Penalty Kick Analysis

I never believed teachers when they told me you need math in everything, until I used it in Football. Penalties are not purely luck as most people say. A penalty kick is not like a coin toss. On average, 80% of Penalties are converted into goals. But how should the players prepare for a Penalty? Where should the Penalty taker shoot? And where should the Goalie jump?

It is not purely luck. A Penalty requires skills from both the taker and the goalkeeper. Almost 80% of all Penalty kicks are scored. But here we present a study that shows where the penalty takers should shoot more and where goalkeepers should jump more (Credits to Wayne Winston author of “Mathletics”). The most important thing about penalty takers is that they shouldn’t have a pattern in their shooting. If a player shoots one penalty to the right and one to the left, a goalkeeper that has reviewed the shooter’s previous record of taken penalties can expect the direction of the next shot and therefore will have a great chance of denying the goal.

Football clubs are using data analysis more in their strategies, especially in penalty shootouts. The Champions League Final between Manchester United and Chelsea comes to mind every time penalty shootouts are discussed. The shootouts are discussed in details in the book “Soccernomics” where the authors discuss how the players followed the advice of data analysts and how United emerged victorious thanks to data analysis and John Terry’s fall.

Let’s assume that a penalty taker can only shoot left or right. The following statistics show the chance that a penalty will be scored:

Goalie Moves Left & Taker Shoots Left: 58% Chance of Goal

Goalie Moves Left & Taker Shoots Right: 95% Chance of Goal

Goalie Moves Right & Taker Shoots Left: 93% Chance of Goal

Goalie Moves Right & Taker Shoots Right: 70% Chance of Goal

Now we will not go deeply into the mathematical methods to performing this method, but using a variable that represents the probability that the penalty taker shoots to the left of the goal, and using the numbers from the table above, we get two straight lines, one for each option for the goalie. After performing the calculations, the Results are:

The Goalie should jump 58% of the time to the right and 42% of the time to the left.

The Penalty taker should shoot 61% of the time to the right and 39% of the time to the left.

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