Tuesday 29 May 2012

Predicting EPL Finishing Positions.

Sports statistics are able to tell you what occurred on the field of play at a particular point in a game.However,they vary in their usefulness because we aren't always able to say with any degree of certainty how the individual events contributed towards the final outcome of the contest or if they are repeatable skills that are likely to contribute to future success or failure.The last caveat is the most important for those who try to predict future events from past results.

Manchester City won the Premiership in 2011/12 partly because they equaled or outscored their opponents in  all but five of their 38 games and produced the kind of high class performances you would expect from such an expensively assembled squad.Their scoring and conceding record not only tell us how they won their first Championship for 44 years,but given that it was spread over an entire season,we would expect City to produce a very similar level of performance in 2012/13.The upper regions of the EPL changes very little over time and with their vast wealth Manchester City will be title contenders for the foreseeable future.So we shouldn't be surprised if the record of the Champions of one year is a very good predictor of their record in subsequent seasons.

The most basic measure of a team's performance over a season is their final points total and City's rivals United have recorded final points totals of 83,89,87,90,85,80 and 89 in their most recent seven campaigns and their previous raw,uncorrected for the talent spread of the league,totals are good indicators of what is likely to follow from season to season.A similar level of consistency exists lower down the pecking order where Stoke recorded 45 points in their first year of Premiership football and followed up by amassing 47,46 and 45 points in their three subsequent years.

If we plot the amount of points EPL teams get in one season against the total they achieve in the next we find that the previous two examples are far from unique and there is very strong visual correlation from year to year.R^2 is 0.57 for all Premiership teams since 1993.

For such a simple statistics,the correlation is extremely good,the only correction made to the totals was to allow for the occasional 42 game season earlier on in the sample run.However,improvement can be made.Total league points gained by teams over a season are a function of their win/draw record and it has been long recognised in sports such as baseball and latterly basketball and American Football that points/goals/runs differential and particularly points/goals/runs scored and conceded can reveal more about the true ability of a side than can it's raw win loss record.

The ultimate aim of all team sports is to put goals,runs or points on the board,but while more talented sides are likely to be better at scoring themselves and preventing their opponents from scoring,they may find that the goals arrive in inconveniently,unproductive sequences.Therefore teams may have identical goal differences or even identical goals scored and allowed totals,but may have slightly different win/draw records and thus different points totals.One team may win a sizeable number of very close games,whereas a similar team may see series a tight matches end in equal wins and losses.Although their respective win loss records my be different,their goals scored and allowed records may be identical and in these circumstances,it's common to assume that the "better" team is merely the luckier one.

So evaluating teams based on goals rather than league points accrued through their win loss draw records may highlight lucky teams and therefore be more predictive over subsequent years.Adapting this approach for football requires issues such as treating draws as half a win and accounting for the best and the worst teams tending to play in a slightly higher goal environment that the rest of the league.

Goals based league points projections are compared to a team's actual points total in the table for the 2011/12 EPL below.It's worth noting that Manchester City were meaner in defence and also outscored United,so they possibly should have secured the Championship slightly earlier than the 94th minute of the ultimate game.Based on goals,they were probably just over one win superior to United.

Team. Goals Scored. Goals Allowed. Actual
Goals Based Projected Points.
Manchester C. 93 29 89 88
Manchester U. 89 33 89 84
Arsenal. 74 49 70 67
Tottenham. 66 41 69 68
Newcastle. 56 51 65 55
Chelsea. 65 46 64 64
Everton. 50 40 56 59
Liverpool. 47 40 52 57
Fulham. 48 51 52 50
WBA. 45 52 47 47
Swansea. 44 51 47 47
Norwich. 52 66 47 43
Sunderland. 45 46 45 51
Stoke. 36 53 45 40
Wigan. 42 62 43 39
Aston Villa. 37 53 38 41
QPR. 43 66 37 37
Bolton. 46 77 36 33
Blackburn. 48 78 31 34
Wolves. 40 82 25 27

Both the strengths and the weakness of using seasonal goal totals to evaluate the amount of points a team "should"  have acquired over a season is highlighted in the case of Newcastle.Their goal difference of +5 is certainly atypical of the teams in the immediate neighbourhood,it's more indicative of a mid table finish rather than top six.Eight of their league wins were by a single goal margin and if a couple of those wins were turned into draws their points total would begin to fade badly because of the three points for a win system.Spurs,who finished just above Newcastle,scored 10 more goals than the Tynesiders and conceded 10 goals less.They had a much more conventional top six goals profile and they won just 5 games by a margin of a single goal.So Spurs would seem to be a more solid prospect to maintain their form next season compared to Newcastle.

However,Chelsea who finished just below Newcastle again with a conventional top six goals profile had one more single goal victory than did Newcastle.Clearly this approach is capturing other factors as well as simply highlighting streaks of narrow victories that may not be repeated in later years.

Wigan in 2009/10 finished with 36 points.Based on their goals record of 37 scored and 79 allowed they would have expected to have been comfortably relegated with 26 points,proportionally the biggest difference between projected and actual values in the last 20 years of EPL football.However,contained within their record was an 8-0 defeat at Chelsea following an early red card and a 9-1 reverse at Spurs with a full complement of players.The Latics had the good sense to concede 17 of their goals in just two games and for the rest of the season they played and accrued points befitting a competitive bottom six side rather than the relegation certs that their final goals record predicted.The following season Wigan again performed like a "good" bottom six side and they stayed up again with 42 points.In Wigan's case their actual points were more predictive than their record derived from goals scored and conceded.Newcastle's record this season didn't contain anything as extreme as Wigan's two catastrophic defeats,but they did ship five at both Fulham and Spurs and four at Wigan.

In short,rare and extremely large defeats can be shared out over the seasonal record making teams appear much worse than their raw win/draw record.Leading to the latter measure becoming the more indicative measure of future performance.

Having highlighted the issues that exist when using goals scored or allowed to get a projected league points total that attempts to account for an excess of fortunate,narrow victories,the final step is to see if overall these projections give a better prediction for subsequent years compared to using actual points from the previous year.

The plot pairs the goals based points projection with each team's actual points total from the next season for all years since 1993.Visually the fit is similar to the previous plot,but the r^2 is slightly higher at 0.61 indicating a better correlation.Although flaws exist,particularly when teams suffer large margin defeats,either because of red cards or simply by throwing in the towel,it appears that extra information can be captured by investigating a team's seasonal goals record.Newcastle are unlikely to repeat this year's points total of 65,but are equally unlikely to fall to levels close to the 55 points predicted by their goals based projection.Prior to any gain or loss of talent in the transfer window and most likely projection is 7th or 8th with a 2012/13 points total in the mid to high 50's.

Saturday 26 May 2012

The Fundamental Flaw Of Penalty Shootouts.

A week on from Chelsea's Champions League triumph on Bavarian soil over "host" team Bayern and reactions to their overtly defensive display remains mixed.From the Kings Road to Monaco the matter rather than the manner of the victory is the only really pertinent fact from the evening,while neutrals and partisan Germans are still less than enthralled.Consequently,it's easy to imagine that Sepp Blatter's vocal denouncement of the penalty shootout format that allowed Chelsea their victory was also a veiled reference to "anti" football overcoming the entertaining "good" variety.As if the Nou Camp wasn't bad enough.....

