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**Statistics to win penalty shoot-outs**

The last World Cup was a relatively rare one for England, with no heroic defeat on penalties, as normally seems to happen. England are in fact the worst country of any of the major footballing nations at taking penalties, having won only 1 out of 6 shoot-outs at the Euros and World Cup. In fact of the 31 penalties taken in shoot-outs England have missed 10 – which is a miss rate of over 30%. Germany by comparison have won 5 out of 7 – and have a miss rate of only 15%.

With the stakes in penalty shoot-outs so high there have been a number of studies to look at optimum strategies for players.

**Shoot left when ahead
**

One study published in Psychological Science looked at all the penalties taken in penalty shoot-outs in the World Cup since 1982. What they found was pretty incredible – goalkeepers have a subconscious bias for diving to the right when their team is behind.

As is clear from the graphic, this is not a small bias towards the right, but a very strong one. When their team is behind the goalkeeper apparently favours his (likely) strong side 71% of the time. The strikers’ shot meanwhile continues to be placed either left or right with roughly the same likelihood as in the other situations. So, this built in bias makes the goalkeeper much less likely to help his team recover from a losing position in a shoot-out.

**Shoot high**

Analysis by Prozone looking at the data from the World Cups and European Championships between 1998 and 2010 compiled the following graphics:

The first graphic above shows the part of the goal that scoring penalties were aimed at. With most strikers aiming bottom left and bottom right it’s no surprise to see that these were the most successful areas.

The second graphic which shows where penalties were saved shows a more complete picture – goalkeepers made nearly all their saves low down. A striker who has the skill and control to lift the ball high makes it very unlikely that the goalkeeper will save his shot.

The last graphic also shows the risk involved in shooting high. This data shows where all the missed penalties (which were off-target) were being aimed. Unsurprisingly strikers who were aiming down the middle of the goal managed to hit the target! Interestingly strikers aiming for the right corner (as the goalkeeper stands) were far more likely to drag their shot off target than those aiming for the left side. Perhaps this is to do with them being predominantly right footed and the angle of their shooting arc?

**Win the toss and go first**

The Prozone data also showed the importance of winning the coin toss – 75% of the teams who went first went on to win. Equally, missing the first penalty is disastrous to a team’s chances – they went on to lose 81% of the time. The statistics also show a huge psychological role as well. Players who needed to score to keep their teams in the competition only scored a miserable 14% of the time. It would be interesting to see how these statistics are replicated over a larger data set.

**Don’t dive**

A different study which looked at 286 penalties from both domestic leagues and international competitions found that goalkeepers are actually best advised to stay in the centre of the goal rather than diving to one side. This had quite a significant affect on their ability to save the penalties – increasing the likelihood from around 13% to 33%. So, why don’t more goalkeepers stay still? Well, again this might come down to psychology – a diving save looks more dramatic and showcases the goalkeepers skill more than standing stationary in the centre.

**Test yourself**

You can test your penalty taking skills with this online game from the Open University – choose which players are best suited to the pressure, decide what advice they need and aim your shot in the best position.

If you liked this post you might also like:

Championship Wages Predict League Position? A look at how statistics can predict where teams finish in the league.

Premier League Wages Predict League Positions? A similar analysis of Premier League teams.

**Statistics to win penalty shoot-outs**

With the World Cup nearly upon us we can look forward to another heroic defeat on penalties by England. England are in fact the worst country of any of the major footballing nations at taking penalties, having won only 1 out of 7 shoot-outs at the Euros and World Cup. In fact of the 35 penalties taken in shoot-outs England have missed 12 – which is a miss rate of over 30%. Germany by comparison have won 5 out of 7 – and have a miss rate of only 15%.

With the stakes in penalty shoot-outs so high there have been a number of studies to look at optimum strategies for players.

**Shoot left when ahead
**

One study published in Psychological Science looked at all the penalties taken in penalty shoot-outs in the World Cup since 1982. What they found was pretty incredible – goalkeepers have a subconscious bias for diving to the right when their team is behind.

As is clear from the graphic, this is not a small bias towards the right, but a very strong one. When their team is behind the goalkeeper apparently favours his (likely) strong side 71% of the time. The strikers’ shot meanwhile continues to be placed either left or right with roughly the same likelihood as in the other situations. So, this built in bias makes the goalkeeper much less likely to help his team recover from a losing position in a shoot-out.

**Shoot high**

Analysis by Prozone looking at the data from the World Cups and European Championships between 1998 and 2010 compiled the following graphics:

The first graphic above shows the part of the goal that scoring penalties were aimed at. With most strikers aiming bottom left and bottom right it’s no surprise to see that these were the most successful areas.

The second graphic which shows where penalties were saved shows a more complete picture – goalkeepers made nearly all their saves low down. A striker who has the skill and control to lift the ball high makes it very unlikely that the goalkeeper will save his shot.

The last graphic also shows the risk involved in shooting high. This data shows where all the missed penalties (which were off-target) were being aimed. Unsurprisingly strikers who were aiming down the middle of the goal managed to hit the target! Interestingly strikers aiming for the right corner (as the goalkeeper stands) were far more likely to drag their shot off target than those aiming for the left side. Perhaps this is to do with them being predominantly right footed and the angle of their shooting arc?

