Champions League Final Ready Reckoner.

Well done to both Chelsea and Bayern Munich who each defied the odds and made the UCL a much more compelling viewing spectacle overall by denying UEFA the "dream" Spanish final.However,the matchup has thrown up one unfortunate occurrence because the final will be held at the Allianz Arena,Bayern's home ground.

Home field advantage is a universal component of professional sports of every kind,so it seems inevitable that the host will benefit by upto three or four tenths of a goal because of the quirk of the pre determined fixture list.The split of "home" fans to visiting supporters won't reach the levels of a normal home fixture and Uefa could try to lessen Bayern's in built advantage by,say giving the home dressing room to Chelsea,but it's very likely that a sizable home field effect will be present on May 19th.

One off finals are almost always contested on neutral ground,but this presents a slight problem when you try to get an intuitive feel for the likely outcome of the game.Virtually every game has home field advantage incorporated into your perception of the course and final outcome of the game,so your ad hoc skills at weighing up a match up almost always includes a HFA component.Therefore,deciding how much of an advantage one team has over their opponent in a neutral venue final requires you to strip out this universal ever present.....and that's not that easy to do without recourse to a spreadsheet.

Fortunately,this year,Chelsea's bad luck in playing the UCL Final on the ground of their rivals means we can look at this game in a very similar manner to how we view most games throughout the season.Namely,Bayern are at home to Chelsea,who's going to win?

One last wrinkle is that German sides don't often play English one's so to make the comparison even easier,I've framed the evaluation in terms of a one off English FA Cup game.The first named team are the home side on the day and the chances on the right refer to the respective sides progressing to the next round,either in 90 minutes,extra time or through a shootout.

All you need to do is select the matchup below that in your opinion most resembles the task faced by Chelsea when they travel to Munich in May.I consider their task on par with,coincidentally Chelsea visiting Old Trafford and that gives Chelsea a 35% chance of qualifying or in this case picking up the silverware.If you think the UCL Final is the equivalent of Stoke trying to get past Manchester United on United's own turf,then you'll be giving Di Matteo's side less than a 20% chance of taking the podium,the fireworks and the trophy.

Equivalent "Settled on the Day" FA Cup Tie.	Home Side's Chance of Qualifying/Away Side's Chances of Qualifying.
Manchester City at home to Manchester United.	0.58/0.42
Manchester United at home to Chelsea.	0.65/0.35
Manchester United at home to Tottenham.	0.70/0.30
Manchester United at home to Liverpool.	0.75/0.25
Manchester United at home to Stoke City.	0.82/0.18
Manchester United at home to Aston Villa.	0.88/0.12

How Chelsea Defied the (Longterm) Odds.

Pictures can often convey situations much more effectively than any number of words and this seems to be the case with Chelsea's heroic rearguard action in Spain.Heat maps brilliantly show how Barca swarmed around the Chelsea penalty area,see Zonal Marking's marvelous piece on Chelsea's tactical approach to the game. The graphic below illustrates how the Blues laboured under the heavy weight of longterm expectation last night and how each team's chances of getting to the final fluctuated throughout the game.

Scorers:
1-0,Busquets,35'
1-0,Terry (Red Card),37'
2-0,Iniesta,44'
2-1,Ramires,45'
2-1,Penalty awarded to Barca,49'
2-1,Penalty missed by Messi,49'
2-2,Torres,90+1'
Chelsea win 3-2 on agg.

Probabilities can only present us with an estimation of the weighted likelihood of a range of possible outcomes and last night a whole glut of the more unlikely actual realities occurred.

Barca were favoured to progress to the Final at kick off.....and it was Chelsea who went through.

Inferior teams who receive a red card on average concede a lot more goals than they score in the remainder of the match.....and Chelsea "won" the game that started after Terry's red card by 2 goals to 1.

Penalties are more likely to be scored than not.......and Messi missed his.

Many have compared Chelsea's performance with that of Liverpool's when they overcame a 3-0 deficit at half time to beat AC Milan in a penalty shootout in the 2005 final.Below I've posted the graph from that game,charting the fluctuating fortunes of Liverpool that night and the shape of the graphs is very similar.Liverpool faced a slightly superior side on neutral territory and had to overcome the scoreboard,whereas Chelsea managed to stay close in scoreboard terms,but were massively disadvantaged by venue,opponent and a decided lack of defenders for large parts of the game.

Scorers:
0-1,Maldini,1'
0-2,Crespo,39'
0-3,Crespo,44'
1-3,Gerrard,54'
2-3,Smicer,56'
3-3,Alonso,59'
Liverpool win 3-2 on Penalties.

