Passing, Shooting and Tackling In Context.

Over the last couple of posts, I've attempted to use the type of calculations that are used to produce game graphs such as these to numerically describe the average game state experienced by sides from the 2011/12 season on an individual match by match basis. I've then plotted certain match events against these hopefully representative game states to try to identify which on field actions correlate well different levels of game state. As must be repeated throughout this exercise, correlation does not imply causation. Therefore a side may excel at certain things to maintain a positive game state rather than to cause it to come about in the first place or vice versa or more probably, a combination of the two.

The aim is to add context to a team's season long figures and possibly identify individual traits which may define tactical approaches to gaining and maintaining a lead, which otherwise may remain hidden among a variety of different styles. Accurate passing over short distnces is a desired aim of lots of sides, but not all.

In the previous post I looked at how Arsenal become slightly more enamoured with the long, hopeful ball when the game state consistently refuses to turn in their direction. By comparison, Stoke, the leading exponents of long ball football in recent times, are such extreme practitioners of the art that they have nowhere else to go and leave this part of their gameplan virtually unchanged regardless of game states.

I've further looked at pass direction comparisons between these two diametrically opposed sides to see how game state changes the proportion of "negative" backwards and sideways passes each side attempts. I've simply labelled the x axis as progressing from poor to good game states.

To obtain such a strong correlation when examining game by game data, where random variation exists is unusual and the trend, if not the direction of causation appears clear. Arsenal are playing proportionally more forward passes when they have spent a good portion of the match chasing a poor game state. When they have enjoyed lots of positive game states over the 90 minutes, their proportion of backwards or sideways passing has consistently been higher. Possibly indicting a change to a risk averse strategy based on ball retention.

Inevitably, Stoke produce a plot with the opposite slope. They appear to use forward passes (often long) to gain a lead and similar tactics to protect one, by getting the ball as far away from their own danger area as possible. It is only when they are behind expectations and opponents set up to defend that they accrue time and opportunity to play football that involves typically patient build up play.

It is a trait Stoke shared with another struggling side in QPR. Like the Potters QPR only really found the time and space to play, thoughtful probing football when their opponents were content to allow them to.

Most on field actions I've looked at involve some teams taking diametrically opposed approaches to other teams, (making the search to value such metrics equally for all teams slightly futile), but the proportion of shots a side has in a single game invariably follows the same direction for all teams. In short, as a team increases their share of shots in a single game, the more likely they were to have enjoyed better game states.

If you wanted to get Manchester United on the ropes in 2011/12, you had to outshoot them and that inevitably meant you had to be a fellow title contender. The influence of random variation is shown by the outlier relating to 70% of the shots, yet continually poor games states during the 3-2 home defeat to Blackburn.

Liverpool share the plot direction with United, but unlike United, they appeared more dominant in rarely failing to win the shooting battle, yet still found themselves facing poor game states. In a previous post Liverpool were flagged up as being more willing to shoot from distance and an increased number of speculative, low probability shots when trailing or drawing may explain the curve.

There is one interesting outlier in on Liverpool's graph. They barely managed a shot compared Spurs in the latter's 4-0 early season win and ended up facing predictably poor game states. The point should appear even further to the left than it does and if we had accounted for Liverpool's two red cards, that is where it would move. Red cards, a reasonably common occurrence, shift game states, so ideally they should be accounted for.

Stoke look to cut out a pass into the final 3rd. 

We can look at game data from a defensive viewpoint by seeing how the attacking intentions of their opponents are dealt with. Correlations will inevitably be weaker because as we have seen, teams go about winning with a variety of different approaches. Final third pass completion is coveted as a significant indicator for success and this appears to be well justified if we see how successful teams were "in running" when progressively excelling at this skill against relegated side, Wolves.

I've flipped the x axis to prevent the need for some messy recalculation, so a predominately good game state for Wolves appears on the extreme left in this plot. The case for final third completion rates is well made, the more opponents completed their passes and the more Wolves failed to get a toe in, the worse things got and remained so for the soon to be relegated for a second time team from the West Midlands.

I've quickly realised where to look to see if any of these correlations are likely to be universal across all teams and supporters of the final third completion stat will be happy to know that Stoke and Arsenal also follow Wolves' lead here.

The Long And Short Of Games States In The EPL During 2011/12.

