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tag:blogger.com,1999:blog-60599833103256782832014-11-27T20:13:19.415ZThe Power of Goals.Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-77601701698041494132014-11-27T17:16:00.000Z2014-11-27T20:13:19.447ZWhy Uttoxeter Probably Isn't A Hotbed of Swimming Talent.
Occasionally the newspapers publish stats based articles that do not relate to sport, but do serve to highlight some of the dubious assumptions that can be made from such studies.

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In the run up to Christmas, a raft of newspapers, including the Daily Telegraph reported that the drink driving capital of Britain was Llandrindod Wells, a small rural town in mid Wales.<o:p></o:p>

LW had over the last 12 months 1.98 convictions per 1,000 drivers, second to Blackpool with 1.85 such convictions. After establishing the drink driving hotspot, a couple of reasons were then devised to explain the results, lack of public transport and a belief that an offender will not be caught in a rural setting, for example.<o:p></o:p>

However, studies comprising very different sample sizes inevitably lead to conclusions that may fail to represent the true picture. Most famously a study decided that small schools are inherently better than large ones because they appeared in disproportionate numbers at the top of a performance table and is quoted in Daniel Kahneman's book "Thinking, fast and slow".<o:p></o:p>

In short, sometimes samples are too small to come to a reliable conclusion.<o:p></o:p>

LW has a population of just over 5,000. If the town follows national trends around 80% of the population will be able to legally hold a driving licence. So, 1.98 convictions per 1,000 drivers implies that 8 cases of drink driving were successfully caught and prosecuted in LW over the previous 12 months.<o:p></o:p>

If we imagine that one such case went undetected. Now LW has a conviction rate of 1.75 per 1,000 and they fall to 4th in the table. Blackpool is now top and it may seem that seaside towns lead to drink driving.<o:p></o:p>

If convictions drop to 6, LW fall to the middle of the roll of shame with entirely unexceptional conviction rates per 1,000 drivers. However, two extra cases added to the actual total catapults the town to 2.5 cases per 1,000, well above the next worst, Blackpool.<o:p></o:p>

So it is possibly the size of LW population that has contributed to making them a headline in the national press. Blackpool, in contrast has around 118,000 drivers and the conviction rate is much less susceptible to large changes occurring in that headline rate because of small numerical changes in convicted or non-convicted cases. Blackpool has probably prosecuted around 280 drink drivers.<o:p></o:p>

Percentages derived from small sample sizes can bounce around if the raw number of cases alters by just one or two. Just as small schools can be shown to be the best, as in the study quoted in Kahneman's book, they can also quickly become the worst if just a handful of students produce poor results rather than excellent ones.<o:p></o:p>

To keep the blog sports orientated, let's use this dubious method to "prove" that Uttoxeter, population 12,000, a small town on the correct side of the Staffordshire/Derbyshire border is a hot bed of swimming world records.<o:p></o:p>

Around 12% of the population are in the age group that would typically hold a world swimming record. So Uttoxeter has around 1,400 potential champions. They currently have one actual world record holder, Adam Peaty (100/1 to be Sports personality of the Year, but don't let that put you off voting for Adam).<o:p></o:p>

Therefore, Uttoxeter has 0.7 world record swimmers per 1,000 likely candidates. This of course would double if we made the conditions gender specific, but it is still good enough to give it the best headline rate in the country.<o:p></o:p>

So Uttoxeter can be shown to be the place for swimming excellence, but only by using percentages applied to small sample sizes which obscure, rather than illuminate the less startling reality of the situation.
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Sadly, it is a flawed conclusion, based on the exploits of a single outstanding swimmer, especially as the town doesn't currently have a swimming pool!<o:p></o:p>
Mark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-76366457593743126072014-11-17T01:25:00.000Z2014-11-17T17:48:39.676ZIs Wayne Rooney An International Flat Track Bully?
Wayne Rooney reached a landmark 100th cap against Slovenia on Saturday. He joined an illustrious club of England internationals and his equalising goal also cemented his position at the heart of his England's leading scorers.

Sir Bobby Charlton leads the way with 49 goals, followed by Gary Lineker on 48, Rooney then ties with Jimmy Greaves on 44 and Michael Owen completes the list of England strikers to have scored 40 or more goals.

 Player	 Goals	 Caps	 Strike Rate per Game.

 Sir Bobby Charlton	 49	 106	 0.46

 Gary Lineker	 48	 80	 0.60

 Wayne Rooney	 44	 100	 0.44

 Jimmy Greaves	 44	 57	 0.77

 Michael Owen	 40	 89	 0.45

The Manchester Evening News questioned the validity of Rooney's achievement by referencing not only the number of games he has played to achieve his 44 goals, but the strength of the opponents against whom he has played.

The average Elo rating of Gary Lineker's opponents is the highest of the group at 1,701, then Owen, 1,677, Greaves, 1,671, Charlton, 1,653 and finally Rooney, 1,557 impling that he is a flat track bully, who feasted on weak opposition.

However, this approach firstly fails to account for the different goal environments in which the five players scored their international goals.

Charlton and Greaves began their international careers in the late 50's, Lineker first appeared against Scotland in 1984, Owen debuted against Chile in 1998, overlapping with Rooney, who began his road to 100 caps against Australia in 2003.

The top English league in 1957/58 saw an average of 3.73 goals scored per game, this figure had fallen to 2.71 by the time Lineker was debuting for England and had drifted down to 2.63 when Rooney took on Australia.

In short, the goal environment was vastly different in the fifties compared to today, as illustrated in the plot below.

Therefore, Greaves and Charlton, regardless of the average Elo ratings of their opponents, began playing international games at a time when scoring was much more plentiful and it showed a gradual decline as the game moved into another century. This prolific scoring also appeared to spill over into international football.

The average number of goals that were scored in the 57 international games played by Jimmy Greaves was 4.05 goals per game. Charlton's 106 caps contained an average of 3.58 goals per game, possibly indicating that Sir Bobby may have played in more competitive matches than did Greaves. Lineker participated in the least goal laden contests, averaging 2.3 gpg and both Owen and Rooney's respective caps average 2.7 gpg.

During Rooney's 100 caps, England actually scored an average of 1.9 goals per game, conceding 0.82. If we place these average goal scoring rates into a Poisson, they are consistent with a side winning 63% of these matches.

Jimmy Greaves' international career saw an average of 2.58 goals scored and 1.47 allowed by England, this time consistent with a winning percentage of just 61% for a team, if applied to a Poisson.

So a Poisson approach appears to confirm that Greaves' strength of schedule was more difficult than Rooney's. England scored and conceded goals consistent with them winning 63% of the matches when Rooney won a cap, but this fell to 61% in the 50's, and 60's when Greaves played presumably due to more difficult opponents.

But despite Greaves apparently playing against tougher opponents, he also played at a time when scoring, at both ends, was more plentiful.

Just as importantly, Rooney merely participated in 100 England matches. He didn't play every minute. Unlike Charlton and Greaves who played during a period where substitutions were largely not permitted. Charlton was infamously replaced against West Germany in anticipation of a World Cup semi final that never materialised at Mexico 1970 and was also subbed on after half an hour of a 10-0 win over the USA in New York in 1964.

But generally both Charlton and Greaves played from first whistle to last.

Rooney has failed to play the whole 90, or sometimes 120 minutes, in over half of his games, either through red card or being subbed in or out of the game. Therefore, an Elo average of his 100 caps may not reflect the realty of the minutes Rooney has spent in an England shirt.

Wayne could have potentially played over 9,000 minutes of international football in his 100 caps, but he was on the bench for over 1,400 of those minutes. He spent nearly 2 hours of his 100 caps watching his team mates score 10 goals against the likes of San Marino, Liechtenstein and Andorra.

He was absent for a proportion of the time available to be played against the weakest of opponents, who depressed his apparently damning Elo rating, whereas Greaves and Charlton were largely ever present to win their caps.

So the latter two players each played in an era of elevated goal scoring, teams were winning games by scoring more and also conceding more goals. Also we can't even be sure that Rooney's apparent low Elo opponent rating accurately reflects his actual playing time.

The average goals scored and allowed by England during the actual minutes Rooney has been on the field in gaining his 100 caps is 1.84 and 0.91 goals per game, indicating a more competitive playing environment than his 100 caps overall. These rates of scoring are consistent with a team winning just 59% of games.

Under these revised strength of schedule estimates that reflect actual playing time, we could conclude that Rooney has played in tougher matches than either Greaves or Charlton. England's goal differential was consistent with a side expected to win 59% of games when Rooney was on the field. The figures for Greaves and Charlton were 61% and 62%, respectively.

This approach elevates the Rooney opponents to at least the third most difficult faced by the five England 40+ scorers and highlights the deficiencies in drawing headline grabbing conclusions about a player merely from a team rating, devoid of wider context.

 Player.	 % of the Total International Goals Scored Whilst
on the Pitch.

 Gary Lineker	 41%

 Michael Owen	 31%

 Jimmy Greaves	 30%

 Wayne Rooney	 28%

 Sir Bobby Charlton	 20%

A more useful method may be to calculate the percentage of the total team goals scored by a player when he is on the field. We saw in the initial table that Jimmy Greaves scored at a phenomenal rate of 0.77 goals per game. But during his international career, England were often scoring eight or nine goals and occasionally conceding four or five in return.

Other England players were also scoring against these profligate defences at such a rate that overall, Greaves was accounting for 30% of the goals scored by England. This figure is comparable with Michael Owen, forty years later and only slightly above Rooney to date.

Sir Bobby only accounted for 20% of the goals scored by England in his playing time whilst winning 106 caps. And most impressively, Gary Lineker scored over 40% of England's goals scored while he played, in an era when one goal or fewer were scored by England in over 50 of his matches and eight goals were reached by the national side just once.

All five have or had exceptional careers, but branding Rooney a flat track bully on spurious evidence is entirely unjustified.

Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-27865068094075541512014-11-09T12:01:00.000Z2014-11-09T12:01:06.581ZAge Profiles for A Team's Best and Worst Premiership Seasons.The optimum age at which players rise to their peak before making the sometimes rapid decline into retirement or punditry is one of the most neglected areas of football analytics. The lack of readily available data is part of the issue, but assessing player development and then their regression is further confounded by the choice of variables.

Shots, goals and assists are obvious key performance indicators for strikers, although even these will have an aspect of team input, but the choice of which data to assess midfielders and defenders, with their diverse team responsibilities, is more problematic.

Some of the game's best defenders rarely made a tackle.

Therefore, using playing time as a percentage of playing time available as a proxy for player worth may still be the best alternative. A player who is not selected by his manager, either because other squad members are regarded as a better option or who misses playing time through injury, should perhaps be considered as a less valuable asset, either through lack of developed talent or because of age related decline.

