Friday 4 May 2012

Scoring Efficiency and Current Score.

As the Uefa Champions league semi final tie between Chelsea and Barcalona entered it's 186th and final minute,the holders and hosts on the night launched one final desperate assault on the massed ranks of the Chelsea defense.The ball was clipped into the Chelsea box,partly intercepted by Ivanovic and then smashed clear by Cole to the breaking Torres,who raced unchallenged into the box before rounding the keeper to claim a draw on the night and confirm The Blues as Champions League finalists once again.

The tie appeared remarkable for many reasons.Not only had Chelsea played over half the second leg with just ten men and Messi had missed from the spot,but they had also enjoyed less than twenty percent of the possession and had been out shot by a ratio of 3:1over both legs.They had managed just 3 shots compared to Barca's 14 in their 1-0 win at Stamford Bridge and had fared only slightly better in going down 16-7 in the return.But as Fernando Torres had so clinically demonstrated in the final minutes of the tie,having the lion's share of the shots isn't as important as how efficiently you finish them and Chelsea had outscored the Spanish giants by 3 goals to 2 in the column that mattered most.

A slightly less transparent fact about the game was that with the exception of the two minutes between Iniesta's 43rd minute strike and Ramires' 45th minute chip,Chelsea had been either level,ahead or ahead on the away goals rule in the tie and as such they had been able or content to stack their defence.The culmination of this partly enforced tactic saw eight blue shirted players stationed within ten yards of the cleared ball during Barcelona's final attack,while Torres' nearest pursuer was twenty yards behind him when he collected Cole's hopeful punt and all that lay ahead of him was Valdes in the home goal.

Arriving at conclusions on the basis of one game or one incident is usually unwise,but it appeared that Chelsea's 30% strike rate owed something to the simplicity of the Torres chance and Barcelona's 7% strike rate was the result of their opponents being able to pack their backline because they had only been behind in the tie for two minutes.Before we can begin to draw wider conclusions we need to work with a larger and more detailed set of results,therefore I'm grateful to OptaPro for providing a season's worth of shot statistics for Arsenal from the 2010/11 season.

In this case the term shots is interchangeable with attempts on goal,be it with the foot,head or any other body part that results in the ball going wide,being saved,hitting the post,being blocked or resulting in a goal.Once in the possession of the timing of every shot from Arsenal's 2010/11 season,I was able to record the frequency with which the Gunners made their attempts on goal and the efficiency of their attempts sorted by whether they were leading,drawing or trailing at the time of the attempt.If we take the Barca/Chelsea example as an extreme case of a team desperate to score creating more numerous,but poorer quality chances playing a team content with the current match situation who create less,but clearer cut chances,we should see a similar pattern emerge in all teams in larger sample sets if the phenomenon is universal throughout football.

Efficiency and Frequency of Arsenal's Shots.2010/11.

Arsenal's Game Position.2010/11. Average time Between Shots. Shots Needed to Score.
Leading. 6 minutes. 8
Level. 5 minutes. 10
Trailing. 5 minutes. 10

Initially,it appears that Arsenal over the course of that season conformed to this pattern.Over the season they made 654 attempts on their opponents goal in scoring their 70 goals (they were also gifted two own goals).The bulk of these shots (70+%) came from open play compared to less than 20% from free kicks or corners.While they held the lead they attempted a shot every six minutes and they needed 8 such shots to register one goal on average.But when the Gunners were trailing or level they increased their shot taking rate to an attempt every 5 minutes,but they required an extra two shots before they found the back of the net.Arsenal,it goes without saying are among the top three or four sides in the EPL,so while losing is always unacceptable to all teams,a team of Arsenal's quality will almost always feel that they should be taking more from a stalemated game.So from this simple breakdown,Arsenal when in the lead are content or required to defend and this on average reduces the frequency of their goal attempts,but because their opponents are also committing players forward,when Arsenal's chances arrive they are comparatively easier ones.

In contrast when the Gunners trailed or were tied in 2010/11,an unsatisfactory state of affairs for one of the best team in the league,they increased their rate of attempts,but were confronted by a relatively content and packed opposition defence.Their opponents appear to set themselves up as a less extreme version of Chelsea for the bulk of the Barcelona UCL tie.Therefore although the quantity of Arsenal's attempts increased, the likelihood of individual shots being successful declined.

Origins and Outcomes of Shots taken by Arsenal in Differing Game Situations.2010/11.

Arsenal's Game State.2010/11. Shots by Defenders as % of Total Shots. Shots Blocked by Opponents as % of Total. Shots from Corners as % of Total Shots.
Leading. 7.0 19.4 9
Level. 14.7 26.5 15
Trailing. 15.7 29.8 19

This shift of game dynamic becomes more evident if we look at the fate of the goal attempts sorted by game state.When leading,the attacking contribution from Arsenal's defenders is at it's lowest point,but this more than doubles when they trail or are being held.Defenders become much more involved at the attacking end of the field and this could account for both the decrease in time between shots compared to when Arsenal lead and the reduced conversion rate.More players are contributing in advanced positions and more chances are being taken by players who are in the team primarily for their defensive prowess.

Blocked shots are also seen to readily increase as game position swings from advantageous to less so,another sign that Arsenal's opponents are less likely to have bodies around to defend with if they themselves are required to try to retrieve the game.

