The psychological warfare behind every penalty: the numbers, the dark arts and the odds

The psychological warfare behind every penalty: the numbers, the dark arts and the odds

The penalty kick is the rawest distillation of psychology and repetitive practice in football. It’s the game at its most primal and basic. The ball must make it into the goal, beyond the goalkeeper, with no defenders in the way. If the match is still in the balance, a penalty offers a great inroad to applying increased pressure with minimal effort. It requires no real tactics, at least relative to the complexity of an entire match.

When a penalty is part of a shootout, a prerequisite to glory, the stakes are incredibly high and it becomes a different beast entirely. It’s no longer one kick, but a series of them. Some teams and players are great, yet some great players can’t step up. So, what makes an individual – outfield or in goal – good in a shootout? How do we make them better? How are we using various models to map and optimise their outcome? To what effect? And importantly, are penalties still important?

Standing in front of the goal, the ball placed on a spot marked out precisely 12 yards from the goal line, in which the goalkeeper must stay rooted to until the player has made contact with the ball, sounds like the advantage is with the player. It is. Yet, many are missed, in part precisely because it’s an advantage for the player. If they have the advantage, they carry the burden of pressure. 

Looking directly into the keeper’s eye – mano a mano – combat is about to commence. For the player, the crowd can as easily become blocked out as it can become a mental block. The keeper can seem minuscule in the goal, or alternatively, an amorphous yin and yang dazzling the player and his senses into pre-kick psychological submission. Perception and fortitude are very important.

Players nowadays rarely miss. During the Premier League’s 2019/20 campaign, of the 92 penalties taken, only two missed the target. In 2018/19 there were 103, with only three misses and in 2017/18 there were 80 taken, also with three misses. In these respective campaigns, 13, 16 and 21 were saved. Besides the latter being a bad season for penalties, one thing is clear: the taker holds all of the cards.

Most seasons tend to look like the last three in terms of general distribution, however, if we’re to look further back to the advent of the Premier League we can start to gauge shifting trends. In the inaugural 1992/93 season, there were only 61 penalties. One was missed, two were saved. In 1993/94 there were 82 with zero misses and two saves (both from Swindon). Finally, for brevity, in 1994/95 there were 67 taken with one miss and zero saves. 

What has now become clear is that, firstly, there are on average a lot more penalties. This may be down to a multitude of factors, including an evolving style of play, harsher and/or more accurate referees, the better-defined codification of rules or, as many will hasten to say, more diving or playing for a penalty. 

Whilst misses can come down to the role of the goalkeeper, for clarity, I’ll discount those and only factor in the times a goalkeeper was directly responsible for a penalty not finding the net – namely, his save. In the 2019/20 campaign, 14.1% were saved, followed by 15.5% and 26.3% in the season’s prior. 

Looking at the earlier campaigns, the save percentages were 3.3% in 1992/93, 2.4% in 1993/94 and zero in 1994/95. Two conclusions can be drawn from this: players are getting worse at taking them or goalkeepers are getting better at saving them. Without being too certain, the second option seems more likely.

The overall standard of players in all positions is increasing, as are the resources available to scout ahead (particularly handy in penalties). Both players – the taker and the goalkeeper – know more than ever. However, the goalkeeper, with a more technically focused skillset, is becoming better equipped to deal with penalties.

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An extra 4.6 goals (the average penalties per team over the last three seasons) could essentially equate to an extra nine or 12 points, per team, should all find the back of the net. That’s the difference between glory and failure; between another season in the top-flight and a potential decade in the Championship. Clubs know this. That’s why goalkeepers are better than ever at stopping them. 

Evolving Roles

Football has shifted immensely over the last decade or so. Almost every position has been overhauled in the shift from the physical and direct football of the 1990s to the possession-based, high-pressing build-from-the-back that is fairly uniform now. Theoretically, it mightn’t make sense for a goalkeeper to be considered a part of this shift. His job is just to stop goals, is it not?