Of the two,Chelsea were in a very slightly deeper hole as Messi placed the ball on the spot compared to Liverpool's low point just prior to Gerrard's strike to make the score 3-1.

Overall,Well Done to both teams!

Manchester United 4 Everton 4,Game Graph.

United's 4-4 draw with Everton was a roller coaster ride for both halves of Manchester and contrasted with the most recent 4-4 EPL game where Arsenal took a casual ski lift ride to the top of the mountain in the first half and Newcastle then hurtled downhill to a near impossible victory in the second.I've included both games in graphical form below.

Both games also neatly demonstrate the flaws and the strength of a weighted goals approach to goal scoring.Barton and Best in the Newcastle game and Fellaini and to a degree Jelavic all scored goals that barely raised their respective team's Expected points off the floor,but without their goals their team mates wouldn't have been able to score their more highly valued later goals.

Weighted EP shows who was lucky enough to get the vital goal and dismisses those who scored when trailing by 2 or more because,unlike Sunday trailing teams are much more likely to go onto lose.It's magnificent as a descriptive statistic,but it suffers from tracking short term goal scoring luck over a single season.Players don't alternate their scoring between high and low leverage situations,they are likely to get runs of high or low "value" goals and players should probably be judged more on scoring ability alone than on an ability to score "clutch" goals that may be just a random,short term pattern.Which is why I suggested we develop a context neutral goal scoring stat to sit alongside it's "clutch" counterpart here.

Manchester United 4 Everton 4.

Scorers:
0-1,Jelavic,34'
1-1,Rooney,41'
2-1,Welbeck,57'
3-1,Nani,61'
3-2,Fellaini,67'
4-2,Rooney,69'
4-3,Jelavic,83'
4-4,Pienaar,85'

Newcastle 4 Arsenal 4.

Scorers:
0-1,Walcott,1'
0-2,Djourou,3'
0-3,v Persie,10'
0-4,v Persie,26'
0-4,Red Card,Diarby(Arsenal),50'
1-4,Barton(pen)68'
2-4,Best,75'
3-4,Barton(pen),83'
4-4,Tiote,87'

A team of Man United's quality would have had to entertain a team of Everton's quality an average of 3,000 times before you would expect them to score exactly four goals and not take all three points and as 4-4's go,the Arsenal/Newcastle one was about 3 times as likely to have occurred as was the ManU/Everton one.
Everything is now set up for next Monday,especially as the mid season scoring lull appears to have been replaced by the customary late season scoring glut with City scoring 12 in their last three and United 10 in their last four.

Quantifying Goal Scorers.....Revisited and Expanded.

There has been some amazing work done regarding quantifying the worth of significant events that occur during a football match.The most obvious of these being goals,both scored and allowed.Much of the analysis is based around the concept of in game win and draw probability and it's derived younger brother,the Expected Points added.I include both of these concepts in my game graphs,they are also integral in determining the chances of teams progressing in various cup competitions and also the wider vista of final league position.Omar and Ford have also pioneered this approach,click on their names to read some of their posts.

The rush to provide a more context dependent explanation of goals scored can be illustrated in the following two examples.After 89 minutes of the then goalless early season game local derby between WBA and Stoke,Ryan Shotton nipped in front of a hesitant Ben Foster and prodded home a controversial winner.Stoke were looking likely to take a point from the game,but following Shotton's smash and grab raid,three points became the overwhelming favourite and the travelling Stoke fans were jubilant.

Compared this goal to Seb Larsson's 59th minute goal against The Potters a month later.It was the 4th goal in a 4-0 stroll for his Sunderland team,it merely confirmed a comfortable victory for the Wearsiders and added very little to his side's expected points total prior to his strike.Sunderland fans were no doubt happy to see another goal,but it hardly defined the afternoon,Bramble's 5th minute opener and to a lesser degree Woodgate's 11th minute own goal had already done that.

In terms of Expected Points added it is no contest.Shotton's is worth almost 2 extra points and Larsson's is worth virtually nothing.As a descriptive statistic expected points is second to none,it brilliantly capture's the importance of Shotton's goal and the relatively unimportance of Larsson's.But does it also do a disservice to the Swede.Scoring a goal against Stoke is probably about as difficult as scoring one against WBA and it's very doubtful if a player has much control over when,during a match his goal will be scored.After all,team's can only consistently improve the rate at which they score the opening goal by becoming a better side.They don't appear to be able to break out of the expected first goal rate for a team of their quality merely by trying to score first more often.Therefore,it doesn't seem fair that Larsson should be "punished" because two teammates and an errant opposing defender has managed to grab a goal or two before he has.

What's needed is a number that can be set alongside the current Expected Points Added stat to give credit to the scorer for his actual act of scoring,but is not dependent as much on the game context when he scores it.

