How Well Might Total Shot Ratio in Football Travel ?

One of the most familiar of the crossover stats from hockey to football is total shot ratio. It is often used as a proxy for "dominance" of possession and supposes that a side that is constantly out-shot or out shoots their opponent will eventually reap their just rewards.

The majority of the football based research has been focused quite naturally on the English Premier League, most notably by James Grayson, who demonstrates both the repeatability and predictive nature of the stat for the EPL.

Very little of the detailed validation that James has undertaken for the EPL has been done on any other the other world leagues, but this hasn't prevented a combination of a respectable TSR and a relatively low league position earning a non EPL side team an "unlucky" tag.

If we first consider the case of possession, It has largely been discarded as credible measure of team strength. Barcelona's use of the tactic, with varying degrees of success, suffered at the feet of Bayern Munich in the 2013 ECL semi final.

Spain's finest held the majority of the ball, but fell to a 7-0 two legged thrashing. And in more humble surroundings, Stoke mostly under Pulis, graciously allowed themselves to be continually "dominated" on all fronts, even at home, but still won enough games to safely avoid the drop each season.

Stoke Shrug & Say No to TSR or Possession Stats.

However, despite possession's decidedly mixed record of success, it is possible to construct a scatter plot of possession against match outcome that does appear to present a pleasingly angled line of best fit that appears to show more possession positively linked to more success on the field.

It is only when the top three or four teams are removed from the plot that the correlation for the remaining teams becomes largely random.

The constant presence of a handful of sides which dominate in a league, not only in wins, but in possession and shots by simply outclassing the majority of their opponents, therefore, may potentially create a misleading correlation, where only a weak one exists for the majority of teams.

So might the illusion of possession being generally correlated to results be repeated to some degree, in some leagues for TSR.

The Scottish Premiership has largely been a two horse race between Rangers (until their demotion following their liquidation) and Celtic. The league has an unusual format, comprising of 12 sides and the table splits in two once each team has played three matches against each of their rivals, enabling a 38 game season to be played out.

In common with the EPL, a Scottish Premiership side's TSR in the first half of the season appears to show a strong correlation to goal difference in the remainder. Therefore, TSR appears to do a good job of predicting a useful future quality of teams in Scotland's top flight.

The coefficient of correlation is a very healthy 0.71 for the four seasons from 2010/11 onwards. However, the scatterplot is fairly lopsided, there is very nearly daylight between the six points in the top right hand corner, four Celtic seasons and the only two from Rangers, and the rest.

As with possession, where a strong correlation is inferred because of the constant presence of atypical sides which partly outclass the rest, have Celtic and Rangers exaggerated the implied predictive power of TSR for the remainder of the teams, outside of the "Old Firm" by helping to create an impressive r value?

If we crudely remove the six "Old Firm" points from the plot, the scatter plot and the coefficient of correlation between past TSR and future goal difference for the remaining ten per season Scottish sides alters dramatically.

If we remove Rangers and Celtic, r falls to 0.14 as does the predictive power of the relationship. TSR may still tell us something about the remainder of the season for these non elite sides, but without a highly likely combination of a regular, out shot, defeat by either Celtic or Rangers, our conclusions become much less dramatic.

The separation of abilities in the EPL is perhaps less stark than in Scotland's top flight, but a division along the lines of Simon Gleave's "Superior seven and threatened thirteen" has largely existed over the last decade.

Once again, the coefficient of correlation is high if we include all Premiership sides and although the clustering of teams at the middle and bottom isn't as pronounced as in Scotland, there does appear to be an effect.

If we remove every game involving at least one of Simon's superior seven, we get a truncated season in which the threatened thirteen only contest home and away matches against one of the twelve remaining teams from this group.

If we now split the season in two and regress a threatened thirteen side's TSR in the first half of the season to their goal difference in the remainder of the season, the coefficient of correlation again falls. This time from 0.73 to 0.29.

Admittedly, the sample size has also fallen in both cases when the very best sides are removed, but the confidence with which TSR is used indiscriminately across and perhaps within leagues to evaluate certain types of sides perhaps should be questioned.

Just as the past possession record of sides is largely irrelevant to many future outcomes, (even when we can easily produce a scatter plot between possession and outcome to create the illusion of a strong, universal relationship), previous team TSR might also be much less of a factor in the prediction of some types of games.