Well, no. The goalkeeper has developed from shot-stopper, largely indebted to reaction, physicality and intuition, into a studious and analytical monster capable of leading play from his six-yard box. Navigating his way through the post-modern footballing landscape like a champion boxer, focusing on intense repetition, mental-physical problem-solving and well-drilled athleticism, the goalkeeper embodies everything football has and will become.

Existing at the apex of modern analytical and scientific football, a goalkeeper’s focus is ever more intense in honing their tools. What seismic shift made the goalkeeper’s penalty-stopping ability follow the trajectory it has? One of the defining goalkeepers of the early Premier League era, Peter Schmeichel, could give us a clue.

Before any changes are made, there must be a belief that they can be. Belief in improvement usually comes down to attitude. If you embed a growth-orientated mindset into your training, you’ll improve. If you don’t, you likely won’t. But remember, this was a time when analysis existed in its infancy, eschewed by many top managers. A player may have improved their attributes, but something like a penalty was still pseudoscience. 

Schmeichel detailed his approach, accepting that even the player can’t control how everything will play out: “In order to gain a little bit of control, or at least to think I have a little bit of control, I would rather not know anything at that point. When it comes to penalties, including in shootouts, for me it is simple. I have already decided. This is what I am going to do. I don’t care who kicks the ball. In a shootout, I’m still going to go left, right, right, left, right. That is what I am going to do. So that gives me the idea, or impression, that I am actually in control.”

Schmeichel’s quote doesn’t quite acknowledge that he, as a player, didn’t believe in technicality, but that the prevailing idea back then was that penalties were a kind of black magic and to succeed required sorcery and superstition. The Dane’s was to never change his mind. No matter what.

The Triad

More than a physical battle, Schmeichel seems to think of it as a psychological one. The invisible battle for control. From a player’s perspective, he wrote: “It’s a situation where you have no control. You don’t put the ball on the spot. You don’t make the run-up. You don’t decide how long the run-up is. You don’t decide which foot he is going to kick with. You don’t decide the angle of the approach. You don’t decide when the referee blows his whistle.”

It’s hard to disagree with any of that. Schmeichel says he believes in luck. Luck is uncertainty. Uncertainty is chaos. In his mind, his approach is not to impose order onto chaos, but to embrace it like a Discordianist in gloves. This highlights one of the key changes. Football, through analysis, data and analytics, is beginning to do what science started to do with nature centuries ago – codifying and controlling it, shining light onto the dark arts. 

Chaos is no longer accepted in football and just rolling with it is a philosophy that, beyond the scintillating Real Betis side under former manager Quique Setién, doesn’t fly. Penalties are more routinised than ever. A player knows what the goalkeeper is likely to do, he’s seen it so many times on video. The goalkeeper knows who is most likely to step up and what they’ll do with it. In many ways, the outcome is settled well before the ball is even kicked. The telepathic trash-talking in the build-up holds a lot of weight. 

Read  |  A history of football’s dark arts’

Into the modern-era and there stands a general consensus as to today’s most reliable goalkeeper from a spot-kick: Flamengo’s Diego Alves. When he left Valencia in 2017, the Brazilian stopper was a LaLiga record-holder, saving 24 penalties in his time there. Alves signed to Valencia from Andalusian side Almería where his record was even more ridiculous. He’d faced 18 penalties, saving 12 of them. 

Of his final total of 24 saves, he’d faced 50, allowing 24 past him with two missing the target. Alves, at the pinnacle of penalty-stopping performance, is a perfect case study. The thing with Alves is that he doesn’t do anything particularly different to others, he just does certain things better.  

In his own words, penalties are “a psychological battle between the goalkeeper and the taker”. As with other psychological battles in a sporting context, football is less about ostentatious displays of distraction as it is subtle tweaks to the dynamics of the situation. A roaring goalkeeper hammering the crossbar makes him appear more unsettled than unsettling. A sly remark gnaws at you. Epictetus, the Godfather of Stoic philosophy, wrote, “Any person capable of angering you becomes your master.”

Think of Conor McGregor – love him or hate him – as being the foremost purveyor of psychological warfare in a one-on-one context in contemporary sports. The Irish mixed martial artist earned the ‘Mystic Mac’ label on account of his ability to call the outcome of a fight before it took place. His prescience isn’t due solely to his unique skillset, but his unique mindset.

