Expected Points calculation,so we can compare the cumulative pre game EP totals with the actual totals gained by the host and then sort them by referee to see if any patterns begin to emerge.All EPL games from the 2004-05 season until the present were included and any referee who officiated 30 games or less was excluded.The vast majority of the referees appear to officiate in games which on average produce actual cumulative points tallies that are extremely close to the pre game expectations.Mark Halsey for example officiated in 121 games and pre game estimates would have suggested that the home team would gain 198.5 points from those games.They actually gained 198 points.So from these figures we would have to conclude that Halsey was officiating in a way that corresponds very closely to the way officials have refereed in the past.Overall 13 of the 21 referees featured in the table saw their groups of matches produce home points that were within 4% or better of their expected value and the majority have been rewarded by being appointed to take charge of the FA Cup final.

Games officiated by Peter Walton saw the home side's actual points under perform the expected value by nearly 8% (two refs produced higher discrepancies,but their game tallies were each much less than Walton's total of 134 games).Again a caveat must apply.Firstly,these results could have arose through random chance or alternatively Walton may actually be one of the few officials who is able to resist the subconscious influence of the home support and it is his colleagues who are out of step.At the other end of the spectrum Mark Clattenburg is the ref with most games in the survey who saw an elevated points tally for the home teams he officiated.Home teams gained an average of 7% more points than expected when he was in charge.The most prestigious game either Clattenberg or Walton have taken charge of is the Community Shield.

Points accrued by home teams compared to pre game expectations sorted by referee.2005-11.

REFEREE.	PreGame Expected Points for Home Teams.	Actual Home Team Points.	% Difference.	Number of Games.
L Mason.	145.3	157	8.0	86
M Clattenburg.	210.1	224	6.6	124
L Probert.	126.0	134	6.3	72
K Friend.	56.9	60	5.4	33
U Rennie.	81.3	83	2.1	50
C Foy.	247.4	251	1.4	145
P Dowd.	251.5	255	1.4	152
M Dean.	274.1	276	0.7	169
M Halsey.	198.5	198	-0.3	121
M Riley.	178.7	178	-0.4	118
M Atkinson.	256.4	254	-0.9	151
A Marriner.	177.6	175	-1.5	109
H Webb.	294.2	289	-1.8	177
A Wiley.	244.0	239	-2.1	145
R Styles.	186.3	180	-3.4	111
G Poll.	104.6	101	-3.5	61
S Bennett	231.4	222	-4.1	139
P Walton.	231.7	214	-7.6	134
M Jones.	109.0	100	-8.3	60
S Atwell.	69.8	62	-11.2	36

* denotes a cup final referee.

If we repeat the exercise by tracing the points haul for all pregame favourites a similar pattern appears.14 of the listed refs see their games come in at within 4% of the expected points total.Game favourites are not always readily identifiable,for example when a relegation candidate entertains a mid table team.So in the majority of these games there's not a huge amount of subliminal pressure to ensure that the "right" team wins.Games overseen by Phil Dowd have coincided with the likes of Arsenal,Chelsea and ManU failing to fulfil their pre game expectations,while Lee Probert controlled matches has seen the favourites overachieve.

Points accrued by match favourites compared to pre game expectations sorted by referee.2005-11

REFEREE.	Pre Game Expected Points for Favourites.	Actual  Points won by Favourites.	% Difference.	Number of Games.
L Probert.	133.2	149	11.8	72
A Wiley.	278.4	296	6.3	145
C Foy.	274.1	290	5.8	145
R Styles.	213.2	222	4.1	111
K Friend.	60.6	63	4.0	118
M Riley.	191.1	199	4.0	33
M Halsey.	226.1	234	3.5	121
S Bennett.	268.8	276	2.7	139
G Poll.	111.1	113	1.7	61
U Rennie.	93.7	95	1.4	50
M Clattenburg.	235.5	236	0.2	124
D Gallagher.	63.2	63	-0.3	34
P Walton.	259.8	256	-1.5	134
M Dean.	313.6	309	-1.5	169
M Atkinson.	279.1	272	-2.6	151
A Marriner.	212.0	205	-3.3	109
L Mason	163.2	157	-3.8	86
M Jones.	113.3	109	-3.8	60
H Webb.	324.8	310	-4.6	177
S Atwell.	69.5	62	-10.8	36
P Dowd.	287.7	255	-11.4	152

From the previous table is is evident that the interpretation and implementation of the laws in the EPL are very largely consistent with previous seasons.There are very few refereeing performances that deviate greatly from the expected outcome over a large enough batch of games.The fewer the games the more likely it is we will see batches of games that appear atypical and even where outlying officials have controlled large numbers of games the possibility for freak sequences to appear is real and present.

