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The Guardian
a day ago
- Sport
- The Guardian
Soccer has changed, but the drama and dynamics of penalties remain
England's victory over Sweden at the women's Euros came after one of the worst penalty shootouts in history (or at least, worst in terms of how many penalties were missed; in terms of drama, it was arguably one of the greatest ever). Of the 14 penalties taken, only five were scored. That led, predictably, to the usual tedious criticism of the women's game and suggestions that the penalty spot should be moved closer to the goal. Which is, of course, nonsense. Four of the five penalties that were scored were excellent, hit firmly into the corners, and the other, the kick that turned out to be the winner, was smashed sensibly and without fuss, straight down the middle by Lucy Bronze as the goalkeeper Jennifer Falk dived out of the way. Two nights later, as Germany beat France in a shootout, 12 of the 14 penalties were scored. In the Women's Super League last season, 90.32% of penalties were converted. Nobody has used those examples to suggest moving the penalty spot further away to give goalkeepers more of a chance. Sign up to Soccer with Jonathan Wilson Jonathan Wilson brings expert analysis on the biggest stories from European soccer after newsletter promotion It is one of the great fascinations of soccer that, since penalties were introduced in 1891, the spot has remained 12 yards from goal as the size and shape of the penalty area has changed. It turns out that being one-and-a-half times further from the goal than the distance between the posts creates a scenario that feels fair and has a remarkable balance. That may in part be the result of familiarity, but at almost every level of the game in the 135 years since, roughly three-quarters of penalties have been scored. That is to say, the contest between striker and goalkeeper remained constant – a relative lack of power in the striker at junior level, for instance, matched by a lack of size in the goalkeeper. Before the Germany v France shootout on Saturday, only 12 of 29 penalties had been scored at the Euros – 41.38%. After the shootout, that percentage had risen to 57.14%. With small datasets there's always a danger of interpreting random variations as patterns, but it did seem that panic had set in. Even before the high tension of England against Sweden, Norway's former Ballon d'Or winner Ada Hegerberg had missed two penalties in the tournament, including, critically, in her country's quarter-final defeat to Italy. That, perhaps, was enough to plant a seed of doubt, which blossomed in England and Sweden's shootout, when both sides suffered a collective loss of nerve. Anxiety is contagious and far from unknown in penalty shootouts: it happened, for instance, to Barcelona as they missed four out of four in a shootout against Steaua Bucharest in the 1986 European Cup final, and to Manchester United as they missed four out of five against Sunderland in the 2014 League Cup semi-final. The England-Sweden contagion then seemed to escape the confines of its own shootout, as Spain missed two penalties in beating Switzerland on Friday and Germany missed a penalty against France in the 90 minutes. The shootout is perhaps the area of soccer in which psychology matters most. In the 2006 World Cup, Germany's goalkeeper Jens Lehmann made great play of consulting notes he had scribbled on hotel notepaper and hidden in his sock before each Argentina penalty in the quarter-final. It turned out that, of the seven players he had jotted down, only two actually took penalties, but the belief he had specific knowledge was enough to unnerve Argentina, who lost the shootout 4–2. Goalkeepers increasingly have data to help inform their decisions. Germany's keeper on Sunday, Ann-Katrin Berger, had notes taped to her water bottle. On TV, the names of only two French players were clearly visible: Amel Majri and Alice Sombath. In both cases, Berger was advised to dive left. She did and on each occasion saved the kick. Given Berger's notes were shown clearly several minutes before the end of normal time, could somebody have informed the French staff who could then have passed on the message for at least some of their takers to change plan? Or would asking a player to vary from their preferred method of conversion itself make them more likely to miss? That's part of the glorious game theory of penalties. At the moment, it feels like an arms race. VAR set goalkeepers back for a time, denying them the skip forward they habitually took as the penalty was taken. But goalkeepers have now worked out how to advance with one foot, the other remaining in contact with the goalline. As strikers have learned how to stagger their run to wait for the keeper to move first, so keepers have more data and can predict such subterfuge. In the Premier League last season, 83.13% of penalties were converted, which is on the high side historically, but actually a drop of just over 6% from the previous season. The season before that, only 74.75% were scored. In fact, what is striking when looking at penalty conversion rates over the past three decades is how little pattern there is – from a low of 65.75% in 2001–02 to the high of the season before last, and all points in between. Penalties are missed, penalties are scored, the taker's cause is developed, and then the keeper's, and sometimes panic sets in, yet somehow the proportion of penalties scored largely remains at 75-80%. Balance remains. This is an extract from Soccer with Jonathan Wilson, a weekly look from the Guardian US at the game in Europe and beyond. Subscribe for free here. Have a question for Jonathan? Email soccerwithjw@ and he'll answer the best in a future edition.