A hungry desire to get to the very top, at all costs, permeates everything McGregor does. There is no chance. It’s all a part of a design. Heir to the throne of Mohammad Ali, McGregor is a sharp talking wit. Like Ali, he can call a fight to its minute. Winding up lethal Brazilian José Aldo, the Irishman said, “It will be over before you know it. Just please show up December 12th.”

Only 13 seconds into the fight, McGregor knocked Aldo out – the Brazilian’s first loss in a decade – a testament not to the limited arsenal McGregor was able to utilise on the night, but the unsettling verbal exchanges that penetrated Aldo’s mental guard.

Alves, like McGregor and Ali, knows the power of behavioural psychology and persuasion. Tipping the scales from the usual save rate of between 15 to 20% to just under 50%, he indulges in some small talk of his own. Overt displays like boxing’s trash-talking would be admonished by football associations around the world, so the crafty Brazilian has adapted to football’s more demure etiquette. 

Facing off against the formidable Cristiano Ronaldo, which has happened four times, Alves coming out trumps in three of those, he knew stopping a powerful and accurate strike from the Portuguese attacker would be difficult so resorted to manipulating the odds in his favour. “Don’t shoot to my right,” Alves said to Ronaldo as the Portuguese attacker’s Real Madrid side were 2-0 down.

Not one to succumb to pressure – despite what is often said of him – Ronaldo makes it count when it most needs to. He opted to do things his way and why not? It had worked countless times before. Ronaldo stuck to his guns, shot right and Alves saved. His side clawed it back to get a single point, but this left them four behind Barcelona with only two games left. Alves had talked them out of the title. 

Another part of Alves’ tactics of deception are his movement. Alves seems to lure penalty takers like a matador holding the muleta. Coaxing a player to one side, the Brazilian lures the ball towards him by moving at a crucial point in the taker’s run-up – when they have hit a trajectory and pace that any change of mind would almost certainly spell disaster. The point of no return; the perfect time to cast doubt in the mind of the taker. 

He moves jaggedly side-to-side, erratic enough to distract, but calculated enough to appear larger than his frame. The impression is that, in the split second it takes for him to move to either side, he has guessed your direction already. In a sense, he has. It’s the final split-second doubt, the inability to wholeheartedly commit, that often kills the goal. 

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Beyond psychology, this movement lends itself to the placement of his feet. They’re never planted, always being in a position with a charged kinetic energy capable of exploding out either side, covering the largest portion of the goal he can. Alves looks at the player as he does this, as if testing the water and provoking a subtle sign. If he hypothesises the direction correctly, eliciting a barely visible response from the player, he’ll commit that way. This is where Alves differs from Schmeichel. Both understood the chaos. The Dane sought to embrace it, Alves to manipulate it.

Valencia’s goalkeeping coach José Manuel Ochotorena boils Alves’ success in penalties down to a few factors: “Diego is a goalkeeper who dominates very well. [He has] intuition and reflexes and control of the situation.” Reflexes are involuntary actions that take place without the brain, for example your knee kicking when it’s tapped by a doctor. These are evolutionary movements in-built for protection and can’t be trained.

Reaction, though, can be trained, largely by repetitive practice to various stimuli. It is reaction, more than reflex, that a goalkeeper relies on. By repeating actions they become almost automatic (easily confused with ‘reflexes’) and habitual. Processing time shortens and new neural pathways begin to form to facilitate these changes. 

On the other hand, intuition isn’t something learned as easily. Of the triad of penalty-stopping powers – reaction, intuition and psychology – the latter is the easiest to work on. Whilst it’s not recommended to go as far as some have, like Argentina’s Sergio Goycochea who urinated on the goalline (even when he didn’t need to) for luck, there are some other great psychological examples that could provide food for thought.