If we divide each game into individual minute sections,there are three major game affecting things that can happen within that minute.These are,you can score a goal,you can concede a goal or much more commonly neither team will score and the importance of these events will depend on the time remaining and the current scoreline.So at the moment we are still very much in expected points territory.

If we further dissect Shotton's goal and run through all three possibilities,we find that as already noted roughly 1 expected point became 3 with his goal,but had no one scored in that minute Stoke's current EP of around one would have remained virtually the same.However,there was also the potential for Foster to sprint off his line,grab the ball before Shotton's arrival,punt the ball downfield and create a goal for WBA.Had this taken place,WBA's "goal" would have been equally leveraged and Stoke's EP of one would have crashed to almost zero.So the potential points swing,from a Stoke perspective when tied in the last minute of a game is just under 3,comprising those points they potentially receive from scoring a game breaker and those they lose through conceding at the other end.

But it doesn't end there.The overwhelmingly likely event is no goal being scored,so to find the average potential points swing for a team in the last minute of a tied game we have to include the likelihood of the two goalscoring and one no goalscoring scenarios actually occurring.If we now factor in the 90%+ chance of no one scoring we find the potential swing in this particular scenario from the perspective of one team is......very small.If we now repeat the scenario calculations for the Larsson goal we find that the potential swing in the minute that he scored his goal,leading 3-0 after 59 minutes is......even smaller still.

Our final step in the preparations to take the game situation context out of goal scoring is to calculate the potential swing for every minute of a match and for every potential scoreline differential.Hopefully,it's obvious that this figure will be larger in tied games late in the day than it will be in blowout victories also late in the day.The importance of these doable calculations lie in their use in defining an average potential swing in expected points for a football match.

We can then use this average figure as the baseline for every context specific scoreline that occurs throughout a game.The potential EP points swing for Shotton's minute in the sun at the Hawthorns,when divided by the average for all possible scenarios will generate a number in excess of one,while Larsson's minute will generate a number that will be less than one.

What we've done is describe,numerically the environment of the minute in which a player scored and it describes not only how important it would be for his team to score a goal,but also how damaging it would have been had they conceded or how neutral it would have been had they merely held station.

Shotton scored a high EP worth goal in a potentially high leverage situation....for both teams.If we divide the worth of his goal by the leverage potential of that particular minute,we will get a figure of around one.Larrson scored a very low worth EP goal in a situation of very low potential leverage,so his EP/situational EP will also be around one.In short this approach values the act of scoring and doesn't penalise players who score goals that appear unimportant,or indeed score the first goal in an epic comeback,such as the Newcastle Arsenal 4-4 from last season.It greatly reduces the effect of game situation,while retaining a flavour of the potential leverage that was present at the time of the goal.

This concept isn't new.It is used in baseball and faltering attempts have been made to incorporate it into the NFL.Hopefully I've made a decent attempt at showing how it can be used in football and why it should be used alongside the current weighted goal scoring metrics to give a fuller interpretation of a player's scoring talent where game context may inflate or reduce that estimation.

I'll stick some numbers up in due course.

Chelsea or Barca.Who Exactly are Favourites to go through?

Maintaining a European Super League table that shows how teams from all the major leagues compare to one another is a relatively straightforward,if tedious task.Just as the various domestic Cup competitions combined with the constant movement through promotion and relegation in individual leagues provides a number of collateral form lines throughout each division,Europa and Champions League games provide a similar network of games to provide a means to compare teams from different countries.

Stoke have played Valencia,who have played Barca,who have played Chelsea is just one interconnected and circular formline that can easily branch off and stretch as high as the Bundesliga and as low the English League Two.Solving the reams of simultaneous equations that a matrix of actual inter European club games can generate is best tackled with a fast computer,but once the process is up and running it becomes fairly easy to dovetail each European league inside another.

Southampton and Reading seem to be fairly typical representatives of the likely promoted Championship sides,so it's not surprising to see their pre transfer window incarnations slotting in around 16th place in the current EPL based on collateral cup form this year.Stoke for all their Europa League success would be a mid table Serie A side,relegation threatened Bundesliga one and would probably be looking forward to life in the Segunda Division had they started 2011/12 as a Primera liga side.

But of most immediate interest for this kind of analysis is how Chelsea are likely to fare when they travel to Camp Nou next week in defense of their 1-0 league earned from a possession deficient,defensive rearguard display,punctuated by a liberal use of the longball and ruthlessly efficient finishing.Not dissimilar to the kind of performances from Stoke that is so roundly condemned in post match interviews.