In conclusion, we seem to get high r values for the relationship between TSR at half season and future goal difference in the remaining games, in leagues where there are a couple of consistently dominant teams, in every aspect of play.

Barca and Real Madrid in Spain, Bayern Munich in Germany, Celtic and a soon to be reunited Rangers in Scotland, the superior seven in the EPL.

The coefficient of correlation for the previous four full seasons, for EPL, Spain, Germany and Scotland are, respectively 0.77, 0.73 0.68 and 0.71.

In France, where dominant sides are less in number and also less dominant, r is 0.51, in Italy it is 0.53.

And most pertinently perhaps, in the bottom tier of the English football league, where runaway winners are rare, r for TSR to future goal difference from the mid season point over the last four seasons is barely 0.4.

So at the very least, the clear assertion that TSR is a good indicator of likely future performance, in every league and within every league at every level, ranging from the English Championship to the MLS and the Egyptian league to the Australian professional league, should also be backed up by the kind of thorough and rigorous validation that James has carried out for the EPL.

Without that, the strength of any possible correlation can only be guessed at.

Weighted Shots v Unweighted Shots As A Predictor of Future Goal Difference in the EPL.

Tom Tango has recently presented an alternative to Corsi in hockey that weights shots differently depending on whether they resulted in goals, saves, misses or blocks.

One of the logical tests of the new metric is see how well it correlates to useful team information, such as future goal difference, compared to projecting from previously used metrics, such as unweighted shot differential or ratios.

The expectation voiced in many hockey circles was that because the "Tango" correlated almost perfectly to the traditional Corsi metric, the added information hoped for by weighting different types of shots would be negligible, at best.

In a typical concise and insightful post, here, Tango addresses the issue of the virtually perfect correlation between both metrics. Pointing out that using basic shot data from identical samples to test the correlation to out of sample data, such as future goal difference, gave different coefficients of correlation depending on whether the Corsi or Tango was used.

In short, weighted shots showed higher r values, despite the strong correlation between the two metrics.

 r Values for Weighted & Unweighted Shot Differential and Ratios when Correlating to Future Premiership Goal Difference.

After X Games	r for Total Shot Ratio	r for Shot Differential.	r for Weighted Shot Differential
2	0.49	0.51	0.57
6	0.70	0.71	0.77
10	0.70	0.71	0.76
15	0.74	0.74	0.80
18	0.73	0.74	0.80
20	0.73	0.74	0.79
24	0.72	0.73	0.77
30	0.65	0.66	0.69
34	0.55	0.55	0.56

Tango's defence of his new metric can be summed up in this extract from the linked post.

"But more amazing is that even though the correlation of Corsi to Tango (both based on the same samples) was close to r=1, when we correlate each to out-of-sample data (in this case, goal differential from OTHER games), Tango correlated at r=.50, while Corsi was r=.44.  Or if you prefer r-squared, it’s .25 to .19, respectively."

I have therefore repeated the exercise for the Premiership, using three flavours of shot based metrics in one part of the season and testing the correlation between these at an individual team level and goal difference for teams in the remainder of the season.

And the weighting of shots also appears to make a difference in soccer as well as in hockey. Correlation peaks around mid-season, but at every stage, weighting proved a superior correlation to goal difference in the remainder of the season compared to unweighting.

It also makes intuitive sense to reflect the extra information present in a goal compared to just a shot.

Using Weighted Shots To Predict Goal Difference in Subsequent Games.

As a follow up to the previous post, here is the changing relationship between a side's weighted shot differential compared to their opponents, for goals, shots that went wide and shots that were saved after a certain number of matches and the goal difference in the remainder, as suggested in the comments by Tango.

The EPL has 38 games,

So, for example, the projection for the goal difference in games 3 to 38 inclusive is found by multiplying the oerall GD in games 1 and 2 by 2.9, adding the differential of shots that went wide after two games multiplied by 0.43 and adding the save differential after two games multiplied by 1.24. The constant is universally close to zero.

r for each regression after each number of games is in the final column and peaks at mid season.

Correlation Between Shot Type Differential in Previous Games & Goal Difference in Remaining Games.