Blatter explained his dislike of the shootout in terms where "team essence" was sacrificed to individual "one on one" duels.This convoluted reasoning is certainly at odds with FIFA's recent views on the subject where a spokesman (Mr S Blatter) in 2010 suggested that penalties should be used after 90 minutes of deadlock as opposed to the current 120 minutes,thereby reducing the ability of "team essence" to come to the fore even more.Presumably the logical extension of this drive towards team inclusiveness would also be the abolition the various Golden Boot and Glove Awards and the attendant lavish hospitality.

Blatter has entrusted Bayern Munich President,Franz Beckenbauer the task of coming up with an alternative.His suggestion will be eagerly awaited,once the raw disappointment of Saturday night has disappeared and fortunately for Chelsea any rule change is unlikely to be retrospective.Happily,Didier Drogba can leave for China as a true Blue legend and following his stint of torch carrying,a true Olympian,to boot.

It is certainly easy to poke fun at FIFA,but for once Blatter's views may have substance,even if his motives are less transparent.The penalty shootout is certainly a flawed device,but not for the reasons he states.Individuality will always exist inside team sports and if no decisive result is possible after 90 or 120 minutes of predominately combined effort,then allowing football to go "one to one" is the only real alternative.

The flaw in shootouts arise because the event is highly stacked in favour of the attacking participant.The "team essence" of football is made from both attacking and defensive parts and while it is undeniable that the majority of fans enjoy the attacking element more,both parts play a similar role in overall team success.Different goal environments may skew conclusions very slightly,but overall a goal saved is equivalent to an extra one scored.Defence and attack are equal partners in creating Blatter's semi mystical "essence" and when the time comes to break a stalemate,both should be treated equally.

A clear shot from twelve yards is converted over 75% of the time and while these figures drop slightly overall in shootouts as a result of less recognised penalty takers stepping up to participate,the advantage remains with the shooter.Also few national teams and even fewer clubs sides with have more than a couple of regular penalty takers.Therefore,almost inevitably the majority of such contests will be decided by a player failing to perform a task that he is not well versed in under match conditions.

So under the present format,the taker has the advantage,but because he is "expected" to score he can only disappoint the fans by missing.Conversely the keeper is continually at a disadvantage,even when the lesser kickers start to appear,but he can be the hero by making an "unexpected" save or by causing the shooter to miss.It's a difficult choice to decide who has the easier role.

Ideally we should try to even up the chances of the player scoring or the keeper saving the shot and while trial and error from different shooting distances would give us the answer,we can make an educated guess by looking at goal likelihoods from varying distances in open play.We saw here  that a shot in open play from 12 yards,the distance of the penalty spot,has around a 25% chance of resulting in a goal.These shooting events are of course extremely varied,from one on ones to crowded goalmouth scrambles,but with limited data we have to make do,as long as we accepted the conclusions as being tentative.If we compared the success rate of 75% for the unopposed shot from a penalty to the 25% rate from open play,we can start to see how the presence of a defence on average degrades a player's shooting ability.The likelihood of scoring from the same distance is increased 3 fold from the spot.

If we now take this 3fold rule of thumb we can find the distance from the goal where the chances of scoring unopposed by defenders would be around 50%,thus giving the attacker and facing keeper an equal chance of success.Conveniently,this distance appears to be around the 18 yardline.A 16% chance of scoring in open play from exactly the edge of the box could realistically be expected to approach 50% if the shot was undefended by all but the keeper.

We now have a perfectly balanced contest between the champion of the defence,the keeper and the attacker's champion,the shooter.Neither expectation nor advantage lies with one party or another and therefore success by either is all the more exciting for the crowd because the outcome is a coin toss,albeit one decided greatly by skill.The mechanics of the new shootout could also be varied because scoring is no longer the most likely outcome.Personally I'd go straight to sudden death with shots taken by three nominated strikers who had taken part in at least 10 minutes of the match.But most importantly we now have the ability to settle a tied game requiring a winner by a piece of comparable skill from either the kicker or keeper.

Thursday 24 May 2012

Xavi Isn't Bad For Barcelona.

A couple of weeks ago we had the "proof" that Andre Villas Boas was the superior Chelsea manager because he had averaged 1.70 points per game compared to Roberto Di Matteo's inferior 1.50 ppg.

Casting aside for a moment the legitimacy of ignoring RDiM's Champions League and FA Cup exploits,the major concerns of the methodology used centered around the lack of any adjustment for different strength of schedules faced by the two mangers and more tellingly the small sample sized used in the studies.

RDiM hadn't yet overseen a dozen Chelsea league games and therefore his points per game total was liable to fairly large swings until his sample size increased.If we take an extreme example,a manager who has been in charge for just one game will have taken either 0%,33% or 100% of the available points and only as he  plays more games will other percentages become available to him.

To further reinforce the danger of making bold statements based on little evidence,by the time Chelsea had collected the Champions League trophy,they had played one more league game,at home to Blackburn,which they won.

If they win their opening game of the 2012/13 season and RDiM is still in charge,his Chelsea will have taken 21 points from 12 league games and will have a better points per game strike rate than AVB's Chelsea.So stand by for the "RDiM is a better manager than AVB". articles.

Facts like these are fun trivia,but the direction in which they are heading can switchback or soar in the relation to the paucity of data.Report them,enjoy them,but don't draw hasty conclusion from them that rapidly become today's informed opinion and if a conclusion is required from small data sets,then add as many caveats as you can.

Which brings us to the startling conclusions of one particular post that informs that Barcelona are a better side without/when Xavi doesn't start.The methodology is strikingly similar to that used to show AVB as superior to RDiM.In the 12 league games where Xavi didn't start,Barcelona scored more goals per game,let in less goals per game and had a higher win ratio compared to the 26 league games in which he did start.

If we start with the data used,all of the objections that existed with the flawed Chelsea study are again present here.Namely,small sample size (12 games are being compared to 26).No account is taken of the strength of schedule (Xavi actually played against a marginally better group of teams than those he was on the bench or rested for).

In terms of goals scored and conceded,the batch of sides Xavi played against were more prolific than those where he didn't start and similarly,the opposing defences he started against were more secure than those where he didn't.

So even if we neglect issues around sample size,the data is still raw and skewed against Barcelona's number 6,especially as one of the goals credited to "Barcelona,without Xavi starting" appears to have been scored by a late substitute going by the name of....Xavi.

One of the most powerful thoughts a football blogger can carry,with a hat tip to Simon Gleave's tweet is that "random chance exists. Season also not long enough to remove effect." So if you want to see how Barcelona play with and without Xavi,you should go back more than one season,so that the skill component of the individual results is given an opportunity to overwhelm the random element.

Xavi has,after all played for their first team since 1998 and if his declining influence on matches is true rather than just an artifact of data mining,then it is unlikely to have developed suddenly this season.

Trends would become apparent earlier,unless we have a readily identifiable incident,such as a player returning from a longterm injury.

If you search through a limited,season long amount of games consisting of countless teams and leagues,random patterns will emerge and often they will appear to implicate even great players as being the causative agent.However,data trawling and then assembling a story is rarely rewarded with the effect persisting in larger samples.We see patterns where none exist and single causes where many add to the effect.