In this previous post I used a numerical description of a side's games state, incorporating current score, time remaining and opponent strength to try to identify any strong, team specific tendencies that occurred throughout the ebbs and flows of individual games within the 2011/12 season. An overview of each side's on field actions may broadly outline their preferred approach and highlight strengths and weaknesses, but the way in which teams adapt to protect a lead or reverse a deficit is often obscured. In overlaying the changing game states onto individual matches we may be able to identify these switches in emphasis without the need to march through the ever changing game state for each match on a minute by minute basis.

The coarsest of tactical divisions involves the use of the long ball, as exemplified by such teams as Stoke and Bolton and the use of shorter, more intricate passing movements employed by the like of Arsenal. It is very rare to see the Gunners attempt to send more than ten percent of their passes long, whilst Stoke's proportion of long balls rarely dipped below 20% of their overall total passes in 2011/12.

The contrasting styles of Stoke and Arsenal are well known, but a more interesting question is to what degree to Arsenal adopt a more traditionally English style when their widely admired passing game comes up short and where do Stoke go to if their direct Plan A stalls ?

If we plot the extent to which each side was content or otherwise with their overall game state in each of their  38 matches in 2011/12 against long ball tendencies, the league splits into roughly three equal groups. There was a group of teams which showed a steady increase in the use of long balls in games where they faced less favourable game states. Arsenal fell into this category, along with all of their fellow title and European contenders.

A second group of teams, most notably including Liverpool saw the reverse occur. Elevated proportions of long balls coincided with matches where they had enjoyed the best of the game states and when they struggled they had enjoyed, or been allowed to enjoyed the freedom to pass shorter proportionally more often.

Passing Style In Contrasting Game States, 2011/12.

Team's Playing Proportionally More Long Balls In Poor Game States.	Team's Playing Proportionally More Long Balls In Good Game States.
Arsenal.	Everton.
Manchester United.	Liverpool.
Manchester City.	Fulham.
Tottenham.	Aston Villa.
Chelsea.	QPR.
	Bolton.

Correlation does not imply causation, and a more intimate examination would be the obvious next step. But for the first group, it is easy to imagine that the preferred style of more skilled sides would revolve around ball possession and short passes. However, there comes a time in anyone's depleted game state where the ticking of the clock leads to the temptation to attempt a more direct approach. Arsenal breached their 10% long ball barrier in half of their ten least impressive matches as measured by overall game state dominance. Their ten best game state performances didn't see long ball % once better 9% of total.

US Import, Reo-Coker hoofs it long for Bolton in 2011/12.

The second group definitely need granular evidence before solid conclusions are reached. Did Liverpool get into good games states and also maintain that advantage with long balls, (Suarez's hat trick goal at Norwich, 40 yard pass followed by a 50 yard shot, suggested they made good use of the long ball in 2011/12). Or did they accumulate lots of short passes when trailing and faced with packed defences ?

Stoke appear in neither group. Their output of long balls were indifferent to game state as measured on this game by game basis. That might imply the non existence of a Plan B, a thought long held by some Stoke fans over their present time in the Premiership. That would be a poor legacy to Tony Pulis' rapidly ending tenure at the club. I prefer to think that I haven't quite found it among Opta's copious amounts of data.

Game States And Attacking Tendency.

One of the biggest challenges in football analysis is to add context to the ever increasing raft of available figures. A team's objective at the beginning of a game will range from securing all three points, if they are the superior side in the match up, to avoiding defeat, if they are the inferior team on the day. How they achieve these various aims will greatly depend on the match situations they face, defined primarily by the current score and time remaining. In short Game States are hugely influential, along with opponent quality in determining the kind of match statistics that a side may record.

The largest, readily available source of match by match data was released by MCFC and Opta last year and contains over 200 categories of in games statistics for each side for every game played during the 2011/12 season. It is therefore, in the absence of more detailed play by play data, an ideal source to test the observation that teams will prioritize different actions during different game states.

The most obvious place to begin is how teams attempt to score their goals, but first we need to quantify a teams current desire to increase or open their account. Current score is a good starting point, but time elapsed is also a major factor. A side's approach to rescuing a single goal deficit will be different if just ten minutes has elapsed compared to a match entering it's final ten minutes. Similarly, a team's inbuilt strengths and weaknesses, as well as their preferred style will also impact on their approach. Finally, relative team strengths add to the game's dynamic. It has been well documented that a mid table team drawing away to a title contender is likely to be a satisfactory game state for the former, but not the latter.