**Win the toss and go first**

The Prozone data also showed the importance of winning the coin toss – 75% of the teams who went first went on to win. Equally, missing the first penalty is disastrous to a team’s chances – they went on to lose 81% of the time. The statistics also show a huge psychological role as well. Players who needed to score to keep their teams in the competition only scored a miserable 14% of the time. It would be interesting to see how these statistics are replicated over a larger data set.

**Don’t dive**

A different study which looked at 286 penalties from both domestic leagues and international competitions found that goalkeepers are actually best advised to stay in the centre of the goal rather than diving to one side. This had quite a significant affect on their ability to save the penalties – increasing the likelihood from around 13% to 33%. So, why don’t more goalkeepers stay still? Well, again this might come down to psychology – a diving save looks more dramatic and showcases the goalkeeper’s skill more than standing stationary in the centre.

**So, why do England always lose on penalties?**

There are some interesting psychological studies which suggest that England suffer more than other teams because English players are inhibited by their high public status (in other words, there is more pressure on them to perform – and hence that pressure is harder to deal with). One such study noted that the best penalty takers are the ones who compose themselves prior to the penalty. England’s players start to run to the ball only 0.2 seconds after the referee has blown – making them much less composed than other teams.

However, I think you can put too much analysis on psychology – the answer is probably simpler – that other teams beat England because they have technically better players. English footballing culture revolves much less around technical skill than elsewhere in Europe and South America – and when it comes to the penalty shoot-outs this has a dramatic effect.

As we can see from the statistics, players who are technically gifted enough to lift their shots into the top corners give the goalkeepers virtually no chance of saving them. England’s less technically gifted players have to rely on hitting it hard and low to the corner – which gives the goalkeeper a much higher percentage chance of saving them.

**Test yourself**

You can test your penalty taking skills with this online game from the Open University – choose which players are best suited to the pressure, decide what advice they need and aim your shot in the best position.

If you liked this post you might also like:

Championship Wages Predict League Position? A look at how statistics can predict where teams finish in the league.

Premier League Wages Predict League Positions? A similar analysis of Premier League teams.

Following on from the data released a couple of weeks ago about Premier League clubs’ financial data, the data from the Championship (England’s second tier) have just been published by the Guardian. These are from 12 months ago (the most recent data available). The Championship is famously very competitive – so it will be interesting to see if the same wages and league position correlation that we see in the Premier League also holds here.

**Wage Bill 2012-13 Season (millions of pounds)**

Using an online scatter plot program we can get the following graph:

Here the league position is on the x axis and the wage bill is on the y axis. In this case if there was a correlation between wages paid and league position we would expect the slope to be negative (as greater wages would lead to a lower league position). From the graph we can see a pretty weak correlation:

Correlation coefficient (r): -0.3451690473979

Regression line equation: y=24.59-0.43x

The correlation coefficient shows that there is a weak negative correlation.

If we compare this to the scatter graph for the Premier League for the same period (this time the wages are plotted on the y axis – though this will not affect the calculations!)

We can see a stark difference. This time the correlation coefficient is -0.73, which shows a pretty strong negative correlation. So what does this show? Well, it confirms what many people already think about the 2 leagues – the Premier League is overall quite predictable – just by looking at the relative wage bills you can get a pretty good idea about league positions. The Championship on the other hand is really pretty unpredictable – wages seem to have only a weak correlation with league position. Indeed Wolves had one of the highest wage bills and yet finished 2nd from bottom.

**Championship Debt Timebomb**

This remarkable graphic shows the terrible state of the finances for most Championship clubs. It shows wages as a percentage of turnover. Spending 50% of turnover on wages is generally considered a sustainable model for football clubs – yet every club in the table is above this – and the vast majority are spending 95% or more of their turnover just on wages. Bristol City (who were relegated) were spending a staggering 190% of turnover on wages – i.e nearly twice their total turnover!

This is again quite a contrast to the Premier League, where clubs seem much better run:

Whilst most clubs are spending more than 50% of their turnover, there are only 3 clubs spending more than 90% – and only QPR (who were relegated) spending more than their turnover.

So, the Championship is a much more unpredictable league – but also a financial basketcase.

If you liked this post you might also like:

Premier League Wages Predict League Positions? A look at the Premier League data.

Does Sacking a Manager Improve Results? How an improvement in team results is often just down to a statistical result – regression to the mean.

Maths Studies IA Exploration Topics – A large number of examples of statistics investigations to explore.

**Premier League Finances – Debt and Wages**

This is a great article from the Guardian DataBlog analysing the finances for last season’s Premier League clubs. As the Guardian says, “More than two thirds of the Premier League’s record £2.4bn income in 2011-12 was paid out in wages, according to the most recently published accounts of all 20 clubs. The Guardian’s annual special report of Premier League clubs’ finances shows they spent £1.6bn on wages last season, most of it going to players.”

The first graph (above) shows the net debt levels for different clubs.

The second graph shows the total turnover:

The third graph shows wages as a proportion of turnover:

and the last one is particularly interesting – as it ranks clubs on their wage bills and their league position. This would be an interesting piece of data to test for the strength of correlation:

I’ve used an online scatter plot to calculate both the regression line and the correlation coefficient:

Which clearly shows a strong positive correlation. This would be an interesting exercise for both IGCSE or IB students (especially Maths Studies).

For even more data, a club by club full breakdown is also provided by the Guardian here. I have also made the data above into a word document to be used as a some A4 posters – and you can download that here: Premier League Debt

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