How Hughes Has Changed Stoke.

When this afternoon Tony Pulis momentarily takes his seat in the home dugout as his new charges Crystal Palace entertain his former employers, Stoke City, he will be much more familiar with the players taking the field for the visitors, rather than for the hosts.

His replacement at the Britannia Stadium, Mark Hughes may have a shared heritage, but his preferred brand of football is far removed from that served up by Pulis in his time at Stoke. The exceptional, but ultimately limited success Pulis achieved during his two spells in the Potteries has been well documented and former skipper Danny Higginbotham describes the route one, possession poor, approach from the inside in this recent article for the Guardian.

Prior to this season, Stoke were outliers in virtually every statistical area as Pulis expertly identified areas of the game where he could eek out a tiny advantage that played to the strengths and more often the limitations of his squad. When Hughes was presiding over QPR, the league's most optimistic distance shooting side, Pulis' less frequent, but higher valued attempts, often executed from deep inside the six yard box, were providing continued Premiership football for the least admired member of that exclusive club.

Evolution, not revolution has been a constant promise, both this term and in Pulis' latter days at Stoke, and Hughes has resisted the temptation to make wholesale signings in the opening half of his first season in charge. It is likely that around eight of the starters for Stoke this afternoon will have been regulars under Pulis and this gives us an opportunity to take a look at the numbers recorded by those players firstly under Pulis and now under Hughes.

Marko Arnautovic, a rare addition to Stoke's 2013/14 squad.

Whilst shots and goals from distance, particularly from the boot of on loan Oussama Assaidi have been a feature of 2013/14, it is in the area of passing, both in terms of completion and accuracy, that the biggest change has occurred in the re vamped Stoke side.

Under Pulis, individual players were likely to see their rate of passing attempts fluctuate across seasons, simply through natural variation. For example, captain Ryan Shawcross made more frequent pass attempts in 2012/13 than he had done in 2011/12, whereas his central defensive partner, Robert Huth was broadly consistent across both campaigns. Overall, the common players in each season made a pass every 3 minutes and 9 seconds in 2011/12 compared to one every 3 minutes and 20 seconds a year later. A difference, certainly, but not a significant one. The chances that passes made in those two seasons where drawn from the same tactical pot reaches almost 40%

Passing Frequency and Accuracy Under Pulis and Hughes.

Player.	Minutes/Pass. Under Hughes 2013/14	Minutes/Pass. Under Pulis 2012/13.	Mins/Accurate Pass. Under Hughes.	Mins/Accurate Pass. Under Pulis.
Charlie Adam.	2.0	2.3	2.6	3.2
Peter Crouch.	2.6	2.4	4.1	4.1
Jonathan Walters.	3.4	3.4	4.9	4.7
Ryan Shawcross.	2.6	3.7	3.5	5.7
Geoff Cameron.	2.5	2.9	3.4	4.5
Steven N'Zonzi.	1.6	2.0	1.8	2.4
Marc Wilson.	2.0	3.2	2.6	5.2
Andy Wilkinson.	3.7	3.8	5.1	5.7
Glenn Whelan.	1.7	2.9	1.9	2.5
Robert Huth.	3.0	4.6	3.7	7.1
Matty Etherington.	3.3	4.0	4.0	4.9

If the difference in passing frequency seen in Pulis' final two campaigns is insufficiently extreme to indicate a major shift of emphasis, the same can not be said when comparing Tony's final year with Mark's first. The increased passing frequency currently displayed by Stoke is very unlikely to be a random draw from a typical Pulis season and the same is true of passing accuracy.

In short, under Hughes, Stoke are almost certainly passing more frequently and finding their intended target more often. Things have changed. Glen Whelan was making a pass every 3 minutes of playing time under Pulis and under Hughes that frequency is well below 2 minutes per pass and the majority of his team mates are showing a similar directional trend.

Of course, Glenn Whelan hasn't suddenly become a much better passer in his declining years, Stoke are simply playing a more conventional passing game, the average distance of their passes is also significantly shorter this term. Years of propping up the "definitive" tables for passing accuracy has been replaced by respectable midtable mediocrity for Stoke's previously unfairly vilified outfielders.

Tactics often make the statistics.

The first meeting between the sides, prior to Pulis' appointment was a close fought affair. Palace struck the important first goal, but Stoke's expected goals from their superior numerical attempts made them worthy winners, statistically and in reality. However, despite Stoke's apparently safe current position of 12th and Palace's 20th, the meeting is still very much a relegation contest.

The plan was that Stoke would turn into a more attractive passing side, maintaining their status by precariously staying out of the clutches of relegation, while Pulis animatedly prowled his technical area.That scenario becomes reality today....just not quite in the way everyone hoped it would.

Begovic Scores! We Draw!

All of the best photographers appear to have a sixth sense about when a worthwhile picture opportunity is about to arise. It was therefore no surprise that my camera had just been returned to my rucksack when Asmir Begovic (a goalkeeper) scored for Stoke (after 13 seconds) against Southampton at the Britannia Stadium on Saturday.