Each of these contributing factors can be broadly described numerically and whilst they are less reliable than using methods such as these, which attempt to track the ever changing game states, they are adequate.

Identifying how content the top sides in the Premiership are with the current score is relatively easy. As with all sides, losing isn't a satisfactory state, (although this is also time dependent) and neither in general is a stalemate for the very best sides. It appears that such sides increasingly shoot from greater distance as these unsatisfactory conditions persist. I therefore compared how the ratio of long range shots to total shots varied by game state on a match by match basis for all EPL teams from 2011/12 to see which sides shared this preferred approach. The teams where the correlation was strongest are listed in the table below.

Swansea demonstrate a tendency to shoot from distance when behind.

Swansea attempted 35% of all their shots from distance in matches where their game state was consistently poor compared to below 25% when they were at their most dominant. Teams which aren't listed showed no game state dependent preference in these particular categories.

Attacking Intentions In Unfavourable Game States For EPL Sides 2011/12.

Sides Which Shoot Proportionally More From Distance In Poor Game States.	Sides Which Cause Opponents To Make Proportionally More Headed Clearances In Poor Game States.
Swansea.	Spurs.
Fulham.	Chelsea.
Liverpool.	Aston Villa.
Wigan.	Newcastle.
Sunderland.	Liverpool.
Spurs.	Everton.
Manchester City.	Blackburn.
Arsenal	Bolton.

In contrast, the second listed sides forced their opponents to make proportionally more headed clearances when they themselves struggled by their own realistic expectations. Possibly indicating a different attempted method to turn around a match centred around more frequent aerial attacks, or at least an approach which  results in more opportunities to loft the ball into dangerous areas of the pitch.

Opponents finding themselves successfully defending an acceptable match position against Spurs had to deal with over 60% of clearances with their head. Those figures dropped to below 20% when Spurs were the team in control of the game.

There may be slight issues of correlation verses causation in these figures which a more granular approach would address, but the trends for sides to alter their approach depending upon games state appears strong, especially as game by game figures have been used. A lack of homogeneity of approach by teams seeking to turnaround a poor situation is indicated, reinforcing an expected lack of correlation overall between individual match events and game results.

Leading When It Really Counts.

The fundamental building blocks of football analysis are fairly well established. Goals are the rare, but intrinsically valuable currency from which virtually every other match outcome can trace back their origins. Likelihood of winning, the outcome of most interest, is strongly correlated to the ability of each side involved in a game to score and prevent goals. The ability to explain the past and predict the future with reasonable accuracy, in larger enough game samples is well within reach.

Fortunately, shorter term variation from these expected norms are also common place and it is this random noise that prevents football from becoming a sterile exercise in number crunching. Consequently, a team which, for instance suddenly shows an elevated home field advantage may be recording these figures through random variation or through a fundamentally different approach at home compared to away. The temptation is to try to rationally explain the latter, when the cause is almost always predominately due to the former.

Time spent leading, drawing or losing hasn't really received the exposure of home field advantage or outright match results, but along with most data recorded in football, it can significantly alter the course of side's season by departing from the line of greatest expectation and help to deliver randomly driven season long highs or lows that are rarely repeated.

Teams cannot chose precisely how many goals they will score and concede over a set number of games, nor can they decide how those goals are distributed within games. But if they could the optimum return for a six to three goal count spread over three matches would be achieved by way of three 2-1 wins. A less favourable outcome would result if all six goals were confined to just one of the three matches. Similarly for lead time, three games where a first minute concession was only overcome by two injury time replies would result in greatly differing lead times compared to a scoring sequence where goals were scored early and conceded late.

So variation is to be expected, even in large numbers of matches and if this variation results in better than expected outcomes, we may overrate sides on the seemingly soundest of evidence, only to be disappointed when they revert to a level of results more in line with their actual skill levels.

Lead time, combined with goal distributions is a prime candidate for causing such miscalculations. As with goals, teams aren't entirely in control of when they lead during a match. Obviously and ideally a side would like to lead going into second half injury time and see the result through for three points. A team gets no added points for leading for a large portion of the match if they then succumb near to the final whistle. In short, is the ability to hold a lead for longer a better indicator of repeatable skill than the other extreme of gathering points with late winners ?