Poor or contentious decisions are often seen as the result of incompetence or malice,but more often they result from a subconscious desire by the officials to please the majority ( in the case of home field teams) or satisfy the consensus opinion (in the case of favourites).Managers often criticise officials often unjustly,but always to gain a possible advantage in future games where the previous,often well publicised vent will subconsciously "encourage"referees to favour their side to atone for previous mistakes.

Judging by the above results EPL referees are largely immune to such pressures or if they do allow their judgement to be swayed it is within the bounds of historical limits and therefore relatively consistent between referees.

Measuring the Fun in Football.

The win probability for each team is tracked on a minute by minute basis throughout each game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.


Expected Points graphs do a very good job of illustrating the ebbs of flows of a soccer match and the large swings caused by the relatively rare occurance of a goal is particularly evident.However,they can also be used to quantify more subjective aspect of a game such as entertainment value.

There are a number of factors that contribute towards a game being more or less entertaining and these can be captured by reference to an EP Graph.Swings in fortunes during the game,late winners,spirited comebacks and impressive performances by an unfancied underdog each can contribute towards making a game worth watching and all can be tracked.

While it would be possible to track all of the movements in EP during the match,it's much more useful to be able to simply and quickly get an idea of how eventful a game has been by just looking at the EP graph.One such method is to sum each team's highest EP during the game and divide it by the sum of each teams lowest EP during the 90 minutes.

Under this approach the ManU Basel 3-3 draw scores an Entertainment Value (EV) of around 23.ManU's highest Expected Points Value was almost 3 just after Welbeck's second goal,Basel's was just under 2.6 in the 89th minute just prior to Young's equaliser.United's EP was at a low of 0.24 and Basel's was 0.01.A similarly switchback game where Blackburn came from behind to defeat Arsenal 4-3 earlier this month scores an EV of 14.

Blackburn 4-3 Arsenal,full of incidents and a great come from behind win and a Entertainment Value of 14

By contrast,Tottenham's wide margin all the way 4-0 win over Liverpool scores an EV of just over 3,as does Swansea's 3-0 canter verses WBA.The Welsh side's dour 0-0 draw with Sunderland totals only 1.3.

Little incident in a fairly standard goalless draw for a EV of 1.3

Winning Contribution in Soccer.

Expected Points graphs are the natural tool to visualise how many league points a team is likely to acheve during certain phases of a game.However,if we are interested in their chances of winning (or drawing) the match then plotting success probability is much more useful.

As the game progresses a team's success probability will ebb on flow dependent upon such things a current score,relative strengths of both team and whether a red card has been shown.By adding a team's chances of winning the match to half it's chances of drawing the game we can chart a teams expected success probability at various stages of the match.

At full time a team will have either won,gaining a success probability of 1.0 or drawn the game and shared the win equally with it's opponent gaining 0.5 wins each or of course lost.

By looking at the changes in success probability from the start of the game to full time,we can start to assign how much success probability should be attributed to the 11 or more participating players.

There are generally four fundamental stages to consider.

1) Change in SP due to time elapsed.

Each team will start a game with a likely success probability (SP) based on their relative strengths compared to today's opponents.This can be calculated by taking a weighted view of both team's recent results.How far you go back in time is a matter for individual taste,but I would suggest the last 25 games as a bare minimum requirement.
Since goals,both scored and conceded determine football games,it's sensible to expess the relative team merits in terms of how many goals each team will on average score in today's game,given the relative merits of both attack and defences.We can therefore use the pre game goal expectancies for both teams to calculate the expected success probability at the start of the game.This is the starting point and it's also team specific for today's game.

As the game develops without any goals occuring,the pregame goal expectancies for each team will start to decay.Thus we can re calculate each team's SP up to the point when a goal is scored.What generally happens is that a much superior team will see it's SP trend downwards towards 0.5 (as the teams are still level) and an inferior oppenent will see it's SP trend upwards.We can assign this change in SP respectively to each team along with any changes that occur in the lulls between significant events such as goals,penalty awards or red cards.

2) Goals scored.

To state the obvious,goals change games.If you score you always increase your success probability.The real bone of contention is how to distribute the credit for the goal between the scorer and the creator,similar to the situation in American Football where the QB throws a TD to his WR.I currently split the credit 80/20 in favour of the scorer.Some goals will be relative tap ins,although as Torres demonstrated recently,there maybe no such thing as a tap in,while other goals may result from a relatively simple pass from a team mate.