There were clues available that would have indicated that Mark Hughes had a plan. All teams have a preferred end to attack in the second half and there appears to be a tacit agreement between captains that if the visitor wins the coin toss, he will take the kick off, rather than earn the early game wrath of the home supporters by turning the teams around. Therefore, the undercurrent of discontent that accompanied the sides swapping ends after the coin toss on Saturday, turned to slight bemusement as Southampton lined up to take the kickoff.

Stoke had turned themselves around.

The geography of the Britannia Stadium makes it an ideal site for endurance training. The prevailing wind regularly blows in from Trentham, funnels itself through the two open corners at the south end of the ground and then struggles to exit at the single open corner to the left of the Boothen End, tipping a hat to the statue depicting the three ages of Sir Stan as it carries on towards the city.

Stoke now have a chequered history with near gale force winds. In the distant past it has removed the roof of the Butler Street Stand (along with our best striker to pay for the uninsured infrastructure), but the worst it has managed at the Britannia was the late postponement of a game against WBA. On Saturday it provided Stoke with the opening goal by way of partial payback.

In the subsequent press conference, Mark Hughes acknowledged the deliberate decision to play with the wind during the first half, citing the importance of scoring first, which is encouraging. However, it is (hopefully) unlikely that his keeper was considered the most likely scorer. Hughes' apparent encouragement for his sides to shoot from distance, so vividly demonstrated at QPR, must have some bounds.

Following the kick off, Southampton chose to attack Stoke with a series of intricate passes. This quickly broke down, the ball was rolled back to Begovic, who launched a wind assisted punt goalwards. Both Southampton defenders chose to ignore the golden rule of defending, namely "never, ever let the ball bounce" and Boruc was left embarrassed by a slick bounce on the wet surface.

Begovic is the fifth keeper to score in the Premiership and invariably such goals require additional help or unusual circumstances. Tim Howard's effort against Bolton was a replica of Begovic's goal, but Peter Schmeichel, when playing for Villa opened the goalkeeping Premeiership goal tally from the more advanced position of the opposing penalty area. So modelling the likelihood of a keeper netting is going to be hugely situational.

We may have more luck trying to quantify the quickfire timing of the goal.

Stoke v Southampton, two minutes 13 secs from history being made (not shown).

The chance of a goal being scored increases slowly, but inexorably as time elapses as caution and fitness, gives way to adventure and fatigue. Your chances of seeing a goal during the sixty seconds that comprise the 8th minute is only 80% of your chances of seeing one in the 80th.

However, three "sixty second" intervals are completely atypical compared to this gradual cranking up of goal expectation. The 45th is the second most goal laden "minute" followed by the 90th and the reasons are clear. Injury time extends both minutes well beyond sixty seconds leading to two big spikes. Therefore these increased rates are purely artificially created by traditional timing considerations. The second half starts with the first second of the 46th minute, even if the first half stretched well beyond 45 minutes of actual time.

The barren blip that comes with the first minute, by contrast is entirely real. If you chose any sixty second period in the first ten minutes, you are likely to see around 0.7 to 0.8 percent of the total goals scored during the match, on average. But if you plump for the first 60 seconds of a match, you will be lucky to see much more than half of the typical early minutes goal percentage.

Again, the reasons are fairly plain to see. Every game starts with a kickoff. The ball is about as far from either goal as it can possibly be and all eleven players are positioned between the ball and their goal and this formation of maximum protection for each goalmouth is guaranteed to occur during the first minute in every match. Hence the scoring is not only at its lowest because of the usual ebb of intent and desire to score, it is atypically lower because of the requirement to start the game with a kickoff.

So, pulling all the information together, around 0.5% of goals come in the first minute, the first 13 seconds are likely to see less than a pro rata division of this goal expectation because of the guaranteed safe starting position for the ball. A back of the envelop calculation using these figures and the average scoring expectation over the history of the Premiership gives an average goal expectation for the first 13 seconds of a Premiership match of around 0.0015 of a goal. The chances of scoring twice or more in 13 seconds is impossible, therefore a goal in the opening 13 seconds should, under these informed gu-estimations happen around once every 666 matches.

So, unlikely as Begovic's goal was purely from a timing perspective on that particular Saturday afternoon, we should expect to have seen around a dozen such goals scored before the 14th second has elapsed over the 8,326 game history of the Premiership.

Begovic's strike was the sixth such effort, so maybe the primeval order at kickoff takes slightly longer to descend into chaotic normality than I accounted for or Premiership audiences have just been slightly unlucky.

If you have to miss a minute of a match and you want to reduce your chances of missing a goal, chose the first minute, (although you may be really unlucky a miss club history in the making), but at least on Saturday any tardy spectator got to see a match featuring two keepers whom had both scored a career goal, (although Boruc's strike came from the altogether more likely source of the penalty spot).

The Last Days Of Tone.

Often those nearest to a situation are the first to realise that something is wrong and few visitors to the Britannia Stadium in 2013 could fail to sense that Tony Pulis, perennial runner up behind Sir Alex Ferguson in the "most secure manager" stakes, was a dead man walking.

