Penalty kicks elicit a spectrum of emotions from players and fans alike. That's why it's no surprise that both teams were in tears at the end of this year's Champions League final.

A grueling, tightly contested match that saw Atlético Madrid come from behind against Real Madrid to tie the game 1-1 to ensure extra time before the game was ultimately decided from the spot.

After the first seven shots were successfully converted, the game's deciding moment came when Atlético's right back, Juanfran Torres, struck the post, giving Real's Cristiano Ronaldo an opportunity to win the match

He did not disappoint — for the second time in three years Real defeated their city rival to capture European glory.   

What played out over the course of more than 120 minutes in Milan, however, was more than just human drama. It was a mixture of mathematical probability and human fallibility. A reminder that science has its limits because it can't account for the one thing that makes sport worth watching — its unpredictability.

For it's clear that both teams were following a strategy, with all five Real Madrid kickers electing to shoot to the same corner (keeper's left) and all four of Atlético's selecting the other (keeper's right).

A zero-sum game

Economists, in particular, have long studied the penalty shootout. Steven Levitt, of Freakonomics fame, co-authored a paper on best kicking strategies. What fascinates economists like Levitt about the penalty is that it provides a real-world example of game theory.

Developed in the 1940s by mathematician John von Neumann, game theory attempts to predict human behavior. In the case of soccer both keeper and penalty taker must make a choice — where to dive and where to shoot. Victory is determined by whether the ball enters the net, making this scenario a zero-sum game perfect for economists.

Simon Kuper and Stefan Szymanski explore the world of analytics and soccer in their 2009 book Soccernomics. One particular story they tell bears a striking resemblance to this Saturday's match: the 2008 Champions League final between Manchester United and Chelsea.

Playing the odds

Just like with Real and Atlético, it's clear that Chelsea in particular had a specific gameplan in 2008. Kuper and Szymanski tell the story of a Basque economist by the name of Ignacio Palacios-Huerta who had gotten in contact with Chelsea's manager Avram Grant.

Palacios-Huertas had analysed the tendencies of United's keeper Edwin van der Sar and gave Grant some straightforward advice:

  • it's crucial to win the coin toss (which Chelsea failed to do) because the team that shoots first wins 60 per cent of the time  
  • never shoot the ball at mid-height — go either high or low 
  • right-footed players should shoot to van der Sar's left because the Dutchman has a tendency to dive right when facing them.

While there is no direct evidence that Chelsea opted to follow Palacios-Huerta's recommendations, every one of Chelsea's shooters except one (more on him later) played the odds and shot to van der Sar's left. 

But right when it looked like the Blues were about to win, captain John Terry slipped on the wet grass, sending his shot against the post as van der Sar dove in the opposite direction.

The human element

Terry's miss was one of two intangible instances that would haunt Chelsea on this day. The second came in the seventh and final round of the shootout when van der Sar, with a singular act of gamesmanship, ruined Chelsea's strategy with only a finger. 

Having seen all previous six shots go to his left, van der Sar was aware that something was up. Suddenly, he fixed his eyes upon Nicolas Anelka, Chelsea's next shooter, stretched out his arms and began pointing to his left.

Doubt could clearly be seen across Anelka's face as he realized that van der Sar had discovered his intentions.

Uncertain of what to do, Anelka abandoned the team's strategy, striking the ball to the right where van der Sar happened to be waiting. Worse still, he gave van der Sar a relatively easy save by hitting the ball at mid-height.

It's difficult to imagine Juanfran not suffering the same indecision as Anelka. How could he be certain that Real Madrid's keeper Keylor Navas — like van der Sar for United — had not deciphered his teams strategy?

Perhaps this doubt caused him to aim further to the keeper's right than he had intended, causing him, like Terry, to strike the post.

This polemic captures what makes the penalty shootout simultaneously maddening and compelling. Once a player is standing behind the ball, 12 yards away from sealing one's fate, the best-laid plans can easily give way to doubt or a single human slip.