Domestically,Chelsea have regressed for most of the year.At the start of the season only Manchester United were superior to them in England,but they've now slipped behind the likes of City,Arsenal and possibly even Spurs.At the end of 2010/11,across Europe they were better than every Italian side,all bar three in Spain and two in Germany,but a season of turmoil has seen them fall behind Milan in Italy,the top four,possibly five in Germany and a host of Spanish sides.Barca have themselves fallen below the high standards they set in 2010/11,but their demise from best team in Europe/the World to merely second best still leaves them towering above most other teams.If Chelsea had spent their year playing in La Liga they would probably currently occupy one of the congested positions around the top 10 and as such would be in the region of a goal and a half inferior to Barca.

If we add an additional four tenths of a goal to Barca's rating to allow for home field advantage that takes their supremacy in the return leg to around 1.8 of a goal and that equates to a 79% chance of winning the match by any score inside the 90 minutes.Any win for Barca by a single goal,bar a 1-0,will see them win on the night,but be eliminated on the away goals rule and there's about a cumulative 9% chance of any of these scores occurring.A 1-0 takes the game to extra time,a 15% chance and if Barca "win" the 30 minute mini game by any score they obviously progress.It's a 48% chance that Barca score more goals than Chelsea in extra time.

If they "draw" the 30 minute mini game by any score other than 0-0,they again win on the night but are eliminated on away goals.If no goals are scored in extra time and the 30' period ends as a 0-0 "draw",then the game progresses to penalties,where I've assumed neither team will have an edge.A goal less extra time has a 41% chance of occurring.

We now have assembled all the routes to a Barca qualification,along with their respective probabilities and if we add and multiply where appropriate we find that far from being favourites,as claimed by Pep Guadiola immediately after the game on Wednesday,Chelsea are still under dogs.Guadiola's side have in excess of a 54% chance of winning the game without the need for extra time,a 7% chance of winning in extra time and a 3% chance of needing a penalty shootout.Giving a grand total of 65%,much more in line with the views of professional oddsetters than the mind games that were being practiced after the game at The Bridge.

Chelsea 5 Spurs 1.Who Made the Biggest Mistake?

Chelsea 5 Spurs 1,FA Cup Semi Final. 

How win probability can make sense of the game's two big talking points.

Scorelines can often hide a multitude of events that could have changed the course of a match and despite 2012's final score closely resembling the 5 goal thrashing handed out to Bolton by Stoke a year earlier,this game was far from one sided and potentially could have been even closer still.

Virtually all of the post game comment revolved around referee Martin Atkinson's inexplicable actions in awarding Chelsea a second goal despite being poorly positioned and receiving no conformation from his assistant.None of the players involved in the goal line scramble have subsequently confirmed that the ball crossed the line and Atkinson appears to accept that he erred in awarding the "ghost" goal.

Trailing 1-0 to Drogba's 45' strike,Spurs weren't in a particularly healthy position just prior to Atkinson's ill considered intervention.Their chances of turning the game around inside the 90 minutes of regulation time was no better than 8%,but they where right to be more optimistic about the likelihood of taking the match to 30 minutes of extra time.That possibility was just greater than a 20% chance and once into extra time they would hold a 23% chance of winning in the extra 30 minutes allowed.It was a coin toss as to whether extra time would peter out into a penalty shoot out,where there would be nothing to separate Spurs' chances of reaching the final from that of Chelsea.If we combine all the possible routes that were available to Spurs in their quest to return to Wembley in a fortnight's time,they total 18% or roughly a 9/2 chance.

 Once Atkinson had blown his whistle to award Mata his goal the 90 minutes odds for Spurs all crashed.They  were about 60/1 to overturn their now two goal deficit inside the 90 minutes and they were about 15/1 to take the game to extra time.Overall the "goal" combined with the three minutes that had elapsed since Chelsea's opener had dropped their 18% chance of appearing in the FA Cup final down to only 5%.Their potential chances in extra time hadn't changed,but their chances of getting that far or completing a turn around in the 90 minutes certainly had.

Spurs' chances when trailing 1-0 just prior to the 48' "ghost" Goal by Mata.

Game Period.	Spurs' Win Probability.	Spurs' Draw Probability
Spurs' W/DP in 90 minutes.	8.0	20.9
Spurs' W/DP in Extra Time.	23.1	51.3
Spurs' WP in Penalties.	50.0	NA

Spurs' combined chances of Qualifying for the FA Cup Final,18%

Spurs' chances when trailing 2-0 immediately after the "Ghost" Goal.