This isn't to say that a 30 year old Frank Lampard is inferior to a peak aged midfielder at a lesser club, but generally we might expect that a team that is stocked with youth or near sell by date talent may perform at lower levels than that same team when it operates with more players at their peak.

In these posts, I looked at when players are most likely to dominate playing time in the Premiership and while goal keepers inevitably defy logical appraisal, the peak for strikers would appear to be in their mid twenties, with midfielders and defenders peaking slightly later.

A logical next step is to see if the results achieved by a team is even casually related to having players at their perceived peak denoted by playing time and whether this performance falls away as less mature and aging performers take more of a centre stage.

I looked at teams which had played at least six seasons in the Premiership and collected the amount of playing time allotted to a range of age groups in the most successful season for that club and then their least successful EPL season.

I then combined the age profiles of these Premiership clubs best season as well as their worst season to see if their lack of maturity or aging may have played a role in their peak and trough of performance.

For, example, Arsenal's best performance in the EPL was unsurprisingly their 2003/04 undefeated season, where their points per game tally was over 2.5 standard deviations above the league average for that season, their worst performance so far followed soon afterwards in 2005/06 when they were just 0.75 standard deviations above average, when finishing fourth.

In total I have a group of 22 sides, comparing their best efforts to their worst, profiled by age related playing time.

The plots have been combined in two year intervals to try to make any conclusions more visible. Defenders perhaps excel as much through experience as raw physical attributes. Defending is as much about organisational skills as it is about speed and stamina. Therefore, generally defenders tend to gain proportionally more playing time later in their career, even if they have peaked physically, compared to strikers or midfielders.

A higher proportion of defenders aged from 25 to 28 played in the combined successful seasons, while more raw youth and 30+ defenders appeared when charting the 22 sides nadir.

Midfielders appear to show a similar trend. The physical demands of a midfield position generally results in players in their mid twenties being afforded proportionally more playing time and the peak at 25-26 years appears to show that a successful season by the standards of each of the 22 teams, was on average also marked by a higher proportion of midfielders from that age group.

Thereafter, older aged midfielders account for proportionally more playing time in every age group on the occasions where the sides under performed most from their usual standards.

For strikers, again 25-26 year old predominate in successful seasons. They then see proportionally even more playing time in the next two years, possibly as a result of favourable recent impressions. But much of these appearances by strikers in their late twenties also coincide with a season of dramatic under performance by their side, possibly indicating that some strikers can show sudden and precipitous reductions in talent levels as age creeps up on them.

Raw youth and players who retain some ability, but have seen it reduced by aging may be a necessary component of a team's make up at times because of restricted squad sizes and transfer restrictions. Or they may be selected in the belief that they currently possess more helpful ability than they actually do.

Whatever the reasons for the selection of players possibly removed from their peaks, there does seem to be some evidence that these occasions also correspond, on average, with a large degree of under performance by the side over the course of a season. Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-37207624773258428452014-11-06T11:19:00.002Z2014-11-07T10:15:26.087ZTo the Lucky the Spoils.
Before the start of the 2014 NFL season I wrote this previewwhich highlighted the factors that are most strongly correlated with winning.

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Turnover differential, the amount of times you take the ball away from your opponent, compared to how frequently you gift the ball to them by interception or fumble, is unsurprisingly strongly correlated with game result.<o:p></o:p>

Possessions are roughly equal numerically during a game. So if you end an opponent's drive by a turnover, you inevitably deprive them of potential points, while often increasing your own scoring potential from your subsequent drive because of good field position.<o:p></o:p>

A side having a turnover differential of +2 in a match will see that team winning over 80% of such games. Any higher and the win percentage rises to 90%+.<o:p></o:p>

Therefore, the importance of turnover differential is both huge and widely recognised. Former Ravens coach Brian Billick writing for NFL.comuses turnover differential as a major component of a statistic he calls "toxic differential" which also charts big plays, in excess of 20 yards allowed and gained.<o:p></o:p>

Billick describes this combined statistic as controllable, which implies that a team that has done well in such categories as turnover differential in the past will continue to do well in the future and in doing so will reap the expected positive results.<o:p></o:p>

However, if we look at season to season correlation between turnover differential for teams, there appears to be virtually no persistence. <o:p></o:p>

That is not to say that there is no talent associated with turnovers. For instance an experienced NFL quarterback may be consistently less prone to turning the ball over than a rookie and some side may encourage a gambling cornerback to go for interceptions. But there is also likely to be a large degree of luck and randomness involved in turnovers.<o:p></o:p>

This is perhaps most visible when sides are attempting to recover or secure a fumble. The ball can pass through numerous hands before it is finally claimed.<o:p></o:p>

In 2013, seven sides had a turnover margin of +10 or more averaging a turnover differential of +14 and their combined winning record was 0.65. This season, the same seven teams are on course to average a turnover differential of -1 over a 16 game regular season and their current combined win% has fallen to 0.53.<o:p></o:p>

At the other end of the scale the five sides that had turnover differentials of -10 or worse have improved their average differential from -15 to a projected -5 and their winning % from 0.36 to a current 0.42.<o:p></o:p>

So a big driver of game outcome, turnover differential is likely to be partly a product of luck, especially at the extremes and a side that has benefitted from extreme splits may not be as fortunate in the future.<o:p></o:p>

The team with the best current record in the NFL is Arizona. Their 7-1 record in one of the NFC's toughest divisions the NFC West has been achieved with a +9 turnover differential compared to their -1 in 2013.<o:p></o:p>

The Cardinals may have worked to improve their turnover differential. The narrative from within the dressing room is understandably one of renewed confidence and positivity. And Billick, who has won more Super Bowl than most people on the planet, may be correct in that turnovers are largely controllable. But consistently, turnovers do appear to be at least partly due to luck for the majority of teams.<o:p></o:p>

Arizona may not be quite as worthy of their current 7-1 record. Pythagorean estimates, which chart points scored and conceded and partly account for the perceived luck that exists where teams win lots of close matches, has the Cardinals as a 5-3 team.<o:p></o:p>

The NFL season is of course geared towards the Super Bowl and Arizona are currently fifth favourites trailing behind division rivals Seattle, who currently trail the Cardinals by two games. So there is an acceptance, even within their own division that Arizona are perhaps not the 7-1 team that they appear, especially if their turnover differential returns to more normal levels.<o:p></o:p>

However, this may not matter to Arizona, even in the post season against quality opponents. If they play 0.5 football for the remainder of the season, their 11-5 record should get them into the playoffs and if they play to their Pythagorean estimates, a 12-4 could land them a top two seeding.<o:p></o:p>

The turnover record of seeded teams and the implication that turnover differential is a transient quality, appears to highlight the amount of influence random chance has on deciding the destination of the Super Bowl.<o:p></o:p>

Over the last ten seasons, number one seeded sides had an average regular season turnover differential of +13.5, number two seeds, 11. The figure was 8 for number three seeds and around 5 for 4th, 5thand 6th seeds. Playoff teams need to be good, but top seeds need to be good and perhaps also lucky.<o:p></o:p>

Average Turnover Differential For Seeded Teams Since 2003.

 Post Season Seeding.	 Average Turnover Differential.

 1	 13.5

 2	 11.0

 3	 8.3

 4	 5.1

 5	 5.5

 6	 5.4

So turnovers and possibly, by implication, luck played a role in gaining a team a high seeding. And that seeding comes with huge benefits. A top seeded team has two guaranteed home field games to reach the Super Bowl, while a 6th seed needs to negotiate three road games to reach the same destination.<o:p></o:p>

If we assume (probably unrealistically) that the difference between 1st seed and 6th seed has come about purely by chance, the rewards of the playoff schedule will see the number one seed attempting to overcome odds of 5.0 to lift the trophy, compared to a road weary 25.0 for the similarly talented sixth seed.<o:p></o:p>

So Arizona may have been fortunate so far. But they have already banked a 7-1 record and a tangible, if perhaps undeserved reward awaits their lucky run if they can use their present record to secure a top seed.<o:p></o:p>

It is perhaps ironic that in the most popular sport in the country that widely acknowledged the influence of random chance on sporting events, the luckiest teams are rewarded with a big post season advantage.

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Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-13857342967083098802014-10-25T08:44:00.000+01:002014-10-25T08:45:15.083+01:00Subbing Your Striker.Substitutes provide a fascinating look into the changing dynamics of a football game.

Scoring accelerates as the game progresses and in this post from 2012 I looked at the tag of "super sub" that had become attached to Edin Dzeko and how it owed much to the higher goal scoring environment in which he commonly played.

Individual players may tend to produce elevated scoring rates as a substitute not only because of the higher goal environment, but also because they will usually be playing against a minimum of seven tired opponents. Playing time for substitutes also tend to result in smaller sample sizes, leading to extremes of good or bad scoring rates.

Small sample sizes will inevitably throw up prodigious scoring rates for individual players, whereas those which inevitably fall well below normal scoring rates will tend to be neglected. The former, high scoring group of players will therefore often be used to represent the scoring feats of substitutes as a whole.

To attempt to remedy this, it seems sensible to firstly compare the records of all starting strikers who play for the entire game, all those who are subbed out and all those who take their place, to see if there is the expected benefit from playing exclusively during the later minutes of a match.

Peter Odemwingie looks forward to a period of elevated match scoring.

These results are taken from the 2011/12 EPL season and are restricted to players who were designated as out and out strikers. I looked first at the scoring rate per 90 minutes for the three different groups of strikers, as well as their conversion rates.

 Striker.	 Goals Per 90+ Time Allowed.	 Goals Per Attempt.

 Plays Entire Game.	 0.356	 0.126

 Subbed Out.	 0.346	 0.139

 Subbed In.	 0.387	 0.113

The average amount of playing time for the subs in this sample was 18 minutes, added time probably stretches this to 21 minutes. And as suspected, as a group they score at rates that are above either those of the strikers who were substituted and those whom played the entire game.

However, there are a multitude of factors that may alter the scoring rate of this minority group of strikers. They may be thrown onto the pitch in place of a midfielder to help chase an game, which may lead to them scoring at a high rate than usual, even allowing for the late stage of the game. But additional goals may be ceded at the other end.

Similarly, strikers subbed out of a match may have been replaced by a defensive midfielder, to help close out a game where more goals and the possibility of an increased scoring rate were there for the taking.

Allowing for these micro details of game state and managerial intention would require painstaking analysis of each individual match, but we can perhaps design a proxy to reduce the effect of goal environment and these other variables.

