Maradona’s penalty legacy
A new study explores Maradona, the art of randomisation and the ‘invisible foot’
When Diego Maradona died, Professor Ignacio Palacios-Huerta had an idea. Ignacio is my friend; he’s also an economics professor and penalty expert, author of the seminal 2003 academic paper on penalties, Professionals Play Minimax.
In it, he examines whether players make random choices with their penalty-kicks. His finding was that most players make choices that do not depend on their own previous penalty, or the goalkeeper’s previous penalty decision, or on past outcomes. And whenever there is a discrepancy among a player’s penalty choices, he can spot it.
Ignacio decided to look back at Maradona’s penalty strategy and see if he followed the Nash equilibrium of game theory (made famous in the movie A Beautiful Mind): this states that a player can achieve the desired outcome by not changing their initial strategy based on how they think their opponent might act. Game theorists love penalties as they are a zero-sum game (someone has to win and someone has to lose).
There were a few reasons he wanted to do this research. Firstly, no-one has put these two geniuses together before (that’s Nash and Maradona, not Ignacio and Maradona). Scientists love testing out a theory, so why not do it with one of the greatest players ever? And from an educational point of view, we both agree that using Diego Maradona to help teach game theory can be effective.
The purpose of Ignacio’s investigation was to answer two questions: 1, were Maradona’s chances of scoring a penalty statistically identical whether he kicked to his natural or non-natural side? And 2, were his choices serially independent, or did they depend on what happened in his previous penalties?
Maradona was involved in 109 penalty-kicks in his career.
Maradona scored 90 penalties in all, at a conversion rate of 82.5% per cent. Towards the end of his career, he missed five penalty kicks in a row for Boca during Argentina’s 1996 Torneo Clausura, which were among the last seven penalties he kicked. Before that point, his conversion rate was up to 86 per cent. “Those five curses signalled the end of my football career,” he wrote in his autobiography, Yo soy el Diego de la Gente.[The story of these five penalties is worthy of a separate piece, which includes some tremendous trash-talking from River Plate goalkeeper German Burgos; as is Maradona’s role in the 1990 World Cup semi-final penalty shoot-out win over Italy, which is explored in Asif Kapadia’s brilliant film, Diego Maradona.]
Ignacio was able to watch 94 of the penalties (of which 80 were scored, at 85 per cent conversion), and from that, he examined Maradona’s strategy of game theory.
Maradona takes his penalties left-footed: he kicks 55 per cent to his natural side (with 85 per cent conversion rate) and 45 per cent to his non-natural side (with 86 per cent conversion). [He only kicks four to the centre of the goal, and because of the angle of his run-up, for the purposes of this study kicks down the middle are counted as natural side.] He rarely kicks his penalties with power, preferring to roll the ball into the net. Here’s a video of some glorious Maradona penalties:
Ignacio then pulls out his party trick: examining the sequence of actions that Maradona chooses, in the order in which they occurred. He measures each aspect of Maradona’s penalty choices: his probability of kicking natural or non-natural, the goalkeeper’s probability of diving to that side, the scoring probabilities and the runs, defined by a succession of identical choices followed and preceded by a different choice. Ignacio goes so deep into this that here is a sample equation in the paper where L=Maradona’s strategy. Enjoy!
L = G[a0+a1lag(L)+a2lag2(L)+b1lag(L)+b2lag2(L)+c1lag(L)lag(L)+c2lag2(L)lag2(L)]
For those who couldn’t work it out (come on!), Ignacio himself explains his conclusion:
“The results of the tests are remarkably consistent with equilibrium play in every respect: 1, Maradona’s scoring probabilities are statistically identical across strategies. And 2, he generates serially independent sequences and ignores any possible strategic links between past occurrences. As the ultimate test of Nash’s theory, the empirical evidence shows that Maradona’s behaviour is consistent with Nash’s predictions.”
As always with Maradona, there is a twist. In one interview, Maradona explains that his strategy is GK-Dependent. He says:
“I used to wait for the goalkeeper. As I’m seeing the goalkeeper, I can’t hit it too hard, as I’m already on top of the ball. The run-up with my foot, it isn’t enough to hit the ball hard. If it goes slowly, it’s knowing if the goalkeeper will move to his right or left. So I extend the leg and watch the goalkeeper. You risk not getting the ball there though, but I usually managed pretty well.”