Yahoo
2 days ago
- Sport
- Yahoo
Soccer has changed, but the drama and dynamics of penalties remain
England's victory over Sweden at the women's Euros came after one of the worst penalty shootouts in history (or at least, worst in terms of how many penalties were missed; in terms of drama, it was arguably one of the greatest ever). Of the 14 penalties taken, only five were scored. That led, predictably, to the usual tedious criticism of the women's game and suggestions that the penalty spot should be moved closer to the goal. Which is, of course, nonsense. Four of the five penalties that were scored were excellent, hit firmly into the corners, and the other, the kick that turned out to be the winner, was smashed sensibly and without fuss, straight down the middle by Lucy Bronze as the goalkeeper Jennifer Falk dived out of the way. Two nights later, as Germany beat France in a shootout, 12 of the 14 penalties were scored. In the Women's Super League last season, 90.32% of penalties were converted. Nobody has used those examples to suggest moving the penalty spot further away to give goalkeepers more of a chance. Related: Ann-Katrin Berger follows up biblical miracle with penalty heroics for Germany | Jonathan Liew It is one of the great fascinations of soccer that, since penalties were introduced in 1891, the spot has remained 12 yards from goal as the size and shape of the penalty area has changed. It turns out that being one-and-a-half times further from the goal than the distance between the posts creates a scenario that feels fair and has a remarkable balance. That may in part be the result of familiarity, but at almost every level of the game in the 135 years since, roughly three-quarters of penalties have been scored. That is to say, the contest between striker and goalkeeper remained constant – a relative lack of power in the striker at junior level, for instance, matched by a lack of size in the goalkeeper. Before the Germany v France shootout on Saturday, only 12 of 29 penalties had been scored at the Euros – 41.38%. After the shootout, that percentage had risen to 57.14%. With small datasets there's always a danger of interpreting random variations as patterns, but it did seem that panic had set in. Even before the high tension of England against Sweden, Norway's former Ballon d'Or winner Ada Hegerberg had missed two penalties in the tournament, including, critically, in her country's quarter-final defeat to Italy. That, perhaps, was enough to plant a seed of doubt, which blossomed in England and Sweden's shootout, when both sides suffered a collective loss of nerve. Anxiety is contagious and far from unknown in penalty shootouts: it happened, for instance, to Barcelona as they missed four out of four in a shootout against Steaua Bucharest in the 1986 European Cup final, and to Manchester United as they missed four out of five against Sunderland in the 2014 League Cup semi-final. The England-Sweden contagion then seemed to escape the confines of its own shootout, as Spain missed two penalties in beating Switzerland on Friday and Germany missed a penalty against France in the 90 minutes. Related: England's Hannah Hampton hits the headlines in latest act of unlikely career The shootout is perhaps the area of soccer in which psychology matters most. In the 2006 World Cup, Germany's goalkeeper Jens Lehmann made great play of consulting notes he had scribbled on hotel notepaper and hidden in his sock before each Argentina penalty in the quarter-final. It turned out that, of the seven players he had jotted down, only two actually took penalties, but the belief he had specific knowledge was enough to unnerve Argentina, who lost the shootout 4–2. Goalkeepers increasingly have data to help inform their decisions. Germany's keeper on Sunday, Ann-Katrin Berger, had notes taped to her water bottle. On TV, the names of only two French players were clearly visible: Amel Majri and Alice Sombath. In both cases, Berger was advised to dive left. She did and on each occasion saved the kick. Given Berger's notes were shown clearly several minutes before the end of normal time, could somebody have informed the French staff who could then have passed on the message for at least some of their takers to change plan? Or would asking a player to vary from their preferred method of conversion itself make them more likely to miss? That's part of the glorious game theory of penalties. At the moment, it feels like an arms race. VAR set goalkeepers back for a time, denying them the skip forward they habitually took as the penalty was taken. But goalkeepers have now worked out how to advance with one foot, the other remaining in contact with the goalline. As strikers have learned how to stagger their