World Cups seem to bring something magical to the penalty shootout. Look at the performative genius of Germany’s Jens Lehmann reading penalty tips from a scrap of paper during the 2006 quarter-final shootout as a shining example. Developing a life of its own, the piece of paper has been deeply mythologised in World Cup folklore and, after being sold to a businessman for €1m at auction, now resides in a museum.

What was it about this piece of paper that so captivated audiences and bewildered potential scorers? No one really knows and therein lies its power. Without developing a treatise on the power of the unknown, it is easy to imagine the unsettling effect it had on players – the content unknown – that seemed to throw them. 

There was nothing that could be written on it that Lehmann couldn’t have remembered from pre-match analysis, or that a player or coaching staff couldn’t have jogged his memory with. Having this knowledge embodied as a talismanic parchment, a lightning rod for all the opponent’s doubt and fear and later controversy, was powerful.

Its content clearly the distilled knowledge of every penalty ever, of who will kick it next and where it’ll go – it’s the most extreme cases that our mind reaches out for in the fog of the unknown. The opponents were baffled. Of course, it wasn’t anything of the sort. It was just a rushed note, barely legible, scribbled onto a page from one of those free writing pads found in hotels.

Juan Román Riquelme had a theory about it: “There wasn’t anything on it. It was all about delaying the kicks that bit longer and making our penalty-takers think he knew where they were going to shoot. He was very sharp in the way he tried to put our players off.” Considering the Germans ended up 4-2 victors, the medium was most definitely the message for him.

Lehmann had, in fact, taken notes that morning, writing down the names of seven players – only two of those actually took penalties – and the direction he thought they’d go. It worked. He saved Roberto Ayala’s penalty and guessed the correct way for Maxi Rodríguez’s too. But what was most beneficial here? The analysis that led to his decisions or the effect the note had on his opponents? Maybe Riquelme actually got closer to the truth of the note than the truth itself.

Louis van Gaal is a pioneer. His groundbreaking tactics are one of the major signs on Dutch football’s innovative roadmap. Unsurprisingly, he knew how to make big calls in big moments, such is his legendary self-belief. Few moments came in more important than the 2014 World Cup shootout his Netherlands side went into against Costa Rica. 

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With a semi-final place at stake, the goalless match seemed destined to end in an upset for the Netherlands. Costa Rica won their difficult group featuring England, Uruguay and Italy before beating Mexico, whilst the Netherlands, try as they might, seemed unlucky and unable to score against the in-form Keylor Navas. Facing him in penalties wasn’t a prospect many would revere in the wake of his performance during the 120 minutes.

Opting for a last-minute sleight-of-hand, Van Gaal, in the 120th minute, substituted goalkeeper Jasper Cillessen for Newcastle’s Tim Krul. Krul, having faced down 20 penalties in the Premier League, had saved only two. What was the ‘Iron Tulip’ thinking? 

Gary Lineker said the Dutchman would “live or die” by his decision. He wasn’t wrong. Krul pulled out all of the stops. He approached every single Costa Rica player in a reasonably aggressive manner to a chorus of boos from the Costa Rican fans. The Dutch giant bounced on the line and reached up for the crossbar. After saving the second and fourth effort from Costa Rica, he wheeled away in the sheer jubilation of victory as the most hated and loved man in that stadium. Penalties always feel cruel for one side. Both sides felt Krul this time. 

Clearly Van Gaal had accounted for this possibility. Krul guessed the correct side for each penalty taken, indicating the research that had gone into it. Still, though, Krul did all that he could to get under the player’s skin, his boorish behaviour in the box and choice words for the players – indicating to them that he knew exactly where they’d put the ball – seemed to psyche them out. The stakes couldn’t have been much higher and the psychological effect of disruption more clear. 

These goalkeepers, as a by-product of their accumulated success, also developed a rare psychological edge – that of reputation. Only a handful occupy a similar stratosphere to these men and with that comes an element of fear for potential adversaries. As with players who score, they become self-perpetuating myths. 

Knowing the amount of effort that goalkeepers and their teams dedicate to perfecting their particular skillset could easily skew how we understand the penalty, making us think it’s more equal than it is. That couldn’t be more wrong. Over three-quarters of the shots taken end up in the back of the net. So, the next question is: what defines a good penalty taker and how can they stay ahead of the rapid curve of goalkeeper improvement?