To try to answer this we first need to create a baseline which correlates time spent leading (and ideally drawing) to points accrued over a season. Modelling the data along the lines of this post from last year, appears to highlight a subtle difference in the importance of time spent leading for the poorer teams and the rest. A team with a winning chance of around 20% or less sees their chances of leading peak just after the halftime break, whereas those with winning chances of 20% or greater see their chances of leading constantly rising until the full time whistle.

For example, a side with a 10% chance of winning a game has a greater than 11% chance of leading that game after an hour.

By contrast strong favourites will see their chance of leading the game consistently rise until full time is reached.

The inability of poor sides to hold onto a lead when faced by much stronger opposition has implication for the use of time spent in the lead as an indicator of overall ability. The relationship between lead time and expected points is likely to be different for changing team quality, particularly for those poor sides which spend proportionally more of their lead time mid game (when no actual points are awarded) and less at the game's end (when they are).

We can produce average expected points for differing team quality derived from actual lead/draw time and actual points gained for whole seasons and equally for a single match. The most memorable game from last year's EPL was the last to finish, Manchester City 3 QPR 2. City spent little more than ten minutes leading this game and almost an hour all square. The majority of points scoring outcomes from games with these type of lead/ draw times are going to be draws, occasionally, as happened last season to City, a team will snatch an unlikely win.

Expected Points Based On Lead/Draw Time Comparable To Manchester City's Final Game With QPR.

Type of Team.	Average Expected Points from Such A Game.
Big Four Side.	1.2
Other Top Ten Side.	0.9
Bottom Ten Side.	0.8

The ability of top four sides to lead when it matters is illustrated by the line of best fit for three types of team. A top side which had the lead/draw time in a single game identical to Manchester City in 2011/12's final game would expect to average 50% more points than a bottom 10 side under identical circumstances.

Lead/draw times are good indicators of expected points and possibly better future performance indicators than actual points totals, but they also depend on team ability.

On a game by game basis from last year, Manchester City's lead/draw time would have resulted in a typical big four team accruing 86 points, three short of City's actual total. So they gained three more points than expected. By contrast, United's lead/draw time resulted in 89 actual points compared to an expectation of 88. A case of City getting slightly luckier than United ?

The sight of poorer sides leading mid game, but losing when it really counts has been common theme of United's games this season. Newcastle, Villa and Southampton each led mid game, but United led at the final whistle. The champions trailed for over 100 minutes in those three games and led for less than 5 minutes, figures that would see even the best struggling to take much more than a single point on average, yet United ended up with all nine points.

Around par for the course last term, this time around United have stretched their points total way beyond repeatable levels with a glut of timely scores. By trailing to seven teams after an hour, but losing to just four by full time, they are respecting the spirit of what a team of their quality may expect to achieve, but hardly the letter of the law. A six and five split would be much nearer to a typical Big 4 expectation.

They deserve to be champions, but they have also been, at times extraordinarily lucky as well. Their current lead/draw time is characteristic of a side just approaching 80 points rather than one powering on towards 90.

It's most likely not a trick they will consistently be able to repeat.

Last Year's Model.

How many games should you look at when you are trying to estimate the likely true worth of a football team? It's a question that is often raised, especially in a betting context and is one that we can try to intuitively answer by reference to a team which we already know a great deal about. Manchester United are almost certainly this year's best Premiership side. The manager of their closes rivals has already conceded the title, even if the feeling is not universal within his coaching staff.

If we go back a couple of days to take evidence of United's fitness to be regarded this year's best side, the evidence is far from compelling. A late and disputed draw at West Ham hardly smacks of greatness. If we quite reasonably increase the sample size to two matches by pushing back to last Sunday, a win at Stoke hauls the points total to more respectable levels for the champions in waiting, but skip back another week and a loss at home to rivals Manchester City returns the win/draw/loss record to mediocre levels.

It is only when we regress towards Christmas and ignore a patchy cup record that United's record begins to appear worthy of their current position. More, it would seem is better, even if we have to pay the price of recency within the numbers.

After just a single game the balance between random variation and recognizable, repeatable talent is heavily weighted in favour of the former. It only through gathering evidence from more matches that the balance begins to shift and the results we measure begin to better describe a side's ability. How we use these measurements made over differing timescales can help to verify the strength of our belief in the validity of each set of figures and the most obvious way to test our faith in our faith in a measurement of a repeatable skill is to use such figures to make predictions about future performance.

