Monday, 28 November 2011

Penalty Kicks in the EPL.

Irishman,William McCrum is widely credited as being the proposer of the penalty kick in football.Borrowed from it's near cousin,rugby football,the penalty kick was introduced to punish foul play near to the goal line and was implemented in 1891 following an incident where Stoke City were denied a score by a Notts County hand.The Football League's current oldest teams neatly combining to invent gamesmanship. Appropriately,Stoke were almost immediate beneficiaries of the new Law when they were awarded a spot kick to tie the match in the dying minutes of game against Aston Villa.Unfortunately,but perhaps unsurprisingly to Stoke supporters,justice still wasn't given a chance to prevail.The Villa goalkeeper cunningly booted the ball out of the ground and by the time it had been retrieved the referee had called fulltime and ended the game.Cue more tinkering with the Laws to allow time for a penalty to be taken.

Not everyone was happy with McCrum's addition to the game,the public school educated Corinthians were unable to contemplate that a gentlemen would ever deliberately try to cheat an opponent and so they deliberately shot their penalties wide of the posts.However,their moral stance wasn't embraced by anyone else and the Irishman's invention became the single most dramatic event that can occur during a game.Ironically,McCrum was not only a visionary,he was also a goalkeeper.

A then non league Burton Albion convert at their now defunct Eton Park.

Fast forward to today and the penalty kick has become a pivotal point of many games.The low scoring nature of football means that a large proportion of scores are important and do induce large swings in "in game" win probabilities.They are also great theatre containing an ever changing cast of heros, villains and a hint of conspiracy often played out over a relatively protracted timescale where audience participation is almost obligatory.Allegiances and differing lines of sight and perspective change radically a person's honest opinion of what happens on a football pitch.With subjective interpretation inevitably playing a part in the awarding of fouls,one man's penalty can often appear to be another man's corner kick.As the Manchester United Newcastle game so aptly demonstrated at the weekend.

Few will feel much sympathy with Manchester United following Saturday's controversial and almost certainly incorrect decision to allow Demba Ba a chance to equalise from the spot as there is an ingrained opinion amongst supporters of other teams that ManU,especially at Old Trafford receive more than their share of decisions,including penalties.The Red Devils certainly have had the lions share of spot kicks awarded in their favour over the seasons.Eight of the ten penalties awarded in their games in 2009/10 were given to them,six out of six in 2007/08,seven out of eight in 2002/03.Sir Alex is no doubt wondering what went wrong last year when they were given just five out of 11.

To see if there is any justification in the paranoia surrounding the awarding of penalties,we must first construct a reasonable explanation as to how they are won.When Manchester United were given eight penalties in 2009/10 they also scored over 80 EPL goals,so they obviously did the majority of the attacking in their games.Goals are the inevitable by product of attacking football,so are corners and also,it would be reasonable to assume are penalties.We would therefore expect the number of penalties a team receives to be intimately linked to the number of goals they score. I therefore took the penalty data for EPL teams that had been members of the EPL for three seasons or more spread over the last decade or so and averaged the percentage of penalties those teams were awarded and compared it to the percentage of goals they had scored in their games over the same period.

The relationship between the percentage of goals a team scores in matches and the percentage of penalties those teams also receive.

As we can see the relationship is very strong.Teams which score more frequently also gain proportionally more penalties.The sample size isn't large and penalties are relatively infrequent events,occurring on average once every 5 games,so it's probably unwise to take the plot entirely at face value.The slope of the graph does tentatively imply that rather than enjoying an overly generous glut of penalties,the better teams fair slightly worse proportionally compared to their lesser rivals.However,the graph does enable a route to estimating the likelihood of a game having a penalty and then extending this to include who is the more likely to receive the award.

Future games can be conveniently expressed in terms of how many goals on average each team will score in a matchup.For example a typical "top vs bottom" clash would see one team scoring 2 goals and the other averaging 0.8,this is happily the same currency we've used to plot the graph above.The better team will average just over 70% of the goals in this type of game and therefore by reference to the graph they can also expect to receive around 70% of the penalties awarded.If we assume any game has around a 20% chance of seeing a penalty awarded,we can therefore deduce that the favoured team has around a 1 in 7 chance of being given a spot kick in a game of this type.A similar calculation gives the outsider a 1 in 16 chance of getting the verdict.


  1. Hi Mark,also love the blog.
    Great anecdotes and you explain the maths stuff really clearly.
    Used to watch the Brewers back in the day,where did you get the photo??

  2. Thanks for that,I try to keep a balance between how much of the maths I include.
    I've taken all the photos on the site,the Burton one comes from the mid '80's