Corners are another by product of attacking play,they are goal attempts that are deflected wide or come about as the result of last ditch tackles.So once again the increase in Arsenal attempts from corner kicks when they trail is an indication of more attacking intent from them,coupled with more defensive efforts from the opposition.

Defining the game state in rudimentary terms such as leading,level or trailing works reasonably well for a team at the top of the tree such as Arsenal.They are not going to be happy drawing with the likes of Stoke at the Emirates or even at the Britannia,so we can probably guess which team will be pressing and which team will be throwing resources to their defence in these situations.But other matches are harder to define.If Wigan are level at Wolves after an hour,which team is likely to be most happy?It's difficult to decide where the attacking impetuous is most likely to be coming from.Therefore we need a more analytical way of defining each side's game position when the shots are being taken.

At the start of a match the combination of the pre game strengths of each side along with the venue will enable you to decide how many points on average each team would emerge with from the game should each teams meet over a large number of repetitions.As the game progresses,the chances of each team winning or drawing will change depending on factors such as time remaining and current score and with it will change their Expected Points totals.By comparing a team's current Expected Points total with their pre game expectation we can develop a numerically based estimation of the game situation.

For example when Arsenal entertained Aston Villa in May of 2011,they kicked off with an average of 2.33 Expected Points.By the time Jack Wilshere's left footed shot missed the target from a corner in the 58th minute,with Villa 2-0 to the good,Arsenal's Expected Points had fallen by over 80% of it's original value to just 0.32.

Arsenal's Predicted Conversion Rates for Shots taken in Differing Game Situations.2010/11.

Current Arsenal Game State as % of Initial Expected Points.2010/11. Best Fit % of Shots
which Result in Goals.
-100 7.3
-80 7.9
-50 8.9
-30 9.6
-10 10.4
0 10.8
+10 11.3
+30 12.2
+50 13.1
+80 14.7
+100 15.9

So as a final refinement,I've taken all 654 goal attempts by Arsenal during last season and recorded both their initial EP and by how much their EP had either risen or fallen at the time of every goal attempt.I've also recorded whether or not the shot resulted in a score and then I've regressed the outcome against the change in Expected Points when the shot was taken.This allows for a predicted strike rate derived from the best fit of the regression line for shots made by Arsenal in the 2010/11 season for a range of different game positions described by the rise or fall in Expected Points compared to pre game estimates.In short,how efficient were Arsenal in relation to whether they were doing better or worse than expected at that point in the game.The same pattern that was present when using the more subjective "leading,trailing,level" approach is again present.Shot's taken when Arsenal's games position is precarious have much lower strike rates than those taken when they are already leading and the more comfortable the lead,the better the strike rate.

Hopefully this preliminary analysis can begin to illuminate goal attempts and conversion rates.It's undeniable that there is a difference in finishing quality between the best teams and the worst teams in the league.Arsenal will always tend to have more efficient strikers with better strike rates than the lesser lights of the EPL.However,it would seem that game position is more likely to drive a team's game by game variation from their normal,average strike rate.

When goals are scored,the way a game is being played begins to change.Teams who were prepared to play for a point have to open out if they go behind or can become even more defensively orientated if they score first and it appears that these alterations can impact upon the quality of the chances that they then present to their opponents.

The proportion of goals a team scores is closely associate with the quality of that team and in the long run better teams will scored proportionally more goals than their inferior game opponents.However over shorter timescales random chance can intervene to allow teams to either over or under achieve and this may lead to good sides trailing for longer periods than you would expect or poorer teams leading more frequently.For example Manchester City are currently top of the EPL,but for a run of five matches recently their universally inferior opponents opened the scoring against Mancini's side.

 If the effects of leading or trailing on a team's shot conversion rates as seen in Arsenal's season is repeated league wide,these atypical scoring runs can in turn distort a teams shooting efficiencies.As a consequence,teams may appear to show unexpected improvement and we may conclude that they have improved by increasing their goals to shots ratio.When in fact they have only benefited from a semi randomly occurring run of goals and they have been able to supplement their strike rate by then playing against teams who are more concerned with attack than defence.The arrow of causation can often run counter to the direction it appears to take.

Random chance plays an extremely important part in deciding low scoring sporting events such as football,especially over a relatively short run of matches,so it's important not to mistake a fortuitous grouping of scores with a real and tangible matter how compelling the evidence.

All data kindly provided by OptaPro.


  1. Just a heads up, it was Bosingwa, not Cole, who made the clearance to Torres in the Barcelona-Chelsea game. Really enjoyed the post though!

  2. Cheers,mate.
    I know the commentator says "Bosingwa",but he appears to be wearing number 3....which would make him Cole?? from the squad numbers.The youtube video I've seen wasn't particularly clear.
    So I tossed a coin and Ashley won :-).

    Glad you liked the post.

  3. Oh I've just watched it again and you're quite right, it is Cole! My bad!

  4. How do you come up with your value of expected points at the beginning of a match?

  5. Also wondering have you ever been offered a job in this field? Your work is far more impressive than anything else I've seen..

  6. Hi Pierre, the initial expected points is based around team specific goal scoring rates which then use the Poisson distribution to predict likely correct scores and ultimately win,draw and loss percentages for both teams. Then you simply total the probability of getting 3 points or one point

    I've done a bit of informal work for a couple of non EPL sides.