Manchester United Get Their Just Deserts at Old Trafford.

The Patrick Vieira row over referees appearing to favour big,well resourced teams who originate from Manchester and are fighting for the Premiership title when deciding  whether or not to award penalties continues to rumble on.We've shown here that both sides from across the blue and red divide can benefit from the occasional lapse in refereeing concentration,but also that over the stretch the better teams do more attacking and therefore get the lion's share of the attacking spoils.For once Graham Poll also put one and one together and came to the same,almost certainly correct conclusion that better sides get more goals,more corners,more shots and more penalties.

To be fair to Vieira he did qualify his remarks by singling out Old Trafford as a venue where opponents find penalty decisions difficult to get,so instead of looking at both home and away matches,I've concentrated solely on home games.We saw previously that if Premiership sides scored say 60% of the goals that were registered in their matches,they could expect to gain a very similar proportion of the penalties awarded in those same games.And the following graph paints a very similar picture if we look at only a team's home games.

 I've looked at the last six season including the present one and although the correlation isn't quite as tight because I've used slightly fewer teams and games,the previous trend is still present.The proportion of penalties you are awarded at home is intimately connected to the proportion of goals you score at home and for much of this sample it is a one to one relationship as before.If you get half your game's goals you should expect to get around half of the penalties that are awarded. Manchester United at Old Trafford scored 80% of the goals over the period I looked at and they received 73% of the penalties,sample size caveats apply,but you could decide that there's the possibility that they were actually short changed.Or maybe the referees invoked their own mercy rule in games where United were romping to victory.

A penalty that is given for a simple trip in the box with little immediate threat being exerted towards the goal is often difficult to take if your side is on the receiving end.But the decision is no different to the steady accumulation of free kicks that happen as a superior side launches wave upon wave of attacks and no side at present is superior to the likes of Manchester United and City,especially on their own turf.So it is very likely the bulk of the penalties will go to these sides when they play at home.Some visitors to Old Trafford even manage to concede two penalties in 15 minutes,Stoke for example back in January.

Vieira's complaint arose from a penalty that wasn't given,but the relationship that exists between United's goal scoring ability and their penalty acquiring talent obviously also applies in reverse to United's defence.They allowed only 20% of all the total goals scored in matches at home and so they would expect to concede about 20% of the spot kicks that were awarded.So the award of a spot kick to United's visitors should be a relatively rare event,four United penalties to every one for the visitors and it's scarcity shouldn't be a sign of anything sinister.No doubt Fulham were disgruntled because of the spot kick they didn't get on Monday.But basing a conspiracy theory on an isolated incident at the tail end of a season ignores the bigger picture.One contentious decision is simply an anecdote.

Vieira goes on to say that the same bias occurs in both Spain and Italy,but again the figures say not.As the following two graphs illustrate the same type of relationship between attacking endeavour and reward exists in both Serie A and La Liga.

These graphs don't differentiate between venue,but are identical in form to the plot for the EPL indicating that it is very likely that attacking intent on the continent reaps a long term penalty kick reward and miserly defences largely avoid conceding spot kicks.

Time of Possession in the EPL.

Time of Possession is fast becoming one of the hot topics in the world of football stats and such is it's current pre eminence that it has become almost the number by which a team is judged.Barca of course are the darlings of ToP and such teams as Arsenal and Swansea are praised for their accurate passing style that also boosts their time in charge of the ball.Mystification along with a faint hint of disgruntlement accompanies any example of a side who win the game's ToP,yet fail to win the game.Hopefully this post will make a convincing argument as to why you should expect a significant proportion of ToP winning teams to actually lose the individual game and why game long ToP shouldn't even be considered as a "real" stat.

Teams use possession for a variety of reasons,some defensive and some attacking in nature.The temptation to stereotype teams on the basis of one particular trait should be resisted,but it's hard not to see Barca and Swansea as polar opposites in possession terms.The former use possession and a host of world class attacking players to score goals,whereas The Jacks use it to prevent their opponents from scoring.Swansea held scoreless the first four EPL teams to visit The Liberty,picking up 8 points in the process and almost 40% of their games has seen their goal remain intact.Tellingly,they have also failed to score themselves in a similar percentage of matches.

On average most other teams use possession in a way that doesn't emphasis extremes of attacking or defensive philosophies and in addition current score can influence how teams accrue or cede the ball.A side who hold a comfortable lead may add to their possession statistics by passing the ball around in less congested areas such as defence or another may happily defend in depth and in numbers,but in doing so concede possession.In short the ways in which a team can decide to try to increase or reduce their time on the ball is dependent upon game situation,are numerous and often depend upon team tactics and there in lies the fatal flaw of trying to interpret ToP.