To conclude,if we correct all of Barcelona's 2011/12 league stats for opponent strength and split them by Xavi starting or not,we do see the apparent under performance.In the 12 games where Xavi was on the bench at kickoff,if not at fulltime,

Barcelona would have expected to get just over 32 points from those particular games and they got 33.In the larger 26 game sample where he played from the start,they would have expected to get in the region of 66 points and they got just 58.

So it looks bad for Xavi.However,if we start to pull out random 12 game samples from the 26 games where Xavi started we soon get a group of matches where the "Xavi starts" Barca plays as well and sometimes better than the "Xavi doesn't start" Barca.Randomness can produce outstanding results from within a sample of merely great ones,just as easily as Xavi can be made to appear as the agent of Barcelona's decline by a selection of games data mined from a 14 year career.

This approach has as much legitimacy as suggesting that Manchester City are relegation certainties based on their five points from five EPL games during March and April 2012. 

In short,12 games does not define a team's true ability and one player alone doesn't account for all of that change even if it did.I think Xavi's worth is unlikely to take a hit this summer.

Sunday 20 May 2012

How Headed Goals Can Shape A Season.

After serving up 82 minutes of highly organised,if largely unappreciated defensive resilience to their German hosts,Chelsea fell behind to Muller's far post header from just inside the six yard box,courtesy of Kroos cross.The otherwise excellent Petr Cech was unable to lay a decisive glove on the ball as the centre forward's header flew first downward towards the turf and then upwards to nestle into the net via Cech's glove and the crossbar.

Five minutes later and The Blues were back level again following Drogba's thumping near post header from a similar distance.The effort being given welcome extra impetuous by Boateng's hefty shove into the back of Drogba just prior to the Chelsea striker making contact with ball .Neuer,like Cech previously managed to lay a hand on the ball,but it was already destined for the net.

Rewind nearly a week,91 minutes and 14 seconds into Manchester City's seemingly abortive attempt to land the Premiership title and Dzeko plants another decisive header into the net from inside the six yard box.As Silva's inswinging corner arched into the area it was clear that Dzeko was the clear favourite to make contact with the ball and although few would have anticipated the frenzied finish that would result,many fully expected City's replacement striker to bury that particular chance.

Headers,most especially those from close range appear to be extremely difficult for defences to deal with.Uwe Seeler excepted,most similar chances fall to players who are already facing the goal,there's no need to collect and control the ball and it is usually difficult for a defender to put in an effective challenge.From the keeper's perspective the ball is already well off the ground,he has little chance to "read" the strikers intentions and the ball can be struck downwards,as in the case of Dzeko and Muller or upwards as in the case of Drogba.

As goalscoring chances go,a header from close range would appear to be an almost cast iron opportunity to score,so using Opta data from EPLIndex and additional stats from the now defunct Guardian Chalkboards,I've tried to quantify headed goal attempts and illustrate their importance to certain teams.The data is naturally incomplete and almost certainly biased towards the teams I followed most closely via the chalkboards,but hopefully will be a starting point for more detailed analysis.For brevity,shots will refer to efforts made with the feet.

The most obvious benefit from directing an attempt at goal is either a score or the creation of a secondary chance from a forced save and rebound.So I initially used regression to estimate the likelihood that my basket of teams would see their effort hit the target.

How likely is a Shot or a Header to be On Target.

The usual caveats apply,sample sizes are patchy at some distances and the line of best fit is merely an extrapolation.However,at first shots appear to be a more productive option from all distances within the penalty area.Unsurprisingly,both headers and shots have a high probability of hitting the target when taken close to the goal line,but the accuracy of headed attempts falls away rapidly as we move outside the six yard box.Just over half the shooting attempts made from the edge of the box require a save or result in a goal,compared to below 20% for headers from such an "extreme" distance.

The anecdotal evidence at the start of the post suggests that in goal terms,headers are likely to be more to the fore from closer range.So now we'll look at how likely goals are from various attempts inside the box.

How Likely is a Shot or a Header to Result in A Goal.

Immediately we see the potency of close range headers.For the vast majority of the distance to the edge of the six yard box a header is more likely to result in a goal than is a shot from the same distance.If we return to the anecdotal evidence provided by the Manchester City QPR Championship decider,Dzeko's header left Kenny little time to react to the direction of the shot,whereas Aguero's winning shot from a similar distance a minute later at least afforded the QPR keeper the opportunity to anticipate where the strike was going and it also originated from the more conventional ground level.Saving close range shots appears to be a more equal duel between the skill of keeper and attacker compared to headers where the balance is more in the attacker's favour.

Only individually tailored team stats can identify teams which prioritize attacking this sweet spot in the penalty area,but EPLIndex do allow teams to be sorted according to the amount of goal attempts that originate either inside or outside the box.It's certainly a leap,but not an unreasonable one to assume that an increased proportion of shots from inside the box would also imply that the team also made proportionally more of their attempts from closer to the goal.Below is a table showing each team's cumulative shots,headers and goal attempts with various other body parts for the last four completed EPL seasons.

Which Teams Make A Higher Proportion of Their Goal Attempts from Inside The Penalty Area.
EPL 2008-2012.

Team. % of  Attempts from Inside the Penalty Area. % of All Attempts that Resulted in Goals.
Arsenal. 62.9 11.5
Stoke. 61.8 9.5
Aston Villa. 60.9 10.0
Wolves. 59.0 8.5
Blackburn. 58.3 9.3
Newcastle. 58.0 10.6
Manchester United. 57.7 12.0
Manchester City. 57.4 11.9
Everton. 56.0 9.9
Liverpool. 55.6 9.3
Bolton. 54.7 8.6
Norwich. 54.5 10.1
Swansea. 53.3 9.2
Chelsea. 53.2 10.0
WBA. 52.8 8.1
Fulham. 52.0 8.5
Sunderland. 51.2 9.0
Tottenham. 50.9 9.0
Wigan. 50.1 7.0
QPR. 45.2 7.8

The presence of Arsenal as the team making the biggest proportion of their goal attempts from inside the box won't surprise many.The image of Arsenal passing the ball and some would say the buck,before finally shooting has become an enduring emblem for both advocates and detractors of the style demanded of his charges by Wenger.Similarly the bombarding of the opposing penalty areas by Tony Pulis' Stoke is also a well worn cliche of their time in the Premiership.But no doubt fans of the respective teams will be aggrieved and amused that their heros achieve very similar attacking end products by employing polar opposite approaches.

Arsenal have probably achieved perennial Champions League participation by taking their scoring chances in an area where success is at it's highest,while Stoke have achieved survival relatively comfortably by shooting less,but also maximizing their production in this scoring sweet spot.As a consequence of their defensively orientated style,Stoke's attempts are always among the lowest in the league,but their conversion rate almost always exceeds that of their immediate competitors.

Indeed,whether by accident or design,The Potters also play in the most productive area of all,namely inside the six yards box and in the air.Below I've listed the number of goals they scored in and around the six yard box,in the most prolific area of the graph during their first two seasons back in the top flight.They were undoubtedly less skilled than virtually every other squad in the league at the time,so every chance made was precious and with a combination of Delap's throw,set pieces delivered with pace,tall players and an ability to make it difficult for keepers to command their box,they produced a rich harvest of goals,the majority of which came in front of a bemused keeper from the heads of Huth,Shawcross,Fuller and Sidibe.The data is taken from Stoke's yearly review DVDs.