The Odds

Some penalty takers relish the opportunity, others not so much. Like goalkeepers, there are techniques to manage this, mantras to calm players, superstitions to follow. Keeping the fact that the odds are firmly stacked in the taker’s favour in mind is very important. Nobody would turn down a 75% chance at success. To score a single goal in football, a low-scoring game, is often the difference between winning and losing. But being the clear favourite also brings about pressure, which for some is too great.

Playing a game of odds, data analysis has been able to provide heat-maps denoting the success of a ball struck into a particular part of the goal. Although the type of shot – powerful or well-placed – and all the other factors that could influence how a penalty plays out, such as run-up, record, opponent or importance have been omitted, these maps give a rough guide as to where a potential goalscorer should aim.

A plethora of great penalty takers all, seemingly counterintuitively, put their shot in zones with average success. Where they derive their magic from is something subliminal and, like a goalkeepers intuition, tend to be something a player has or doesn’t have. For the vast majority that don’t, picking the right spot is important. Similar to the way we would approach buying stocks in a company, there is a risk-reward trade-off that a player must make in terms of where they place the ball. 

Most shots that hit the target along the top third of the goal will make it past the keeper. Whether that’s a scintillating swerver into the top corner or a lace-of-the-boot ball through the middle, aiming up is a high-risk, high-reward strategy for takers. 

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Due to the myriad of variables, particularly judging conversion rates for players who have taken say ten penalties as opposed to 25 – never mind in what league, against what goalkeeper and with what importance – it’s difficult to say for certain who the best is. There’s the tried and tested Roberto Lewandowski or the yet-to-miss Alfred Finnbogason. Both deserve a more comprehensive breakdown, but that’ll come after a player who few would argue with – Matthew Le Tissier. 

Upon retirement, the Southampton icon had taken 49 penalties for the side, netting 48 of them. That miss, coming against Nottingham Forest’s Mark Crossley, saw Le Tissier strike the ball fairly centrally, making for an easy save. There was no more drama to it than a poorly hit case of human error surfacing. It probably haunts him to this day, although vengeance didn’t take long. Later on in the same match, he beat the keeper with a spectacular long-range effort. How did the Guernsey-born attacking-midfielder develop such mastery from 12 yards out? Simple. He loved taking them and practised by betting against the youth goalkeepers. 

Le Tissier said of his methodology: “I would get one of the youth team goalkeepers at the club to go in goal and I’d offer them money for every one they could stop. I would take maybe ten penalties and offer a fiver or tenner for every penalty saved. That money was going to make a lot of difference to him, so he’d be trying his best. I didn’t want to give money away, so obviously it put pressure on myself to score, otherwise I’d be skint.”

He knew he was the penalty taker so practised them incessantly. In a distillation of Aristotle’s thoughts, Will Durant synthesised an otherwise verbose philosophical passage written by the Greek as, “We are what we repeatedly do. Excellence, then, is not an act, but a habit.”

It didn’t hurt that Le Tissier also relished the opportunity to take them and implement his tried-and-tested technique of hitting the ball with the inside of his foot to the goalkeeper’s left, always aiming a yard in from the post. Should things get a bit sticky, say the goalkeeper moved early, the penalty master always kept his body open enough to be able to whip the ball into the opposite corner as a plan-B.

Le Tissier’s idea was to approach the ball confident in your plan, regardless of intimidation from other players whilst remaining flexible, developing the ability to make a last-minute switch. The Southampton legend’s dichotomous approach – it’s either left or right – captures the essence of the penalty at its purest. As we saw earlier on, though, goalkeepers weren’t as adept at stopping them as they are now. For modern players facing modern goalkeepers, there’s a bit more to it.

Learning

If pressed on picking one man to take your penalty from today’s best, a great many football fans would probably pick Robert Lewandowski. There are players whose success percentage is higher – although not by much – but none who have yet managed to maintain a 90%+ scoring record on over 25+ penalties. Remember, this is against goalkeepers with the access to data that Le Tissier never had to face. 