There does appear to be some method behind substitutions in the EPL. In this post I suggested that younger, less experienced players are proportionally substituted out of a game more frequently than more experienced players, even with such likely factors as a fitness advantage.

So there may be perhaps a systematic overall approach from EPL managers to substitutions.

Therefore, I looked just at substitutions where a striker replaced another striker, matched the pairings together and treated the combined statistics of the departing player and the newly introduced substitute as those of a single 90 minute + injury time playing event. Albeit made up of two different individuals.

This partly eliminated occasions where a side was aggressively attacking their opponents. If we compare this composite "player" combined from a subbed out and subbed in striker to a striker who plays for the entire game, we might see if the manager is getting optimum return from his ability to make substitutions by looking at like for like changes.

There were just over 300 occasions where a striker replaced a striker in 2011/12. We could speculate that more often a less talented striker was replaced by another less well thought of attacker, but with fresher legs, while the side's premier striker remained for the entire 90 minutes.

The "subbed out/subbed in" group of matched attacking players scored 115 goals in 309 matches of 94 minutes allowing for injury time. A rate of 0.356 goals per 90 minutes.

Strikers who played the entire 94 minutes, scored 277 goals in 746 games. Also a rate of 0.356 goals per 90 minutes.

Either through accident, design, a quirk of this data set or a combination of all three, in 2011/12 EPL managers were able to get goal scoring returns from a substitute striker and the striker he replaced that were identical to those returns from a striker who was considered worthy of the full 90 minutes, under broadly similar match conditions.

A case of expertise and experience eking the optimum return from a side's strike force?Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-20764946685821693802014-10-17T15:17:00.001+01:002014-10-17T15:21:12.340+01:00Your Biggest Opponent Might Be Your Teammate.
In attempting to answer the question "how good is a striker?", the focus unsurprisingly falls on their goal scoring abilities. Raw goal scoring totals have been replaced by such statistics as "goals per 90 minutes" to reflect playing opportunity, often with corrections to remove penalty kicks and to allow for the different scoring environments that are present later in a game.<o:p></o:p>

Latterly, actual goals have been replaced by expected goals, based on the likelihood that an average player would score with a shot or header from a particular location on the pitch.

The ability to get into good scoring positions may be as important as the successful execution of a chance. <o:p></o:p>

Random variation may in the short term produce actual goal tallies that flatter or under value a player and so his "virtual" goal per minute numbers may be a better indicator of his likely long term scoring potential.<o:p></o:p>

The difference in talent levels at the very top level of finishing is likely to be very small and the ability to outwit the defence and fashion a chance may be more important than short term goal scoring achievements.<o:p></o:p>

The opposing defence is quite naturally considered the natural opponent of a striker trying to amass expected goal value, but often there is also another factor that might cause his numbers to rise or fall.<o:p></o:p>

Liverpool was fortunate to be able to call on two exceptional strikers, last season. Both Suarez and Sturridge reached impressive, respective goal totals, both real and expected. In addition, both missed playing time for a variety of reasons. But Liverpool was able to call on at least one of the pair for every Premiership game.<o:p></o:p>

Suarez's suspension left the striking stage clear for Sturridge at the start of the season and then the roles were then reversed when the latter missed a run of matches from early November to mid-January.<o:p></o:p>

While in tandem, the two strikers could possibly be competing for the best chances created by their teammates, while in the other's absence, each may have laid claim to the majority of the prime opportunities.<o:p></o:p>

Therefore, I looked at each goal attempt made by Suarez and Sturridge over the 2013/14 Premiership season as defined by shot location and type. And, reflecting the wider picture, these primary parameters were significant indicators of whether a goal was likely or not to be scored.<o:p></o:p>

I then added a variable to differentiate between when both Suarez and Sturridge were on the pitch and when just one of the strikers was present. This new variable was also a significant indicator of likely success, reducing the likelihood of a goal being scored when the duo were playing together.<o:p></o:p>

In the case of Sturridge, his expected goal per game number falls from 0.9 when he flies solo to 0.67 when he partnered Suarez. A fall of nearly 30%.<o:p></o:p>

The same is seen for Suarez, 1.1 expected goals per game alone and 0.75 when paired with Sturridge. Once again, this is a fall of around 30%.<o:p></o:p>

We are looking at nearly 300 total attempts, but the results may just be a quirk of this dataset. However, on a shot by shot basis, it does appear that the players are taking a bigger proportion of low expectation attempts and fighting over the prime cuts when both are playing. <o:p></o:p>

Suarez's average goal expectation per attempt fell from 0.23 to 0.14 when Sturridge joined him on the field. Sturridge's comparative figures went from 0.27 to 0.18 per attempt.<o:p></o:p>

This is a single case involving two extremely high class finishers and there are at least eight other outfielders to consider, but it perhaps seems that the pair as a duo may have been shooting sometimes, when the position was too heavily defended.<o:p></o:p>

This may have had implications for Liverpool's strategy when both played, although it is now a moot point.<o:p></o:p>

Perhaps more pertinently, each player appears to depress the expected goal record of the other by their considerable presence on the field. And this may have implications for player assessment as well as projection at future clubs, where the most difficult opponent to overcome in posting impressive scoring statistics may well be your teammate.

Luis Suarez debuts for Barcelona in the near future. <o:p></o:p>
Mark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-7061009537884731362014-10-10T09:37:00.004+01:002014-10-10T09:37:42.134+01:00Chelsea Impressive Start to the Season.Chelsea have been impossible to ignore this season. They have either been bullying teams in their own six yard box or jostling for space in their own technical area.

Either way they have been posting extremely impressive raw shooting data and even when their relatively benign strength of schedule is accounted for, they are the Premiership's best performing side to date.

And when you additionally incorporate the distribution of big chances they are creating they pull even further ahead of their challengers.

The strength of schedule is one of the issues looked at in this post http://www.pinnaclesports.com/en/betting-articles/soccer/epl-shot-analysis-week-7?ito=twitter

And their slew of big chance are put under the spotlight here

http://www.bettingexpert.com/blog/chelsea-quality-chancesMark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-29468174009911966352014-10-05T10:04:00.000+01:002014-10-05T10:27:12.968+01:00A Round Up of September's Articles.A round up of September's articles which try to make use of the new information we are gradually gathering about the Premiership teams as we reach half a dozen games.

Swansea and Villa were obvious targets as two sides who were running hot, but don't have the underlying statistical indicators or recent history of being a top six team to maintain their current positions. Gary Monk was Manager of the Month in August and Roy Keane was celebrated as a more effective assistant than he was in the role of manager.

They have a combined five points from a possible 24 in September.

Newcastle and WBA were both noted as probable mid table teams who were out of place at the foot of the table and the record of promoted teams was used to heap on bit of praise on Leicester.

Just click the links below.

A Look at Leicester City

When the Weather Becomes a Significant Factor in the NFL

Chelsea's Hot Start to the Season

Swansea and Villa May not be as Good as their Early Season Results Suggest

Scoring First in the EPL and why Newcastle are probably in a False Position

A Round up of Week 5 in the EPL, Plus a Look at Red Cards.

Why Aston Villa's Narrative Needed A Bit of Statistical Context.

Sir Geoff Hurst > James Milner.

also check out Marvellous if you can get BBC iplayer where you live. You don't have to be a Stoke fan to enjoy the life story of Stoke's onetime kit man (& clown) Neil Baldwin.Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-90418093229387939962014-09-27T10:38:00.001+01:002014-09-27T10:38:19.576+01:00Leicester City's Premiership Season So Far.Leicester City's season to date has been a fascinating mixture of unimpressive rates of chances allowed and created, a devilishly difficult opening series of matches and a perfectly welcome return of eight points from five matches. Enough for 7th spot so far.

In this post I look at how expected goals placed in context, along with their record from last season's Championship can give a better idea of what the remainder of the season holds for the Foxes...

Click here to read more. Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-63678033380566477162014-09-09T12:04:00.000+01:002014-09-09T13:14:31.468+01:00Sir Geoff Hurst's 49 Caps Still Beats James Milner's 50.Last night saw the start of England's inevitable qualification for the finals of Euro 2016. Victory over Switzerland was a welcome opening result, achieved in fairly comfortable manner once the players took the advice of ITV's summarizing commentator, Andy Townsend, by scoring a goal.

The insightful commentating team also observed that by replacing the largely anonymous Jack Wilshere after 73 minutes, Manchester City's James Milner had not only gained a milestone 50th cap, but he had also eclipsed the 49 caps won by England's World Cup legend, Sir Geoff Hurst.

Without wanting to belittle Milner's excellent achievement in an era when competition for England caps is perhaps greater than when the then plain Geoff Hurst was winning his, many would consider the tallies of each player far from comparable.

For those not Born in the Fifties or earlier, Hurst's England career spanned seven seasons and was inextricably linked to matches against the then West Germany. He made his debut in a friendly against them in 1966, scored a World Cup final hat trick at Wembley later that year and limped out of international football with a single 1972 cap against the same side in the first leg of the European Championship quarter finals again at Wembley.

Nearly 50 years of hurt, but Jules Rimet still gleams in the company of two Stoke City World Cup legends.

His international career spanned an era when substitutes were not permitted and a side began and ended the match with the same eleven players. Fewer should serious injury occur during the game.

Limited substitutions had been introduced by the time Hurst won his 49th and final cap, but for a part of that career, gaining a cap meant you had to be selected in the best eleven and there was no option to gain a cheap cap in the final closing minutes from the bench.

In contrast, James Milner, no doubt because of his admirable versatility, has gained many of his 50 caps as part of the multi-substitutions that have become an irritating feature, particularly of friendlies. Or as a late defensive option to protect a lead in competition matches.

28 year old Milner's international career has currently lasted one fewer year than Hurst's, although Hurst only played in the opening international of 1972. And even with the retirement of Lampard and Gerrard, Milner would appear to be vulnerable to a new generation of midfielders.

Perhaps surprisingly, the number of internationals in which Hurst and Milner could have potentially played during Hurst's seven seasons or Miner's six to date are very similar.England played 64 matches from Hurst's debut in 1966 to the end of his international career in 1972. Winning the World Cup in 1966 of course helped.

And the side has played 61 during the course of Miner's international career which began in 2009.

So England played 5,790 minutes of international football from the moment they first capped Sir Geoff to the moment they discarded him for Rodney Marsh. And during that time Hurst played 4,371 of those minutes.

England has played 5,520 minutes during Milner's time as an international player and through either being replaced or coming on as a substitute or nor being selected at all, the Manchester City star has missed 1,771 minutes of potential playing time even when winning a cap, playing 2,819 minutes in total.