I wonder how his penalties can be totally randomised in line with Nash equilibrium if he’s only reacting to goalkeepers making the first move? Ignacio makes the reasonable point that we should not always believe everything that Maradona says – after all, he has the data, and about 33 per cent of Maradona’s penalties actually go in the same direction as the goalkeeper’s dive. Ignacio says:
“Well, he is not exactly reacting, despite what he says. He is a good randomizer, and as such, once he randomizes, he will not change the direction he kicks the ball. He himself admits this when he says that ‘you risk not getting the ball there’. Does he want us to believe that, as the best player on earth, when he aims to kick the ball to the right, it sometimes goes to the left?
“The data clearly show that Maradona’s penalties are taken using the proverbial ‘invisible foot’. That is, he keeps goalkeepers indifferent to their diving sides [ie no goalkeeper facing Maradona has a diving preference], and the goalkeepers keep Maradona indifferent to his kicking side [he doesn’t have a preferential side; his scoring rate is statistically the same on both sides]. Also, as goalkeepers facing Maradona as a group behave randomly, so ‘reacting’ to a random sequence also generates a random sequence.”
So there you have it. Put one of the world’s greatest ever players alongside the world’s greatest penalty professor and the result: proof that Maradona plays Minimax. His penalty choices are perfectly randomised. And the clue was there for us all along: the letters from the word ‘random’ can be found in ‘Maradona’.
Thanks to Professor Ignacio Palacios-Huerta, whose academic paper on this subject, Maradona Plays Minimax, has just been released.
Sergio Aguero apologised after his Panenka penalty was saved in Manchester City’s defeat to Chelsea. Did he really need to? Fans were extremely riled up by his miss, accusing him of showboating and, in some newspaper reports, of trying to humiliate the opposition goalkeeper. No way! The kicker is just trying to score, nothing else, and has made a decision that gives the best chance for that (Panenka himself is horrified at the thought of disrespecting the goalkeeper). In Aguero’s case, it didn’t work. But it was nothing to do with showboating or trying to humiliate anyone. No need to apologise, Sergio!
Poor old Roberto Baggio. His penalty miss in the 1994 World Cup final against Brazil still haunts him. In a rare interview last week (only his fourth since retiring 17 years ago), he said: “I still have not forgiven myself. Religion could help me in that moment. I could have killed myself that day and yet I wouldn’t feel anything.” Missing that penalty (and let’s not forget that Franco Baresi and Daniele Massaro had also missed for Italy) actually fitted his career narrative. As Italian novelist Vanno Santini told me: “Baggio’s miss embodied Italy’s struggle to combine beauty and victory. He came out of it purified.”
Big drama in La Liga where Real Madrid was awarded a penalty only to see VAR step in and Sevilla get a penalty for a foul earlier in the move. It’s the first time this has happened in La Liga, and it would be in one of the most important of the season. Ivan Rakitic made no mistake from the spot…Madrid awarded a penalty at one end, but play is brought back for a Sevilla penalty at the other! 😱 Incredible scenes, and Rakitic converts to put Sevilla 2-1 up! ⚪🔴
This might cheer up Sergio and Roberto: a penalty from Romania’s second division match between Cluj and Reccea. The score was goalless when Reccea took this penalty. Cluj won the game 3-2. Thanks Emy for sharing this!
Please share any penalty thoughts or further questions to me either by commenting below or at @benlyt.
If you enjoyed this post, please spread the word about Twelve Yards and share this with your network. Recent pieces include: how Neymar honed his technique after FIFA changed the rules, explaining Real Madrid’s penalty drought, how Diego Alves became the penalty scourge of La Liga, Pep Guardiola’s surprisingly impressive record in penalty shoot-outs, which players will be next to score penalties with both feet, the Chilean defender who hates penalties but keeps scoring, the Argentine penalty tradition sweeping across empty stadia in Europe, why Lionel Messi is average at penalties, how Robert Lewandowski became a penalty killer, who really invented the two-touch penalty (and Robert Pires relives his trauma), why it’s better to aim high than low, the great Ederson penalty debate, an interview with Antonin Panenka, how to define a true Panenka, how to end Antoine Griezmann’s run of five missed penalties in a row, penalty records in empty stadia, and Barcelona’s first shoot-out win in 23 years. Thank you!
Ben Lyttleton is the author of Twelve Yards: The Art and Psychology of the Perfect Penalty