Origins of Stoke's Goals,2008-2010.

Stoke's EPL Season. All Goals Scored from Inside Six Yard Box. Headers Scored from Inside Six Yard Box Total Goals.
2008/09. 20 14 38
2009/10. 18 10 34

The aim of good analysis is to discover areas of the field where you have the biggest advantage and then devise methods to deliver the ball into those areas,either via intricate patterns as in the recent case of Arsenal or more direct means such as Stoke's.Bolton under Allardyce famously deduced where the ball was most likely to be cleared to following a set play or corner and then always positioned a player there to pick up the second ball and judging by Saturday's UCL Final teams as diverse as Bayern Munich,Chelsea and Stoke know where to hit their lofted crosses to maximize their chances of netting.

Friday 18 May 2012

How Costly Was The Woodwork To Liverpool?

The end of the season has recently spawned a cottage industry whereby the wrongs suffered by teams over the course of the year are righted and those sides are assigned their "rightful" place in the Premiership.Firstly we saw Arsenal's rash of unfavourable decisions charted,corrected and the Gunners elevated to runners up spot by a media eager to see conspiracy where there was simply randomly distributed errors of judgement.The press inevitably ran with the story even though the methodology was badly flawed and a big chunk of many team's rich  history comprises the result of miscalculations by both players and officials.For every piece of silverware there is an offside goal allowed to stand against you because the officials mistook a programme seller for the last line of defence.Reducing football to an endless visit to the television match official's replay booth merely serves up the punctuated spectacle that is rugby.

This year we have the saga of Liverpool's fondness for striking the frame of the goal.The average number of times an EPL side struck the post or bar in 2011/12 was around 15,so Liverpool's total of 33 was certainly excessive.Glen Johnson has come out in print with the view that had all of those shots counted as goals,then The Reds would have found themselves around 15 points better off,on the cusp of Champions League qualification and,one presumes,not currently seeking a new manager.

The number of times a team hits the woodwork is fairly strongly related the the amount of attacking they do,so we should expect Liverpool to be among the league leaders when it comes to striking the "woodwork".Stoke,for example attack rarely,but they do it with above average efficiency,realising that points are gained by goal difference rather than simply goals scored and as a consequence tallied just 7 such strikes last year.While the Premiership's top scorers,Manchester City's rate was three times that of The Potters.

If we are to indulge in the fad of revisionism,how should we go about it to remain fair to all teams in the division and not just realign the achievements of one team under the spotlight.Firstly,simply counting a woodwork strike as a goal and adding it to the final score is far too simplistic.Had Suarez scored in the 12th minute at home to QPR instead of striking the post,there is no guarantee that the game would have finished 2-0,comprising the early "goal" Liverpool should have scored and the later one they actually scored.Changing earlier events can only advance the team to a difference level of likelihood that they will eventually win the game.We have to include the small possibility that QPR spurred on by falling behind can pull off a remarkable come from behind they would do later in the year in the reverse fixture.

Twelve minutes in and scoreless,Liverpool would expect to take on average 2.4 points from QPR at Anfield,if we change Suarez's striking of the post to a score,their expect points jumps to 2.8.That's short of the 3 points they achieved for the actual 1-0 where they didn't lead early.So revisionism comes at a cost as well as a benefit.

Secondly,Liverpool are undoubtably outliers,but correcting this aberration by converting all their post and bar strikes to goals and making the team outliers at the other side of the line is wrong.The assumption being made by Johnson and others is that each shot that struck the woodwork was a"goal" that got unlucky.It could equally be a shot that was going to miss the target all together,but then got "lucky" and hit the frame instead.

The third problem is that Liverpool weren't the only team hitting the bar in their games.One of the most highly leveraged "woodwork" incidents happened in the 84th minute against Fulham when Downing hit the post with the game still scoreless.Liverpool's expected points prior to Downing's strike was 1.3,had he scored it would have jumped to 2.7.A difference of 1.4 longterm points in just one incident and comparable to the potential benefit Fulham would have gained three minutes earlier when Dempsey struck Liverpool's woodwork.

Lastly,although 33 strikes appears as though it should have a major effect on a team's final points tally,the raw numbers fail to identify that some games contained multiple hits and some even led instantly to goals.Liverpool were denied in this manner in less than half of their games.Above average without doubt,but a far cry from the near one event per game had each attempt been spread out more evenly.Over a quarter of their total woodwork hits came in four games against Everton,QPR,Villa and Chelsea,all games they went onto win anyway.

So if we are going to estimate a value for the amount of points Liverpool lost because of their bad shooting luck in 2011/12 we need to try to allow for all of these competing factors and we'll start by being unrealistically generous to the Carling Cup holders.Below I've listed all the games where Liverpool struck the bar or post and I've calculated the expected points just prior to the shot and immediately after,only I've assumed that the ball has hit the woodwork and gone in for a spectacular goal.Where games contain multiple events I've credited Liverpool with the event that would have been most advantageous to them in terms of advancing their expected points.Games are arranged with the highest leveraged situations listed first.

How Liverpool's Expected Points would have changed if their Woodwork Strikes had been Goals.

Opponent. Expected Points Prior to Woodwork Strike. Expected Points Had Goal Been Scored. Extra Points if Goal Had Resulted from Shot.
@ Fulham. 1.26 2.73 1.47
@ Arsenal. 1.27 2.28 1.01
Villa. 0.96 1.95 0.99
WBA. 1.87 2.76 0.89
@ Everton. 1.97 2.67 0.70
Newcastle. 2.06 2.67 0.61
Arsenal. 2.38 2.84 0.46
QPR. 2.39 2.83 0.44
@Bolton. 0.12 0.54 0.42
Swansea. 2.44 2.8 0.36
@QPR. 2.68 2.96 0.28
Sunderland. 2.66 2.92 0.26
Wolves. 2.78 2.98 0.20
Chelsea. 2.84 2.99 0.15
Norwich. 2.83 2.97 0.14
@Norwich. 2.87 2.99 0.12
@Villa. 2.9 2.98 0.08
@WBA. 3.0 3.0 0
Total. 39.3 47.8 8.6

So had Liverpool unrealistically converted the majority of their bar or post shots into goals instead of an Expected longterm average of 39 points,they would have taken nearly 48 points from those games.If we add that to the actual 21 points they tallied from games where they didn't strike the woodwork,Johnson's claim of challenging for UCL participation almost becomes a reality,as they now are level on points with 4th placed Spurs with 69 points.

However,the reality would almost certainly have been much less dramatic.Liverpool underperfomed all statistical models,the 39.3 Expected Points just prior to the shots hitting the post in reality yielded only 31 actual points.Events such as their failure to defend a two goal lead at QPR were much more the cause if this type of under performance than bad luck with the woodwork.Furthermore every team hits the woodwork sometimes during a season,Liverpool should expect some of their shots to hit the bar and bounce to safety.

We can simulate these more realistic expectations in such a way as to decrease the amount of rebounding shots whilst increasing the amount of goals Liverpool might have scored,such that they are no longer an extreme outlier.If we do this over a large number of iterations and also randomize the likelihood that Liverpool will receive either high or low leveraged extra goals,the average extra benefit Liverpool would have gained by being more normal in terms of hitting the bar or post,would have been around three points.