So proportionally, Hurst, as expected eclipses Milner, playing 75% of the available time compared to just over 50%, despite earning one fewer cap.

However, this approach doesn't address the longevity of both player's international careers. A one cap wonder could easily beat both figures, while playing at least 72 minutes in gaining just a single cap.

We can allow for this by measuring a player's international career, not in caps, but in the proportion of international years they represented their country. For example, in 1970, Hurst played in 11 of England's 12 matches, once as a substitute, replacing Mike Jones of Leeds after 73 minutes of a goalless, Wembley draw with the Netherlands.

Therefore, Sir Geoff played 917 of a potential 1080 minutes or 85% of England's 1970 international year. Over his career, If we repeat this process for all of Hurst's international years and sum them, we find that he played a total of 4.6 international years taking into account opportunity to play, as defined by the total number of England matches that year and actual playing minutes achieved.

James Milner's most successful international year was 2012, when he played in 11 of 13 games, many as a replacement, but his playing minutes accounted for just under 70% of England's 2012 international year.

Cumulatively, Milner's 50 caps have been gained through him playing 2.7 years of England football to date compared to the 4.6 years of international football gathered by Hurst.

In short, the opportunity to play international games was broadly similar across each player's career, but Hurst was on the field for proportionally much longer and gained more "international playing years", if fewer caps.

Milner may have one more England cap, but he has a long way to go to catch Sir Geoff in actual achievement, even discounting a World Cup hat trick.

Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-88486872913914851932014-09-06T10:30:00.000+01:002014-09-06T11:04:50.111+01:00A Round Up Of August's Articles.August sees the NFL gearing up for an early September start, so this month's articles are split between American football and the association variety.

As well as partially sharing a name for their sport, the NFL and the EPL also return to centre stage at roughly the same time and share many of the often ignored traits which can influence the result of a sporting contest.

Seasonal results are often taken to wholly represent team ability, with all vestiges of luck erased, but this is rarely the case.

Does luck even itself out over a season? Not really.

Even a 38 game EPL season can see teams raised or lowered to finishing positions that do not fully reflect their true abilities, especially among the also-rans where teams of similar talent tend to cluster.

The NFL runs to just 16 games for those teams which fail to make the playoffs.

Being splendid one season in a statistical category that is strongly related to winning, in reality can also be a case of simply being both merely good and lucky. So there is often a need to separate the persistent from the transitory when using last year's form to predict this years.

Stoke warmed up for the shock of the season by winning virtually none of their previous 2014/15 games.

There is also an eagerness to draw definitive conclusions from early season results. So shot location and goal expectation models, which use increased sample data, can be used to simulate individual games, as well as the season to date, in an attempt to see if a team's current league position is consistent with the shots they have created and faced so far.

Are Swansea performing better than Southampton just because they are above them in the table?

And Manchester City may gain some slight comfort from shot simulations that imply that, despite their lacklustre showing at home to Stoke, they should still have been beaten just once in every 10 trials.

On to the articles, click the links for the whole article.

Premiership Football.

What are the limitations of predictive models for soccer betting?

Using Goal Difference to predict Premier League team points for 2014/15

Who Will Top the EPL at the End of August?

Shooting models, expected goals & Pinnacle Sports' alternative EPL table

A shot based appraisal for Week 1 of EPL games

Understanding shot data and expected goals

Why Swansea may not be as good as they appear in the EPL

Based on shot models Villa & Swansea have been lucky so far this season

American Football.

How to predict the CFL Grey Cup winner

Canada plays football as well and despite the differences, it also shares many of the uncertainties with a close cousin, the NFL.

What are the HFA factors that may affect NFL betting?

Gaining an edge over the bookmaker using NFL HFA data

Ubiquitous in sport, but the NFL has a few additional wrinkles of its own. Would you really like to start you game day preparation at 6 am, whilst your opponents have a lie in or play in the noisiest stadium in sport after a long haul flight?

How to predict the 2014 NFL Superbowl winner

Which factors are likely to persist from last season and the myth of being handed a tough schedule.

July's articles are available here.

Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-19526832989625664732014-08-08T11:18:00.002+01:002014-08-08T11:22:35.755+01:00A Roundup Of July's Articles.I've included links to some of the articles I've written over the previous month, which have been published by Pinnaclesports and BettingExpert

As ever the aim is to highlight the impact that random variation can have on sporting contests and the dangers of mistaking random noise for actual repeatable talent.

Was the Suarez deal good for Liverpool?

How easy is it to win the Manager off the Month Award?

Predicting Premiership Points Totals.

The Value of Direct Free kicks.

What Possession figures in reveal in football

Will the top Premiership teams suffer a post World Cup Hangover?

Can Total Shot Ratio help to predict match outcomes?

Are Corners Really Worthless?

The all Madrid Champions League Final.Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-19428210584474457022014-07-08T12:04:00.002+01:002014-07-08T12:04:51.192+01:00How Good Was Tim Howard's Performance Against Belgium?Tim Howard's 17 shot stopping effort against Belgium has been hailed as the "best ever" World Cup performance. But how good was it and what do displays, such as Tim Krul's penalty shootout heroics say about knee jerk reactions based on small sample sizes.

read more here.

http://www.bettingexpert.com/blog/what-howard-and-kruls-goalkeeping-heroics-says-about-evaluating-performanceMark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-52076324560850442342014-06-10T11:16:00.001+01:002014-06-10T11:19:48.483+01:00A Partial Explanation.By way of an apology to those who have recently visited the blog expecting a new post or two. A couple of events have prevented me from posting as frequently as previously, one of which I'll share.

Firstly, I have been extremely grateful for the opportunity to write for BettingExpert.com for the last couple of years and my content continues to appear there, along with many other fine insights.

In addition, Pinnaclesports.com have also given me the opportunity to explore my interest in how uncertainty and the use of stats impacts on our ability to not only explain, but also try to, imperfectly, predict sporting outcomes. Again my articles can be found here.

Feel free to browse the blog or email any points to my address on the home page. Or if you want some insight into the expected refereeing styles at Brazil 2014, why stats should be treated as noisy, rather than beacons of truth or a quick way to calculate where goal difference may tie break a WC group, head over to the aforementioned sites.

 Finally, thanks to Andrew, Michael and Simon and everyone who has kindly re-posted my posts.

Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-34296636489473513032014-04-21T12:00:00.000+01:002014-04-21T12:19:30.261+01:00Which Summer Premiership Buys Bloomed in the Spring?The summer and winter transfer windows afford Premiership teams their only chance to substantially strengthen their squads with quality players. Considered judgement is made and opinions are backed with hard cash to acquire players who will hopefully form a nucleus for a successful squad for the foreseeable future.

In a sport with notoriously short term agendas, it is perhaps unfair to attempt to assess the winners and losers from last summers transfer spending spree, but in the spirit of the current awards season, we'll give it go.

Transfers, of course involve defensive players, mid fielders and attackers and in view of the lack of really objective measures at the moment for the defensive side of the ball, a rating system based on player statistics would prove problematical. Therefore, we perhaps should fall back onto a much more valuable resource in evaluating a successful transfer, namely the experienced opinion the man at the top, the manager.

Playing time can be used as a good proxy for talent in assessing such things as ageing characteristics. Premiership teams have reasonably deep squads and a player who is appearing regularly is likely to be one of the top performers within his team.

However, playing time alone, requires context as well if we are looking at the success or otherwise of a transfer. The playing time achieved by a player is likely to be correlated to his transfer fee. Better players cost more and overall should perform to a higher level than those who cost less.

Age will also be a factor. Most players who attract a fee are generally aged in their twenties, but a player just out of his teens may be bought as much as a future investment than as a potential ever present in the current season of his purchase. By contrast, a player in his mid twenties would be more likely to be purchased as an immediate and useful full time starting player, before age related injury and depreciation sets in.

The third major consideration revolves around the talent levels of the side making the transfer. A £5,000,000 purchase for a promoted side would be a considerable investment and the expectation would be that the player would command a regular starting spot and considerable projected playing time. Whereas, a similarly priced player would be much less likely to make a similar impact at a top side, where talent levels would be higher. He may even initially be purchased as loan fodder with which to inconvenience the ambitions of his parent club's rivals.

These parameters can be used to create a baseline for playing time for particular transfer profiles.

For example, if a struggling Premiership side, had paid around £8 million for 24 year old in the summer transfer window, the average expected playing time, based on historical precedent, for your purchase would be around 60% of the time available in his first season. A more experienced player, nearing 30 would be expected to be on the field for the same side nearly 70% of the time.

Compare that to under 40% of playing time if a similar transfer had been to a top four side instead.

 The Ten Best Transfers Made in the Summer Window, 2013/14.

 Player.	 Club.	 Cost.
(£ millions)	 Age.	 Proportion Of Playing Time.%

 A Elmohamady.	 Hull.	 2	 26	 97

 S Caulker.	 Cardiff.	 8	 22	 100

 E Pieters.	 Stoke.	 3	 25	 88

 C Davies.	 Hull.	 2.25	 29	 97

 J McCarthy.	 Everton.	 13	 23	 81

 L Bacuna.	 Aston Villa.	 3	 22	 79

 M Olsson.	 Norwich.	 2.5	 25	 85

 T Huddlestone.	 Hull.	 5.25	 27	 93

 D Lovren.	 Southampton.	 10	 24	 80

 N Redmond.	 Norwich.	 3.2	 20	 62

Above, I've listed the summer purchases whom have bettered their projected playing time by the greatest amount and thus may be considered to have exceeded the hopes and expectations placed in them by their new club.

Hull's Amhed Elmohamady tops the list, although he and Hull had the advantage of a season long loan to bed in at the KC Stadium during their Championship season of 2012/13. Therefore, England prospect, Steven Caulker should probably take the accolade. His transfer fee was four times that of Elmohamady, but he is considerably less experienced at 22 and under this simple metric, his ever present status at an inferior team, Cardiff, only just failed to overhaul the Hull player for outright leader.

A couple of modestly priced, relatively mature (in age anyway) players follow closely, Erik Pieters at Stoke and Curtis Davis, again continuing the apparently impressive team building done by Hull in the summer window.

Steven Caulker prepares to say "Pob Hwyl" to Spurs and "Helo" to Cardiff.

Of the higher priced purchases in the top 10, McCarthy at Everton and Lovren at Southampton stand out and mega pound, but relatively successful purchases bubbling just below, include Fernandinho at Manchester City, Eriksen and Paulinho at Spurs and Bony at Swansea.

I've omitted keepers, purely because they tend to have few pretenders to their place in the starting lineup, but Mignolet, Mannone and McGregor (at Hull) top the list of newly acquired stoppers.