It is a secondary statistic that has been derived from a composite of many other primary stats that are fundamental to a team's success,often opposing in nature and quite often related to the talent pool of individual sides.Teams get possession by being good at making tackles or interceptions,they keep it by passing well,they use possession to create chances,they score goals by converting chances and they win games by scoring more goals that they allow.So we have a chain with match result at one end time of possession at the other,but in between are statistics that are ability based,context dependent and often better indicators of match success.

ToP is an amalgam of other more informative numbers,so why look at ToP when you can look at the components that go towards defining it.

If we use shot per game allowed and conceded as an example of a fundamental football statistic,we can show why this is a much more powerful measurement of a team's ability than time of possession even though we can use both to come to very similar conclusions about a team's ability.It's reasonable to assume that for the vast majority of teams,increased possession will lead to more goal attempts by that team and less from their opponents and this appears to hold true over a 38 game season.As we can see,the differential between attempted shots and shots allowed becomes positive and increases in size as possession passes 50%.

If we now chart a team's seasonal success rate,that is it's number of wins plus half it's number of draws all divided by it's number of games against average shot differential over the season we can see that the correlation is both strong and in the expected direction.Each data point represents one team's season consisting of 38 games,or 31 for the present year.

Team possessions plotted against success rate produces a similar graph,although the correlation is not quite as strong.The similarity isn't a surprise as we have speculated that one of the aims of a team while in possession is likely to be shot creation for itself and prevention for the opposition.

So if we now use both of these graphs to work through a real life example we can demonstrate the different levels of information we can deduce from a derived stat such as ToP and a talent based one such as shots per game.In 2010-11 Newcastle's average ToP was virtually 50% and it's shot per game differential was zero.So on average they kept the ball for as long as their opponents and on average they attempted as many shots as they allowed.From each of the above graphs we therefore can predict that their success rate for the season would have been 0.5.However,it was only 0.46.

Now if we came to our conclusion that Newcastle's actual results under estimated their probable ability based on historical results from the shots per game model,we can look back at their 2010-11 matches to see if they were short changed by short term luck during the season.And we find that their success rate in games where they were out shot by their opponents was 0.37.They were outshot on average by 9 shots per game to 14,comprising 20 games and based on the season long graph we can possibly say that they very slightly overperformed in those 20 matches.In the remaining 18 games,Newcastle out shot their rivals by 14 shots to 8 and their success rate was 0.55.An improvement compared to when they lost the shots per game duel,but probably well below what an average team would expect with such a record.Indeed if we look at individual games,Newcastle managed to lose five games where they outshot the other teams.A quarter of such contests.

We can explain such situations were a team has more shots,but loses the game thus.Teams will have an historical average rate at which they turn shots into shots on target and ultimately goals.On a particular matchday these rates will fluctuate around their historical means because one game represents a very small sample size,especially in a low scoring sport,such as football.It's therefore to be expected that the vagaries of short term luck will in a season's worth of games see some teams being overly unfortunate in the number of games where they have more shots in a single game,but end up scoring less of the goals.That may have contributed to Newcastle's lower than expected success rate based on their shots per game stats.

By using ToP we can also deduce that the Toon should have had more wins or less losses in 2010-11,but we have no way of knowing which factors may have contributed to the short fall.Even if we isolate games where they dominated possession and lost,we still don't know if they shot inefficiently,played Swansea style keep ball and succumbed to a late goal or just made individual errors.ToP tells us nothing that other fundamental game stats won't tell us with more illumination.

If we can put ToP into context it may become a valuable addition,but in it's present catch all,game long form it struggles to compete.

for more great thoughts on time of possession,check out 11tegen11 and 5 AddedMinutes.

Predicting the Game's First Goal Scorer.

The importance and value of scoring the game's first goal has been well documented on this blog and elsewhere.Omar has written about the subject here and I have discussed the subject here and used illustrations from previous seasons to highlight how a team's final results are affected by the frequency with which they score first.If a team finds the net before it's opponent then they can begin to dictate the immediate course of the game.

In matches where the gap in quality between opponents is small,the first strike can greatly shift the balance of expectations.If we consider the case of two evenly matched sides then an opening goal from the the home team after half an hours play will shift the Expected Points total for that side from around 1.6 points to 2.3,a jump of 0.7 of a point.At the first whistle,the home side would have typically had about a 44% chance of ending the day with win bonuses all round,but by keeping out the visitors for 30 minutes before scoring themselves,they have increased the chance of a positive outcome to over 70%.Their visitors could have expected to average a tick over 1 goal per such encounter.But by failing to take their chances so far they would expect to average only 0.8 of a goal during the remainder of the game by the 30 minute mark and they trail by a goal as well.The afternoon is looking like it is turning into one of the more positive outcomes for the home side from the myriad of possible game scenarios.If we reverse the scoring and allow the visitors first blood,the importance remains.Their pre game win probability rises from 30% to 60% and their Expected Points rise from 1.15 to 2.05 points.