So rather than facing the agony of probably missing the chance of UCL football on goal difference to Spurs under The Glen Johnson Model,they suffer the agony of being pipped by Everton by a point for seventh under mine.

Monday 14 May 2012

How Bolton Slipped into the Championship on Survival Sunday.

Bolton's fans arrived at the Britannia Stadium on Sunday hoping for an unlikely escape but prepared to enjoy a Premiership swansong and a relegation party.The final spot in the bottom three lay between themselves and Etihad bound QPR and of the nine possible permutations involving the two games only one,a Bolton win coupled with a QPR loss would keep Bolton in the top tier.

Stoke started the brighter of the two and the home crowd had barely finished their 10th minute tribute to their departing talismanic number 10,Ricky Fuller when they opened the scoring.Walters miscontrolled a fine chance just inside the six yard box,but recovered quickly enough to bundle the ball out of Bogdan's hands and over the line.Referee,Chris Foy looked towards his assistant for help,received none and almost inevitably awarded yet another controversial decision in the Potteries.

13 minutes in and Bolton's pre game chances of avoiding the drop fell from around 25% to below 10%.

Bolton immediately discarded any pretense at caution and the game became stretched as they went in search of goals and two arrived in bizarre fashion five minutes before the interval.Immediately after QPR fell behind to Manchester City,Stoke's Huth,restored to his unnatural full back position clattered an attempted clearance against Mark Davies' legs and into the net to restore Bolton to their pre game survival odds.Namesake Kevin then fired in a nearpost cross that was punched into his own net by a ring rusty Sorenson.Wanderers were now odds on to survive with a success probability in excess of 0.6.

Cisse's equaliser in Manchester briefly swung the odds back towards the London team,but Barton's meltdown and ensuing red card flipped the favourites again.Mackie's barely believable go ahead goal at the Etihad then booted Bolton back to square one once again and the unwelcome news visibly drained both team and supporters.A brief rendition of "Blue Moon" from the Bolton fans failed to produce any change in the QPR scoreline and Bolton's early exertions began to leave gaps for Stoke to exploit.Etherington sliced over from ten yards before Couch fell under Bogdan's challenge and Jonathan Walters scored the goal that ultimately kept QPR above the relegation line.Just over ten minutes of the season remained and Bolton's survival chances were down to 4%,due in no small part to QPR's lead over City.

Had Bolton believed that Manchester City would produce a miraculous injury time turnaround,they would no doubt have pressed forward with much more urgency as time expired.Two half chances and a barrage of corners was all they could produce in the final ten minutes.Although how much the knowledge that the Bolton game had already finished with QPR still level at the Etihad contributed towards Aguero's late,late winner only Rangers' players will know.

I was at Sunday's game and took advantage of the bright day to take some photos,including the goal that ultimately relegated Bolton,although true to form ref Chris Foy managed to get in the way of a clean shot!

A collage of photos from Sunday's Bolton Stoke game.

A few people have asked for a line plot of the probabilities,so here it'is.Personally I find it slightly more difficult to interpret.Major events such as goals or red cards are always major dislocations,but the can appear as more gradual changes on a line plot with a variable axis.

How Manchester City Won the Title.

Quite simply the most amazing finish to any league season and any numerical attempt to quantify the agony of the twists and turns is rightly doomed to failure.

Manchester City fans were no doubt suffering pangs of doubt long before Manchester United became narrow favourites to capture the title when Mackie defied a numerical disadvantage to fire QPR ahead after an hour at the Etihad.

But the final crushing disappointment was handed to the Manchester United players and fans,who stood on the pitch at The Stadium of Light with a near 90% chance of being crowned Champions,only to see Aguero deny them at the absolute death.

How the Title Was Won.

20',Rooney,Sunderland 0-1 Manchester United.
38',Zabaleta,Manchester City 1-0 QPR.
48,Cisse,Manchester City 1-1 QPR.
55,Barton,Red Card,QPR.
66,Mackie,Manchester City 1-2 QPR.
90+2,Dzeko,Manchester City 2-2 QPR.
90+4,Aguero,Manchester City 3-2 QPR.

Rooney's opening goal at The Stadium of Light only edged United slightly closer to the title because the likelihood of a City win over QPR was at that stage still very high.

Zabaleta's opening goal for City gave them a near 95% chance of beating QPR from that situation,so it meant that Mancini should have had a very relaxed half time dressing room.

However,the second half started badly for the blue half of Manchester and Barton's red card excepted it just got worse and worse.......until the very end,of course.

Cisse's goal still left them half the match against inferior opposition to find a winning lead,so even at level terms they were still title favourites,although the nature of the mistake that led to the strike demonstrated that the nerves were starting to twitch.

Barton's 55' dismissal was a big bonus for City,especially as Tevez appeared less than blameless in the incident.

City,with the inevitable exception of Balotelli did well keep their discipline during the highly charged minutes it took to finally remove Joey from the pitch.

It also meant that City's game would finish after United's game at Sunderland and possibly crucially,Bolton's at Stoke.

They had a numerical advantage for around 40 minutes and that's worth just under an extra goal in a comparable 11v11 match.

The remarkable Mackie goal was the strike that finally flipped favouritism in favour of United and the clock rapidly became The Reds' friend.

By the 90th minute City's odds of depriving United were in the region of 4% and this was reflected in the betting markets,but Dzeko's point blank header lifted their chances to almost 25%.

The impossible was now merely improbable.

Time constraints were now so severe that within the minute City's relatively healthy new position had decayed to barely half of it's new found wealth as final whistles were being blown around the country.

Possibly the most significant one was blown by Chris Foy,35 miles away at The Britannia Stadium where Stoke had relegated Bolton and saved City's current opponents QPR.

Newly bereft of any incentive to take anything from their match with City, QPR then capitulated for a second time in two injury time minutes and Mancini, Mike Summerbee, Noel Gallagher and those of the 48,000 who hadn't already departed The Etihad could begin a victory celebration.

Friday 11 May 2012

Chelsea's League Form Under Villas Boas and Di Matteo.

This season's highest profile managerial departure rather predictably came at Chelsea following their 1-0 defeat away to WBA on the 3rd of March.The defeat left Chelsea three points adrift of fourth placed Arsenal,seven shy of Tottenham and confirmed their irrelevance in the Championship race where Manchester City were already swinging away in a 20 point lead over The Blues.

After an opening day draw at Stoke,an early season run of four wins in all competitions hadn't been bettered and fatally for Villas Boas two mid season four game sequences of winless games had recently stretched to one of five games.In the currency most usually used to describe a team's well being,his Chelsea team had averaged just 1.7 points per game.Fantastic if you were managing a mid table team on a budget,but a totally unacceptable level of form for a team used to challenging for top spot.

Abramovich must enter every season with a mind to a replacement candidate for his top job should the need arise and Roberto Di Matteo was swiftly promoted from within.He has now taken charge of Chelsea for ten Premiership matches and has interspersed this mundane fayre with a Wembley rout of their near rivals,Spurs and Cup Final victory over Liverpool and has plotted a course past Barcelona to reach the Champions league final against Bayern Munich.