This isn't the post for a detailed description of a predictive football model. suffice to say the path from Poisson to match odds is well worn and the inputs derived from goals scored and conceded via rates rather than simply raw numbers is only slightly less trodden. In short, workable models to predict football matches through individual team scoring rates are relatively simple to produce.

Below I've generated odds for a randomly selected group of matches (they were actually played on Boxing Day 2007) and the averages used for the Poisson have been found using the previous 35 matches for each team, the previous 20 and lastly, the previous six matches. The figures in red are typical bookmakers prices for the relevant matches for the home win, away win a draw.

Poisson Generated Odds Using Last 35 Games.

Game.	Score.	H. Win.	A. Win.	Draw.	H. W.	A. W.	Draw.
ManC v B'burn.	2-2	0.44	0.29	0.27	0.45	0.26	0.29
P'mouth v Ars.	0-0	0.28	0.44	0.28	0.21	0.52	0.27
Che v AV.	4-4	0.62	0.11	0.27	0.68	0.11	0.22
Eve v Bol.	2-0	0.77	0.08	0.15	0.56	0.17	0.27
Tot v Ful.	5-1	0.71	0.13	0.16	0.66	0.12	0.23
Wig v New	1-0	0.32	0.41	0.27	0.35	0.36	0.29

Poisson Generated Odds Using Last 20 Games.

Game.	Score.	H. Win.	A. Win.	Draw.	H. W.	A. W.	Draw.
ManC v B'burn.	2-2	0.54	0.22	0.24	0.45	0.26	0.29
P'mouth v Ars.	0-0	0.30	0.42	0.28	0.21	0.52	0.27
Che v AV.	4-4	0.55	0.16	0.28	0.68	0.11	0.22
Eve v Bol.	2-0	0.78	0.08	0.14	0.56	0.17	0.27
Tot v Ful.	5-1	0.66	0.16	0.18	0.66	0.12	0.23
Wig v New	1-0	0.35	0.41	0.25	0.35	0.36	0.29

Poisson Generated Odds Using Last 6 Games.

Game.	Score.	H. Win.	A. Win.	Draw.	H. W.	A. W.	Draw.
ManC v B'burn.	2-2	0.80	0.08	0.12	0.45	0.26	0.29
P'mouth v Ars.	0-0	0.28	0.39	0.34	0.21	0.52	0.27
Che v AV.	4-4	0.58	0.12	0.31	0.68	0.11	0.22
Eve v Bol.	2-0	0.85	0.05	0.10	0.56	0.17	0.27
Tot v Ful.	5-1	0.89	0.02	0.08	0.66	0.12	0.23
Wig v New	1-0	0.43	0.36	0.21	0.35	0.36	0.29

Testing a new model usually requires a couple of obligatory steps. A large number of matches are used to determine the hopefully predictive inputs and then these are tested on a new set of out of sample games so we can be satisfied that we haven't overfit the predictors and modeled noise as much as signal.

However, as a workable shortcut we can use the bookmaker's expertise to arrive at an approximation of our model's validity. Once shorn of the overround, bookmakers odds are excellent indicators of the true odds of an event occurring. If you gather up all the 4/7 shots, they are going to win just over 60% of the time. So if your odds are close to the quoted odds, that is invariably a good sign. Likewise if one model is consistently closer to the quoted odds than another, then that model is probably more reflective of reality than the other.

Poisson generated odds using goal scoring and conceding data from the previous 35 matches were closer to the bookmakers raw odds in 11 out of the 18 prices (denoted by green numbers in the table above), three other odds were tied (denoted by blue). If I used 20 game figures only three occasions saw that model beat the other two, with two ties. Finally relying on data from just the last six matches, not only produced only one "result" and one tie, but the odds generated were also extreme.

Bookmakers deal in signal, not noise and then shorten their prices to allow for any slight miscalculation. A side's six game record demonstrates much of the former and less of the latter and so is less likely to model reality.

Ageing Patterns By Position In The Premiership.

When it comes to evaluating player performance, we have currently only scratched the surface. The amount of individual player data that is becoming available is but a snapshot of that player's true, core ability. So we have to deal with issue of sample size, along with the need to measure what is truly important in producing team wins on the pitch.