For clarity, there are a few who are close. Sébastian Haller, Bas Dost, Harry Kane and Paulo Dybala are four such examples who are on their way to Lewandowski’s level, whereas a few nearing the end of their careers – Giampaolo Pazzini, Ryad Boudebouz, Luka Milivojević and Mark Noble – are not far off, although seem unlikely to pull even.

What marks Lewandowski’s 33 out of 36 (92%) penalty record aside, like Cristiano Ronaldo’s 82 of 98 (84%), is their sheer consistency. Many of these aforementioned players are lethal from the spot, someone you can really rely on to cash in on the opportunity, but over a period of time, when one miss can easily become two in a row, no one remains as proven in the game today.

Hearing a name like Lewandowski at the top would hardly be a surprise. He’s been a talismanic presence in the Bayern Munich squad for six years – a true striker with all of the physical and technical attributes to boot. Penalties, though, are a different domain. Torino’s Andrea Belotti or Juventus’ Gonzalo Higuaín share many of his attributes. Both can lead, both can score, yet those two rank amongst the poorest penalty takers in European football, netting with 65% accuracy and 70% respectively over 20 and 23 attempts.

“Everything is about mentality,” Lewandowski says. Again, this boils down to confidence. The Polish goal-machine often picks his side in the build-up to the penalty, partly due to what he’s seen of the keeper so far, but partly due to intuition. Other times, he’ll simply pick a side before the match and not change that because of how it feels. 

In an interview with Deutsche Welle, Lewandowski espouses the benefits of mental fortitude – to remain focused and calm in the face of overwhelming pressure. Even as the inner battle rages, the tumultuous ebb and flow of fight-or-flight, you must be perceived as in control through your external demeanour and body language. Don’t turn your back on the goalkeeper and don’t run at the ball as soon as the whistle blows.

Should a player commit either or both sins, the goalkeeper is better placed to phase them through intimidation. Then comes the run-up. Something Lewandowski and Cristiano Ronaldo have in common – as well as Max Kruse and Alfred Finnbogason who have yet to miss from the spot – is the staggered approach. Varying from stop-start to an uneven acceleration, this technique does two things to boost a taker’s chances.

Initially, it gives the player a split-second to analyse where the goalkeeper looks like moving to. Whether it’s the lean of his trunk or a raised heel, a perceptive eye will pick up on this and inform the taker’s decision. Like Le Tissier, these players are adept at last-minute changes. Secondly, it’s a smoke-and-mirror, sort of like how a goalkeeper moves on the line. Hoping that the goalkeeper will be blatant enough is the hope, but if that doesn’t work, the run-up could provoke enough confusion for the goalkeeper to question his own commitment. It’s a marginal gain, but one that many of the best taker’s capitalise on.

This might well be Lewandowski’s way of doing it, or Ronaldo’s – motions and approaches fairly unique to them – but there are certain rules, as governed by statistics, that should influence what a taker does. Most importantly, it was the aforementioned approach of hitting the ball high into the top third of the net. Then there’s the question of left or right. Or, even better, natural versus unnatural.

A taker is more likely to score by hitting the ball to their natural side, like Le Tissier said, which means a right-footed player directs the ball to the left side of the goal, with the inverse being the case for left-footed players. Directing the ball to your natural side gives you a favourable outcome of 77% success as opposed to 70% on your unnatural side. Hitting the ball down the middle, although appearing riskier, still trumps either side. 

These numbers, unearthed through vast quantitative research, neglect more subtle factors such as the strength of the keeper’s hand (right versus left). Prior knowledge of this can give you vastly improved odds on a more immediate scale, especially if you’re as comfortable hitting the ball into either side of the net. 

When the goalkeeper correctly picks the side, 70% of penalties are still successful when shot to his weaker side, which for a right-handed goalkeeper is the right side of the goal from the penalty-taker’s perspective. Just over half, at 55.2%, will find the net if the goalkeeper guesses correctly and onto his strong hand – the left side of the goal from the taker’s perspective. 