Game Period.	Spurs' Win Probability.	Spurs' Draw Probability
Spurs' W/DP in 90 minutes.	1.6	6.4
Spurs' W/DP in Extra Time.	23.1	51.3
Spurs' WP in Penalties.	50.0	NA

Spurs' combined chances of Qualifying for the FA Cup Final,5%

If the Atkinson incident was infuriating for the Spurs fans,players and management,they were about to be subjected to the most bitter sweet moment in the history of the FA Cup.Spurred onto the offensive as trailing teams often are,Adebayor broke clear of the Chelsea defence,knocked the ball wide of the onrushing Cech and was felled inside the box by the Chelsea keeper.A penalty and a red card for Cech was a formality until Gareth Bale who had been supporting Adebayor's break ran onto the loose ball and calmly stroked the ball into the net.Atkinson awarded the goal and correctly allowed Cech to stay on the pitch,although he probably should have yellow carded the keeper for his challenge on Adebayor.

2-1 to Chelsea,11 verses 11 and 40 minutes of normal time to go.

It was a perfectly natural reaction from Bale.....but was it the correct one to give his side the best possible chance of getting to the final.Immediately you sensed he would have been better ignoring the ball and allowing Atkinson to award the penalty and dismiss Cech.

An almost unique situation and Bale had only a split second to decide what to do,but everything pointed to a red card and a penalty favouring Spurs more than just the goal.Firstly,penalties are converted at rates in excess of 70%,so they were odds on to score.Next the game still had almost 40 minutes to run making a red card alone worth almost 7 tenths of a goal to Spurs.And lastly,the possibility of extra time increased the potential benefit that Spurs would gain from a Cech dismissal.

If we do the win probability maths we find that the two different scenarios aren't even close and I've listed the individual win probabilities for all scenarios in the tables below.By scoring the goal,Bale lifted his team's chances of qualification to 17% just shy of the levels they were at prior to Chelsea's second goal.But if he'd resisted the open goal and Spurs were lining up a penalty kick against 10 man Chelsea's second choice keeper,their chances of reaching Wembley again in May would have stood at a substantially greater 34%.Never should a goal by your team have been celebrated with such less enthusiasm as this one.

Incredibly by scoring Bale had halved his team's chances of getting to a cup final.Had he resisted the chance we could have seen a clued up Chelsea defender desperately trying to slam the ball into his own net before Atkinson could blow his whistle to award the spot kick.


Bale Scores in the 56' to make the score Chelsea 2 Spurs 1.

Game Period.	Spurs' Win Probability.	Spurs' Draw Probability
Spurs' W/DP in 90 minutes.	6.8	20.6
Spurs' W/DP in Extra Time.	23.1	51.3
Spurs' WP in Penalties.	50	NA

Spurs' combined chances of Qualifying for the FA Cup Final,17%

Bale Shuns the chance,Cech is Red Carded and Spurs are awarded a Penalty.Chelsea 2 Spurs 0.

Game Period.	Spurs' Win Probability.	Spurs' Draw Probability
Spurs' W/DP in 90 minutes.	15.8	27.2
Spurs' W/DP in Extra Time.	41.2	49.0
Spurs' WP in Penalties.	50	NA

Spurs' combined chances of Qualifying for FA Cup Final,34%.

Both incidents were honest mistakes and Atkinson would certainly reverse his if given the chance,but how many could say,hand on heart what course they would have taken faced with Bale's dilemma,even in full possession of the Win Probabilities for each outcome.

How Dangerous are Manchester United Late in the Game.

Stoke City have now played Manchester United four times at the Britannia Stadium during their Premiership career and in three of those four games The Potters have managed to arrive at around the 80th minute with the game all square.The remaining 13 or so minutes of those three games haven't been the most rewarding from a Stoke perspective,as first Tevez in 2008 and then Hernandez in 2010 claimed late winners and only recently did Stoke manage to hold onto their hard earned point.The home side's hoped for cumulative haul of three points became one and the Red Devils increased their points tally at 80 minutes from three to seven.

Watching from the stands there certainly feels like a certain air of inevitability about the possibility of a late United winner.The pressure becomes unrelenting and but for an uncharacteristically skied chance by Ryan Giggs in injury time of the latest encounter,Stoke would be on the wrong end of a 0-3 when playing United to an 80th minute stalemate at home.

Three points for a win was introduced with the intention of persuading teams to take an attacking stance instead of settling for a draw.Two wins and three defeats initially compares favourably with an unbeaten run of five draws,the latter nets a team 5 points instead of 6,an increase of 20% for the former.However,this oft made calculation usually omits to mention that the five opponents in this scenario have also seen their cumulative points total leap from 5 points to 9,an increase of 80% in their case.So denying an opponent an extra two points can still be a better option than a gung ho attempt to turn draws into wins at the expense of more losses.

