Portugal (National Football)

# Penalty Dilemma: Evaluating Shootout Strategies and Cristiano Ronaldo's Decision

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Frank WagnerCorrespondent IJune 29, 2012

Now that we are a few days removed from Portugal's loss to Spain in the semifinals of Euro 2012, let's look back at the circumstances of the loss with clear heads.

Specifically, what I would like to discuss is the "team decision" to have superstar Cristiano Ronaldo shoot fifth for his team and subsequently, not get a chance to shoot.

Did other things go wrong for Portugal in the shootout?

Yes, of course.  Anyone who saw Bruno Alves walk up to the spot only to be sent back by Nani could tell you that.  However, a problem like that seems to be beyond planning.  Perhaps Bento should have tried to send someone else up for Alves, but it's hard to blame him seeing as he had already submitted his order to the referee.

Pure mathematical analysis of the situation has been thrown around quite a bit over the past few days. Admittedly, I partook in such talk in an attempt to start a discussion on the matter.  However, there has been a dearth of adequate rebuttals to this argument, so I will provide it.

As an avid football fan with degrees in mathematics, I have researched the subject of penalty shootouts.

The subject of game theory [incidentally, whose father was that guy from "A Beautiful Mind" (no, not Russell Crowe)] is perfect for this.  In a nutshell, it is the study of optimal strategies.  Hence, using this, we can analyze what the coach should do with his lineup, what a kicker should do at the spot and what a keeper should do on the line.

To make a long story short, in terms of the coach, the optimal strategy is to put your best kicker first, second best second, third best third and so on and so forth.

(If you are interested, the video to the right is an analysis of the kicker vs. goalie dilemma.  It's extremely simplified, but for the purposes of a video, it gives a good idea of the type of analysis.)

So, did Paulo Bento and Cristiano Ronaldo really think that CR7 was the fifth-best penalty taker on the team?  Almost certainly not and if so, they are a little less than sane.  Thus, from a mathematical perspective, Portugal's "team decision" was plain wrong.

This was the argument made after the match, and one that I referenced in my article on Wednesday in the Ronaldo and Bento slides.

Now, while the facts of mathematics are alluring and seemingly irrefutable, I will make my case against them with one clear fact: the restrictions of the study of game theory.

In this branch of mathematics, different levels of players (and especially their nerves) are just not taken into account.

In no way am I trying to disrespect the rest of the Portuguese team, but let's say that, hypothetically, everyone on the team besides Ronaldo was an average penalty taker except for the instance of a deciding kick.  If Bento somehow knew this, putting Ronaldo first would clearly be against his best interest.  After all, as much of an advantage as Ronaldo gave him after the first kick, no one would be able to finish it off.

Jasper Juinen/Getty Images

Of course, it was probably not as cut and dry as this scenario, as Portugal is filled with world-class talent.  Still, this example shows that the mathematical argument isn't without holes; instead, they should be treated as guides.

Hence, there may have been some sound logic behind Portugal's "team decision."

In Chelsea's Champions League final victory over Bayern Munich in May, superstar Didier Drogba was chosen as the fifth taker and made the winning penalty.  In Liverpool's 2005 Champions League final victory over AC Milan, captain and penalty-master Steven Gerrard was selected as fifth, but his team won before it even got to him.  Thus, this type of selection was not unprecedented.

In fact, in Portugal's most recent shootout, they knocked England out of the 2006 World Cup with their fifth kick.  Who took that penalty?  You guessed it: Cristiano Ronaldo.

So what is the difference between these decisions and Portugal's decision on Wednesday?

I have seen some argue that those two club sides and Portugal's 2006 side had better penalty takers than this Portugal did.  However, according to the line of thought outlined above, this makes Portugal's decision even more valid.

In the end, the only thing that that makes Portugal's decision second-guessed while Chelsea's and Liverpool's are lauded, is the simple fact that Portugal's failed while the clubs' succeeded.

Sure, that is a very big difference.

But before you sharpen your knives on CR7 and Bento and call their decision unthinkable, think of it from their point of view.  At worst, this was a very tough decision that, while they had logical reasons to believe in, they missed on.

No, unthinkable would be leaving Ronaldo out of the top five altogether.

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