3) Goals conceded.

Allowing goals always decreases your SP and again we need to apportion the "blame".Harsh though it may seem,I've given the keepers 20% "credit" for the goal.The remaining 80% I've distributed between the 10 outfielders.55% of remaining fall in SP is divided amongst the defenders.I've chosen this figure because if we use goals scored as a proxy for "attacking play" we find that forwards score 55% of the goals,midfielders 35% and defenders 10%.Therefore it seems reasonable to flip these percentages when  trying to apportion the less transparent skill of defending.Blaming forwards partly for goals conceded may seem strange,but firstly the proportion of fault is relatively small, they do actively defend at corners and goals often develop from failure to maintain possession higher up the field.

4) Red Cards.

It's not harder to play against ten men that eleven,it's easier.Reduced in numbers,a team finds it harder to score and harder to prevent goals being scored against them.A red card reduces that team's SP  and the entire amount by which the SP is reduced counts against the transgressing player.

These are the (very) bare bones of a system to apportion blame and credit for team wins or draws amongst the individual players.So lets use a real example.I've chosen the Fulham Man City game from last week to illustrate the methodology and I've started with a pared down Success probability graph,illustrating the six major incidents from the game.Namely,kick off,two goals apiece and full time.

Significant Events from the Fulham Man City Draw.

Goals.
0-1,Aguero ,18 mins,assist,Silva.
0-2,Aguero,46 mins,assist,Dzeko.
1-2,Zamora,56 mins,assist,Dempsey.
2-2,Murphy,75 mins,assist,Zamora.


Subs.
Kasami on for Duff,61 mins.
Ruiz on for Dembele,84 mins.


Zabaleta on for Silva,69 mins.
Johnson on for Nasri,81 mins.
Tevez on for Aguero,83 mins.


A deeper look at some of the SP changing events from the game.


Kick Off).

Man City are the away side,but unsurprisingly given their vast investment are still considered more likely winners.If this game were to be repeated a large number of times I'd expect Man City to score on average 1.9 goals,concede 0.8 goals,win just over 60% of the time and draw just over 20% of the time.
So at kick off Man City have a SP of 0.741 compared to Fulham's 0.259.Just prior to the first Man City goal after 18 minutes,City's SP has declined to 0.722 and that fall is shared amongst the 11 starting players.Fulham's has risen to 0.278 from 0.259 and that is also shared amongst their starters.

Aguero's first goal).

Aguero scores from a Silva assist and Man City's SP goes from 0.722 to 0.902.80% of the credit goes to Aguero and 20% to Silva.By contrast Schwartzer is debited 20% of the 0.18 his team's SP has fallen,another 44% is shared by each member of the back four,28% by the four midfielders and 8% by the the two strikers.

Murphy's equaliser).

His goal raises Fulham's SP from 0.07 to 0.39 of which 80% is attributed to him and 20% to Zamora,who set up the chance.

Last 20 minutes).

Fulham's SP rises from 0.39 at the time of the Murphy goal to 0.5 at the final whistle,this is shared amongst the players on the field at the time of the goal.Man City's players lose the same amount as their SP falls to 0.5 from 0.61 as they were still the most likely winners with the game tied at 2-2.

A summary of each players win shares from the game.

FULHAM.

Player.	Win Conribution.	Comments.
Schwartzer.	-0.018	Conceded 2 goals,but benefitted from Fulham being big underdogs and claiming a point.
Kelly.	0.005	Unless they score,assist or are sent off,defenders score identically.Tackles won for example would re distribute the SP.
Baird.	0.005
Hangeland.	0.005
Riise.	0.005
Duff.	0.006	He was substituted while Fulham were still trailing,so didn't reap the completed comeback rewards.
Sidwell.	0.015
Murphy.	0.271	A late equaliser is always going to be a big SP mover.
Dempsey.	0.030	Assist for Zamora goal.
Zamora.	0.145	His goal could have just been a consolation.Assist for Murphy's leveller.
Dembele.	0.016
subs.
Kasami.	0.010	Limited game time,but gained from coming on before the equaliser.
Ruiz.	0.007
Total.	0.5

MAN CITY.