The purchase of a footballing, "pass first and pass often" midfielder in Steven N'Zonzi had merely whetted the appetite for a more pleasing and less risk averse football of the type often displayed by visiting teams to the Potteries, but hardly ever from the hosts. The heady "all in it together" days of 2008, when news of newly promoted Stoke's "relegation" reached me while watching county cricket at Derby after a mere 45 minutes of the season had elapsed were long forgotten as Pulis struggled to implement the long promised change in footballing direction.

0-3 to Bolton at halftime at the Reebok, was sufficient evidence for Irish bookmaker Paddy Power to pay out on Stoke's certain demise. Once in real money and once in mint flavoured ice cream by way of apology as City comfortably avoided the drop by finishing above their opening day conquerors.

The methods Pulis used have been well chronicled here. Super efficient, (by virtue of their shot origin) but relatively rare finishing and a team committed to defence, (mostly without the ball) was a small price to pay for keeping a mid table Championship side, at best in the top flight. Suddenly, "long throw" no longer immediately conjured up long forgotten footage of Ian Hutchinson's windmill arms.

If cloth was initially cut accordingly, the promise of a three (later four) year plan to play more expansive football was mooted. Team's with limited resources, aims and ultimately achievements often gather most of their points in low scoring encounters, whereas those of grander ambitions display a more rounded ability by gathering greater proportions of their points in higher scoring contests. And as such Stoke's first, memorable taste of home Premiership football was a sham. A 3-2 win over Villa contained typical Potteries goals, one from a set piece (a penalty), one from Ricardo Fuller's rare individualism and an injury time winner via a six yard header from a long throw. But winning points in high scoring affairs was never part of the initial game plan.

Stoke's points gathering profile was stuck firmly in the typical rut of a team destined perennially for the bottom five places, although it was testament to Pulis' implementation of his extreme brand of football, that he never once finished as low as this. Only once, in 2010/11 and including a run to the cup final, did Stoke's exciting, dual wing play lift their points scoring profile closer to the midtable levels that they were actually achieving. A seasonal quest for safety now came with a few pleasing extras.

 Adam and Crouch prepare to Implement Plan A one last time.

However, the source of Pulis' initial success proved the downfall of his greater ambitions. The Premiership is unforgiving especially outside the top six, where random fortune can see almost any side relegated. It is not an arena where change, especially dramatic change can be easily applied. The purchase of more quality and the change to a more pass orientated style, showed willingness, but Pulis is rightfully proud of a record that has never seen his sides relegated and ultimately, when points became hard to come by, the cage won out over the more elegant pass and go.

N'zonzi passed like a "normal" Premiership midfielder ( see Devin's Opta post), was voted Stoke's young player of the year and promptly asked to leave. Tony Pulis, however, beat him to the door, but not before maintaining his record of keeping sides afloat in their chosen division. Fittingly, the random element in football favoured the Welshman in this last difficult season as Charlie Adam, an upgrade with no real role, scored a paltry three goals, but scored each one in 1-0 home wins. Three became nine and Stoke survived in 13th, but with the points gathering profile of a bottom five side. Back to the beginning.

The parting of the ways was both amicable (in public at least) and inevitable and Tony Pulis will remain a major figure in Stoke's 150+ year history. Stoke are currently without a manager, but more importantly, a side with the rump of two distinct and seemingly incompatible styles. Sorting out the latter will prove much more urgent and difficult than resolving the former.....Although "Hughes Out" banners have already been moved on from the west car park, in anticipation of any imminent announcement.

How Teams Win from the MCFC Data.

The data released by MCFC, Opta and Gavin Fleig has now been out in the wild for a couple of weeks and it has already been put to good use both in graphical form and as the basis for game by game analysis, most notably by Ravi Ramineni at Analyse Football .

The data as presented in the csv file largely describes the actions made by players in a game. For example the number of forward passes made by Salif Diao for Stoke at the Emirates. One, as it happens. It is therefore a fairly simple task to accumulate match data comprising the total number of forward passes made by Stoke on that day against Arsenal. Once again Ravi's suggestion regarding the use of pivot tables in excel or Datapilot in Open Office is an excellent one.

We can therefore begin to build up a profile of the actions made by teams during games and try to marry these actions to game result to build up a picture of how teams achieve  the results they do. This aim can be best achieved by looking at the stats differential between both teams in the match. Goals are strongly correlated to game success, but as Blackpool discovered, you must also be proficient at preventing goals. The defensive and preventative side of the game can often be overlooked, even though it has a similar level of importance in determining match outcome. In short it is goal difference that is the stronger indicator of success or failure compared to simply goals scored.

Below I've listed the strength of correlation between success over a season as measured by wins plus half draws divided by games played and various recorded events from the MCFC data and then I've listed the correlation between success and event differential. The closer the correlation is to 1.0, then the stronger the correlation.

How Match Events And Their Differentials Correlate With Seasonal Success.

