John Nash, the mathematician portrayed in the movie
A Beautiful Mind
, could have helped Real Madrid and Valencia on Wednesday night when their Super Cup semi-final went to penalties.
Nash was one of the pioneers of game theory, and penalties, which Gattuso associated with "luck" and Ancelotti said that he practiced little, fall squarely within the domain of this area of mathematics.
The shooter and the goalkeeper go to the penalty knowing that what they get out of it depends on what the opponent fails to achieve.
It is the type of situation that game theory deals with: the result that a participant obtains depends on his interaction with others and on how his different interests come together there.
"A penalty kick is a game of strategy," says London School of Economics professor Ignacio Palacios-Huerta.
“Left, right or center.
And you should enlist the help of game theorists to prepare them.
With the money that is at stake, it is incredible that almost no team has these types of experts.
Palacios-Huerta, who has built an extensive database with thousands of launches, and works in the Premier and with national teams, points out two points where he could have helped on Wednesday.
One is the type of shooter you see in shootouts, many of them not used to shooting: their numbers show that they have a very strong tendency to choose their natural side.
Between 65% and 70% of the time.
And the other: “Benzema took two penalties.
When you look at the data of hundreds of players, you realize that in a second launch there is a probability between 70% and 85% that they will not repeat ”.
The Frenchman had one in the 39th minute and chose the goalkeeper's left, who dived to his right.
Already in the tiebreaker, Benzema took Madrid's first penalty, and changed places: to the right of the goalkeeper, who went to the other side.
"Wouldn't it have been good for Mamardashvili to know that, the probability of a pitcher changing in the second?" Palacios-Huerta suggests.
🥊 THIS IS HOW THE PENALTY SHOT HAS FINISHED!
🆚 @realmadrid - @valenciacf
📺 @MovistarFutbol#superSupercopa pic.twitter.com/Ta1NWhbmNr
– RFEF (@rfef) January 11, 2023
Although it is also true that there is between a 15% and a 30% chance that it will repeat.
In the World Cup final an almost like this was seen: Mbappé had three, and for all three he chose the same thing: the goalkeeper's right, who despite being Dibu Martínez did not catch any.
In the hours before the semifinal, Ancelotti said that his team did not prepare the batches much, which is the case, but only in part.
He also said that his players practiced at the end of training.
That is preparation.
Luis Enrique commissioned his players before Qatar: “You have to reach the World Cup with at least 1,000 penalties taken on your teams.
If we wait for the concentration, you don't have time”.
Ancelotti pointed out that the recreation of pressure, an essential ingredient in batches, escaped him.
But daily practice does give them something: “There I can evaluate and choose the five, taking into account those who want to shoot and those who don't want to shoot.
Sometimes there is difficulty in finding five.
That's where the mental aspect comes in.
It is impossible in a training session to replace the atmosphere of a penalty shootout, ”he explained.
At this point, there are coaches who are more confident in being able to find help for their footballers, such as the English coach, Gareth Southgate, a particular case.
His career, and part of his life, was marked by a penalty he shot at the post in the Euro 1996 semi-final at Wembley.
He failed and Germany agreed to the final.
When he took charge of the England team, he began to look for ways to systematize the process, reduce uncertainty and try to ensure that his footballers did not suffer something similar to his.
The English federation even resorted to Palacios-Huerta.
Southgate developed a meticulous liturgy far removed from the Ancelotti method.
The batches were rehearsed at each concentration, and during the last Euro Cup, for example, the ritual was repeated almost every day.
They would gather the players in the center of the field like a tie-breaker, make them walk from there to the box, pick up the ball, place it, wait for a whistle and then decide when to shoot.
Breathe and visualize
They trained them not to do it right away, but when they found their moment, for which they trained them with breathing exercises and visualization.
Everything was planned: who would be in the band at the end of overtime, who would give instructions, who would be the pitchers.
Despite everything, England lost that European Championship against Italy on penalties.
The preparation of these launches has become more sophisticated in recent years, and according to Palacios-Huerta's records, the accuracy has dropped from 80% to 75% in 10 years, which he attributes to the improvement in the goalkeepers' work.
This fall has also had an effect on another of the mythical figures of the tie-breaks, revealed in one of his first works (he has studied more than 1,000 batches).
The one who threw first won 60% of the time.
Now he has seen that this advantage has dropped to 55%: “But there is an equal advantage.
The important thing is that there are more chances shooting first, no matter how much it is”.
Ancelotti is nowhere near Southgate's obsession, but some of his decisions seem in line with these findings.
“The key has been that I have put the three most experienced first, the three coldest [Benzema, Modric and Kroos]”, he explained.
Before, the best player reserved the last one, but in addition to the fact that many times he didn't get to shoot, the advantage detected by shooting first suggests that going ahead on the scoreboard adds pressure to the one behind.
That is why it is convenient that the best go before.
Although Madrid have not looked like meticulous England in recent years, they have not lost a shootout in a decade.
The last was in the Champions League semifinal against Bayern in 2012. Since then they have won three: two against Atlético (2016 Champions League final and 2020 Super Cup final), and Wednesday's against Valencia.
13 shots, 13 goals.
Before Gayà took the final penalty that Courtois saved, the Madrid players hugged and laughed in the center of the field and Benzema raised his arms an instant before he kicked the ball.
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