#Knockouts time at the #FIFAWorldCup, and we know how important taking Penalties are in this case. How can we not have a math story on penalties? So, here is story #54 on Football and Penalties.

Say ‘#Penalty #shootout’ and the following questions come to mind:

1> Who should take penalties?

2> In what order should they take the shootout?

Before we go on, few backdrops:

The penalty shoot-out is used to break tied games in the knock-out stages of soccer competition. 

The shoot-out, which consists of an alternating series of penalty kicks, is won by the team with the highest goal tally after 5 kicks per team. 

In the event of a tie after five penalty kicks each, the shoot-out progresses to 'sudden death'. The team to strike first is determined at the end of extra time by the toss of a coin.

Now to the main course:

As each on-field player can be awarded only a single penalty kick, the line-up order in which the penalty kicks are taken allows for the possibility of tactical influence on the final outcome. 

Tim McGarry and Ian Franks did a probability analysis of the penalty shoot-out in soccer from which they identified the following:

*They ranked every player in order of their penalty-taking ability. They ranked the goalkeepers in order of their penalty-stopping ability.

*They, then showed that the best five ranked penalty takers from the on-field players should be assigned to the first five penalty kicks in their reverse order of ability <Surprising?!>. That is, the fifth-best penalty taker should take the first penalty kick, the fourth-best penalty taker should take the second penalty kick, and so on. 

*In the event of sudden death, the next highest-ranked on-field player should be assigned to the next penalty kick until the shoot-out ends.

These findings indicate that the tactical substitution of on-field players for higher-ranked penalty takers, including higher-ranked penalty stoppers (i.e. goalkeepers), with a view to an impending penalty shootout, should be given due consideration. 

They showed that these results are of practical importance as they are shown to maximize the likelihood of winning the penalty shoot-out under certain initial conditions.

Well, let us wait and watch what happens in this World Cup and if this holds true!

Source:

<1> On winning the penalty shoot-out in soccer by Tim McGarry and Ian Franks July 2000 in Journal of Sports Sciences.

#math #mathstories #story54 #football #worldcup #penaltyshootout #probability #sports