run to wait for the keeper to move first, so keepers have more data and can predict such subterfuge. In the Premier League last season, 83.13% of penalties were converted, which is on the high side historically, but actually a drop of just over 6% from the previous season. The season before that, only 74.75% were scored. In fact, what is striking when looking at penalty conversion rates over the past three decades is how little pattern there is – from a low of 65.75% in 2001–02 to the high of the season before last, and all points in between. Penalties are missed, penalties are scored, the taker's cause is developed, and then the keeper's, and sometimes panic sets in, yet somehow the proportion of penalties scored largely remains at 75-80%. Balance remains. This is an extract from Soccer with Jonathan Wilson, a weekly look from the Guardian US at the game in Europe and beyond. Subscribe for free here. Have a question for Jonathan? Email soccerwithjw@ and he'll answer the best in a future edition.
The Guardian
2 days ago
- Sport
- The Guardian
Soccer has changed, but the drama and dynamics of penalties remain
England's victory over Sweden at the women's Euros came after one of the worst penalty shootouts in history (or at least, worst in terms of how many penalties were missed; in terms of drama, it was arguably one of the greatest ever). Of the 14 penalties taken, only five were scored. That led, predictably, to the usual tedious criticism of the women's game and suggestions that the penalty spot should be moved closer to the goal. Which is, of course, nonsense. Four of the five penalties that were scored were excellent, hit firmly into the corners, and the other, the kick that turned out to be the winner, was smashed sensibly and without fuss, straight down the middle by Lucy Bronze as the goalkeeper Jennifer Falk dived out of the way. Two nights later, as Germany beat France in a shootout, 12 of the 14 penalties were scored. In the Women's Super League last season, 90.32% of penalties were converted. Nobody has used those examples to suggest moving the penalty spot further away to give goalkeepers more of a chance. Sign up to Soccer with Jonathan Wilson Jonathan Wilson brings expert analysis on the biggest stories from European soccer after newsletter promotion It is one of the great fascinations of soccer that, since penalties were introduced in 1891, the spot has remained 12 yards from goal as the size and shape of the penalty area has changed. It turns out that being one-and-a-half times further from the goal than the distance between the posts creates a scenario that feels fair and has a remarkable balance. That may in part be the result of familiarity, but at almost every level of the game in the 135 years since, roughly three-quarters of penalties have been scored. That is to say, the contest between striker and goalkeeper remained constant – a relative lack of power in the striker at junior level, for instance, matched by a lack of size in the goalkeeper. Before the Germany v France shootout on Saturday, only 12 of 29 penalties had been scored at the Euros – 41.38%. After the shootout, that percentage had risen to 57.14%. With small datasets there's always a danger of interpreting random variations as patterns, but it did seem that panic had set in. Even before the high tension of England against Sweden, Norway's former Ballon d'Or winner Ada Hegerberg had missed two penalties in the tournament, including, critically, in her country's quarter-final defeat to Italy. That, perhaps, was enough to plant a seed of doubt, which blossomed in England and Sweden's shootout, when both sides suffered a collective loss of nerve. Anxiety is contagious and far from unknown in penalty shootouts: it happened, for instance, to Barcelona as they missed four out of four in a shootout against Steaua Bucharest in the 1986 European Cup final, and to Manchester United as they missed four out of five against Sunderland in the 2014 League Cup semi-final. The England-Sweden contagion then seemed to escape the confines of its own shootout, as Spain missed two penalties in beating Switzerland on Friday and Germany missed a penalty against France in the 90 minutes. The shootout is perhaps the area of soccer in which psychology matters most. In the 2006 World Cup, Germany's goalkeeper Jens Lehmann made great play of consulting notes he had scribbled on hotel notepaper and hidden in his sock before each Argentina penalty in the quarter-final. It turned out that, of the seven players he had jotted down, only two actually took penalties, but the belief he had specific knowledge was enough to unnerve Argentina, who lost the shootout 4–2. Goalkeepers increasingly have data to help inform their