One of the most obvious indicators of a player's worth has nothing to do with his skill set. It's his age. Football demands a mixture of physical ability and various skills and in this guest post, I look at how the decline in the former leads to older players gradually, then dramatically disappearing from the Premiership scene (except for goalkeepers!).

In Defence Of Corner Kicks.

The fluid nature of football makes it tempting to concentrate on the occasions where the whistle is blown, the play stops and the game is restarted with a set play. A penalty kick provides a side with an excellent opportunity to register a goal and therefore they have received the lion's share of the attention, but the spotlight is increasingly falling on corner kicks, particularly their value in terms of scoring likelihood.

Many have pointed out the low rate of conversion from corner kicks. Most recently Tijs Rokers wrote in the excellent, data driven blog "The Sixteen" about the three percent goal success rate from such set pieces in the Dutch league, a figure that is consistent with scoring records in the Premiership. One goal every 30+ corners, where teams rarely average much more than 5 or 6 corner per game can therefore make corners appear almost insignificant incidents, even in such a low scoring sport such as football. Increasingly, corners are becoming unloved and even the very act of launching the ball into a crowded and well defended box is being portrayed as an outdated and inefficient throwback.

So let us try to redress the balance.

The Futility of Corners ?

Corner data is still relatively patchy, but the two most usually quoted numbers are success rate, denoted by first contact by an attacking player and conversion rate. Unfortunately, despite it's enticing description, the former is completely uncorrelated to the latter. Here's a (painful) example. Villa had two corners last week at Stoke's Britannia Stadium. The first was deemed "successful", but didn't result in a goal and the second in the 85th minute of a stalemated relegation scrap was "unsuccessful" because a Stoke defender got first contact and cleared the ball from the near post. It was further scooped ten yards beyond the edge of the area. At which point Lowton smacked a dipping volley just under Begovic's bar. An unsuccessful corner by one definition which resulted in the winning goal from a corner by another. A wider plot of corner conversion rates against the percentage of first contact by attacking players confirms that Lowton's enigma is far from unusual.

Therefore, any attempt to extend the definition of a successful corner beyond the raw conversion rate is likely to prove fruitless using the current, limited and confusingly defined data.

To rehabilitate corners as an attacking threat we need to reexamine their apparently underwhelming 3% conversion rates. When comparing the effectiveness of different approaches to goalscoring it is essential that we are comparing like with like. Corners are merely attempted assists which sometimes result in a goal attempt and sometimes do not. Understandably, the obvious nature of a set piece has led to corners which don't result in a goal or even an attempt, appearing prominently on the ledger which records corner efficiency.

The yardstick of chances created from open play, to which corners are often unfavourably compared isn't similarly tainted. Goal attempts from open play appear to have higher success rates than goal scoring rates from corners. But the comparison is flawed because attacking moves which break down before a shot is attempted (the equivalent of a corner which is successfully cleared) are very rarely included in the analysis of chance creation from open play. To do so would require a thorough interrogation of play by play data from every Premiership game, along with video analysis.

In short, a two on one attacking situation which breaks down and is cleared by the lone defender is merely logged alongside numerous other unsuccessful final third passes, it is unlikely to be flagged as a failure of chance creation from open play. Whereas when a defence successfully clears a corner, it is marked down as a set piece failure. Football analysis is as much about trying to accurately record what didn't happen as it is about recording what did occur and in this regard corners and other set pieces are victims of their own conspicuousness.

If we want to damn corners because of a 3% conversion rate,we are selectively cherry picking our data. Ideally, on the negative side, we must also include the occasional threat of conceding on the counter, along with the likelihood that possession is going to be lost. On the plus side, we should include the likelihood that the defence may only temporarily relive the pressure by clearing the ball up field and may not totally eliminate the danger by regaining a full, controlled possession.

And we also need to perform the same reckoning for supposedly superior alternative strategies and include the less readily available turnovers and partial loss of possession and even counter attack goals which occur for example in open play. Only then can we start to fairly compare corners as precursors to a chance against their open play equivalent.

Set plays may still prove less efficient than other strategies, but the importance of having a mixed strategy is evident in other sports. NFL sides are rarely equally proficient at moving the ball on the ground and through the air, but the need for an opponent to prepare for both can see the existence of a team's weaker discipline aid the enactment of it's strength.