The adoption of a more attacking outlook where a stalemate is looming would therefore appear to make more sense if it was used by the better team in the match up.Ideally you want to turn more draws into wins than you do into losses in case the extra points you allow your opponents come back to haunt you later in the season.Indeed the final 10 minutes of a stalemated game would appear to be the perfect setting for the best teams in the league to take advantage of the rest.The inferior opponent will at best have eight tiring starters and three,fresh but inferior substitutes.Maximizing effort combined with a widening of skill differences between the teams may combine to see goals flow more freely for the superior side as time expires.

 To see if Manchester United and by inference the rest of the best EPL sides can turn late draws more efficiently into wins,we will start with a typically league average result from tied games after the 80th minute.Two equally matched sides will typically score around a quarter of a goal each in the last ten minutes plus injury time of an EPL game and this will give each side an Expected Points total of 1.16 points from that position.If we take a look at United's record when being held to a draw to the 80th minute,as you'd expect we find that they perform considerably better than an average side.

Man Utd's record when level after 80', EPL 2005-2012 (57 games) and likely record of an Average Side.

Team.	Wins	Draws	Losses	Points per Game.	Goals Scored in Final 10' per Game.	Goals Allowed in Final 10' per Game.
Man Utd.	22	30	5	1.68	0.43	0.12
Average Team.	10	37	10	1.17	0.28	0.28

United have found themselves level with just 10 minutes of regulation remaining on 57 occasions since 2005-06 and while an average side pitched against a team of similar quality to their own would expect to turn 10 of those games into wins and 10 into defeats,The Red Devils scored game clinching goals in 22 of the 57 matches and succumbed in only five.Points per game were almost 50% above average and goals scored and allowed were similarly elevated and depressed,respectively.So United do appreciably better from similar conditions compared to average sides,but that's no more than we should expect.The are perennially one of the top two sides in the EPL and as such are the best team in virtually all of their match ups.

At any time during a match each team will have an associated win and draw probability depending upon the score and the time remaining.Therefore,it is possible to calculate the Expected Points that ManU had in every game where they went into the 80' still level with their opponents and we can compare this total to the actual cumulative total of points they actually achieved in those games.As an illustration I've charted all games from their 2005-06 season below.

The EPL is increasingly a league comprising a bulk of similarly talent mid to lower table sides,with a cream of three or four outstanding sides rising above the herd and the occasional visitation by the Ghost of Derby County at the bottom.Therefore,any attempt to model game outcome will tend to more accurately reflect the mediocre sides which make up the majority of the teams,as opposed to the Derby's and the ManU's of the EPL.If we find that teams at the extremes appear to diverge from our predictions we should at least entertain the possibility that our model has not accurately captured how good or how bad some teams can sometimes be in certain circumstances.

ManU's Game by Game Record when level after 80' in 2005-06.

Opponent.	Goal Time.	Scored by	ManU's EP at 80'	ManU Points at FT.
Man City.	No Goal.		1.58	1
@Liverpool.	No Goal.		1.21	1
Blackburn.	81'	Blackburn.	1.66	0
Spurs.	No Goal.		1.48	1
Everton.	No Goal.		1.66	1
@Birmingham.	No Goal.		1.58	1
@Arsenal.	No Goal.		1.19	1
Liverpool.	90'	ManU	1.27	3
@Wigan.	90'	ManU	1.46	3
Sunderland.	No Goal.		1.86	1
Middlesbro'	No Goal.		1.69	1

With this caveat in mind we can fully let loose our Expected Points model on ManU overall over the seven almost complete seasons from 2005-06 onwards and over the 57 tied games at the 80' minutes.Cumulative Expected Points totals from pre game estimates for every ManU league game since the opening day of the 2005-06 season predicted that the often Champions would accumulate 580 points over that timescale and that compares very well with the 590 points they actually achieved.Therefore on a game by game basis,spread over nearly 250 games a relatively simple goals based model can accurately capture a lot of information about how an outstanding team such as United can perform.

If we now look at the 57 tied games and total the Expected Points for each of the 57 games we find that our model expected United to gain 85 points from a position of equality at the 80th minute mark.The reality was that they overachieved by 11 points and gained 96.In short over a run of 250 completed games,United overperformed against the predictions of a reasonable robust model by under 2%.In more extreme conditions of the final ten minutes of a tied game they overachieved by almost 13%.

How a Goals Based Model predicted United would Perform in various Game Scenarios since 2005.