However,critics of Di Matteo are quick to point out that his points per game haul is inferior to that of Villas Boas.In the Premiership Chelsea have average 1.5 points per game since the mid season sacking and although they have around a 36% chance of qualifying for next year's Champions League as holders,they cannot do so by their EPL position where they can finish no higher than 6th.Had they kept accumulating points at the pre sacking rate of 1.7 per game,they would current have around 65 points,making their chances of qualification through the EPL route somewhat on par with the chance currently enjoyed by Newcastle.

Points per game averages can be skewed by the arbitrary awarding of three points for a win.Few would argue that a win is three times better than a draw,so a more objective approach is to look at a team's success rate,where a draw is treated as half a win.If we do this for each portion of Chelsea's season we again see AVB coming out on top of RDM in performance in the Premiership with success rate mirroring the difference in points per game for each manager.

So by both standards,AVB appears to have got more out of Chelsea on a league day than did RDM in subsequent midweeks and weekends.

Chelsea's EPL Raw Points Per Game and Success Rate Record,2011/12.

Chelsea Team Performance. Villas Boas. Di Matteo.
Points per Game in Premiership. 1.70 1.50
Success Rate in Premiership. 0.61 0.55
Success Rate.All Games. 0.60 0.74

We could leave the analysis there and conclude that AVB was unlucky to be sacked and his replacement has failed to even reach the level of performance that he extracted from an ageing Chelsea team,ripe for change.
However,RDM's detractors have failed to credit him for the additional cup games he has overseen.If we include FA,Carling Cup and Champions League matches in the records of both managers,we not only increase the sample sizes of the games we are looking at,but we also see a large shift in the two success rates.Di Matteo is now the more successful coach and by a significant margin and although his record now contains relatively easy games against Birmingham and Leicester,these are counterbalanced by two games against Barcelona.

We can continue this theme of strength of opponent by returning to only EPL games and once we correct for opponent strength even the argument that AVB outperformed his replacement in EPL matches begins to look much less secure.The average league position of Chelsea's opponents at the time when the game was played when AVB was selecting the side was 11.5,by contrast RDiM's Chelsea faced sides with an average league status of just over 9th.So latterly Chelsea have gained less points per game,but they have on average faced stronger opposition.

We can attempt to quantify this effect by devising match odds from 30 game rolling averages for each team in all of Chelsea's EPL league games played so far this year and compare the expected results against the actual results for the reign of each manager.If we do this we shouldn't be surprised to see that The Blues have underperformed all season,but this declining EPL track record was slightly more pronounced when AVB was in charge than when RDiM was selecting the side once opponent strength was accounted for.So under a system that takes into account who Chelsea played,RDiM is now also the more successful Premiership coach as well as bettering AVB overall.However,...............

Chelsea's EPL Record Corrected for Opponent Strength.

Chelsea Performance. Andre Expected. Andre Actual % Under
% Under
Points Per Game in Premiership. 2.11 1.70 19.4 1.84 1.50 18.5
Success Rate in Premiership. 0.74 0.61 17.6 0.65 0.55 15.4

........this post shouldn't be taken as a declaration that AVB was inferior to RDiM because we simply don't have enough data points to be sure.The 27 EPL games for which the former was in charge is barely enough to gain a decent estimate of a team's worth and the ten game league stint enjoyed so far by his replacement is of insufficient size to make any definite statements.But it should demonstrate that points per game averages are no more than rough estimates,even over dozens of games and are often completely misleading as a means of presenting an opinion about a team or manager.The two men's points per game average alone will tell us very little about their relative quality.Indeed if Chelsea beat Blackburn at the Bridge on Sunday,DiM's average will approach that of his predecessor partly because he has been in charge for so few league games.

At the very least a rudimentary correction for opponent strength needs to be made and even then any conclusions should be tentative rather than definitive.                

Wednesday 9 May 2012

How Will the Final Relegation Spot be Decided?

Every possible scenario for Sunday's relegation showdown and their associated probabilities of actually occurring.

Scenarios Whereby QPR Avoid the Drop.

Gained by QPR.
Gained by Bolton.
for this Scenario.
QPR Points Total.
Bolton Points Total.
3 3 0.02 40 38
3 1 0.01 40 36
3 0 0.02 40 35
1 3 0.03 38 38
1 1 0.03 38 36
1 0 0.04 38 35
0 1 0.23 37 36
0 0 0.36 37 35
Cumulative Probability. 0.74

Scenario Whereby Bolton Avoid the Drop.

Points Gained by QPR. Points Gained by Bolton. Probability
for this Scenario.
Seasonal QPR Points Total. Seasonal Bolton Points Total.
0 3 0.26 37 38
Cumulative Probability. 0.26

How Will the Premiership Title be Won?

Every possible scenario that can be played out on Sunday and their associated probabilities of actually occurring.

Scenarios Whereby Manchester City Win the Title.

Points Gained by Manchester City. Points Gained by Manchester United. Probability for this Scenario. Seasonal Man City Points Total. Seasonal Man Utd Points Total.
3 0 0.12 89 86
3 1 0.18 89 87
1 0 0.02 87 86
3 3 0.53 89 89
1 1 0.02 87 87
0 0 0.00 86 86
Cumulative Probability. 0.88

Scenarios Whereby Manchester United Win the Title.

Points Gained by Manchester City. Points Gained by Manchester United. Probability
for this Scenario.
Seasonal Man City Points Total. Seasonal Man Utd Points Total.
0 1 0.01 86 87
1 3 0.08 87 89
0 3 0.03 86 89
Cumulative Probability. 0.12

Tuesday 8 May 2012

Bolton's Injury Woes.

As the 2011/12 Premiership prepares for it's final Sunday of action much is still left to be decided.Arsenal,Spurs and Newcastle are each eyeing third spot with varying degrees of optimism and the automatic admission to the Champions League that success will bring.Elsewhere matters at the top of the table will depend upon the result of QPR's visit to the Etihad Stadium and to a lesser degree on the outcome of events further north at The Stadium of Light,where Manchester United take on Sunderland.

Many have discounted the possibility of former Manchester United player and Manchester City manager,Mark Hughes' QPR taking anything from their match with City and so the relegation spotlight will once again fall on the Britannia Stadium and Stoke's match with 18th placed Bolton.Last year it was Wigan who made the trip down south to the Potteries requiring a draw or perhaps even a win to secure their safety and they duly delivered with a solitary single goal in the 78th minute.This time around,Bolton don't have the luxury of playing out a stalemate,they must take all three points and then hope that Manchester City win the title with 89 points courtesy of a win over QPR.

Little has separated Bolton from Stoke since the latter's return to the top flight in 2008/2009.The Potter's uneasy reintroduction to top flight football came during a 3-1 defeat at the Reebok on opening day in 2008 and the two sides finished within a place of each other come the end of the year.Stoke were three places above the Trotters the next year,but both teams ended the next year side by side again.Seasons do ebb and flow,but both teams ended each of the last three completed years comfortably above the drop zone.So what has changed this term that has seen Stoke perform largely to expectations,but Bolton enter the weekend as very short odds to drop into the Championship.

We saw here that the amount of playing days lost by a team due to injuries can at least in part explain that team's success rate over the course of the season.(Success rate is merely all a team's wins plus half of their draws divided by their total number of games).We further demonstrated that a team who experience a particularly low rate of injury attrition in one year and then a much higher rate in the subsequent season can experience a noticeable decline in that subsequent campaign.