Match Event.	Correlation With Seasonal Success.
Goals Scored.	0.78
Goals Scored/Allowed Differential	0.94
Shots On Target.	0.60
Differential.	0.73
Headed Goals.	0.03
Differential.	0.27
Goals From Corners.	0.27
Differential.	0.45
Successful Passes ex Crosses.	0.54
Differential.	0.54
Successful Final 3rd Passes	0.62
Differential.	0.65
Touches In Opponents Box.	0.56
Differential.	0.73
Shots On Target Inside Box.	0.57
Differential.	0.73

As it's simplest level the differential column now includes the defensive contribution to winning instead of merely the offensive output. Scoring goals on it's own is a major factor for success for a lot of the Premiership teams, but a stronger correlation can be found if we included goals allowed as well. By presenting the wider picture of events we can begin to understand how free scoring Blackpool spent just one season in the top flight and barely scoring Stoke have survived since 2008/09. Concentrating on having a strong defence can be both cost effective and successful and a partial antidote to a lacklustre attack.

The figures, which are far from exhaustive, outline the kind of things the majority of the successful teams excel at over a season. However, care must be taken to avoid making broad statements that do not apply to all teams. Those teams which adopt tactical approaches that are at odds with the majority of other teams will inevitably be flagged up as outliers who have been incredibly fortunate to survive, when in reality they have exploited a niche market that has allowed them to prosper.

Headed Goals...A vital contribution for some teams.

One particularly striking result is the apparent zero correlation between headed goals and success followed by only a slight improvement if we look at the differential between headed goals scored and headed goals allowed. However, if we dig a little deeper, rather than being a worthless artifact of a bygone age, headed goals are actually vital to a minority of teams.

Scoring headed goals is a much cheaper, if less efficient method of moving the scoreboard than taking the ground route. You can create headed chances with little more than tall attackers or defenders and a delivery system, (long throws, set pieces or crosses). Creating Barca style goals from intricate passes usually requires expensive skill throughout the midfield and attacking areas. So headed goals are vital to the prospects of Stoke and Norwich and previously Bolton and Blackburn. These teams make the best of their meagre resources, but are in the minority in prioritizing headed goals both scored and conceded and therefore cannot greatly influence the regression correlation.

Aggregated game stats can shed some light on the type of things some teams are doing and are allowing to be done to themselves over the course of a season. But the picture is broad and sweeping and much fine detail is lost due to lack of game position context and tactical approach of some teams over a season.

By looking at differentials we can strengthen the correlations between season long success, so lastly I'll look at how success as measured by individual wins on a game by game basis relates to positive on pitch actions for each team. Are these broad correlations observed on match day?

Final 3rd completions are widely regarded as the preferred tactical approach for the majority, but not all teams. So it seems reasonable that if this approach is effective, teams will be winning more often if they complete passes in their opponents final 3rd and limit their opponents in this area. Regressing differentials for final 3rd passing, we do find a clear and strong game by game correlation for the EPL as a whole last season. Below I've plotted the line of best fit for final 3rd differentials and the likelihood that the home team won the match.

For example if the home side out passed their opponents by 50 passes in a game, there was a 50% chance that they also won the game and the greater the differential the greater the likelihood that they also won the game. Correlation doesn't imply causation, but it does strengthen the case for final 3rd passes being an important component of some team's armoury. There will of course also be exceptions in this game by game analysis with Stoke, certainly and Newcastle, possibly plotting a different route through a tactical independence from the majority of the rest of the league where the importance of final 3rd completions is diminished.

Getting Out Shot Isn't Always Bad News.

With the influx of readily available data, shooting efficiency has quickly become the mainstay of much of the statistical analysis of both football teams and individual players. The rate at which a keeper keeps out shots, the ratio of goals to shots for strikers and team conversion rates are now a common and welcome addition for debate. While any advance in the quantity of data is to be welcomed, this all encompassing approach does have it's drawbacks. In judging a keeper or a striker simply on his shooting or saving success ratio we are hoping that sheer weight of trials are leveling out the quality of the attempts. The accuracy of our conclusions depend on keepers facing roughly the same overall quality of attempts or players or teams being presented with chances of roughly the same difficulty. An improvement compared to the previous goalcentric models perhaps, but still a not inconsiderable leap of faith.

Euro 2012 well demonstrated that there are numerous ways to play football and teams as diverse as Stoke and Swansea can achieve virtually identical seasonal points tallies in the Premier League by employing polar opposite approaches. By using raw counting methods and applying it to such statistics as team shots, we may capture the general trend, but we are destined to miss almost all of the finer detail that may differentiate between the Midland's best EPL team of recent times and their Welsh cousin.

Therefore a parallel approach is needed using more granular data or we risk dismissing alternative playing styles as mere outliers or the product of excessive luck. Everyone is comfortable heaping praise on the all conquering Spanish club or country sides, who are perceived as maximizing their talent with a style and philosophy that is both successful and pleasing to the eye. But we still need to try to explain why less attractive teams appear to prosper, especially if their success appears to contradict the new statistics that are currently used to define desirable team talent.

