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Jul 16, 2014
Jul 16, 2014

A shot location model for soccer

A shot location model for soccer
A soccer team’s quality is most conveniently measured by the rate at which they score and concede goals. Goal difference shows a strong correlation to overall success as measured by league position or points accrued per game and Poisson based approaches can be used as a basis to predict future score lines and ultimately match odds.

Rarity goals makes their prediction hard

One drawback with goals is their relatively rarity. English Premier League teams in a typical season average around 1.4 goals per match compared to ten times that amount for shots, including blocked efforts. Therefore, shots – partly because of their greater frequency – are increasingly being used as an alternative to goals as a way of measuring team ability. Sample size is an important consideration in analysis and shots provide more copious amounts of data over the same timeframe than do goals.

The use of shots, in such crossover stats from ice hockey as total shot ratio, does present renewed challenges. Although larger sample sizes are useful, not all shots are created equally, especially in a sport where the playing surface is large and attempts can be made with both the feet and the head. Consequently, different tactical approaches may not be fully picked up by counting simple shot numbers.

How tactics can skew shot data

For example, Stoke City under Tony Pulis regularly found themselves outshot and appeared to over perform in terms of goals scored and allowed. The temptation was to attribute this over performance greatly to luck, rather than the advantageous positions from which Stoke took their shots and their tactical setup that saw opponents forced into taking more frequent attempts from distance, where the chance of scoring was greatly reduced.

Similarly, QPR in their relegation year in 2012/13, shot often, but mainly from distance. 78 of their shots had between a 1 and 2% expectation of resulting in a goal. The cumulative goal expectation from these efforts was just a single goal and that was the return they achieved.

Goals – How, where & why

How, where from, and under which circumstances, an attempt is made can have a huge influence on the chances of a goal being scored. An appreciation of the likely success rates of different types of shots is therefore, useful when assessing teams solely on their shooting record.

The major factors that contribute to a shot being successful are:

  • shot type – foot or a header
  • distance from goal – vertical distance from the goal line & horizontal distance in yards from the centre of the goal

Logistic regression can be used to formulate the relationship between a categorical dependent variable and a variety of inputs. So it is useful in predicting how likely it is that a certain type of shot from varying positions on the pitch will result in a goal.

Intuitively, greater distances, wider angles and headers rather than shots with the feet, will reduce the chances of scoring and this is confirmed by using a logistic regression approach to shot location data from the English Premier League.

Goal propensities by shot type

As an illustration, a typical shot in open play from the penalty spot has about a 24% chance of being successful, but this generic probability falls to just below 10% if the chance is taken with the head. If we move out to the 18 yard line, while maintaining a central position, the expected conversion rate for a shot tumbles to just over 13% compared to less than 5% for a headed attempt. So even with very little defensive pressure, Robin van Persie’s equalising World Cup header against Spain was both brilliantly executed and comparatively rare.

Actual penalty kicks are converted at much higher rates than ordinary shots and headers from 12 yards out, typically slightly under 80%. So the absence of any defensive pressure and the choice of kicker would appear to contribute this increased rate.

Penalties are rare, but high value events and their award makes a goal more likely than not, but attempts directly from free kicks are much less clear cut in their worth to sides. The conversion rate from direct free kicks in the EPL is around 5%.

If we take 2011/12 as typical, 5.2% of direct shots from free kicks resulted in a goal, 25% required a save to be attempted, not always successfully, 36% missed the target and 39% were blocked. In 2012/13 scoring rates was slightly higher at 5.7%

Goals & free kicks

There are numerous pre-shot advantages of taking a direct shot from a free kick compared to a similar effort from the same position in open play. The choice of taker lies with the attacking side, so the best dead ball striker gets the chance and there is tentative evidence that finishing ability is a repeatable skill. He is allowed time to prepare and take the shot at his leisure and the box is unusually well populated with team mates, who may act as decoy runners to confuse the keeper.  The defence can counter with a defensive wall and a ready keeper.

The 5.3% conversion rate in the Premier League from 2007/08 to 2012/13 for direct shots from a set play compares poorly to a general conversion rate for all shots of between 9 and 10%. This has led to suggestions that direct shots from a free kick is an inefficient use of good field position and they would better serve the success of a team if they were taken short to maintain possession and attempt to create a shot closer to the goal.

However, as with all statistics, context is essential. The clearest comparison to shots taken directly from a free kick is open play shots from outside the penalty area, where the average shot location in each case is broadly similar. Under these conditions the direct free kick becomes a valued, if rare addition to a team’s scoring potential. Success rates for open play shots from outside the box rarely improve beyond 3%, making a direct free kick upwards of 70% more likely to result in a goal than a similar effort from open play.

Therefore, for a player to spurn the opportunity to win a free kick by staying on his feet when fouled or a team to resist the temptation to attempt a direct shot, a chance must be generated that is appreciably closer to the goal than the position of the original offence.

This analysis also omits any residual value of shooting from a free kick, such as goals scored from rebounds or maintaining good possession from the initial shot.

These simple mathematical models that use readily available, if tedious to collect inputs, such as shot type and location can not only highlight the true relative value of a variety of scoring methods, such as shot taking from direct free kicks, they are also reconnecting shot volume to goals.

Goals & predictive models

Predictive models that use goal expectations of actual shots and headers are becoming increasingly useful, especially if additional variables, such as shot placement are included. A team’s cumulative goal expectation based on their much more numerous chances created may be a better indicator of team talent than their actual record of goals scored and conceded over the same period, which may owe much to the vagaries of chance. The important application for betting on soccer outcomes should barely need emphasising.

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Having graduated with a degree in Chemistry, Mark embarked on a career with a major UK brewery. However, his love for sports and numbers was always at the back of his mind. He has been writing about the statistical side of sports, mainly soccer and NFL, for over 20 years and has a particular interest in the randomness and uncertainty inherent in the numbers.
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