After x Games	Goal Difference  Coefficient	Shots Wide Differential Coefficient	Shots Saved Differential  Coefficient	Relative Weight for GD	Relative Weight for Wide Shots	Relative Weight for Saved Shots	r
2	2.9	0.43	1.24	1	0.1	0.4	0.57
3	2.5	0.59	0.92	1	0.2	0.4	0.67
4	2.3	0.40	0.71	1	0.2	0.3	0.72
5	1.9	0.38	0.57	1	0.2	0.3	0.76
6	1.8	0.33	0.45	1	0.2	0.3	0.77
7	1.6	0.25	0.37	1	0.2	0.2	0.79
8	1.4	0.24	0.30	1	0.2	0.2	0.79
9	1.2	0.22	0.27	1	0.2	0.2	0.76
10	1.1	0.17	0.24	1	0.2	0.2	0.76
11	1.05	0.15	0.19	1	0.1	0.2	0.77
12	.99	0.15	0.16	1	0.1	0.2	0.78
13	.91	0.13	0.14	1	0.1	0.2	0.81
14	.82	0.11	0.14	1	0.1	0.2	0.81
15	.75	0.09	0.14	1	0.1	0.2	0.80
16	.72	0.09	0.12	1	0.1	0.2	0.81
17	.6	0.06	0.14	1	0.1	0.2	0.81
18	.55	0.02	0.15	1	0	0.3	0.80
19	.46	0.02	0.14	1	0	0.3	0.78
20	.43	0.01	0.13	1	0	0.3	0.79
21	.39	0.01	0.12	1	0	0.3	0.78
22	.36	0.01	0.10	1	0	0.3	0.79
23	.31	0	0.09	1	0	0.3	0.76
24	.28	0	0.09	1	0	0.3	0.77
25	.25	0.01	0.08	1	0	0.3	0.75
26	.20	0.01	0.08	1	0	0.4	0.74
27	.17	0.01	0.07	1	0	0.4	0.72
28	.15	0	0.07	1	0	0.4	0.70
29	.13	0.01	0.05	1	0.1	0.4	0.69
30	.13	0.01	0.04	1	0.1	0.3	0.69
31	.11	0.01	0.03	1	0.1	0.3	0.66
32	.08	0.01	0.03	1	0.1	0.3	0.64
33	.06	0.01	0.02	1	0.2	0.4	0.60
34	.05	0.01	0.02	1	0.1	0.5	0.56
35	.04	0	0.02	1	0	0.5	0.48
36	.02	0	0.02	1	0	0.7	0.40
37	.02	0	0	1	0	0.2	0.32

The Weighting Game.

Shot counts verses goal counts as a predictor of future performance is a debate that that is being fought out not only in football, but also in hockey. Sample size is at the heart of the issue. Goals are obviously more important in terms of who wins the match, but they are relatively rare events. Whereas shots accumulate at a faster rate, building up sample size, but play only an intermediate role in deciding the outcome.

It is perhaps unfortunate that a distinction has arisen between shots and goals because they are merely classifications of a single larger group. Namely, they are all goal attempts, but with different actual outcomes.

Goals are shots (or headers) that result in a goal, saves are on target shots that are saved and misses are shots that go high or wide of the target.

The most recent rumblings from hockey arises from renowned sabermetrician, Tom Tango's use of different types of shots (he includes blocked efforts also), from the first half of a season to predict goals or specifically goal differential from the second half.

He uses the different types of shot differential, with appropriate weightings in the first half of a season to predict goal differential in the second. The post can be found here and the application to football is obvious.

I have therefore updated a similar approach using data from Joe B's football data site (So no blocked shot data as a separate category). The aim was slightly different. I set out to determine the final goal difference for EPL teams, based on their goal difference and shooting differential at various times during the season.

Final goal difference is strongly correlated to finishing position and with the odd exception finishing position is also related to team strength. And knowing where a side is likely to finish well before they actually arrive at that position is an obvious advantage if we wish to know how they are likely to perform during that 38 game journey.

I therefore split goal attempts into shots that went into the net (or goals), attempts that were saved and off target attempts and totaled the cumulative differential between each Premiership team and their opponents from the second match of the season until the penultimate game.

For example, after 14 games, Arsenal currently have a +7 goal difference, a +91 differential in shots that went wide and +34 differential in shots that were saved.