Player.	Win Contribution.	Comments.
Hart.	-0.021
Richards.	0.015
Kompany.	0.015
Lescott.	0.015
Clichy.	0.015
Silva.	0.097	Supplied an assist and had left the field before the equaliser.
Barry.	0.021
Toure.	0.021
Aguero.	0.259	Two goals.
Dzeko.	0.063
Nasri.	0.056	He wasn't on the pitch at the very end when City's SP was slipping away quickly and,as a forward he wasn't heavily penalised for Fulham's goals.
subs.
Zabaleta.	-0.039	Appeared when City still led,but couldn't help them protect the lead.
Tevez.	-0.007	Appeared with the game stalemated,but couldn't grab a winner.
Johnson.	-0.008
Total.	0.5

This initial system rewards or penalises players for being involved in events that are integral to the score and the final result.Consequently,players who aren't involved in game changing incidents tend to score similar shares.As in American Football,it' quite easy to assign a number to depict how influential a quarterback has been to the game,but much more difficult when dealing with a lineman.An improvement to players being scored as a unit would be to re distribute the unit's total by using stats such as tackles made or passes completed.The problem here is that these kind of stats,even if they correlate well with talent,aren't readily available in an easy to use format.So at the moment it's a work in progress and the more obvious contributors to the fore.

Games from Around the World.The MLS.

The win probability for each team is tracked on a minute by minute basis throughout each EPL game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.

Philadelphia Union 4-4 New England Revolution.

Scorers:
 9'  0-1 Soares.
21' 0-2 Lekic (pen).
26' 0-3 Zerka.
28' 1-3 Torres.
33' 1-4 Feihaber.
54' 2-4 Adu.
80' 3-4 Le Toux (pen).
90' 4-4 Le Toux.

How Red Cards Affect A Soccer Match.

After penalties and goals,red cards are the next most significant event that can take place during a soccer match.They are both dramatic and potentially game changing and they aren't quite as rare as you may imagine.Around 15% of matches feature one or more red cards,so statistically speaking you are more likely to see a red card than you are a 1-1 draw.

The team which is reduced in number suffers by scoring less goals than they would have done had they kept a full complement of players on the pitch and they also concede more goals than would have been so.

One of the most effective ways to model the expected progress of a soccer match is to calculate the average number of goals each team can expect to score at today's venue and against today's opponents.We can then use the Poisson distribution (with few tweaks) to calculate a multitude of predictions about the likely route the game will take.This is the basis for the game graphs on this site.However,if we want to carry this approach past the initial whistle we also need to know how the expected average number of goals each team will score today decays as the game progresses.Initial clues for a possible way forward lies in the distribution of goals scored in each half of play.In England approximately 45% of goals come before the interval and 55% afterwards.In fact if you plot the number of goals scored in various 10 minute segments over the course of a contest you'll find that the later segments see more goals than the earlier ones.In short the rate of goal scoring increases with time.

The best fit for goal expectancy throughout a game is;

Goal Expectancy during the Game = Initial Expectancy * (Proportion of game left)^0.85

where the initial expectancy is the average number of goals you expect the team to score in today's match up at the start of the game.If the initial expectancy is set to 1 and the proportion of the game remaining to 0.5,you'll get the answer 0.55,the observed fraction of second half goals.

This method gives us a route to determine the effect of a red card on the remaining goal expectancy of each of the two teams involved and thus the expected course of a match post that red card.As we have seen,red cards occur in about 15% of games.However they tend to occur later in matches,Kevin Pressman's red after 13 seconds and Vinnie Jones' yellow after three being exceptions.This makes collecting data for earlier game times problematical,often no data exists.What we can do is collect the average time of every red card and also record the average  goal expectancy for the team receiving the red card and their opponents immediately prior to the incident.If we then record the average number of goals the red card side and their opponents actually went on to score,we will have the average change in goal difference between the sides pre and post the dismissal.

We find that over the last 6 seasons one average dismissal occurred just after the 60th minute and the average change in goal difference amounted to 0.61 of a goal.About 64% of the 0.61 difference occurred because the side with 11 players scored more than they would have expected to score prior to the card and the rest came about by the infringing side scoring less.

We can surmise that the change in goal differences bought about by the card decays at the same rate as ordinary goal expectancy.61 minutes means that about 36% of the game remains,so by plugging the figures into the equation we can find the amount by which two teams will see their goal expectancy difference changed by if the red card is shown at the very start.Usefully we can find out how much goal expectancy a team loses overall from a red card over an entire game.

The answer is about 1.45 goals.