In football, a less nimble central defender may be exposed in a open play ground duel, but his presence in a side may relate to the need to defend half a dozen corners and a similar number of other set play crosses. One dimensional teams, even sometimes the very best, are often easier to frustrate and even occasionally defeat. Barcelona may struggle to implement their brand of possession based football when deprived of certain outlandishly talented players. Many cite the example of Spain as a successful, yet flawed one dimensional team.

Proportionally, some teams also rely more on set plays than on chances taken from open play. It is hard to imagine Stoke surviving in the Premiership for as long as they have done without the ability to "score off a corner". Corners, even before we begin to treat them on a level analytical playing field, are often essential elements for less talented sides, where producing numerous, higher conversion, open play chances may prove difficult for their overall quality of playing staff.

Corners are individual, discrete events, but in determining their worth we should take care not to fully remove them from the fluid game that is football.

Can Wigan's Fat Tail Save Them Again ?

Last night's victory for City in the Manchester derby is unlikely to materially alter the destination of this year's Premiership title, so aside from the FA Cup, Premiership watchers will only have the relegation fight and European qualification to occupy their thoughts in the remaining months of the season.

Few outside of the Potteries will be too upset to see Stoke fall back into the Championship. Finally bereft of Delap's prodigious long throw and seemingly unable to keep a fully fit and favoured group of cross supplying wingers on the pitch, Pulis' difficult second album may prove to be his swansong. Their niche tactical position has not survived the inevitable churning of playing personnel and a requirement to play in a more conventional Premiership style has seen their points total becalmed in the mid 30's since January.

Heading For The Championship?

Simon Gleave over at Infostrada has pioneered a very effective comparison method for season on season performance which looks at a side's record in like for like matches across the present and previous seasons. Relegated sides are replaced by the equivalent promoted side from the Championship. So for any nervous Stoke fans it is perhaps slightly comforting to know that in like for like matches this season, Stoke have dropped but one point compared to last term.

Simon Gleave ‏@SimonGleave2h

Looking at the ISG coefficients, perhaps interesting to note that Stoke have only one point fewer than last season. @MarkTaylor0 @eatmystoke

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Those of us more inclined to pessimism will look more towards Stoke's remaining six matches which accounted for ten of their 45 survival points, last term. Small sample sizes often yield extremes of performance and a repeat of such a points haul may seem unlikely against sides such as a Manchester United team smarting from a derby defeat, a Spurs team fighting for third spot and a visit to an upgraded Blackburn in the guise of newly promoted Southampton. Adding a small underperfoming subset of results to Simon's model wouldn't greatly impact on the usefulness of the model as a whole, but the effect on Stoke could be dramatic.

To further rattle the nerves of any Potter, I've plotted the frequency at which Stoke and Wigan, one of their main rivals for the final drop spot, turn six game sequences into points over each side's tenure in the top flight over the last 10 seasons. Stoke's most frequent outcome is a point a game and overall both sides have averaged similar end of season totals. Wigan, however possess particularly fat right and left hand tails, indicating a record of abject runs, mixed with Champions League contending sequences.

Whether this is a repeatable trait or as seems more likely, just random fluctuation that could appear among the late season records of any of the currently struggling teams, it does highlight the risks inherent in leaving yourself vulnerable over a small number of games. (The risk is increased for Wigan's rivals because cup commitments has also left the Latics with a game in hand over most of the relegation pack).

Fat tails, as the financial sector has discovered can herald very nasty surprises. Wigan will be looking to a repeat of their right hand tail heroics for another reprieve, while Stoke will be eyeing the opposite side of the graph and also hoping for a points haul not too distant from their "like for like" performances over the season to date to stabilize an ever decreasing gap between themselves and their north western rivals.

But the long run has mostly gone this season and anyone still fighting for survival will have to pitch their own talent levels against not inconsiderable doses of random chance. Neutrals alone, should enjoy the ride.

Game State and Goalless Games.

It goes without saying that a goal scored changes the balance and dynamics of a football game. In the widest, most general terms, the average opening goal scored by an average home side against similarly mundane opponents adds about eight tenths of a league point to that teams long term points expectation. So scoring first is always good for the team taking the lead.

What is less obvious is the overall effect the concession of the opening goal has on their opponents. The relative ability of opponents can readily be expressed in terms of goal expectancy, the value of which is reduced as time elapses. It is reasonable to assume that once a goal has been scored, the remainder of the game proceeds in accordance with the present values of these decayed goal expectancy values.