Team.	Predicted Points Over All Games	Actual Points Over All Games.	Predicted Points at 80' in Tied Games.	Actual Points in Games Tied at 80'.
ManU 2005-12	581	590	85	96

The sample size of tied games is 57 and although this appears impressive it is only the last 13 or 14 minutes of those 57 games.So the reality is that United's presumed large over performance in late game stalemates has been detected in only 800 minutes of football or around 8 and a half games.I've found similar figures in Arsenal games over the same timescale,so we can combine the figures and say that over performance appears to occur late in tied games where the tied,soon to be over performer is a very top EPL side and this has been seen in the equivalent of a 17 game sample.

SAF,Master of the Last 10 Minute Drill?

In such circumstances,the top side will almost always be dissatisfied by the current stalemate,their opponents by contrast will most likely be pleased with a point against top class opposition and so they are likely playing passively compared to aggressively.We have already speculated that tiredness and the differing quality of substitutions will have resulted in the quality between the side being at a peak and additionally tactical approaches by the better side may see them aggressively seeking the win.In short the final moments of such games are fundamentally different from other game situations,which is why an unaltered predictive model may consistently under estimates very good side in these circumstances.

SAF has been quoted as saying that the title race starts in March,although this excellent post on Ravi's Analyse Football makes a great case for that claim being mere mind games from Sir Alex,but there is at least tentative evidence that United under Fergie have a very effective last 10 minute drill in tied games.

Arsenal 1 Wigan 2 Game Graph.

Relegation threatened teams can string status saving runs together at the end of the season.Part of the reason can be down to a side facing an unbalanced schedule over the last couple of months of the season compared to their rivals.You'd rather have a raft of mid table drifters than a host of Champions League aspirants.So that makes Wigan's recent run all the more noteworthy.Their last five games have been against Liverpool,Arsenal,ManUtd,Cheslea and Stoke,(there's always one outlier) and their record of four wins and one moral victory has now made them a longshot to face the drop.The upcoming games against Fulham,Newcastle,Blackburn and Wolves will go someway towards levelling out the challenged they've faced so far and provide enough points to beat the drop again.

Scorers:
0-1,Di Santo,7'
0-2,Gomez,8'
1-2,Vermaelen,21'

The game graph and match itself raise some interesting points.

Wigan's points expectancy when they took the lead at 1-0 in the seventh minute was almost identical to Arsenal's when they went 2-0 down in the eighth minute.

Once Arsenal pulled a goal back in the 21st minute Wigan remained underdogs until just before the 40th minute.

Pre game estimates of how many goals will be scored are much better indicators than any in game scoring spree.Extrapolating the scoring rate from the first 20 minutes would have seen around 14 goals being scored in total.Extrapolating the pre game expected scoring rate to the last 70 minutes would have seen five goals scored in total.For more on this see here

As 2-0 leads go,this was potentially one of the least secure.Not only were the trailing team a top four side and their opponents hovering around the drop zone,but Wigan had managed to leave Arsenal over 80 minutes on the clock.The Latics were about an even money shot to hold on for the win and a 3/1 shot to have to settle for a draw directly after their second goal,but they became only slightly better than a coin toss to take anything from the match after Vermaelen's header.For more on 2-0's see here and here

The contest also demonstrated how a team can dominate possession and lose.  

Bale Shouldn't Have Scored.

Bale's done some great things this season,but he'd have been much better turning his back on the 56' chance and letting Cech receive his marching orders and taking their chances from the spot.

Spurs' win and draw chances in 90 minutes.

Sizing Stoke City.

Just an excuse to post this very poor,camera phone photo of Stoke's 1972 League Cup winning team as they paraded the cup around the Brit before the recent game against Norwich.

Their 2-1 victory over Chelsea 40 years ago in the 1972 League Cup Final at Wembley was rightly commemorated by a pitch side appearance from many of the victorious squad prior to Stoke's home game with Norwich.Any tears that appeared in the eyes of older fans were no doubt down to the typically biting wind that funnelled between the two open diagonal corners of the Brit.But it was difficult not to recall in your mind's eye the glorious images of the red and white striped heroes as they were half a lifetime away on a balmy day in London as they casually strode around the Britannia pitch complete with the ancient trophy.

Stoke's 1972 winners 40 years after the event. 

Which team was fit to lace the others boots was predictably split down generational grounds,but there was a less controversial comparison between the 1972 side and the current Stoke side.The cliche around playing Stoke is that opponents enter the Land of the Giants,but with half the present side measuring in at 6 foot or less,it's never been a particularly accurate assessment.What is undeniable is the change in height,weight and body shape that has occurred across all teams over the 40 years that separates Stoke's last meaningful trophy success and the present day.

