Revealed – The Scientific Formula For The Perfect Penalty Kick

Chris Wright

28th, May 2010


By Chris Wright

Time for a confession. I was never that good at maths (an 8% overall score at A Level will testify to that), and a serendipitous birth defect is the only reason I can count to eleven on my fingers confidently – so you must forgive me the copy-and-paste nature of this article.

Anyway, at the behest of Lucozade, a scientific study has been carried out to determine the formula for the perfect penalty (to mark the 120th anniversary of the spot kick) and their findings are as follows…

Clear? Just in case you share the same pitiful gift for numbers as I do, I’ll let Nick Morgan, Lucozade Sport‘s Lead Sports Scientist, explain his conclusions;

“The formula really reaffirms the importance of practicing penalties. With ‘Technique’ elements accounting for half of a player’s final lps, having a mental image of your perfect penalty could prove decisive in such a pressure situation. It’s the small differences that can make a big difference.

So just how does the penalty formula work? Firstly, analysis highlighted several key variables that increase the likelihood of a successful penalty kick.

Secondly, these were grouped into the two-part formula, the first part being ‘Player’, the second being ‘Technique’.

For example, a ‘Player’ variable might be that right footed players have more success than left footers, a 71% vs. 52% success rate, while a ‘Technique’ variable would be the fact that 87% of penalty kicks aimed in the lop left corner of the goal are successful. See Notes to Editors for a full overview of these variables.

Finally, the indicator function (I) was applied to these variables. The indicator function turns these real-world observations into the 0s and 1s needed to generate mathematical outcomes, and in this case will deliver an overall likely penalty success (lps) score between 0 and 2, 1 for ‘Player’ and 1 for ‘Technique’.

For example, if a player had three of the four ‘Player’ attributes, his score would be 0.75/1. If that player then used two of the five ‘Technique’ elements to take the penalty, his score would be 0.40/1. Thus the lps would be 1.15/2, giving that player a 58% chance of a likely penalty conversion.

The ‘Penalty Spotlight’ study also uncovered a host of additional insights that further cement the importance of penalty perfection. For example, the team that misses the first penalty goes on to lose the shoot out a huge 78.5% of the time, and while almost a third (64%) of all shoot outs go to the full five penalties, all five are scored a mere 18% of the time.”

Nope, me neither.

Still, they should probably post a copy of their findings over to England‘s World Cup training camp in Austria – just in case.