So if a reasonably typical EPL team starts the game a man down within seconds they can be expected to score on average 0.5 of a goal less than they would have done with 11 players and concede 0.95 more goals resulting in a swing in overall goal expectancy of 1.45 of a goal.The figure of 1.45 goals can be re plugged into the decay equation to determine the respective figures at any time throughout the course of the game.For example a dismissal as early as the 33rd minute will cost a team a goals worth of expectancy,split between goals they don't score and extra ones they do and this number can be incorporated into the in game probabilities for that particular game.   

The Most Amazing Soccer Comeback.............Ever!

No blog with "goals" in the title can be complete without the inclusion of the most amazing comeback in the history of soccer if not sport as a whole.

Charlton 7-6 Huddersfield. English League Division Two,1957-58.

Charlton went into their Division two league match against Huddersfield on 21st December 1957 as strong favourites,all that changed when their captain was stretchered to hospital with just 20 minutes gone.The use of substitutes in English football was still 8 years away,so the injury was as bad as a sending off.The incident flipped the game in favour of the visitors and ten minutes later they took the lead.

They'd doubled their advantage by half time and a Charlton goal early in the second half seemed little more than token resistance to the home crowd,who were steadily drifting away due to the worsening weather.Their pessimism appeared to be rewarded as Huddersfield then piled on the goals and held a commanding 5-1 lead with just 30 minutes left.The omission of their up and coming young striker,Denis Law seemed fully justified.

As the pitch conditions continued to worsen a miracle materialised.Johnny Summers,Charlton's winger cum centre forward for the day added four more goals to his earlier strike and Johnny Ryan chipped in with another to see Charlton to a barely believable 6-5 lead with just 5 minutes left.Almost as astonishingly,Huddersfield then pegged the score back to 6-6,but Ryan completed the most dramatic of turnarounds when he turned Summers' cross into the Huddersfield net.

7-6 is about a 1 in 1.5 million occurrence,7-6 after playing for 70 minutes with ten men about a 1 in 2.5 million chance.The game has been charted in terms of success probability as three points for a win was still 23 years away and it's proponent was still winding down his career as a Fulham player.

Scorers.
Injury,Ufton(Charlton),21'
0-1,Massie,27'
0-2,Bain,35'
1-2,Summers,47'
1-3,Bain,49'
1-4,McGarry,51'
1-5,Ledger,62'
2-5,Ryan,63'
3-5,Summers,64'
4-5,Summers,73'
5-5,Summers,78'
6-5,Summers,81'
6-6,Howard,86'
7-6,Ryan,89'

England at the World Cup.The Best and the Worst.

A couple of graphs from the past featuring England at their ultimate peak and their lowest low.

Expected points artificially inflates the in running gap between teams because of the choice of three points for a win.Therefore for each of these games I've plotted "success probability" instead.This weighs a win as 1.0 success points and a draw as a shared 0.5 a point each.This approach more accurately tracks how close each teams are to winning the match rather than reflecting the amount of league points teams are likely to accrue.

England 0-1 USA,World Cup Group Stages Brazil 1950.

England didn't consider the FIFA World cup important enough to enter until the competition had been in existence for twenty years,so 1950 was their first appearance at the finals.The team consisted of some of the biggest names from England's long history.Mortensen,Finney and Wright played in the match,while a recently arrived Matthews watched on from the stands.The later to be Sir,Alf Ramsey played fullback.

The USA team,consisting of part time players and coached by a Scottish born manager,were unconsidered 500-1 shots to lift the trophy (England by contrast were just 3-1),but they scored the game's only goal in the 37th minute.Some English newspapers thought the scoreline had been misread and assumed that England had won 10-1.They hadn't.

Scorer:United States,Gaetjens 37'.
.........................................................................................................................................


England 4-2 West Germany.World Cup Final 1966,Wembley Stadium.

Redemption of sorts for Alf Ramsey,soon to be Sir Alf.A fullback in the defeated England team from 1950 in Brazil,his "wingless" wonders" made full use of home advantage and some generous officiating to usher in "30/40 years of hurt" for England fans.
The game was a magnificent example of two equally matched teams producing a tense contest,as first one team then the other saw their advantage quickly nullified before controversy swung the game massively in England's favour late in the day.The graph gives a strong impression that it was all over after 101'.It certainly was after 120.

Scorers.
0-1,Haller,12'
1-1,Hurst,18'
2-1,Peters,78'
2-2,Weber,89'
3-2,Hurst,101'
"they think it's all over...."
4-2,Hurst,120'
"it is now".

Blasts from the Past.....Newcastle 4-4 Arsenal.