Inevitably there is a bottom ten, but a metric based partly on appearance minutes is obviously susceptible to injuries.

Everton's Kone prove the least successful summer purchase, a £6 million pound, 30 year old player should be expected to play nearly half of the available minutes at a top 6 side in his first season. Although injuries are partly out of the control of a team or player, his history and age perhaps suggested the price paid was too high for the potential risk. He has been absent through injury since mid October.

Cardiff's John Brayford was a non injured failure from Derby. The fee was relatively modest, £1.5 million, but as a 26 year old he would have expected to feature in around 45% of playing minutes. Instead he failed to play a single minute and is now out on loan. Cardiff suffered a similar disappointment with the transfer of Peter Odemwingie, a more costly and older investment who failed to impress enough to command a regular starting place and his swap move to Stoke was bi-laterally agreed in the winter window.

Palace, Sunderland, and Villa spent moderately, but with a fair few underperforming individual returns at this end of the ledger and big priced summer disappointments, some partly injury mitigated, include Fellaini at United, Osvaldo at Southampton, Jovetic at Manchester City and Lamela at Spurs. Mark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-55783079368068343942014-04-18T08:26:00.000+01:002014-04-18T09:47:53.745+01:00Luck Can Make An Average Team Appear Special.It is very easy to be drawn to extreme performances, either good or bad when looking at the analytical side of football. Exceptional performance stands out, is always highlighted in the media and talked about by the fans. It's difficult not to get carried along.

Liverpool's title charge and the consummate ease by which Crystal Palace cruised to 40 points, of course is partly down to the expertise of their respective managers, fans and players, but it is also likely that random fortune also pushed their sides higher, as well.

The temptation, though is to look for the cause to the effect and ascribe 100% of the former to the latter. But the praise is rarely fully deserved and the criticism is often unduly harsh when expected success fails to arrive promptly.

One way to avoid the almost irresistible rush to narrative, is to start with a singularly anonymous team, one that, for a season,at least is steeped in mediocrity. 52 points with a barely positive goal difference has been the average seasonal performance of a Premiership team over the last decade and the Spurs team of 2004/05 exceeded no one's expectations by recording this benchmark.

The side Martin Jol inherited mid term from Jacques Santini finished 19 points clear of the drop, 43 points from the summit, reached the 6th round of the FA Cup before losing to Newcastle and the 5th stage of the league cup before bowing out to Liverpool, despite taking the first kick in the penalty shootout. They failed to defeat any of the then Big 3 of Arsenal, Chelsea or Manchester United and their 52 points were exactly in line with expectations from their pre-match odds over the 38 games.

So the 52 points gained by Spurs in 2004/05 probably reflected the most likely outcome for a team of their ability playing in that season's Premiership. It is a comforting occasion when theory and reality combine to give the illusion of control without the appearance of outlying products of talent and a lop sided portion of random chance.

The range of possible outcomes from a group of games is most easily demonstrated by simulating seasonal outcomes using strength of schedule adjusted match odds. The usual method projects the range of league points that might be posted by a side of say Spurs talent once the vagaries of random chance are given full rein by continual repetition. However, it is a simple process to break down a team's match probabilities into individual slices that quantify the chances of winning or losing by a particular margin.

So alongside the usual range of points projections, we can add another commonly used statistic, namely goal difference.

How Likely Winning or Losing Margin Varies with the Chance of Winning the Game Outright.

 Chance of Winning the Game.	 65%	 46%

 Winning By a Margin of 1	 25%	 24%

 Winning By a Margin of 2	 20%	 14%

 Winning By a Margin of 3	 12%	 6%

 Winning By a Margin of 4	 5%	 2%

 Losing By a Margin of 1	 10%	 17%

 Losing By a Margin of 2	 3%	 7%

 Losing By a Margin of 3	 0.8%	 2%

 Losing By a Margin of 4 	 0.1%	 0.5%

Spurs' cumulative points expectation from the individual match odds for all 38 league games in 2004/05 was that they would get 52 points and typically that would result in a goal difference of small, single figures.

However, just as it is possible, but highly unlikely that an average side could either win or lose all 38 matches, a single iteration may see a side of Spurs' 2004/05 talent deviate from their expected average and in doing so produce atypically higher or lower goal differences.

The most likely goal difference is indeed centred around zero, but there is also a reasonable chance that our league average side might record multiple years when their goal difference drops well into negative double digits or rises to similar positive heights.

If we take the 2004/05 season as a benchmark, Spurs' range of possible goal differences only begins to peter out as they record values matched by Manchester United, who finished 3rd at one extreme and Norwich who were relegated at the other.

Even with thousands of repetitions, sample sizes start to fall as we look at the spread of actual points recorded by the same goal difference. But the spread of points gained with the same goal difference, in this case -2, is similarly wide, if slightly less well defined, falling into the low 40's and as high as the early 60's. If we again look at the 2004/05 season, Everton recorded a goal difference of -1, but won 61 points.

If average Spurs, mk 200405 can produce an impressive array of goal differences from the same talent base and an equally diverse range of league points from seasons with identical goal differences, the random walk should also be apparent within individual seasons.

Below are two final plots that trace individual seasons taken from just a couple of dozen simulations using our generic, average team and patterns and trends, that could be easily mistaken for real changes within the team are readily apparent. Even though they have been generated from the same game odds, used in an identical order.

The first graph could easily be depicted as a promising start that stalled after around a dozen matches and then got progressively worse as the side stumbled over the survival finishing line, before the season ends on a low point and four consecutive losses.

While the second plot, again drawn from the same match probabilities, show an almost polar opposite. A poor start is gradually arrested and followed by an impressive second half of the season, containing a 12 game winning streak and likely UEFA Champions League qualification, probably in the first qualifying round.

Two very different outcomes to essentially the same talent laden season, made possible by the random distribution of rewards in a short 38 game period.

Fortunately, even when we try to chose a mundane, everyday side to illustrate how the same talent base can produce very different results, an event often intervenes to proved a potential narrative where none really exists.

Santini left to be replaced by his assistant, Jol after 12 matches. Jol's first match in charge was a 4-5 loss at home to rivals, Arsenal. And each of these graphs provides convenient inflexion points at or around 12 matches and it would be incredibly hard to resist attaching the cause of a managerial departure to the effects seen in either plot.

Even if we knew that both were merely produced as one possible reality out of many with the help of a spreadsheet. Mark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-3994888609331305392014-04-17T17:13:00.000+01:002014-04-18T09:58:21.861+01:00The Race For 1st and 4th.A quick piece of housekeeping to follow up the relegation post after the weekend games.

Liverpool's win over Manchester City failed to settle the title race, but it did tilt the odds strongly in favour of the victors. The Reds and particularly Chelsea, then watched on as Sunderland came within minutes of taking all three points from City on Wednesday night, before gratefully settling for a draw.

The title now lies in the hands of Liverpool and Chelsea, win out and that side will be crowned champions by virtue of their head to head meeting at Anfield at the end of April.

Title Odds as of 17 April 2014.

 Team.	 Liverpool.	 Chelsea.	 Manchester City.

 Title Likelihood.	 65%	 22.5%	 12.5%

Chelsea will be the outsiders of three at Anfield, behind Liverpool and the draw, hence the large preference for Liverpool to take the title. However, match odds of around 47% for a Liverpool victory refer to longterm expectation, rather than a single iteration, so chance and luck will quite likely play a part as they did at Anfield on Sunday.

Goal difference has largely become cast in the title chase. There's around a 5% chance that Chelsea and Liverpool will end the season level on points, but virtually all of these ties would be settled in Liverpool's favour. A 5 goal margin of victory in the head to head would be needed to wipe out Liverpool's current advantage in one swoop, (somewhere in the order of 1,000/1), but even then the sides would also need to finish level, most likely on 84 points. Nine goals is too big a gap to bridge in just four games.

City trail both Chelsea and Liverpool, but have a superior goal difference. If they catch one or both (a triple tie is about a 0.5% chance), they almost certainly maintain or increase their current advantage.

The title is now Liverpool's to lose.

Goal difference is one straw that the blue half of Merseyside are currently clutching after Pulisball found its unlikely vindaloo factor by scoring one more than Everton as Crystal Palace reached 40 points in a 5 goal thriller. Should Liverpool falter, the clamour to crown Tony Pulis manager of the season may prove irresistible and the irony won't be lost in the Potteries, if clever defensive spoiling and set piece efficiency suddenly becomes fashionable five years after its inception.

Roberto Martinez is correct in stating that even Everton's current slender three goal difference superiority could prove decisive in the battle for 4th, although only in a minority outcome. If the teams are tied at the end of the season, Everton win nearly 90% of those occasions by virtue of goal difference. Unfortunately, ties are only likely to occur less than 5% of the time and overall Arsenal took a huge step towards securing UCL football on the back of a favour from their favourite pantomime villain and the honesty in the penalty area of West Ham's Matt Jarvis.

4th Place Odds as of 17th April 2014.

 Team.	 Arsenal.	 Everton.

 Likelihood of 4th.	 85%	 13%

As @mixedknuts over at StatsBomb points out, Pulis is now cast in the role of Kingmaker. Having fatally wounded Everton and greatly inconvenienced Chelsea, he faces both Liverpool and Manchester City, against whom his record with a similarly hard working Stoke side was excellent in matches away from their home comforts.

During Pulis' reign at the Britannia Stadium, a Stoke side that was assured Premiership football next season looked and played very much like any other Stoke side and for all that he departed Stoke on relatively good terms, it must appeal if he could end the season with Palace positioned above Stoke.
Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-61945402858182375932014-04-14T16:48:00.000+01:002014-04-18T09:58:58.690+01:00Yaya Sanogo's "Goal" Would Have Been More Than A Consolation.In a low scoring sport such as football, it is inevitable that perceived mistakes by the officials can be extremely important factors in determining the final scores of matches and even the outcomes of competitions. The introduction of goal line technology is a first step to eliminating error, although as Simon Gleave points out even this welcome addition should also come with an associated error bar.

Most contentious decisions involve the more subjective interpretation of fouls and the awarding of any subsequent penalties. Had Mark Clattenburg or his assistants spotted Skrtel's last minute penalty area handball or taken a less lenient view of Sakho's ill timed, first half tackle or Suarez's persistent infringing at Anfield on Sunday, the title race might already be over, settled in Manchester City's favour.

Offside decisions, by contrast have more in common with goal line innovation, but unlike other sports such as rugby, the officials in football are still given just one shot at calling correctly these often extremely close calls.

The ability to watch two different actions simultaneously, (the pass and the move), while correctly judging the relative movement of the striker and the marker, takes a rare talent and it is testament to the skill of the linesmen and women that the majority of such decisions are correct.