I then regressed these differentials against the final goal difference after the 38th game to get the changing relationship between the three variables and the side's ultimate goal difference after two games all the way up to 37 games played.

All three types of shots are important in predicting the final goal difference of teams. But the relative importance in predicting future goal difference from shots that are saved or go wide, declines in relation to the importance of shots that result in a goal (or goals for short), as the number of games increases.

In addition, the values of the coefficients is also dependent upon how many matches are in the sample. The respective goals, wide shots/headers and saved shots/headers coefficients are 3.91, 0.43 and 1.24 when calculated after just two matches and, as you would probably expect 1.02, 0, and 0 after 37.

So far this season each team has played 14 matches and the coefficients for current goals, wide shots and save differentials when used to predict future final goal difference are respectively 1.91, 0.13 and 0.14. If we use these figures for each team, the final projected league goal difference for each side is as shown below.

Projected Final Goal Difference Using Shot Differentials After 14 Games.

Position	Team	Projected GD.
1	Chelsea	46
2	Man City	40
3	Southampton	31
4	Arsenal	28
5	Man Utd	20
6	West Ham	10
7	Everton	6
8	Liverpool	4
9	Swansea	2
10	Newcastle	0
11	Tottenham	-3
12	Stoke	-4
13	West Brom	-12
14	C Palace	-13
15	Hull	-22
16	Sunderland	-23
17	QPR	-26
18	Leicester	-26
19	Aston Villa	-26
20	Burnley	-29

At the moment these figures are merely another rating system, albeit one that appears to reasonably predict the likely quality of the current side. Villa, for example appear to have been fortunate in the way in which they have won numerous single goal victories. And a wider appraisal incorporating extra shot information reduces their rating compared to their current league position.

To illustrate how the projections have fluctuated for a single team, here's how the projected final goal difference has varied for Arsenal using the updated coefficients after each game week of the 2014/15 campaign to date.

Projected Final Goal Difference For Arsenal from Shot Differentials Updated Weekly.

Games Played by Arsenal.	Final GD Projection.
After 2 Games.	+13
3	23
4	16
5	24
6	25
7	17
8	22
9	24
10	31
11	27
12	26
13	27
14	28

We can demonstrate the use of such ratings and perhaps their predictive potential by converting these weighted shot derived ratings into match odds and comparing them with a reliable benchmark, such as the current bookmaking odds.

Stoke entertain Arsenal on Saturday. Arsenal's projected final goal difference is a rounded up +28, Stoke's is an also rounded up -4. Or +0.74 and -0.1 per game, conveniently in the currency of goals.

Home field is running at 0.38 of a goal. So Arsenal are 0.84-0.38 of a goal superior away to Stoke.

Arsenal should be, based on our projections, 0.46 of a goal superior, on average at the Britannia. If we run this figure through a Poisson, we might get a 47% chance of an Arsenal win, 26% for Stoke and 27% the draw. Best odds, as of Thursday night are 50%, 23% and 27%.

So the projections broadly agree with a robust business model, at least for the Potters and below I've applied the method to the remaining games this weekend.

Odds Derived from Shot Differentials and Final Goal Difference Projections for Week 15.

Game (Home Team First!)	Home Win % (Predicted/Best Price)	Away Win%.	Draw%.
Man City v Everton	67/63	14/16	19/21
Liverpool v Sunderland	62/64	15/14	23/22
Newcastle v Chelsea	19/13	57/63	24/24
Spurs v C Palace	53/63	21/14	26/23
Stoke v Arsenal	26/23	47/50	27/27
QPR v Burnley	47/47	26/25	27/28
WHU v Swansea	49/41	24/30	27/29
A Villa v Leicester	45/43	28/28	27/29
Southampton v Man U	48/36	25/37	27/27
Hull v WBA	39/40	33/31	28/29

The majority of the odds fall within touching distance of those available to bet on and those few that don't do so for rational reasons, such as Manchester United's chaotic "getting to know you" phase, combined with Southampton's recent injuries.

By weighting shot types and applying coefficients appropriate to the number of matches played, it appears possible to project team strength with sufficient accuracy to mimic the bookmakers appraisal of Premiership teams.

Dixie Dean. Head and Shoulders Above the Rest.