There is no doubt that Bolton have been very unlucky with injuries this year.The near tragic,but ultimately uplifting story of Fabrice Muamba's remarkable recovery from a cardiac arrest during Bolton's cuptie with Spurs was a keynote event that touched all of world football.But from Chung-Yong Lee's season ending broken leg in pre season against Newport County to David Wheater's ACL knee injury sustained last week in their 2-2 draw at home to WBA,Bolton have had a steady stream of injured players at the Reebok.

On 38 occasions this term they have listed a first team squad player as injured and the combined playing time lost to these incidents is likely to be in excess of 1600 days.Figures can be hard to come by,so I've taken the date on which a player's injury was listed by Bolton and counted his lost playing time from that point to when he next makes a squad appearance.If we compare these figures to the 2010/11 seasons we can begin to appreciate the burden under which Owen Coyle's team have been asked to play.Only 23 injured players were listed during the previous year and playing days lost was around 500,a third of the total for 2011/12.

Therefore,under the definition I used in the previous post on how teams cope with their injury burden,Bolton had a light burden in 2010/11,but a heavy one in 2011/12.At the end of their 2010/11 campaign,Bolton had amassed 12 wins and 10 draws for a seasonal success rate of 0.45 and a relatively comfortable finishing position of 14th place and seven points clear of the drop zone.However,this position had been achieved with a relatively light injury burden and that was going to change dramatically in 2011/12.

If we refer to the table I publish in the previous injury related post we can see that 0.50 success rated teams with Bolton's two year injury profile on average see their success rate fall to 0.38 in year two.A 0.4 SR team fares even worse,falling to a 0.3 SR team.Bolton fall exactly half way between these two category of teams,having a SR in 2010/11 of 0.45.So everything else being equal we would have expected Bolton to have had a SR in the region of 0.34 in 2011/12 given their long injury list following on from a relatively benign one the previous year.A figure perilously below the average success rate for the final relegation spot in recent times of 0.35.

How Injuries Reduce a Team's Success Rate in Subsequent Seasons.

 Success Rate in 2010/11.  Injury Burden in 2010/11. Injury Burden in 2011/12.  Predicted Success Rate in 2011/12.
0.50 Light. Heavy. 0.38
0.40 Light Heavy. 0.30
Bolton in 2010/11.
Light. Heavy. 0.34

Bolton currently have 10 wins and 5 draws from 37 games for a success rate of 0.34,exactly in line with their predicted SR given their record and injury burden in 2010/11 and their injury burden in 2011/12,had we known it in advance.If they beat Stoke on Sunday they will lift it towards 0.36,but that's still close to the SR rate gained by the best of the relegated trio,so they are fortunate that QPR are involved in a meaningful final contest.

It is dangerous to assign one factor too much significance in a side's apparent decline from one season to the next as often teams can under or over perform against their bi annual injury profile because of a multitude of different and competing factors,but Bolton have certainly faced adversity this term.Managers are often prone to exaggeration,but few will dispute Owen Coyle's view that Bolton have had "a freak season in terms of injuries".

Sunday 6 May 2012

The Premiership Fight for Survival.

On of the joys of supporting a Premiership team from outside of the top half dozen is the prospect of sooner or later being involved in a relegation battle.Football should be dramatic and memorable and if your team isn't up to providing the excitement whilst winning silverware then the only other option is to be scrapping for their lives in early May.This year's basement contest has seen perennial strugglers Wigan string together a phenomenal late season burst to counter their winless midterm run and they are now long odds to fall into the Championship,while surprise package Villa had enough early points to also stumble over the line.

With Wolves already gone and Blackburn accounting for little more than one percent of the survival market,the final drop spot is between Bolton and QPR and the final day rollercoaster ride came a week early on Sunday,as first Bolton and then QPR appeared to be in prime position to avoid demotion.

  The penultimate weekend saw QPR and Bolton facing very similar challenges with home games against Stoke and managerless WBA respectively.The R's final weekend match away at Champions elect Man City is partly counterbalanced by their vastly superior goal difference and Bolton travel to the Potteries to face a Stoke side who can be notoriously generous towards needy causes.

On Sunday,Bolton split the deadlock both at the Reebok and in their head to head with QPR by taking the lead over WBA and their chances of survival climbed to over 60%.Both games saw no further goals until Bolton doubled their lead in the 72nd minute,but their two goal advantage was quickly reduced by Brunt's strike 4 minutes later.However,time was now as much a factor as the size of Bolton's lead and as each game entered the final minutes,their chances of survival was in the region of 90%,while QPR's languished at barely 10%.

Everything changed as Cisse's 89th minute game breaker against Stoke saw Rangers' survival odds rocket to just below 50% and Bolton's in turn plummet downwards to meet it.But worse was to follow for the Trotters as they then fell to a late WBA equaliser and after a day that had promised much they enter the final week with barely a 25% chance of playing Premiership football in 2012/13.

Friday 4 May 2012

Scoring Efficiency and Current Score.

As the Uefa Champions league semi final tie between Chelsea and Barcalona entered it's 186th and final minute,the holders and hosts on the night launched one final desperate assault on the massed ranks of the Chelsea defense.The ball was clipped into the Chelsea box,partly intercepted by Ivanovic and then smashed clear by Cole to the breaking Torres,who raced unchallenged into the box before rounding the keeper to claim a draw on the night and confirm The Blues as Champions League finalists once again.

The tie appeared remarkable for many reasons.Not only had Chelsea played over half the second leg with just ten men and Messi had missed from the spot,but they had also enjoyed less than twenty percent of the possession and had been out shot by a ratio of 3:1over both legs.They had managed just 3 shots compared to Barca's 14 in their 1-0 win at Stamford Bridge and had fared only slightly better in going down 16-7 in the return.But as Fernando Torres had so clinically demonstrated in the final minutes of the tie,having the lion's share of the shots isn't as important as how efficiently you finish them and Chelsea had outscored the Spanish giants by 3 goals to 2 in the column that mattered most.

A slightly less transparent fact about the game was that with the exception of the two minutes between Iniesta's 43rd minute strike and Ramires' 45th minute chip,Chelsea had been either level,ahead or ahead on the away goals rule in the tie and as such they had been able or content to stack their defence.The culmination of this partly enforced tactic saw eight blue shirted players stationed within ten yards of the cleared ball during Barcelona's final attack,while Torres' nearest pursuer was twenty yards behind him when he collected Cole's hopeful punt and all that lay ahead of him was Valdes in the home goal.

Arriving at conclusions on the basis of one game or one incident is usually unwise,but it appeared that Chelsea's 30% strike rate owed something to the simplicity of the Torres chance and Barcelona's 7% strike rate was the result of their opponents being able to pack their backline because they had only been behind in the tie for two minutes.Before we can begin to draw wider conclusions we need to work with a larger and more detailed set of results,therefore I'm grateful to OptaPro for providing a season's worth of shot statistics for Arsenal from the 2010/11 season.