The nippy Grant Holt is flagged for offside (& a couple of fouls, probably).

One such call that may have been incorrectly flagged came with virtually the final kick of Arsenal's recent visit to Everton when Yaya Sanogo's 93rd minute goal was generally thought to have been incorrectly ruled out for offside.

The contest had already been comprehensively won by Everton, who led 3-0 and although replays suggested that Sanogo began his run from an onside position as the pass was made, few commentators thought the decision significant. Even Arsene Wenger's burning desire to see fair play remained in check.

Sanogo's disallowed goal would likely have been the game's final action, so the impact on the match can easily be calculated. It had none. Everton would have won the match whether Arsenal's goal stood or was struck off.

However, in a wider context the "goal" had a significant effect on the UCL ambitions of both Everton and Arsenal. As Liverpool v Manchester City and Fulham against Norwich demonstrated, head to head games against your rivals are immensely important, especially as the season winds to a close. Everything good you profitably do also ends up in the loss column of you rival.

Three points gained are three points that aren't available to your opponents, but less obviously goals scored boost your goal difference, while simultaneously depleting that of your current opponent.

If we ignore for a moment the unlikely resurgence of Spurs or the unexpected implosion of Manchester City, Arsenal and Everton have the fight for fourth place and UCL participation in 2014/15 between themselves. Everton currently top the Gunners by two points with five games each to play.

Everton's two point cushion is partly countered by Arsenal's markedly easier run in. Everton's schedule includes entertaining both Manchester sides and a visit to Southampton, while Arsenal taken on four teams from the bottom half along with Newcastle, which is arguably easier that playing basement teams at the moment.

Arsenal's points expectation from these 5 games is around 11 points compared to just 8 for their rivals and strength of schedule based simulations of the remaining matches give the Gunners the upper-hand prior to Tuesday's rearranged game at home to West Ham.

The Race for 4th on April 14th.

 Teams.	 Arsenal.	 Everton.	 Teams Tied on Points.

 Chance of Finishing 4th	 58%	 30%	 9%

So Arsenal, despite trailing Everton appear to still have the better chance of claiming 4th spot. In addition, a significant, near 10% of the iterations result in both sides finishing with equal points, meaning goal difference would be the tie breaker and Everton currently have the superior figures, +22 to Arsenal's +16.

To break these ties we can run the simulations using correct scores, rather than simple win/draw and loss outcomes and add the margin of victory or defeat onto the current goal difference of each side. Once again Arsenal's easier schedule gives them a potential advantage. They are more likely to win by larger margins and less likely to lose by larger margins compared to Everton who face stronger overall opposition.

However, a current six goal deficit is a mighty obstacle to overcome in just five matches and Everton, in the event of a tie, edge 78% of these occasions where the teams finish the season level on points. Arsenal win 14% of the tie breakers and a further 8% of the 9% still cannot be split by goal difference and we have to move onto goals scored.

Overall, once ties have been broken, Arsenal finish 4th 59.8% of the time, Everton 37.8% with a small percentage left over for any other team. So the current goal difference of each side greatly favours Everton should the need arise.

At which point we should return to Sanogo's disallowed goal in the 93rd minute two weeks ago.

The apparent irrelevance of the event in the context of the single game, (except perhaps to Sanogo) begins to take on a much larger significance over the season as a whole.

Everton's currently superior goal difference shrinks if the match at Goodison finishes 3-1 with a last kick consolation and Arsenal, under these new conditions now win a much larger minority percentage of the occasions when both sides end with the same points tally. 4th place is also settled more frequently by goals scored, which also favours Arsenal who have at present scored three more than their Merseyside rivals.

What Was the Cost of Sanogo's Disallowed Goal at Everton?

 Teams.	 Arsenal.	 Everton.

  4th Place if Sanogo Scores.	 62.0%	 35.6%

 4th if Sanogo's Goal is Ruled Out.	 59.8%	 37.8%

Arsenal's chances of claiming 4th place increase by over 2% points simply due to a single goal. Underlining the importance of seemingly irrelevant goals scored in head to head matches, especially when two teams are locked closely together by both points and the subsequent tie breakers.

Liverpool at 2-0 against Manchester City briefly had the opportunity to press on and overturn City's superior goal difference and in view of their harsh run in, Norwich should be grateful that Fulham won on Saturday by the narrowest of margin, rather than the 5-0 they recorded over the Canaries in 2012/13.Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-31829809787560053372014-04-13T21:31:00.000+01:002014-04-14T08:55:36.979+01:00Norwich Slip Towards The Championship.Just when it seemed the day couldn't get any worse for Norwich following their 1-0 defeat at Craven Cottage, the news arrived that the least likely result from the three relegation shaping games had actually materialized. A win for Cardiff at Southampton should have been expected around 12% of the time and Cala's goal (inevitably "Super Cala" for the punning headline writers) had made the result a reality.

The Canaries knew that defeat would see Fulham emerge as serious contenders to snatch away their Premiership place come May, but they must have hoped that Cardiff wouldn't also advance to within touching distance.

The result also took some of the shine off Fulham's narrow win as they failed to shake off the Welsh side.

Sunderland had begun the day as the most likely of the bottom two to take points from their fixture, but although the Black Cats scored the only goal of their game, it was sadly in the wrong net. Instead Cardiff's unexpected three points revived their hopes and chunks of survival probability were claimed from both Norwich and Fulham.

Leaving so soon? Norwich's EPL Status Hangs by a Thread.

Norwich now lie 17th with 32 points and four matches remain, two points in advance of Fulham and Cardiff a further point back. Their goal difference is superior, but not so far in advance that it would remain so with a series of heavy defeats. The killer for them is a borderline unfair run in that takes in visits to Manchester United and Chelsea and visits from Arsenal and Liverpool. A schedule that would pitch them against three of the top four sides in any normal EPL season before a ball was kicked in August.

Norwich's average points expectation from their final four games is around 2.3 points, compared to 4.1 and 4.4 for Cardiff and Fulham respectively and this disparity is best illustrated by plotting the likelihood that each side will gather particular points totals from theses matches.

Norwich's expectations dominate the left side of the graph where fewer points lie and their rivals dwarf the chances of Norfolk's finest as we move towards the higher totals. Both Cardiff and Fulham's most likely total is four points and Norwich's is a single point.

These totals do need to be viewed with regard to how likely they are to occur, but the plot does reiterate the threat to Norwich from two currently trailing teams, but each with significantly easier final fixtures.

We can further confirm the task facing Norwich by comparing the record this season of teams at the foot of the table in their corresponding fixtures against the Canaries final four opponents to create a general baseline. It gives a small sample sized indication of how difficult Norwich's task may be perceived, even if the reality of their task may be slightly different when framed from longer term results.

Sunderland are yet to visit Old Trafford or Stamford Bridge, but are still pointless from the visits of Liverpool and Arsenal. Cardiff took nothing from the four games, as did Villa. Palace are also pointless with a visit from Liverpool to come. Fulham, Swansea and West Ham took just a single point each and only WBA bucked the trend, defeating United at Old Trafford at the depth of their slump and taking a point from each of the other three fixtures.

Overall, sides from Stoke downwards took just 15 points from a possible 105 against the four sides and venues confronting Norwich. Therefore, the upside for the Canaries appears very limited and now they have two legitimate pursuers.

Despite very nearly half the Premiership still not mathematically free from relegation worries, the main contenders still remain any three from the current bottom four.

Sunderland's failure to take anything from Saturday's home game with Everton has pushed them to near certainties for the drop, even with a brace of games in hand. Cardiff looked all but gone following defeat by Palace, but their against the odds win over Southampton has given them renewed hope, while simultaneously damaging the fortunes of Fulham and principally Norwich.

The results of simulating the remainder of the season is shown above.

On a weekend when honours at both ends of the table could have been virtually settled for the season, every result that needed to happen to prolong the enjoyment of the neutral or the agony of the committed, did happen.

Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-58723436619515232112014-04-11T17:38:00.002+01:002014-04-11T17:38:53.608+01:00Premiership Showdowns at Liverpool and Fulham.Get ready for a weekend of football action by seeing how two pivotal matches could decide the fate of the Premiership title race and the fight to stave off relegation. Norwich's visit to Fulham is followed on Sunday afternoon by Manchester City's trip to Liverpool.

In this guest post I outline what each possible match outcome will mean for each side.

Share the pain or the glory.Mark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-27976372150028358832014-04-07T10:07:00.000+01:002014-04-07T10:35:55.121+01:00Crystal Palace Survival Update.For the length of his Premiership tenure at Stoke City, Tony Pulis always managed to pull of at least one late season victory over a fellow struggling team that virtually guaranteed safe passage through to May. Two goal margin wins at the Hawthorns in Stoke's first Premiership campaign and at QPR in Pulis' last season, sandwiched similarly important victories over the likes of Middlesbrough, Hull and Wolves in the intervening years.

For all his critics at the Britannia and beyond, Pulis never allowed the fans' fingernails to be bitten all the way to the quick and it was frequently Stoke's opponents whom were staring into the abyss on the final day of the season.

Whether that was a talent or just a happy quirk of fate, the Premiership's marmite figure virtually guaranteed himself a shot at a full season in Premiership charge of newboys, Crystal Palace, following a comprehensive 3-0 victory over Cardiff on Grand National Saturday.

Three goal margin wins are an extravagance that rarely appears on the Welshman's CV, where defence is prized above all else and few can disputed the marvelous turn around he has engineered using his tried and trusted approach. When Pulis arrived at Palace after 11 matches, they had fewer points than Derby had at a comparable point in their miserable 2007/08 season when they ultimately finished bottom with just 11 points.

As Palace fan and Infostrada's data guru, @SimonGleave points out on Twitter,

Simon Gleave @SimonGleave  23h

Since Pulis was named, Palace have kept nine clean sheets. Only Chelsea (12) and Arsenal (10) have kept more during the same period. #cpfc

and

 Simon Gleave @SimonGleave  23h

In those 21 PL matches, Palace have conceded 18 goals. Only Chelsea (14) and Man City (17) have conceded fewer in the same period. #cpfc

Whether you use cold hard numbers or gut instinct, the picture is rosy for a second season of Premiership football. Last weeks post combined these two approaches by simulating the fate of each side given they attain a particular number of points.

A fan whom watches his side over the course of a season is well placed to give a valid opinion as to the likelihood of their team taking all three points away at Cardiff, So the wisdom of the (Selhurst Park) crowd can provide a strong indication of the number of league points their side will finish with at this late stage of the season.