However, this isn't quite what happens. Either through a re balance of tactical approaches or a burst of more intense effort from the trailing side, the side which conceded the opening goal becomes slightly more likely to score next goal, if there is one, than if the game had remained scoreless. In short, goal expectancy is a product of relative team talent, but it is also tweaked by the current state of the game.

Some great work is currently being done in this area and I'll link the best at the end of this post. But for now I'd like to flesh out some previous posts of mine to try to understand the subtle changes that occur over a season and also within a single match.

2010/11 was a reasonably successful season for Arsenal. They were in contention for the title well into March, but ultimately fell away to finish 4th. A series of scoreless home draws meant that even a narrow late season win at home to ultimate champions, Manchester United offered more hope to pursuers such as Chelsea than it did to the Gunners themselves.

Their season had peaks and troughs and they spent just over 43% of the time stalemated, led for around 40% of the playing time and trailed for 16% of the time. So in terms of game state as measured purely by current score, the Gunners provided a reasonably sized sample in terms of winning, drawing and trailing.

Goal attempts are a decent measure of a side's attacking intent, particularly if shot location is incorporated to provide the likely chance of success for each effort. In previous posts, I've charted the increased rate at which Arsenal peppered the opposition goal as they moved from a position of supremacy on the score board to a losing position. Those numbers are worth repeating and with the addition of an average goal expectancy, based on x, y data we can see how a team's frequency and potency of attempt might change with the current scoreline.

                Arsenal's Shooting Frequency and Efficiency By Game State. 2010/11.

Game State by Score.	Time Between Shots.	Goal Expectation/Shot	Average Time To Score.
Leading.	5 min 40 secs.	0.106	53 mins 19 secs.
Drawing.	5 min 03 secs.	0.108	46 mins 34 secs.
Losing.	4 min 43 secs.	0.105	44 mins 47 secs.

The table above paints a broad picture of Arsenal's attacking response to certain scorelines averaged over a wide variety of opponents. However, much of the detail and nuances of individual games is lost. Overall, the most ambiguous game state occurs when sides are level and in the case of Arsenal in 2010/11 this was their most common state in which the team found itself.

Game states change dramatically if a goal is scored, but they are also shaped by the relentless passing of time and the quality of the opposition. Arsenal are a top side, so a draw, especially at home is below their pregame expectation. However, even against the poorest teams in the Premiership a stalemate after just 10 minutes of play isn't totally unexpected or even cause for much concern. This isn't the case if the same game is still goalless in the 80th minute. The game is still scoreless, but the game state from an Arsenal perspective is massively different from the one they were experiencing 70 playing minutes earlier.

To demonstrate how game state can change, even if the scoreline doesn't, I've plotted Arsenal's disappointing 0-0 draw at home to Blackburn from 2010/11. At the start of the match, the Gunners would have expected to average just under 2.4 points from such a miss match. As time elapsed back in April 2011 and Arsenal's initial burst failed to produce an opening goal, their current points expectation slowly declined from the optimistic initial total. By halftime their current average expected number of league points stood about 15% below the total at kickoff and is denoted by the red column.

The situation at the interval wasn't satisfactory, but it wasn't dire for Arsenal and after creating a barrage of chances in the first half hour, they had drawn breath slightly. The cumulative goal expectancy of all their goal attempts in the first ten minutes would have averaged a third of a goal, long term. In the reality of this particular trial, the shots had proved fruitless. Their long term goal expectation during each ten minute period is denoted by the green columns.

As the game remained goalless, Arsenal's likely points haul retreated further from their hoped for pregame average. Aside from a barren ten minute spell after the hour (possibly indicative of an inability of even the fittest of sides to maintain maximum effort across an entire 90 minutes) Arsenal's goal expectation from their increasing goal efforts rose in step with their declining likely final reckoning. The final 10 minutes plus stoppage time alone saw four goal attempts and in a goalless game Arsenal played the final 20 minutes as though they were losing on the scoreboard.

Small effects are often magnified and become more noticeable in extreme match ups. Arsenal's experience and reaction to their failure to break the deadlock in a game which they expected to win is mirrored in varying amounts in every game. A draw at any stage of a match will rarely be equally satisfying to both sides. The ticking clock, as well as goals can subtly alter a side's approach to a match.

For more on game states, check out Ben Pugsley and 11tegen11