The first step to improving the information gained from shot data is to be able to attribute a expectancy for each shot or header based on the origin of the attempt. How likely is a shot to result in a save, a miss, a block or a goal. This tentative first step is available from Opta supported apps, such as FourFourTwo's Stats Zone and while data collection is time consuming, the effort is rewarding.

The continued comfortably successful presence of Stoke in the EPL midtable and within the various domestic and European cup competitions regularly provokes reactions ranging from mild bemusement to outright hostility. Especially as they are entering their fifth consecutive top flight campaign while appearing to perform poorly in many of the shot based advanced metrics and possession stats.I'm extremely skeptical about the usefulness of possession data ,but for now I'll use Stoke to illustrate how shot data can reveal hiddens gems about a team's record, but only if we look beyond the general counting stats that are the mainstay.

I've taken every goal attempt propelled and faced by Stoke during the 2010/11 season, their third year back in the top flight. The declining influence Delap's longthrow has been charted here and the goal scoring duties for the campaign lay at the feet and head of £8 million Kenwyne Jones, the largely unheralded £3 million Jon Walters from Championship side, Ipswich, Tuncay, a £5 million flop who would leave in the January window and an ageing and increasingly injury prone Ricardo Fuller. So the striking talent was broadly consistent with that available to EPL teams from midtable and below.

How Many Goals A Slightly Above Average Side Would Expect to Score Given Stoke's Opportunities in 2010/11.

Stoke Attack (480)	Goals.	Shots on Target.	Shots Blocked.
Expectancy.	69	183	117
Actual Performance.	45	135	128
Expectancy per Shot.	0.15	0.38	0.24

My shot conversion model at the moment contains an over representation of good attacking sides, but we are simply using it here to see how Stoke managed to overcome their unbalanced ratio of shots allowed and shots attempted.

Stoke's tactical approach under Pulis has always been one of containment regardless of venue, so the lack of possession is baked into the gameplan. They were outshot in 2010/11 by almost 60 attempts over the season as a whole, but finished 13th with a goal difference of minus two, an extra point away from 10th. The point of origin of each Stoke attempt has been charted and a goal expectancy, accuracy expectation and likelihood of seeing the shot blocked is calculated for each shot. Cumulatively we can then see how many goals an above average attacking team might have scored had they been able to create Stoke's 480 chances from 2010/11.

How Many Goals A Slightly Above Average Side Would Expect to Concede Given Stoke's Opponents Opportunities in 2010/11.

Stoke Defence (539)	Goals.	Shots on Target.	Shots Blocked.
Expectancy.	59	186	142
Actual Performance.	46	182	156
Expectancy per Shot.	0.11	0.35	0.26

The predicted outcomes of the shots Stoke's defence allowed are then similarly treated and by comparing the two batches off shots we can try to see how Stoke managed to score as many as they conceded despite the large excess of shots aimed at their goal by frustrated opponents.

The most significant figure is the expectancy per shot in each table. When Stoke were shooting it averaged 0.15 per attempt, when they were on the receiving end the figure fell to 0.11. So Stoke were creating less shooting or heading opportunities and allowing more, but this was compensated by their shots on average being more likely to result in goals. They were also more likely to be on target, creating rebound possibilities and less likely to be blocked judged on where on the pitch the attempts were taken from.

That Stoke's strikeforce didn't manage to match the goal tally from their 480 attempts that was predicted by a model that contains data from the likes of the top five EPL teams shouldn't be surprising. But Stoke scored 45 goals, omitting own goals in 2010/11 by presenting relatively low numbers of high quality chances to predominantly average or below Premiership strikers. Leading to a average season long total in the mid forties. As a group Stoke players who had a goal attempt two years ago weren't that potent, certainly weren't very accurate and had more shots blocked than the top teams......but they were presented with top drawer chances.

Kenwyne..."...set them up & I'll put some of them away".

An EPL side consists of at least two units and the defence, by contrast overperforms the model. Even though they had an average of two more shots a game to contend with compared to their own team's offensive output, they only conceded 46 goals. Chances created by the opposition were more difficult opportunities, as shown by an expectancy per shot of 0.11 goals compared to 0.15 goals for the Stoke attack. Given Stoke's setup, that was probably a team effort, starting with Jon Walters and working back down the field. Opponents also couldn't match the model's expectation and under shot by 13 goals and that was probably more down to the back four and keeper. Stoke's defensive legion also made many more blocks than predicted, another constant from team's coached by Tony Pulis.

So in this case the more numerous shots allowed were of a lower chance quality and intervention by Stoke defenders, which naturally is currently beyond the scope of one man analysis, further reduced the scoring levels.Stoke's 480:539 shot ratio appears poor, but the raw numbers obscure the hard work of the defence and a gameplan designed to produce quality chances for a team then lacking in attacking excellence.

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.

Quantifying Delap's Long Throws.

One of the central ideas behind  the "Moneyball" approach to running a successful sports team is the identification of undervalued player skills that can contribute greatly to winning matches and then purchasing these skills cheaply and creating strategies that help your team be successful.It can be argued that one of the most high profile and productive examples of such a strategy  occurred in the English Premiership when Stoke manager,Tony Pulis secured English born,former Irish international,Rory Delap from Sunderland on a free transfer.