Above is the updated plot, summarizing the simulated relationship between points and how frequently each team survived in the 2013/14 EPL season. Palace's current total of 34 points is already sufficient for the team to survive in over half of the 10,000 simulations, even if they fail to gain another point. A single draw bumps their survival rate in excess of 80%.

For completeness, here's also the target figures for the remaining struggling teams.

The really good news for Palace is that Cardiff wasn't their easiest game in the final run in. They have a better opportunity to gain additional points in their upcoming home game with Villa and a similarly "easy" away match, comparable to Saturday's win at Cardiff, at Fulham on the final day. So points are there to be taken to push their likely end of season points haul to even more comforting probabilistic levels.

Again by simulating the remainder of the campaign, it's possible to arrive at how likely Palace are to finish with a particular points total and those predictions are shown in the plot above. Each fan will have his or her individual attainable total in mind, but even allowing for a degree of pessimism, the high 30's should be easily reached.

By combining the two plots above, we can arrive at a more conventional graphical depiction of the likelihood that Palace could, through the unlikely combination of a really poor set of results over the last half dozen games, combined with Europa League qualifying form from one or more of the teams currently cut adrift at the bottom, find themselves relegated in May.

So to summarize, Palace has a less than 2% chance of being relegated prior to Sunderland's Monday night game at Spurs. By defeating Cardiff, they almost certainly sealed the Welsh sides fate.

Norwich reacted to an extremely damaging loss at home to WBA by sacking their manager and face a massively important game at Fulham next week, followed by a run in that takes in visits to Old Trafford, Stamford Bridge and visits from Liverpool and Arsenal.

Should Fulham defeat Norwich, the Cottagers may face Palace on the final Sunday having to win to stay up, while the Palace fans celebrate another resounding success for the Pulis sorcery.Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-56870626959546362652014-04-02T08:34:00.000+01:002014-04-02T10:42:20.925+01:00Where To Draw the Line for Premiership Survival.The expectations of football fans at the start of the season can be broadly split into two camps. Supporters of around half a dozen teams can look forward to a season where the anxiety revolves around title aspirations and UCL or Europa league qualification. Some even organise a flypast to celebrate the latter. The remainder of have-nots can't wait to get to the magical 40 points quick enough and reach the generally accepted threshold for continued membership of the top flight.

The 40 point target usually leaves quite a bit of room for error, the mid to high thirties has generally been sufficient to finish outside the bottom three throughout the history of the 38 game Premiership. Only West Ham (42 points) in 2002/03 have been relegated with more than 40 points, although Everton needed a superior goal difference to go with their two score points to survive in 1997/98 and Sunderland found 40 points insufficient a year earlier.

Each of these seasons were atypical of the current EPL. Everton's near miss-hap and Sunderland's demise came in a period when fewer than 80 points were needed to win the title, so "extra" points filtered down the league and West Ham suffered partly through the generous nature of the other two relegated sides, WBA (26 points) and Sunderland (19 points).

This demonstrates that while historical precedence can give a baseline figure, factors unique to particular seasons also wield some influence.

If the likes of Derby, Coventry and Sheffield Wednesday hadn't embarked on unlikely goal scoring sprees against Bolton in 1997/98, Everton would have suffered relegation on goal difference instead of clinging to their top flight status.

And if WHU had swapped an impressive 3-2 win away at Chelsea for a much more valuable win at lowly Bolton in 2002/03 instead of the narrow 1-0 defeat they actually suffered, the Hammers 42 points would have been sufficient and Bolton would have dropped into the Championship with 41 points.

Therefore, goal difference, an intertwined fixture list (14 of the remaining matches are head to heads between teams currently occupying one of the bottom nine places) and the proximity of the relegation candidates to each other, each add layers of uncertainty to the survival target of the threatened sides. And these effects become more apparent as the season winds to an end.

The case of Crystal Palace illustrates some of these factors. Their run in is tough and two matches away at both Cardiff and Fulham present them with one of their best opportunities to pick up points in their remaining matches. If they do take points from these games they will deny one or more of their pursuers the chance to take maximum points. Additionally they have a superior goal difference and this is likely to be the case after 38 games.

Palace's goal difference under Pulis' 20 matches in charge is -4, compared to -15 in the first 11 matches before his arrival. Even if they only limp to 34 points by May, simulations indicate that they will still have just over a 50% chance of beating the drop.

34 points is not only at the lower end of the points estimate for Palace by the end of the season, (their most likely total is 38 points), but it also gives them a better than even money shot at staying up.

But what about their relegation rivals, Sunderland, currently lying in 19th place with 25 points from 30 games. Palace are an obvious target for Sunderland, but their fixture lists don't cross again this season, although their goal differences are very similar. However, they do play WBA whom are also struggling at the foot of the table, but the Baggies have an easier run in than Palace, as well as a superior goal difference. To complicate matters further, Cardiff also visit the Stadium of Light at the end of April.

If Sunderland reach 34 points, (an over-achievement on current evidence), how will all these intertwined factors play out in terms of their survival chances?

The easiest way to unravel this is to again simulate actual seasons and see how often 34 points sees Sunderland safe compared to others marooned at the foot of the table.

The table above appears to indicate that rather than a single survival line at this late stage of the season, each team has its own individual target. The chances of enough teams emerging from the bottom of the pack to relegate Palace if they end the campaign with just 34 points is around 53%.

In contrast, the likelihood that Sunderland will find enough sides to catch should they gain 34 points in a multitude of different iterations of the remaining 64 matches is only 30%. Cardiff, especially with their poor goal difference, need a near superhuman 36 points before they are more likely than not to remain in the top flight, as most of the birds will have flown to a slightly higher perch.

The playing field is level in August, but by May the really struggling teams appear to be required to clear a slightly higher bar just to give themselves a similar shot at surviving the drop.

*although Fulham aren't on the (slightly cluttered) plot, they are of course included in the simulations. Their potential fate is slightly worse than that projected for Cardiff.Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-80650031579403821582014-03-31T16:04:00.000+01:002014-04-02T09:55:54.163+01:00Kings and Kingmakers.If Sunday was a fine day for Merseyside as a whole, Saturday was also almost as good for both halves of the city, despite neither side setting foot on a football pitch.

Crystal Palace against Chelsea, pitted a master of tactical planning, prepared to sacrifice every ounce of entertainment from a match to achieve his desired result against.......Jose Mourinho. Ultimately, Pulis' continuing love affair with a binary scoreline could prove decisive in turning Palace's survival from merely possible to probable. However, the loss of three points in a 1-0 defeat, stalled Chelsea's pursuit of another Premiership title, just when even Jose was daring to dream.

The result of the evening fixture was almost as good for Liverpool, as close rivals Manchester City found a visit to the Emirates as difficult as the respective league positions suggested it should be. Arsenal, with UCL football now in the balance, stirred enough to deprive City of two points and, for the moment, fight off a sustained challenged for 4th from Merseyside's Blue half.

Wins for both Everton and Liverpool the following afternoon, then pressed home the advantage that Saturday's results had delivered. Radio 5 Live's 606 phone-in had a decidedly red hue, with outlandish comparison being drawn between Brendan Rodgers and Shanks and honeymoon flights being cancelled to take in the clash with Manchester City in April.

A bunched finish is more often a sign of overall mediocrity, rather than excellence, so the accolades could perhaps be shelved for a few years, at least. But there is no denying that Liverpool are an improved side and an attacking style that dares opponents to keep up, rather than a pragmatic, defensively stifling approach has captured the imagination of fans beyond their natural heartland.

Chelsea and Liverpool each has six games remaining, City has eight, but the best team doesn't always gain the most points over a short span of matches, as luck and strength of schedule effects kick in. The highest placed side after half a dozen games, more often than not doesn't stay the 38 match distance, so a sprint finish from a reasonably level break, combined with a visit to Anfield for both City and Chelsea will likely see the title odds fluctuate throughout April.

An uninterrupted run of victories would ensure the title for either City or Liverpool, but, in the likely event that a few Palace-like slip-ups lie in wait, the importance of home matches for Liverpool against first, Manchester City and then a fortnight later, Chelsea is clear.

How Results Against Manchester City & Chelsea Could Decide the Title Race.

 Outcome of H2H From Liverpool Perspective.	 % Chance of Liverpool Winning EPL. 	 % Chance of Man C Winning EPL.	 % Chance of Chelsea Winning EPL.

 MC(W) & Che(W).	 71.5%	 27.0%	 1.8%

 MC(W) & Che(D).	 36.0%	 48.0%	 16.0%

 MC(W) & Che(L).	 24.0%	 42.6%	 33.4%

 MC(D) & Che(W).	 37.1%	 59.5%	 3.4%

 MC(D) & Che(D).	 17.0%	 70.5%	 12.5%

 MC(D) & Che(L).	 7.0%	 58.9%	 34.1%

 MC(L) & Che(W)	 11.8%	 86.8%	 1.4%

 MC(L) & Che(D).	 2.1%	 91.1%	 6.8%

 MC(L) & Che(L).	 0.6%	 78.5%	 20.9%

One way to attempt to quantify the importance of the upcoming games is to simulate the remainder of the season and examine the frequency at which each side tops the table under the nine possible combinations of match outcomes for the two huge games at Anfield.

We should have sufficient information to be able to frame reasonably accurate match odds for the remaining 65 matches and use these probabilities to re-run the EPL table without the need to play the matches. Around one season in five, Liverpool might achieve victories over both City and Chelsea and in light of the boost given to their chances on Saturday when their rivals dropped points, such a clean sweep would see them claim the title just over 70% of the time.

As a slight reality check, every combination of results other than a Liverpool clean sweep in these two head to heads makes a Liverpool title odds against. Manchester City still achieve more title winning simulations than Liverpool, even if they lose at Anfield, but Chelsea avoid defeat two weeks later. Chelsea also increase the size of their minority vote with a favourable Anfield experience.

So Liverpool's advantage from playing their closest rivals also has the downside of increasing their strength of schedule in the remaining games. Should City lose to Liverpool, they will have a motivated Chelsea going into bat for them two weeks later.

A fascinating end to the season, with rivals possibly relying on each other to beat whichever side steals a march towards the title. For all the hype surrounding Manchester City's visit to Liverpool in April, it may be their return to the city in May, this time to Goodison Park, that finally clears up the 2013/14 EPL title race.
Mark Taylorhttp://firstname.lastname@example.com:blogger.com,1999:blog-6059983310325678283.post-45171786125651275552014-03-19T13:48:00.000Z2014-03-19T14:05:06.840ZJudging A Side Over One Season.For much of Alan Pardew's reign at Newcastle, his side has provided ample topics of discussion for the analytical community. Their fifth placed finish in 2011/12, with a goal difference of just 5, was widely seen as the product of a decent side getting a bit lucky and their near relegation the following season merely served to reinforce some misconceptions that exist around luck based over-achievement immediately snapping back into ledger balancing under-achievement.