An extraordinary graph with Newcastle's EP spending over 80 minutes at 0.08 or below before leapfrogging Arsenal's EP for the last 7 minutes.This game more than any illustrates that the current EP merely takes you to the current position in the game and the size of that EP is an expression of what happens afterwards ON AVERAGE.

Diaby's 50th minute red card certainly made Newcastle favourites to score more than Arsenal in the remainder of the match ,but the four goal cushion should have been sufficient to enable the Gunners to hang onto the points.The dismissal advanced Newcastle's EP from 0.001 to 0.01 and Arsenal would have won the game from that position 794 times out of 800 and draw it on 5 other occasions.They'd have lost just once.
Countless Geordie fans had already made this mental calculation for themselves and left the ground at half time.

Even when Barton converted a 68th minute penalty the EP barely moved and Best's 75th minute second still saw the respective Newcastle and Arsenal EP at 0.07 and 2.879.

Crucially the clock was now favouring the 10 men visitors and just 5 minutes after Best's strike Newcastle's EP had halved,but Barton's second penalty suddenly made the impossible merely improbable.It had taken 82 breathless minutes to return each teams EP to the values they'd had after Walcott had opened the scoring after a minute.

Tiote's strike was worth just under an EP of 1 (almost 3 and a half times the worth all thee previous goals and the sending off combined) and propelled the home side to marginal EP favourites,but Arsenal held out to ensure that this game wasn't the 1 in 800 when a team gives up a 4-0 half time lead.

Eight goals in total and everyone of them integral to the final result,Tiote's strike claiming the EP plaudits.

Individual Goal Values for the EPL 28th August 2011.

WBA 0-1 Stoke.
Stoke's record of 20 wins,8 draws and one defeat against WBA over the last 20 years was added to with a high value last minute strike from a full back playing as a makeshift striker.Tight,low scoring games are always going to lead to high value goals and Shotton's strike,coming as it did in the last minute was one of the highest you'll see all year.

ManU 8-2 Arsenal.
Big margin blowouts for favoured teams rarely produce very interesting graphs as the team EP quickly approaches 3.This game was very slightly more interesting than the usual rout.United led 1-0 when Arsenal won a 27th minute penalty and a successful conversion would have dropped United's EP from 2.67 to 2.04 and raised the Gunners' from 0.2 to 0.7.However,following the early season trend,Van Persie failed from the spot,60 seconds later the Red Devils were 2-0 up and their EP had climbed to 2.92 and Arsenal's was down at 0.05.A converted penalty may not have changed the ultimate result,but the miss led to a massive EP swing compared to what might have been.
Neither Rooney's hat trick,nor Arsenal's two goals registered much on the EP scale and neither team's EP showed any movement for most of the second half. The 4th red card of the season for Arsenal was meaningless in the context of game EP.

Tottenham 1-5 Man City.
Man City were not as big a favourite as their near neighbours,so there was more EP on offer for a comfortable victory. Dzeko's first three goals easily outscored Rooney's hat trick later in the day.Any potential to accumulate  significant EP had vanished by the 55th minute barring a concerted Spurs comeback and that was never on the cards.

Newcastle 2-1 Fulham.
A fairly standard example of a comfortable home win involving two evenly matched teams was briefly interrupted by a small blip bought about by Dempsey's late consolation.

How much a Team's Expected Points were increased by each Premiership Goal.

SCORER	TEAM	Goal Time (mins)	Pre Goal Points Expectation.	Post Goal Points Expectation.	Increased Points Expectation.
SHOTTON	Stoke	90	1.05	2.81	1.76
BEST	Newcastle	48	1.52	2.44	0.92
DZEKO	Man City	34	1.40	2.27	0.87
WELBECK	ManU	22	2.08	2.67	0.59
DZEKO	Man City	41	2.30	2.79	0.49
BEST	Newcastle	66	2.53	2.92	0.39
YOUNG	ManU	28	2.67	2.92	0.25
DZEKO	Man City	55	2.85	2.96	0.11
DEMPSEY	Fulham	88	0.01	0.11	0.10
ROONEY	ManU	41	2.93	2.99	0.06
ROONEY	ManU	64	2.96	3.00	0.04
WALCOTT	Arsenal	45	0.006	0.037	0.031
AGUERO	Man City	60	2.98	3.00	0.02
KABOUL	Tottenham	68	0.001	0.007	0.006
NANI	ManU	67	3.0	3.0	0
PARK	ManU	70	3.0	3.0	0
ROONEY	ManU	82	3.0	3.0	0
DZEKO	Man City	90	3.0	3.0	0
VAN PERSIE	Arsenal	74	0	0	0