The Prelude to a low,flat delivery

Delap's career started at Carlisle,before he spent four seasons at Derby.Throughout his career he was never a prolific goalscorer and the eight EPL goals he claimed to make him leading scorer for the Rams in 1999/00 was more a reflection on their lack of firepower than his scoring prowess.Never the less,a season later he made his one and only big money transfer move when Southampton paid in excess of £4 million for his services.Once again his employers received good,honest work rate in return for their outlay and a goal a season for five seasons.However,even with such a mediocre scoring rate,Delap still managed to attract the attention of the wider footballing public by scoring the best overhead bicycle kick goal of all time against Spurs in 2004,eclipsing even Rooney's effort nearly a decade later.

A short and unproductive free transfer to Sunderland saw him surplus to a new manager's requirements and within just three seasons he found himself wearing his third different set of red and white stripes at Stoke.Firstly on loan,but with a view to a permanent switch.When a 51/49 touchline collision,ironically against Sunderlnd saw him sidelined for the year only 95 minutes into his loan period,Stoke could have easily turned their back on the proposed deal and sent their stricken loanee back to Wearside,but instead the Potters immediately indicated their intent to honour the deal and sign Delap.Their actions were widely interpreted as an example of old world "word is my bond" business ethics that had led Stoke's owner to create two hugely successful enterprises,with the benefit of hindsight a determination to secure a rare,if not unique talent was also at the heart of the deal.

During a dozen seasons of his professional career, Delap's longthrows had produced one goal at Carlisle,one Derby and three at Southampton,but his move to Stoke was about to take the tactic to whole new levels of production.The Potters hadn't yet narrowed their playing area to maximize Delap's delivery,but he bettered his career assists total in his first full season for his new club.Six of his eight assists broke the deadlock in games,three came away from the Britannia Stadium and Stoke were unbeaten in all eight matches.His throw assisted scores added over six Expected Points to Stoke's points haul in their promotion year and while Expected Points are a partly abstract concept (it quantifies by how much the goal has advanced a team's chances of securing either a win or a draw),it seems very likely that Stoke would have fallen into the playoffs without Delap's contribution.

Expected Points Value of Goals Scored from Delap Throws,2007/08 Championship Season.

Opponent.	Expected Points Pre Goal.	Expected Points Post Goal.	Pre Goal Scoreline.	Increase in Expected Points.	Game Result.
Plymouth	0.583	1.572	1-2	0.99	W 3-2
QPR	1.812	2.477	0-0	0.67	W 3-1
@ Plymouth	1.290	2.071	0-0	0.78	D 2-2
Hull	1.766	2.531	0-0	0.77	D 1-1
Preston	1.837	2.515	0-0	0.68	W 3-1
Scunthorpe	0.352	0.951	0-2	0.60	W 3-2
@Norwich	1.264	2.337	0-0	1.07	W 1-0
@Colchester	2.060	2.627	0-0	0.57	W 1-0
Expected Points added per Appearance	0.14	Total Expected Points added.	6.12	Expected Points added per assist.	0.76

Delap's long throws became an international phenomenon on Stoke's return to the Premiership.A narrow but legal pitch combined with one high profile scalp in Arsenal ensured that the tactic remained on the back pages.A high leverage winning assist in Stoke's first home game of the season turned a single home point into a virtually assured three and settled the nerves of a team who had been comprehensively outclassed at Bolton on opening day.The win loss record when Delap provided an assist was slightly inferior to the previous year in the Championship,but there were two high leverage winning assisted goals at home to fellow relegation candidates,Sunderland and Middlesbro'.In terms of keeping Stoke competitive during a difficult first season Delap's throws were invaluable,especially at home.

Expected Points Value of Goals Scored from Delap Throws,2008/09 Premiership Season.

Opponent.	Expected Points Pre Goal.	Expected Points Post Goal.	Pre Goal Scoreline.	Increase in Expected Points.	Game Result.
Aston Villa	1.004	2.816	2-2	1.81	W 3-2
Eveton	0.079	0.366	0-2	0.29	L 2-3
@Portsmouth	0.235	0.846	0-1	0.61	L 1-2
Sunderland	1.261	2.531	0-0	1.27	W 1-0
Arsenal 1st goal	0.605	1.298	0-0	0.69
Arsenal 2nd goal	2.122	2.772	1-0	0.65	W 2-1
Bolton	2.528	2.924	1-0	0.40	W 2-0
Middlesbro'	1.248	2.744	0-0	1.50	W 1-0
Expected Points added per Appearance	0.21	Total Expected Points added.	7.22	Expected Points added per assist.	0.90

The 2009/10 season marked the first signs of a steady decline in the effectiveness of the tactic.Five additional assists in Stoke's run to the FA Cup quarter finals partly masked the decline in productivity in the league matches.The value of the goals in the context of the scoreline when they occurred decreased markedly from the previous two years as did Delap's assisted Expected Point added per appearance.Teams actively prepared for the challenge posed by the longthrow,advertising boards were moved closer to the pitch resulting in just one assist in the league away from the Britannia and referees began to pay more attention to the aerial bombardment that opposing keepers faced.