Home grown talent was the order of the day in the seventies. The entire back four were born in or around Stoke,Mick Pejic making the comparatively short jaunt in from Chesterton.All four players had also joined Stoke straight from school,meaning that a cup winning defence had been acquired at no cost to the club.Centre forward,John Ritchie was just about another Midlands lad,hailing from Kettering and the bulk of the rest of the side came appropriately enough from either the Red or the White Rose counties of Lancashire or Yorkshire.Only Terry Conroy and substitute on the day,John Mahoney weren't qualified to play for England as they came from as far a field as Dublin and Cardiff respectively.

By contrast with most other teams in the Premiership the Stoke eleven who ran out against Norwich also consisted predominately of home nations talent.However,only winger cum full back Ryan Shotton can claim one of the Six Towns as his birthplace.Fellow full back Andy Wilkinson is a Staffordshire lad,Peter Crouch and Ryan Shawcross were born in the next door county of Cheshire and of the three Irish qualified starters,only Glenn Whelan was born and bred in Ireland.A Bosnia keeper,a German centre half and a Cornish winger is the closest Pulis' line up comes to reflecting the cosmopolitan make up of the rest of the EPL.

Former keeper and present City President,Gordon Banks alone would be able to look down on the majority of the 2012 vintage Stoke side,but would struggle to look his successor,Asmir Begovic firmly in the eye.Full backs were traditionally small and compact and not lean and tall like the present day and for all their undoubted guts and skill both Smith and Bloor physically would hardly get a look in as potential center backs in the present era.Midfield is the area of most similarity across the ages,especially if Pulis had elected to play Pennant instead of Shotton,his versatile,play anywhere central defender.Both units were/are similar in height,although the present midfield would have a little more weight to throw around.Up front,Crouch is an obvious outlier.His strike partner John Walters is not really considered a big forward,but his similarly proportioned predecessor,the late John Ritchie was certainly described as an imposing character in his pomp.

Each player's BMI is included to get a feel for their general physique.As a guide,less than 20.2 is considered underweight,greater than 24.9 indicates overweight.

Comparisons Between Stoke's 1972 and 2012 Sides.

Stoke 1972.	Height	Weight	BMI	Stoke 2012.	Height	Weight	BMI
G Banks	6-1	13-6	24.8	A Begovic	6-5	13-1	21.6
J Marsh	5-8	10-4	21.9	A Wilkinson	5-11	11-0	21.5
M Pejic	5-6	10-5	23.4	M Wilson	6-2	12-8	22.6
D Smith	5-11	12-0	23.1	R Huth	6-3	13-12	24.2
A Bloor	6-0	13-0	24.7	R Shawcross	6-3	12-0	21.0
M Bernard	5-9	10-10	22.1	D Whitehead	6-0	12-1	22.9
T Conroy	5-10	11-0	21.8	R Shotton	6-3	13-5	23.4
P Dobing	5-9	11-9	23.7	G Whelan	5-11	12-7	24.4
G Eastham	5-7	10-6	22.9	M Etherington	5-10	10-1	20.2
J Greenhoff	5-10	11-2	22.4	P Crouch	6-6	11-11	19.1
J Ritchie	6-0	12-4	23.3	J Walters	6-0	12-6	23.6
AVERAGE.	5-10	11-7			6-2	12-4

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.

Blackburn 2-3 Liverpool.

Blackburn's heady mix of ragged defending and potent goalscoring continues to delight the neutral and frustrate their fans as they attempt to keep their heads above the drop line.Around 70% of their games have featured at least three goals,with 3-3's and 4-3's relatively common place.3-2 was the weapon of choice when they overturned the champions elect at Old Trafford and when they defeated fellow strugglers,QPR,but this time they were on the wrong end of the scoreline.

A pulsating game saw each team's Expected Points peak and trough throughout the evening.None more so than in the 25th minute.An early 2-0 lead to Liverpool on the back of Rodriguez's brace had seen the host's EP fall to just over 0.1 of a point,but the penalty award alone bumped it up to nearly 0.4 and upwards again to almost 1.0 as the red card quickly followed.But it settled back down to 0.5 points when Yakubu's tame penalty went unconverted.

The prolonged time spent playing a man down finally cost Liverpool their lead when Yakubu added to his first half header with yet another penalty and the hosts spent the rest of regulation as the team favoured to take most points longterm.That is until Carroll's injury time header sealed a welcome win for the visitors ahead of Saturday's FA Cup semi final derby game.


Scorers.
0-1,Rodriguez,13'
0-2,Rodriguez,16'
0-2,Penalty awarded to Blackburn,25'
0-2,Doni Red Card,25'
0-2,Yakubu missed penalty,27'
1-2,Yakubu,36'
1-2,Penalty awarded to Blackburn,61'
2-2,Yakubu(pen),61'
2-3,Carroll,90+1'