Even if we model the most extreme of mis matches that occur in the current EPL we see similar results.A relegation candidate taking an half hour lead at a title contender's home turf will see their win probability rise from 4% to 26% meaning the most likely result would still be a home win,but it's a massively improved situation compared to pre game.And the inferior team are now more likely than not to return with at least a point.

Scoring the first goal is therefore a good indicator of success on the day and if you look at the teams who have scored the highest proportion of first game goals so far they include most of this year's best teams.Both Manchester sides top the list,followed by Spurs,Chelsea,Newcastle and Arsenal.League stragglers such as Wigan,Wolves,Bolton,QPR and Fulham prop up the first scorer table.Therefore,it seems reasonable to assume that the typical rate at which teams register the first goal is related to their overall scoring record.You can demonstrate this relationship by plotting the proportion of match goals a team has scored over the season against the proportion of first goals each team has scored.

Seasonal Relationship Between Goals Scored and 1st Goals for EPL Teams 2009-11.

A less general method involving a match by match basis,where the respective pre match goal expectancies are compared to the identity of the game's first goal scorer also yields a similar correlation.The line of best fit for two completed season's worth of EPL games also strongly indicates the near one to one relationship between the two.

Line of Best Fit for Proportion of Goals and First Goals Based on a Match by Match Samples.

From a team perspective we are now in a position to predict the likely number of first goals a team of a given scoring and conceding ratio will record.We know that scoring first gives that team a much higher likelihood of winning the game than was the case at the start of the contest.In some cases a team will substantially exceeded or dip below those opening goal expectations and unless we can find compelling reasons for these first goal deviations,the most likely explanation is that the pattern has arisen because of small sample random chance.

So far this season Newcastle are the biggest overachievers in this category.They have scored the first goal in almost 70% of matches,yet they have scored barely over 50% of their game's goals.Their current position is a magnificent achievement,but some of it has probably been achieved through a fortuitous run of opening goals.At the other end of the table,Wolves with only 21% of opening goals despite scoring 32% of their game's goals can count themselves slightly unfortunate at the depth of their current plight.

We can move this kind of analysis a stage further by  looking at the level of individual players.Again the league's leading scorers tend to also top the first goal lists,indicating that a similar relationship exists at the individual level,namely the larger the proportion of goals you score then the more likely your are to notch an opening strike.There's a couple of tweaks needed before the player based data can be used.Firstly,players unlike teams don't play every game,so they shouldn't be penalised for occasions when they are absent and similarly they may enter the match after the first goal has been scored.For example RvP has featured in every EPL Arsenal game,but despite scoring a brace against Stoke he didn't leave the bench until the hour mark,by which time the score was already 1-1.So that game has to be discarded from the sample.

Secondly,position affords strikers more of an opportunity to open the scoring than say defenders.The average time of the first goal in the EPL is just after the 30th minute and this early in a contest defenders will still be prioritising defending.In a quick analysis consisting of the leading scorers from the last couple of years,leading strikers scored around 19% of their teams match goals,but accounted for over 21% of opening goals in those games.A line of best fit therefore can be plotted and used to predict the number of opening goals predominately attack minded players could be expected to score if we know or can estimate their likely scoring rate.

The Rate at which Attacking Players Opened the Scoring in 2011-12 in the EPL.

Player.	Goals Scored by Team.	Goals Allowed by Team.	Goals Scored by Player.	Number of Games  by Player	Number of 1st Goals.	Predicted Number of 1st Goals.
R van Persie	56	38	24	27	8	7.5
W Rooney	60	20	21	24	6	6.8
E Dzeko	35	12	12	13	4	3.6
S Aguero	63	25	15	19	6	3.8
C Dempsey	37	58	12	29	4	4.5
D Ba	33	35	16	23	5	5.9
Yakubu	32	40	13	19	4	3.9
G Bale	50	31	10	26	5	3.9
F Lampard	33	22	10	21	3	4.0
P Crouch	27	36	8	24	2	3.6

For the majority of the goal scorers listed their actual rate of opening goals is very close to their predicted levels.Aguero's tally of 6 is around 30% higher than you would expect from his overall scoring record and the record of Man City when he starts,while Rooney,Ba and Crouch each under perform compared to average expectations.However,we are dealing with very small totals here and any under or over performing trend should be deemed as much more likely to be descriptive as opposed to predictive.

Placing too much credence upon single season numbers may lead to teams and individuals being either over or under rated.A run of randomly superior rates of 1st goal scoring may falsely inflate a team's points total and may not be predictive or indicative of future levels of performance.This may have occurred in the case of Newcastle this year and of Ipswich here.Similarly,opening goals as we have seen are potentially valuable and players who manage a small sample sized glut of such strikes may appear to possess a valuable ability that may or may not exist.Players may be able to control to some degree the amount of goals they score in a season, it certainly is a reasonably repeatable skill across seasons.But the order and thus the importance in which these goals are scored during a game may be much more of a hostage to chance.