This isn’t good for right-footed takers facing a right-handed goalkeeper (the majority). At higher levels, against the very best goalkeepers who are more likely to move to the correct side, almost all advantage is lost for the taker if they pick their natural side and the keeper his strong side. 

Some clubs at lower levels won’t have the resources to find this out beforehand. Don’t worry. You can safely assume them to be right-handed, alongside the other 90% of the world. Even with all this access to data, some of the best players in the world still struggle with penalties.

Lyon’s Memphis Depay is best known for the penalties he does score. They’re the kind of penalties you try against your mates in the park and bring it up every few months thereafter. The Panenka, named after the Czech player Antonín Panenka, is the epitome of the flair penalty. A slow run-up followed by a cheeky chip over the keeper who watches the ball float over him. Pure salt in wounds stuff. 

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Panenka’s unique style came to the world after his successful execution won Euro 76 for the Czech Republic. It was pure romance, pure poetry and a purely mental thing to try. That’s why, in his wake, so many great players have failed. Depay is an exciting player, explosive and tricky with an exuberant personality that manifests in his penalties. When they go in they go viral, but that doesn’t happen much. His record of 8 out of 14, only 57% success, is one of Europe’s worst and a case study of why a penalty must be taken seriously.

Not that all his penalties are Panenkas, yet his misses lack any consistency in approach and execution, seeming more prone to emotion and his eccentric personality. They seem to want that viral video just as much as the goal. Depay isn’t bad at all set-pieces, though. With a fantastic free-kick record as a young player at PSV, he’s gone on to score many more memorable long-distance efforts. So too have Dimitri Payet, Paul Pogba, Yohan Cabaye and Antoine Griezmann. Those four are also amongst the statistically worst penalty takers in Europe.

Don’t worry if your favourite free-kick taker steps up to take a penalty – there’s nothing to say that being good at one makes you poor at the other. What it does confirm is that the two are very different art forms. In what is a sort of set-piece paradox, it only contributes to the allure of how to perfect the art of the penalty, a metric that mathematics has tried to help with.

Maths

Because of the many variables, penalty kicks in football have become the fascinating subject of academic study into game theory. Game theory is the mathematically optimal way for agents in a game to rationally act. It considers that participants want to optimise their results and that the optimal decisions are dependent on the actions of the other participants. The result is that game theory maps complex human behaviour with the goal of understanding and predicting it.

What game theory in football has found, overwhelmingly, is that ‘pure’ strategy – whereby a player will always shoot towards their same preferred side – is not the optimum strategy, simply because goalkeepers would predict it. Adopting a ‘mixed’ strategy – picking different points in the goal – is the optimum.

This might sound straightforward, but it leads to a greater question: how can this be used to aid the success of a player or team’s efforts in penalties? Or the more bizarre question: are penalties, overall, slaves to the same rules as our economic system and our propensity to use nuclear arms?

In a penalty shootout, there’s one winner and one loser. The ball either goes in or doesn’t and, therefore, one team’s gain is another’s loss. This is a zero-sum-game. One theory that has been applied to penalty shootouts is the Nash Equilibrium, created by the same John Nash that was played by Russell Crowe in 2001 film A Beautiful Mind. Nash’s theory was used in the Cold War standoff between the US and Soviet Russia – each side contemplating their own nuclear armament. Many say it helped save the world.

A proposed solution to a non-cooperative game, Nash’s Equilibrium has been extensively studied in penalty kicks, notably by Spanish economist and head of talent identification at Athletic Club, Ignacio Palacios-Huerta. Penalties, with taker and keeper employing mixed-strategy and each party depending on outwitting the other, actually follow Nash’s equilibrium, showing that the seemingly unpredictable is, over a period of time, actually very predictable. That’s not such a bad thing either.

Just like the game ‘rock, paper, scissors’, penalties should be approached using a mixed-strategy. Both ‘games’ have a lot in common. Palacios-Huerta didn’t go out looking to solve the riddle of the penalty, although he’s an avid football fan; rather he chose penalties as his way of illustrating the Nash equilibrium using natural data in a manner slightly more scientific than a playground game.