decisions. Germany's keeper on Sunday, Ann-Katrin Berger, had notes taped to her water bottle. On TV, the names of only two French players were clearly visible: Amel Majri and Alice Sombath. In both cases, Berger was advised to dive left. She did and on each occasion saved the kick. Given Berger's notes were shown clearly several minutes before the end of normal time, could somebody have informed the French staff who could then have passed on the message for at least some of their takers to change plan? Or would asking a player to vary from their preferred method of conversion itself make them more likely to miss? That's part of the glorious game theory of penalties. At the moment, it feels like an arms race. VAR set goalkeepers back for a time, denying them the skip forward they habitually took as the penalty was taken. But goalkeepers have now worked out how to advance with one foot, the other remaining in contact with the goalline. As strikers have learned how to stagger their run to wait for the keeper to move first, so keepers have more data and can predict such subterfuge. In the Premier League last season, 83.13% of penalties were converted, which is on the high side historically, but actually a drop of just over 6% from the previous season. The season before that, only 74.75% were scored. In fact, what is striking when looking at penalty conversion rates over the past three decades is how little pattern there is – from a low of 65.75% in 2001–02 to the high of the season before last, and all points in between. Penalties are missed, penalties are scored, the taker's cause is developed, and then the keeper's, and sometimes panic sets in, yet somehow the proportion of penalties scored largely remains at 75-80%. Balance remains. This is an extract from Soccer with Jonathan Wilson, a weekly look from the Guardian US at the game in Europe and beyond. Subscribe for free here. Have a question for Jonathan? Email soccerwithjw@ and he'll answer the best in a future edition.
BBC News
4 days ago
- Sport
- BBC News
The mathematics of the perfect penalty shootout
Professional footballers sometimes use a mathematical strategy to help them score a penalty, or save one – and it all comes down to randomness. As we reach the latter stages of any major football tournament, penalty shootouts between evenly matched teams seem almost to be an inevitability. An absorbing spectacle for neutral watchers, agonising for the fans of the teams involved, and potentially career-defining for the players – the penalty shootout offers a form of sporting drama almost unrivalled in its acute tension. And so it transpired on Thursday night, when England and Sweden couldn't be separated over normal and then extra time in their Euro 2025 quarter final (read more analysis of the game on BBC Sport). Up stepped Allessia Russo for England to take the first kick putting it just beyond the reach of the diving Swedish keeper Jennifer Falk. But England would not score again for the next three kicks. Falk dived the right way and saved all three. When the camera cut to Falk before England's fifth penalty she could be seen consulting her water bottle on which the names of the England penalty takers and their preferred penalty direction were listed. Fortunately for England, Sweden were equally wayward with their penalties – goalkeeper Hannah Hampton saving two while two others missed the goal completely – leaving the sides tied on two scored and four missed after six penalties each. Up stepped stalwart defender Lucy Bronze to take what would transpire to be England's last penalty; blasting it right down the middle over the legs of a diving Falk. Teenager Smilla Holmberg then skied Sweden's final spot kick to spark scenes of jubilation amongst the England players. (Read more analysis on the shootout on BBC Sport.) In her interview after the game, Bronze (whose mum is a maths teacher, and who achieved a very apt bronze award in the UK Mathematics Trust challenge while at school) discussed why she chose to blast her penalty straight down the middle. "I watched the goalkeeper, and every single penalty she dived quite early. Statistically it's risky for the keeper to stand still… So yeah, I love maths." Bronze's comments raise an important question: can mathematics help players determine how they should take their penalties? What can they do to make it more likely that they hit the back of the net? Should they go high or low, left or right or perhaps down the middle? Should they put their boot through it as hard as they can or should they aim for placement above all else? Does it pay off to opt for a "Panenka" – a chipped penalty kick down the centre of the goal relying on the keeper diving one way or the other? Audaciously brilliant