In this case the term shots is interchangeable with attempts on goal,be it with the foot,head or any other body part that results in the ball going wide,being saved,hitting the post,being blocked or resulting in a goal.Once in the possession of the timing of every shot from Arsenal's 2010/11 season,I was able to record the frequency with which the Gunners made their attempts on goal and the efficiency of their attempts sorted by whether they were leading,drawing or trailing at the time of the attempt.If we take the Barca/Chelsea example as an extreme case of a team desperate to score creating more numerous,but poorer quality chances playing a team content with the current match situation who create less,but clearer cut chances,we should see a similar pattern emerge in all teams in larger sample sets if the phenomenon is universal throughout football.

Efficiency and Frequency of Arsenal's Shots.2010/11.

Arsenal's Game Position.2010/11. Average time Between Shots. Shots Needed to Score.
Leading. 6 minutes. 8
Level. 5 minutes. 10
Trailing. 5 minutes. 10

Initially,it appears that Arsenal over the course of that season conformed to this pattern.Over the season they made 654 attempts on their opponents goal in scoring their 70 goals (they were also gifted two own goals).The bulk of these shots (70+%) came from open play compared to less than 20% from free kicks or corners.While they held the lead they attempted a shot every six minutes and they needed 8 such shots to register one goal on average.But when the Gunners were trailing or level they increased their shot taking rate to an attempt every 5 minutes,but they required an extra two shots before they found the back of the net.Arsenal,it goes without saying are among the top three or four sides in the EPL,so while losing is always unacceptable to all teams,a team of Arsenal's quality will almost always feel that they should be taking more from a stalemated game.So from this simple breakdown,Arsenal when in the lead are content or required to defend and this on average reduces the frequency of their goal attempts,but because their opponents are also committing players forward,when Arsenal's chances arrive they are comparatively easier ones.

In contrast when the Gunners trailed or were tied in 2010/11,an unsatisfactory state of affairs for one of the best team in the league,they increased their rate of attempts,but were confronted by a relatively content and packed opposition defence.Their opponents appear to set themselves up as a less extreme version of Chelsea for the bulk of the Barcelona UCL tie.Therefore although the quantity of Arsenal's attempts increased, the likelihood of individual shots being successful declined.

Origins and Outcomes of Shots taken by Arsenal in Differing Game Situations.2010/11.

Arsenal's Game State.2010/11. Shots by Defenders as % of Total Shots. Shots Blocked by Opponents as % of Total. Shots from Corners as % of Total Shots.
Leading. 7.0 19.4 9
Level. 14.7 26.5 15
Trailing. 15.7 29.8 19

This shift of game dynamic becomes more evident if we look at the fate of the goal attempts sorted by game state.When leading,the attacking contribution from Arsenal's defenders is at it's lowest point,but this more than doubles when they trail or are being held.Defenders become much more involved at the attacking end of the field and this could account for both the decrease in time between shots compared to when Arsenal lead and the reduced conversion rate.More players are contributing in advanced positions and more chances are being taken by players who are in the team primarily for their defensive prowess.

Blocked shots are also seen to readily increase as game position swings from advantageous to less so,another sign that Arsenal's opponents are less likely to have bodies around to defend with if they themselves are required to try to retrieve the game.

Corners are another by product of attacking play,they are goal attempts that are deflected wide or come about as the result of last ditch tackles.So once again the increase in Arsenal attempts from corner kicks when they trail is an indication of more attacking intent from them,coupled with more defensive efforts from the opposition.

Defining the game state in rudimentary terms such as leading,level or trailing works reasonably well for a team at the top of the tree such as Arsenal.They are not going to be happy drawing with the likes of Stoke at the Emirates or even at the Britannia,so we can probably guess which team will be pressing and which team will be throwing resources to their defence in these situations.But other matches are harder to define.If Wigan are level at Wolves after an hour,which team is likely to be most happy?It's difficult to decide where the attacking impetuous is most likely to be coming from.Therefore we need a more analytical way of defining each side's game position when the shots are being taken.

At the start of a match the combination of the pre game strengths of each side along with the venue will enable you to decide how many points on average each team would emerge with from the game should each teams meet over a large number of repetitions.As the game progresses,the chances of each team winning or drawing will change depending on factors such as time remaining and current score and with it will change their Expected Points totals.By comparing a team's current Expected Points total with their pre game expectation we can develop a numerically based estimation of the game situation.

For example when Arsenal entertained Aston Villa in May of 2011,they kicked off with an average of 2.33 Expected Points.By the time Jack Wilshere's left footed shot missed the target from a corner in the 58th minute,with Villa 2-0 to the good,Arsenal's Expected Points had fallen by over 80% of it's original value to just 0.32.

Arsenal's Predicted Conversion Rates for Shots taken in Differing Game Situations.2010/11.

Current Arsenal Game State as % of Initial Expected Points.2010/11. Best Fit % of Shots
which Result in Goals.
-100 7.3
-80 7.9
-50 8.9
-30 9.6
-10 10.4
0 10.8
+10 11.3
+30 12.2
+50 13.1
+80 14.7
+100 15.9

So as a final refinement,I've taken all 654 goal attempts by Arsenal during last season and recorded both their initial EP and by how much their EP had either risen or fallen at the time of every goal attempt.I've also recorded whether or not the shot resulted in a score and then I've regressed the outcome against the change in Expected Points when the shot was taken.This allows for a predicted strike rate derived from the best fit of the regression line for shots made by Arsenal in the 2010/11 season for a range of different game positions described by the rise or fall in Expected Points compared to pre game estimates.In short,how efficient were Arsenal in relation to whether they were doing better or worse than expected at that point in the game.The same pattern that was present when using the more subjective "leading,trailing,level" approach is again present.Shot's taken when Arsenal's games position is precarious have much lower strike rates than those taken when they are already leading and the more comfortable the lead,the better the strike rate.

Hopefully this preliminary analysis can begin to illuminate goal attempts and conversion rates.It's undeniable that there is a difference in finishing quality between the best teams and the worst teams in the league.Arsenal will always tend to have more efficient strikers with better strike rates than the lesser lights of the EPL.However,it would seem that game position is more likely to drive a team's game by game variation from their normal,average strike rate.

When goals are scored,the way a game is being played begins to change.Teams who were prepared to play for a point have to open out if they go behind or can become even more defensively orientated if they score first and it appears that these alterations can impact upon the quality of the chances that they then present to their opponents.

The proportion of goals a team scores is closely associate with the quality of that team and in the long run better teams will scored proportionally more goals than their inferior game opponents.However over shorter timescales random chance can intervene to allow teams to either over or under achieve and this may lead to good sides trailing for longer periods than you would expect or poorer teams leading more frequently.For example Manchester City are currently top of the EPL,but for a run of five matches recently their universally inferior opponents opened the scoring against Mancini's side.

 If the effects of leading or trailing on a team's shot conversion rates as seen in Arsenal's season is repeated league wide,these atypical scoring runs can in turn distort a teams shooting efficiencies.As a consequence,teams may appear to show unexpected improvement and we may conclude that they have improved by increasing their goals to shots ratio.When in fact they have only benefited from a semi randomly occurring run of goals and they have been able to supplement their strike rate by then playing against teams who are more concerned with attack than defence.The arrow of causation can often run counter to the direction it appears to take.

Random chance plays an extremely important part in deciding low scoring sporting events such as football,especially over a relatively short run of matches,so it's important not to mistake a fortuitous grouping of scores with a real and tangible matter how compelling the evidence.

All data kindly provided by OptaPro.