Expected Points Value of Goals Scored from Delap Throws,2009/10 Premiership Season.

Opponent.	Expected Points Pre Goal.	Expected Points Post Goal.	Pre Goal Scoreline.	Increase in Expected Points.	Game Result.
Burnley	2.516	2.873	1-0	0.36	W 2-0
Wolves	2.502	2.878	1-0	0.38	D 2-2
Blackburn	2.401	2.843	1-0	0.44	W 3-0
Arsenal	0.855	1.602	0-0	0.75	L 1-3
@Burnley	1.283	2.123	0-0	0.84	D 1-1
Expected Points added per Appearance	0.08	Total Expected Points added.	2.76	Expected Points added per assist.	0.55

The decline of the previous season was arrested in 2010/11,but the previous highs were never threatened and only four league goals came from Delap assists.However,three were relatively high value scores resulting in a healthy Expected Points per assist.Over half the goals scored following a Delap throw over the last two seasons have come in Cup competitions,reinforcing the thought that the surprise factor of the tactic no longer exists in the EPL.

Expected Points Value of Goals Scored from Delap Throws,2010/11 Premiership Season.

Opponent.	Expected Points Pre Goal.	Expected Points Post Goal.	Pre Goal Scoreline.	Increase in Expected Points.	Game Result.
Liverpool	1.110	2.182	0-0	1.07	W 2-0
@WBA	3.000	3.000	2-0	0	W 3-0
Sunderland	0.808	1.633	0-1	0.83	W 3-2
Aston Villa	0.980	1.802	0-0	0.82	D 1-1
Expected Points added per Appearance	0.07	Total Expected Points added.	2.72	Expected Points added per assist.	0.68

Delap continues to be a regular in Pulis' Stoke City sides in the current season,but the threat from his throws has failed to produce a single league goal so far.Ricardo Fuller,a major beneficiary of Delap's delivery has become a peripheral member of the squad and the expensive addition of Peter Crouch hasn't produced a score to add to the one the pair combined for seven years ago when both were Southampton players.

Expected Points Value of Goals Scored from Delap Throws,2011/12 Premiership Season.


None As Yet.

How Effective were Stoke's Substitutions in 2010/11.

Substitutions provide the manager with his biggest single weapon to alter or consolidate the path a match has taken once under way.Although some substitutions are obviously forced changes because of injury,many more are tactical adjustments based on such factors as historical data relating to tiredness of starters,current score and time remaining.It's therefore understandable that teams will have a genuine interest in assessing the impact their replacements make to the final match outcome.


Attacking substitutions inevitably attract most of the attention because a replacement who grabs an important goal will live long in the memory.However,just as many changes are made with the intention of preserving a lead or a hard earned point away from home and therefore taking a merely goal based approach can fail to capture a large proportion of the effect of juggling your troops.

Hajduk Split Prepare to Ring the Changes at the Brit.

My Expected Points model tracks the average number of league points a team can expect gain in any match up,at any time in the game and under any scoreline.Large changes to each team's current EP totals occur when a goal is scored and I regularly produce game graphs for EPL matches and use the plots to put an Expected Points value each goalscorer's effort.

As an extension of this approach,these graphs can also be used to chart the effect each successive substitution has had on a side's chances of being successful on the field.By recording the EP value at the start of the game for a team and then recording the values at the introduction of each substitute and again at the final whistle,we can see how the EP points has declined or increased during each separate stage of that team's on field make up.

Below I've charted the change in EP for Stoke City over all 38 games of the 2010/11 season.I've recorded the current EP for the team at the time of each substitution,so anyone can easily see by how much the EP changed while the team was playing with the original starting eleven and compare that figure to the change that occurred for example when the team played with two subs on the field.

Sunderland at home must rank as Tony Pulis' most inspired tactical switch of the season.An initial EP of 1.79 points had declined to 0.46 points as they trailed after 67 minutes.However,a single substitution of Andy Wilkinson(a defender) for John Walters( an attacker) resulted in three points with a late winner.This example is one of the memorable,but atypical times when a switch leads to spectacular,goal driven success,but it must be put along side the times when the result isn't as positive.The following week at Birmingham,two late substitutions presumably made to protect a goalless draw ended with a 92nd minute Birmingham winner.
Enforced substitutions are included in this example for completeness,as we can assume that Pulis would not have voluntarily replaced his record signing after just 14 minutes of the season in the away fixture at Wolves.Similarly,Pennant's removal after 12 minutes at the Hawthorns was down to a clash of bodies and not a clash of personalities.

How Stoke's Expected Points Changed with Each Substitution.2010/11 EPL Season.