In this post I looked at the goal scoring record of Wayne Rooney compared to other England international strikers and particularly the difficulty of comparing scoring feats spread across very different eras when scoring environments varied.

The game has undergone many fundamental changes since its inception in the late 19th century, either tactical or through tinkering with the laws of the game, most notably the offside rule. And the effects of these changes can be seen in the average number of goals that were scored in total in league matches contested in the top flight of English football.

The early matches were particularly goal laden, briefly averaging just over 4.5 goals per match, but with noticeable post war peaks occasionally arresting the decline, the average has settled at a level just above 2.5 goals per match.

Therefore, the number of goals a top striker might expect to claim in a season was largely dependent upon the goal environment when he played and the maximum number of games he could and did actually play.

Of course, the holder of the most league goals scored in a division one season lies with Everton legend, Dixie Dean, who scored 60 goals in the 1927-28 season. However, not only was that season played in the midst of a post Great War scoring peak following the relaxation of the offside rule,(an average of 3.82 league goals were scored per match), but the season consisted of a maximum of 42 games.

Uneven numbers of games can be partly accounted for by taking individual goals per game. Dean, as far as I can find appeared to play in only 39 of the possible 42, although his scoring record was bolstered by penalty kicks, a luxury not available to the very earliest players.

Even with the occasional spot kick, Dean's record of 1.54 goals per game is astonishing. But to attempt to level the playing field further we can use the general relationship between the goals per game rate of scoring of the division's top scorers and the goal environment that prevailed at the time, denoted by the average goals scored per game.

For simplicity, the regression indicates that the top goal scorers across the eras have scored their goals per game at a quarter the rate of the average total goals per match during that season.

So Dean, playing when a match might average nearly four goals in total, would have been expected to score a goal a game, were he to follow the habit of the league's leading scorers across the ages.

Leading Scorers Relative to the Goal Environment at the Time

From the table above, even though Dean was playing when goals were more common and the top tier was an expanded version of its current form, his record is unsurpassed. No player gets close to his over performance compared to the expected rate based on the goal environment in 1927.

If Dean had performed to the typical level of a league leading scorer, he would have been expected to claim 39 goals in 1927-28, rather than his actual total of 60.

Virtually every decade of the last two centuries are represented in the list and there is a mixture of the familiar and the not so familiar names in the list of the top division's most formidable scorers.

Why 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.

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.

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.

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”.

In short, sometimes samples are too small to come to a reliable conclusion.

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.

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 4^th in the table. Blackpool is now top and it may seem that seaside towns lead to drink driving.

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.

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.

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.

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.

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.

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.

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.

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!

(Update, we do now).

Is 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	53	119	0.45
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, 1,581 implying that he is a flat track bully, who feasted on weak opposition.

However, this approach firstly fails to account for the different goal environment 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 goals per game and both Owen and Rooney's respective caps averaged 2.7 goals per game.

During Rooney's 119 caps, England actually scored an average of 1.83 goals per game, conceding 0.78.

If we place these average goal scoring rates into a Poisson, they are consistent with a side winning 62% 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 marginally more difficult than Rooney's.

England scored and conceded goals consistent with them winning 62% 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 119 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 119 caps may not reflect the realty of the minutes Rooney has spent in an England shirt.

Wayne could have potentially played around 11,000 minutes of international football in his 119 caps, but he was on the bench for over 1,700 of those minutes.

He spent 2 hours of his 119 caps watching his team mates score 13 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 119 caps is 1.84 and 0.91 goals per game, indicating a slightly more competitive playing environment than his 119 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 58% 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	29%
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 scored in a single game 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.

Age 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.

To the Lucky the Spoils.

Before the start of the 2014 NFL season I wrote this preview which highlighted the factors that are most strongly correlated with winning.

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.

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.

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%+.

Therefore, the importance of turnover differential is both huge and widely recognised. Former Ravens coach Brian Billick writing for NFL.com uses 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.

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.

However, if we look at season to season correlation between turnover differential for teams, there appears to be virtually no persistence.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 4^th, 5^th and 6^th seeds. Playoff teams need to be good, but top seeds need to be good and perhaps also lucky.

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 6^th seed needs to negotiate three road games to reach the same destination.

If we assume (probably unrealistically) that the difference between 1^st seed and 6^th 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.

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.

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.

Subbing 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?