This season the team has largely occupied the dead ground between Simon Gleave's Superior Seven and Threatened Thirteen. They currently hold 8th spot with very little likely up or downside, casting them as mere spectators to the title and Champions League tussles and the relegation grind. So it has been left to their off field employees to guarantee column inches.

Over the previous two and three quarter seasons, Newcastle's success rate, that counts draws as half wins, has averaged out at a shade over 50%. If the Premiership were allowed to meander on without a season's end reckoning, Newcastle since the start of 2011/12 have recorded results typical of a side finishing a 38 game season in 8th or 9th spot, with a goal difference in the region of zero. So, despite the bouts of squad strengthening and weakening during the various windows, might Newcastle have been broadly a "best of the rest" team under Pardew and has their seemingly up and down seasons simply been down to talent and luck interacting in differing doses?

Simulating season long results for one side or a whole league can quickly produce the range of possible outcomes we might expect from teams of a certain quality and it is perhaps a sobering thought, especially for managers that there is a non trivial chance that the best side from the Threatened Thirteen could find itself struggling to top 40 points over a 38 game campaign.

There is almost a 10% chance that a side with a true success rate of 0.5 may recorded 41 or fewer points, the limit of Newcastle's achievement in 2012/13 and a 6% chance that they could rise to the highs achieved in the previous season.

So although a dissected break down of Pardew's previous two completed seasons would give an entirely factual record of the points per game performance of his side in the 2011/12 and 2012/13 seasons, we can be much less sure if that see sawing record accurately tracked the talent of the team.

What we see, isn't a cast iron endorsement of quality or the lack of it, but a combination of randomness and talent.

It would have been easy to over react to the raw results posted by Newcastle in either season and while injury, Europa League involvement, squad churn and tactical change almost certainly impacted on their talent and luck based achievements, it seems unlikely that the 24 point difference between the 2012/13 team and the 2011/12 team truly expressed the quality gap between those two closely related editions of the side.

One way of trying to reconcile an apparent points based performance improvement to any real shift in a sides actual abilities is to utilize to expertise of the bookmaking industry. At the start of the season all of the spread firms publish the expected number of league points they think each side will gather by the end of the season. As the season progresses these estimates will be up or downgraded in line with each side's current rate of accumulation of points.

For example, prior to last Saturday's eventful head to head meeting with Newcastle, Hull had already posted 31 points, almost equal to the general preseason estimate of around 33 or 34 points. Their updated quote suggested they might get about 42 points. So from a performance perspective they were roughly 8 points ahead of where most bookmakers expected them to be.

We have also reached the second half of the season, where a side increasingly completes their head to head appointments and by mid March a team has played a rival home and away between 9 and 11 times. The chances of a team winning or drawing a game depends on not only the gap in quality between the teams, but also the venue. So the expected success rate in a return fixture will depend partly on how each team has progressed or regressed over the 190 or so days between the initial meeting, but also where each match was played.

Above, I've plotted the pre-game quoted success rates for actual Premiership matches, paired by home and away matches. So a home side that is expected to have a 60% success rate at home would likely be quoted at around 40% when they traveled to complete the reverse fixture.

If we look at the actual differences in the quoted success rates for return matches any deviation from this fairly strong, general relationship can be, at least partly attributed to the direction both sides have moved in over the ensuing timescale.

The case of Crystal Palace (or more accurately, Tony Pulis) demonstrate the process. Up until March 19th, they have played 10 teams twice. Stoke, Hull, Manchester United, Norwich, WBA and Southampton each made a return visit to Palace and Palace set off to reacquaint themselves at the homes of Arsenal, Spurs. Sunderland and Swansea.

In eight of those ten matches the quoted pregame success rate in the return was greater than predicted by the success rate in the initial game and the line of best fit from the plot above. Palace's quoted success rate posted by the bookmakers is on average 15% higher over the ten rematches, compared to a typical example from the line of best fit. In short, the recent quotes imply a level of improvement compared to Palace in the opening months of the season.

There are strength of schedule issues, Palace may have played ten teams whose true ability has dipped, but this can be addressed by a least squares approach to the overall loss or gain in success rate of each side, when measured against their actual repeat schedule. The order shuffles slightly if you apply this correction.

Which Teams Have Impressed Enough to be Upgraded from Preseason Estimates?

 Team.	 Average Shift in Success Rate per Game.

 Crystal Palace.	 0.06

 Liverpool.	 0.04

 Hull.	 0.04

 Arsenal.	 0.04

 Manchester City.	 0.04

 Chelsea.	 0.03

 Everton.	 0.02

 Newcastle.	 0.01

 Sunderland.	 0

 Southampton.	 0

 Manchester U.	 -0.01

 Spurs.	 -0.01

 WBA.	 -0.02

 Norwich.	 -0.02

 Stoke.	 -0.04

 Swansea.	 -0.04

 Cardiff.	 -0.04

 Aston Villa.	 -0.04

 Fulham.	 -0.05

 WHU.	 -0.06

The table above shows the strength of schedule corrected, average raw success rate increases or decreases per game as seen in the repeat fixtures played so far by each Premiership team. It's a combination of perceived improvement (Liverpool) or decline (Manchester United) and partly a popularity contest.

Stoke are on course to better most preseason points estimates, but their marmite factor makes them a universally unpopular team, which may account for their apparent downgrading, despite a better than expected transitional campaign. Even punters have to be offered inducements to side with Stoke! But hopefully, most sides in the table have been up or downgraded predominately on the bookmakers interpretation of repeatable form.

To add context to the previous table, I've finally plotted the change in pregame quoted success rate against the rise or fall in expected final league points totals compared to the estimates at the start of the season. Fulham, for instance are on course to be 10 points adrift of preseason estimates and they've been downgraded by an average success rate of ~0.05. Slightly more than you would expect from the plot.

Palace are on course to gain about 36 points compared to the 31 quoted in August, but their position, well above the average line appears to reflect extremely well on current manager, Tony Pulis and less so on Ian Holloway, who was in charge for the bulk of 2013. Pulis, once again demonstrates an ability to turn relegation fodder into lower half scrappers who can take their season to the wire. When he was appointed Palace had 4 points from a possible 33 and were rock bottom.

Steve Bruce's tenure at Hull is also endorsed by the betting movements. Not only were the Tigers underrated, but there appears cause for added optimism above and beyond there current position of relative safety.

Both Merseyside teams have gather more points than expected, but Everton's upgrade still lies below the line of best fit, possibly indicating a reluctance to take their improvement wholly at face value. A caveat that also applies to Southampton.

Liverpool may be the most telling point on the plot. They were expected to gather around 66 league points when the season began, currently they may be able to top 80 points. An increase of around 16 points. However, if we roughly apply their average increased success rate that is currently being applied to them over a 38 game season, their points total increases by just around half of those 16 points. Outstanding, but partly unexpected performance isn't being taken at face value on a match by match basis. It is also being taken with a slight pinch of salt.

The Reds' uptick is as spectacular as the 38 game epic demonstrated by Newcastle, when they nearly claimed a Champions' League spot, but it may be well to remember that single season performances are a product of repeatable skills and also less repeatable variation. Even with points in the bag, a team might not really be quite as good (or bad) as their record might indicate. Mark Taylorhttp://email@example.com:blogger.com,1999:blog-6059983310325678283.post-26836502883173653162014-03-10T16:37:00.000Z2014-03-10T16:41:36.696ZAnalytics Might Need to Get Lucky.Let's try a thought experiment.

Analytics has taken root in the game and you've been tasked with improving the goalkeeping abilities of one of your two goalies. Both are equally talented at every aspect of the game, (you've developed a statistical method that strips away random variation to tell you this, but of course that must remain proprietary). The two keepers are identical in virtually every way, both on and off the field. They are the Fabio and Rafael of the goal keeping ranks.

But there is one facet of the game where a slight improvement may be possible. Namely, saving penalty kicks.

You load up a database with physical and locational data for every type of penalty kick. The pace of approach, the angle of run, the kicker's natural foot, even the flavour of ball being kicked. And the numbers allow you to give the keeper a slight advantage compared to his previous spot kick saving talent levels.

You pass the information onto just one of the keepers because the club has decided to sell the other (now slightly inferior) goalie for a hefty profit. Just to be sure, you trial the keepers over a million penalty kicks (it is a thought experiment, remember) and sure enough, keeper A saves kicks at a rate of 25% and keeper B is stuck at the league average of 22%, (we could have used our proprietary tool to strip out random variation, but I made that bit up).

Prior to this analytical tweaking, your robotic, talent flat lining keepers and their 22% ability to save penalties had faced 43 kicks spread over eight seasons and they had prevented 8 from entering the net. So they'd been a bit unlucky and saved 19%. Even for a true 22% keeper, you are going to save 8 or fewer about 34% of the time.

Keeper B leaves and keeper A, his talent constant, remains the starter for the next two seasons. Buoyed by the knowledge that their keeper can save 25% of the penalties compared to just 22% previously, the defence thinks nothing of fouling opponents in the box and they concede 17 penalties in two seasons....and all but two are scored.

Just 12% stay out of the net! It's a disaster.

Meanwhile, keeper B, by a happy coincidence, also faces 17 penalties and saves 4, nearly a 24% success rate. Inevitably, keeper B is repurchased for a lot more than he was sold and the analytics department closes to finance a couple of days worth of his now considerable salary.

So what went wrong?

The answer is probably nothing. Inferior teams out perform superior ones all the time over limited numbers of trials. The World Series springs to mind. If you pair a keeper who has a 25% chance of saving a kick with one that has an inferior 22% chance over 17 trials, the better keeper will save more kicks on just over half of the occasions. About 17% of the time they will save the same number. But in a not insignificant 32% of the paired trials, keeper B will own the bragging rights.

17% of the time keeper A will save 2 or fewer penalties and 40% of the time your new improved keeper won't beat the raw success rate of 8 from 43 posted over the previous eight seasons by the combined individual might of two 22% penalty deniers.

You've succeeded in your brief to improve a player, but that improvement isn't guaranteed to show itself in 17 repetitions. You still need to get a bit lucky to become the hero.

Moneyball, the movie played around with the chronology of some of the trades for dramatic effect, (once again stats take a back seat to the demands of narrative), but I'm assuming the sluggish start to the 2002 Oakland A's season, when an analytical approach was in full swing and the results on the field were not, is more faithful to the actual course of events.

Chance, might not always love a trier.Mark Taylorhttp://firstname.lastname@example.com