Limited to three movements, dive left, dive right or stay central, the goalkeeper is working within set parameters. Upon stepping up to take a penalty, the taker is aware of these three finite actions of the goalkeeper. Palacios-Huerta found that the ideal taker should take 61.5% of shots to their natural side and 38.5% to the other. In reality, players acted very close to this – around 60% in his findings. Goalkeepers should only optimally favour their strong-hand 58% of the time. In his studies, they did so 57.7% of the time. 

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Utilising game theory is about optimising, hence its popularity in market research and business. For penalties, Palacios-Huerta is clear that “the best approach is to vary your moves unpredictably and in such proportions that your probability of winning is the same for each move.” By analysing 9,017 penalties from various countries between 1995 and 2012, he found that 60% were shot to the right, 40% to the left, and that this is balanced as players are more likely to take advantage of their strong leg (most commonly right).

Palacios-Huerta’s study confirmed that, “In accordance with Mr. Nash’s theory, penalty kicks shot to the left were successful with the same frequency as kicks shot to the right – roughly 80 percent of the time.” Although game theory doesn’t tell players which direction to shoot, it highlights the strength of unpredictability in the penalty format, with emphasis on each penalty being uninformed by the choice of sides from the last. Besides his position in Bilbao, he has also advised Chelsea, Portsmouth, Barcelona and both the England and Netherlands national teams. 

But do teams gain from taking his advice? Chelsea followed his analysis to a tee in the 2008 Champions League final – except for Nicolas Anelka, whose defiance cost them the trophy.

Using game theory has its limits, as it requires that both players execution be flawless, something that can rarely be applied to humans like it can in the machinations of economic practice and biological modelling. Football at the most elite level, when it comes down to a single action like a penalty, is proven by game theory as not being too far off perfect.

Looking through the lens of game theory also magnifies the brilliance of players who consistently statistically over-perform. As Stefan Szymanski and Simon Kuper wrote in Soccernomics, “Nobody is suggesting that footballers have sat at home mugging up on mixed-strategy equilibria. Rather, the best players intuitively grasp the truth of the theory and are able to execute it.” So, all in all – what’s the best strategy?

Optimal Strategy

Overcoming the baseline statistics to be a good penalty taker or stopper means to be consistent. Consistency, if we’re to take advice from the best, comes mainly down to psychology. This could be said about a lot of football, but the fewer number of variables in a penalty increases the significance of individual factors like confidence, decision-making, pre-kick psychology and. for goalkeepers, disruption.

Some strategies do work, but not in a one-size-fits-all way. If you’re the taker, give precedence to your natural side, but with enough confidence in switching to the weaker side should a goalkeeper move prematurely or make a clear tell as to which direction they’ll dive. That, or, focus on hitting the ball to the goalkeeper’s weak side.

Goalkeepers seem to derive even more from the psychological battle and subtle forms of improvement, which is probably why more and more penalties are being saved. The taker needs fortitude and confidence, but the goalkeeper can draw from an arsenal of distraction techniques to psyche out the taker. At the end of the day, the taker is making the choice; the goalkeeper is responding to it. If the goalkeeper can do something to decipher the taker’s intentions, then he stands a good chance of stopping the goal.

As with game theory’s analysis of economics and the stock market – well-oiled machines – the penalty has methods, tricks and tips to improve success. But like markets and economies that (should) act rationally, penalties are fallible, imperfect humans facing off against each other. Therefore, it’s not the system a participant is trying to hack, but what goes on in their own mind and, if they can figure it out, the opponent’s. Due to the taker’s process being slightly more prone to error (mishitting a shot), goalkeepers are becoming the new guardians of the domain, making the most of every factor they can.

A penalty, especially as a part of a knockout-clinching shootout, is crucial. So many have gone down in history for the right or wrong reasons. They’re nerve-wracking displays that we, like players, both love and hate. Still, it’s something that goalkeepers are getting better at stopping, so players need to adjust accordingly. That, or they begin to petition for the return of the golden goal

By Edd Norval @EddNorval

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