While on vacation, I had the opportunity to pick up a few books on football, among which one was Soccernomics. The book is jointly authored by sports journalist Simon Kuper and sports economist Stefan Szymanski. The book explores how the study of statistics and raw data have influenced the modern game.
At one point they talk about penalty kicks. They provide a counter-argument against popular opinion that states that penalties are an unfair way to decide a game because at the end of the day it all comes down to luck. To prove their argument they bring up various examples, one of which is the 2008 Champions League final penalty shoot-out between Manchester United and Chelsea in the Luzhniki Stadium at Moscow.
In that match, Chelsea tried their best to use ‘game theory’ to win the penalty shoot-out. Game theory is a concept allows any kind of team to win a shoot-out, making it look like there isn’t any element of luck involved. Let us delve deeper into what game theory really is.
Game theory was developed by various scientists and mathematicians, one of which was John von Neumann. It is the study of situations in which what one person does depends on what another person does, and vice versa.
This can be explained with real-life examples. Let’s look at the race for acquiring nuclear weapons. Say country A has a close rivalry with country B. Country B isn’t sure whether country A will develop or not develop some kind of nuclear missile, so it uses game theory to predict.
If country A has no nuclear missiles, country B would contemplate doing either of the following two things:
(a) We don’t get a missile. There will always be incidents such as this, and we can live with it.(b) We get the missile. We will gain country A’s respect and they won’t be attacking us again.
If country A has a nuclear missile, country B would contemplate doing either of the following two things:
(a) We don’t get a missile. By the time we’re done making it and they hear about it, we would be in ashes.(b) We get the missile. We will gain country A’s respect and they won’t be attacking us again.
This shows that the equilibrium of the race for nuclear weapons is for both countries to acquire nuclear missiles.
The logic of all football matches is pretty much the same; for penalties, however, it is not. Penalties are, as the authors put it , a ‘zero-sum game’. Any gain for one player is exactly offset by the loss to the other side, or simply put, a +1 for me is -1 for you.
Professionals play Minimax is a paper published in 2003 by Basque economist Igancio Palacios-Huerta, who started recording the way penalties were taken since 1995. It can remarkably be found here, though it isn’t quite on the intellectual level of a common man. Minimax simply means denoting a method or strategy in game theory that minimises the greatest risk to a participant in a game or other situation of conflict. Penalty kicks are a fine example.
Ignacio and Avram Grant, the then Chelsea manager, had a common friend. Upon Chelsea’s entry into the final, the middle-man got them in touch with each other as he knew one could help the other. Grant was instantly mesmerised by Ignacio’s line of work and desperately asked him to help him out. As he sat on the plane to Moscow, he was beyond delighted to receive some good news.
The economist had done an extensive study on United’s goalkeeper and penalty-takers. He then went on to state four main points that would have a direct effect on the shoot-out:
1. Van der Sar tends to dive to the kicker’s ‘natural side’ more often than most keepers did. This meant that when facing a right-footed kicker, the goalkeeper would usually dive to his own right, and when facing a left-footed kicker, to his own left. Chelsea would have a better chance to win the European Cup if their penalty takers kicked towards their unnatural side.
2. A vast majority of the penalties Van der Sar stops are those kicked around the height between 1 and 1.5 meters. Therefore the penalty takers must always aim to hit it just on the ground or high up; never in mid-height .
3. Ronaldo often stops in the run-up to the ball. If he stops, there is an 85% chance he’ll kick to the right-hand side of the goalkeeper because he won’t be able to generate enough power after 120 minutes of football to score towards his left. When a keeper moved early, Ronaldo always scored. The key is to not move.
4. The team that wins the toss has a 60% chance of winning because there is too much pressure on the team going second.
Once you have read this, your entire memory of the shoot-out is changed forever. The Chelsea players mugged up the letter, word for word. There was absolutely no reason for them to go wrong, until Anelka stepped up to take his penalty.
United won the toss, and John Terry tried his best to influence Rio Ferdinand into letting Michael Ballack take the first penalty. Thanks to Sir Alex Ferguson, Ferdinand flatly refused. Carlos Tevez stepped up, calmly placed the ball and scored. Petr Cech really wasn’t given much advice and spent most of the training watching videos of the club’s penalty kicks.
Michael Ballack places the ball, looks at Van der Sar in the eyes and hits it hard and high into the net to Van der Sar’s left. The goalkeeper goes the right way, but due to it not being mid-height, Ballack scores.
Juliano Belletti again places the ball on the left, this time keeping it close to the ground. Another penalty taken on the ‘unnatural’ side. Ignacio, who was nervously watching the game at home with his wife, wasn’t fully convinced Chelsea were following his statistical advice.
Next up was golden boy Cristiano Ronaldo. Petr Cech didn’t move at all. His cold-blooded eyes stared right into Ronaldo’s soul without blinking. Ronaldo paused in his run-up. Right when he made the sudden movement to shoot the ball hard and fast, Cech instinctively jumped to his right and hoped for the best. Penalty saved, and Chelsea were in the driving seat. Igancio’s sceptical wife was left shell-shocked.
Lampard stepped up, and in customary fashion, scored. It will be interesting to note that Lampard has always favoured a really hard and fast shot to his left throughout his career. However, this time he placed it to the right and scored.
Next to make the walk was Ashley Cole who was loudly booed as he placed the ball on the spot. He, however, seemed to disregard Ignacio’s advice. Being a left-footed player, he decided to take a shot towards his ‘natural’ side. Van der Sar did exactly what Ignacio expected and pounced on it. However, Cole’s technique was perfect and the ball just squirmed out of the Dutchman’s grasp as the ball was hit low, just as the economist had recommended.
Next stepped up John Terry. History was indeed going to be made at the end of the night, but the Chelsea captain made it a little too early. He went to his ‘unnatural’ side but slipped and missed as Van der Sar dove the wrong away. Pressure back on because Chelsea had lost the toss.
Kalou steps up, does what the note asked him to do. High, hard and precisely on the side your mind tells you not to shoot at. Chelsea were still in it. But not for long.
Next up was Anelka, but by this time Van der Sar realised something was up. A coach on the United bench figured out that there was some kind of strategy Chelsea were using. Every kick was almost on the same side – five out of six till then.
For the first time, Van der Sar extended his arms to either side. With his left hand, he pointed towards the left corner. “You’re going to put it there, aren’t you? I’m on to you guys and your little plan. Not this time son, not this time,” his gaze said as the two men locked their eyes for a few brief seconds. Anelka now had a problem. As Stefan Szymanski puts it, this was game theory at its finest.
The Frenchman panicked. He had earlier planned to place the ball high on to his right corner and the goalkeeper’s left. However, he shot towards his left and Van der Sar’s right instead. At the end of the day, statistics failed against crude and sheer psychology.
Anelka knew that Van der Sar knew that he knew that Van der Sar tended to dive towards the natural side. As a rain-drenched Ferguson said after holding the European cup, “That wasn’t an accident, his penalty save. We knew exactly where certain players were putting the ball.” A hurt Ignacio spent a sleepless night, as the ignorance of his advice caused Chelsea a European title.
It’s funny how despite being a boy of just 11 back then, I remember watching the game quite vividly. Nobody in the room, including me, noticed Van der Sar pointing towards his left. However, replays clearly show exactly that. While I was busy crying harder than I ever had and my parents were celebrating the happiest moment of their life, I did not realise that all the players except Cole and Anelka had shot towards their unnatural side.
Psychology and statistics. Exploited by few, under-rated by many.
Here are the highlights of perhaps the most riveting penalty shoot-out ever.