if it works, but embarrassing if the keeper doesn't buy the dummy and the ball floats gently into their open hands. When all the rivalries, the personalities and the occasion are stripped away, penalty taking is a very simple sort of game with just two players: the taker and the keeper. Fortunately there is a branch of mathematical sciences, known as Game Theory, dedicated to understanding and interrogating the dynamics of such simple competitions. To use the language of that subject, penalty taking is a zero-sum game: for the taker to score the keeper has to concede and for the keeper to triumph they must ether save the shot or rely on the taker missing. Either way, there is only one winner. As outlined above, the kicker has a variety of strategies from which to choose when taking the penalty and the keeper has a corresponding range of options when attempting to block the shot. For the sake of simplicity though, let's just think about three options for the placement of the penalty kick: to the left, to the right or down the middle – and the same three options that the keeper can use to attempt to save. Let's also imagine, as is usually the case, that both the taker and the keeper make up their minds about what their strategy will be in advance. As four of the seven English penalty takers in the quarter-final shoot out discovered, no single strategy like "always aim right" is going to be optimal, precisely because it makes you predictable and predictability can be exploited, as so expertly demonstrated by Sweden's goalkeeper Jennifer Falk. There is no single best place to put your penalties. In fact, the optimal strategy to use when taking penalties might just be what game theorists call a "mixed strategy". This is an approach in which a player deliberately introduces unpredictability into their decisions to prevent opponents from exploiting patterns. In the context of penalty taking, this would involve the taker aiming at a different, randomly chosen position each time. Not all players opt for this strategy, but even if they do, a perfectly random approach is difficult to achieve. Preferences for a particular placement can sometimes become apparent – hence Falk's notes on England's penalty takers' habits written on her water bottle. A 2002 study found that, rather than consistently favouring one side of the goal, penalty takers in two of Europe's top leagues chose randomly between kicking to the left, the right or down the middle. Remember, though, that this is not the same as simply alternating sides, which is an entirely non-random and easily predictable strategy. Football is by no means the only sport in which a mixed strategy might pay dividends. In tennis, the serve is one of the most potent weapons a player has in their arsenal. Pro players might expect to win about two-thirds of the points on their serve which translates to winning 86% of their service games. For the elite this percentage is even higher. In the recent men's Wimbledon final, defending champion Carlos Alcaraz won 73% (121 of 165) of his service points, whilst world number one and eventual winner Jannik Sinner won 76% (116 of 152) of his. Part of the advantage of the serve comes from its speed, leaving the receiving player relatively little time to react. Typically, there are two options for serves in elite level tennis, either "down the middle" or "out wide". Being able to predict which of these two strategies an opponent will use on their service games would give the returner an advantage, enabling them to anticipate, prepare and execute a return of serve. So again the optimal strategy for the server is to mix things up by randomly selecting between the two options to keep the receiver literally on their toes. Analysing almost half a million serves from over 3,000 matches, Romain Gauriot, an economics researcher at Deakin University in Melbourne, Australia, and his colleagues found that professional tennis players adopt a near-optimal strategy when it comes to switching between the different serve types. Interestingly they also found that junior level players diverge quite substantially from the optimal strategy – serving in a more predictable manner, suggesting that perfecting a mixed strategy is something that pro tennis players have either learned to do, or is a trait that has helped them reach the professional ranks. Beyond the world of sport, mixed strategies have been adopted in a variety of different arenas ranging from politics to business to hunting. It is believed that for hundreds of years, the Naskapi people of eastern Canada have been using a randomised strategy to help them hunt. Their direction-choosing ceremony involves burning the bones of previously caught caribou and using the