Opponent.	Time of 1st Sub	Time of 2nd Sub	Time of 3rd Sub.	EP@Start	EP@1st Sub.	EP@2nd Sub.	EP @3rd Sub.	Final Points.
@Wolves.	14	51	67	1.22	1.22	0.10	0.32	0
Spurs.	64	85	88	1.15	0.34	0.16	0.12	0
@Chelsea.	51	68	86	0.27	0.07	0.07	0.00	0
Villa.	61	65	87	1.51	0.46	0.42	1.16	3
WHU.	66	73	83	1.79	1.49	1.43	1.30	1
@Newcastle.	50	57	67	0.96	0.32	0.29	0.25	3
Blackburn.	77	89	89	1.58	2.62	2.81	2.81	3
@Bolton.	67	86	-	1.15	1.11	1.07	-	0
ManU.	57	66	79	0.78	0.24	0.21	0.15	0
@Everton.	74	77	-	0.73	015	0.14	-	0
@Sunderland.	58	75	-	1.09	0.33	0.23	-	0
Birmingham.	73	89	89	1.79	2.95	2.82	2.82	3
Liverpool.	88	89	-	1.09	2.71	2.74	-	3
@WBA.	12	79	83	1.15	1.10	2.50	2.58	3
ManCity.	45	63	76	1.15	1.12	1.11	1.10	1
@Wigan.	71	83	-	1.44	1.27	1.19	-	1
Blackpool.	70	70	83	2.11	0.60	0.60	0.35	0
@Blackburn.	75	84	89	1.22	2.48	2.64	2.76	3
Fulham.	55	69	80	1.92	0.23	0.13	0.06	0
Everton.	59	80	84	1.44	2.40	2.95	2.97	3
@ManU.	69	69	76	0.37	0.11	0.11	0.10	0
Bolton.	71	81	88	1.79	2.94	2.97	2.99	3
@Fulham.	58	59	63	1.15	0.07	0.06	0.06	0
@Liverpool.	62	65	67	0.74	0.22	0.22	0.21	0
Sunderland.	67	-	-	1.79	0.46	-	-	3
@Birmingham.	79	81	-	1.29	1.16	1.16	-	0
@Arsenal.	78	88	-	0.46	0.10	0.06	-	0
WBA.	65	78	83	1.79	2.57	2.67	2.73	1
@WHU.	52	65	69	1.22	0.15	0.10	0.40	0
Newcastle.	60	81	88	1.65	2.99	3.00	3.00	3
Chelsea.	85	89	89	0.78	0.99	0.99	0.99	1
@Tottenham.	76	76	76	0.84	0.17	0.17	0.17	0
@Villa.	73	75	88	0.96	1.04	1.04	1.03	1
Wolves.	31	72	80	1.91	2.47	3.00	3.00	3
@Blackpool.	56	81	89	1.44	1.29	1.18	1.11	1
Arsenal.	51	73	84	0.78	2.60	2.83	2.93	3
@ManCity.	73	74	-	0.51	0.00	0.00	-	0
Wigan.	72	77	-	1.42	1.20	1.18	-	0

To account for these extreme outcomes and also incorporate the many games when the subs trot on and games meander to a less dramatic conclusion,I've averaged the change in EP per minute for the first choice Stoke and the Stoke side comprising various numbers of substitutes.It's doubtful that a single season is sufficient to allow for any extravagant predictive claims to be made about the astuteness of Pulis' tactics (high value EP goals such as winners late in a match will overhang such small sample sizes),but they do provide an interesting descriptive narrative to that season.

If we take the EP value at a certain point in a match and compare that value to a later point in the match,the two numbers are unlikely to be the same.Sometimes the later value will be higher,sometimes lower,but if the model is valid,on average over a large number of games these individual in game fluctuations will cancel out.If we therefore average the change in EP for a team's starting 11 and find that average is positive,we could conclude that the starting team out performs the model.This could be for any number of reasons.Small sample size is the most obvious,but alternatively the starting 11 could just be better than the substitute laden units that by necessity carry the team to the final whistle and the excess EP is "given back" later in the match.

How Stoke's Starting 11 Compared to Stoke Sides Containing Various Combinations of Substitutes. EPL Season 2010/11.

Average EP change  per minute for Starting 11.	Average EP change per minute for Team with 1 Sub.	Average EP change per minute for Team with 2 Subs.	Average EP change per minute for Team with 3 Subs.
-0.00115	0.00122	-0.00853	0.00425

From a purely narrative stand point,Stoke's starting 11 under performed the model in 2010/11.Playing with one substitute on the pitch they over performed,partly as a result of Walters' lone appearance against Sunderland.On average they under performed with two replacements but bounced back when all three took centre stage.

As a starting point this approach quantifies a team's performance with and without it's substitutes on the park without relying on the actual replacement player doing something noteworthy,such as scoring and it provides an individual game narrative.

* A bold Pulis double substitution today when Crouch and Walters made way for Jones and Jerome with twenty minutes left and the game still scoreless against Norwich.The move paid almost instant reward when soon afterwards Matty Etherington beat Ruddy at his near post for the only goal of the game.Another example of the potency of Stoke when they have all three subs on the pitch or just another data point?