random scorch marks which appear in order to determine the direction for the next hunt. It is suggested that divesting this decision to an essentially random process circumvents the inevitable repetitiveness of human-made decisions. Some academics have argued that this reduces both the likelihood of depleting the prey in a particular region of the forest and the probability of the hunted animals learning where humans like to hunt and deliberately avoiding those areas, although others have cast doubt on how effective this mixed strategy would be in practice. In recent experiments into the impacts of emotional unpredictability, management students were asked to negotiate a hypothetical venture with each other according to some pre-specified rules. In one scenario, negotiators were asked to be relentlessly negative and angry, while in another, they were asked to frequently change their emotional tone between positive and negative. The students whose counterparts displayed emotional unpredictability were made to feel as though they lacked control over the negotiations, leading them to make larger concessions and irresolute demands. More like this: Political leaders employing mixed strategies aim to appear erratic and volatile to manipulate adversaries. One particular mixed strategy, a form of brinkmanship known in political science as the Madman Theory, was the basis of much of Richard Nixon's foreign policy in the late 1960s and early 1970s. The aim, as the name would suggest, was to convince Nixon's communist opponents that he was more than a little unhinged. He reasoned that if his opponents judged him to be an irrational actor, they would not be able to predict his plays and would thus have to make more concessions to avoid the risk of accidentally triggering him into retaliation. More recently, observers have argued that President Donald Trump is also harnessing the power of unpredictability by resurrecting Nixon's Madman ideology in his trade negotiations as well as his dealings in the Middle East and Ukraine. (Read Allan Little's analysis of Trump's use of Madman Theory.) Whether we are on the football pitch, the tennis court or the boardroom, game theory teaches us that predictable decisions can give our opponents the upper hand. Mixed strategies remind us that raw talent isn't everything and that randomness in how our skills are deployed can have a big impact. Staying unpredictable might be our most predictable path to victory. -- For more science, technology, environment and health stories from the BBC, follow us on Facebook, X and Instagram.
Business Recorder
5 days ago
- Sport
- Business Recorder
Swedish coach backs 18-year-old Holmberg after decisive shootout miss
ZURICH: Sweden keeper Jennifer Falk made four penalty shootout saves but still managed to end up on the losing side as England triumphed 3-2 on penalties after a 2-2 draw in their Women's Euro quarter-final on Thursday, leaving the Swedes distraught. Falk played both the hero and the villain, making save after save from a succession of poorly-struck England penalties, but when she had the chance to win it, she fired her own effort way over the bar. With Lucy Bronze finally scoring for England, the pressure piled on to teenager Smilla Holmberg, but she blasted the final effort horribly high to send the reigning champions through to face Italy in the semi-finals. 'It's a tough loss, when it comes in that way too. We were very close, both in the penalty shoot-out and in the game when we led 2-0,' Sweden coach Peter Gerhardsson said. With five Swedes failing from the spot there will not be the usual spotlight on 'the one who missed', but a distraught Holmberg was still comforted by her team-mates. England beat Sweden in sensational penalty shoot-out to reach Women's Euro semis 'Everyone supports her, and not only her – the sadness is not because you are 18, others are just as sad at 27 or 30. What you saw after the shoot-out was support; everyone supported one another,' Gerhardsson said. 'It will be difficult to deal with later, but we in the coaching team made the choice of players, and we have never been cowardly to make a decision, but sometimes things do not go your way.' Pundits in Swedish media immediately criticised Gerhardsson for giving an 18-year-old the responsibility of keeping Sweden in the tournament when more experienced attacking players had yet to take a penalty in the shoot-out. 'It's the coaches who decided that,' he said. 'We have 11 players who can stand there. It's small margins, it's very hard to prepare for, it's been that way all the time. If they miss, someone else should have taken it, and if they score, it was right. 'You can't have that kind of hindsight, you have to make the choice.'
