The science of football

The Beckhams' bash is over, Wayne's on the mend, and Sven's master plan is taking shape (we hope). But with only two and a half weeks to go until the World Cup, have the England team really grasped the football fundamentals? What do they know of free-kick trajectories, of passing permutations, of angular velocity? The game may be an art, but it's also a science - and as Ken Bray explains, every dug-out needs an Einstein

1. Fitness: the key ingredient

Ask any coach at the World Cup for the most important attribute of his team, and you'll get the answer "fitness". Technique is worthless if players can't sustain 90 minutes of hard competition or if they fade completely in extra time.

Not surprisingly, energy consumption is closely related to how far players run in a match, but for many years, this figure was a matter of guesswork. It took the precise measurements of two scientists, Thomas Reilly and Vaughan Thomas of Liverpool Polytechnic (now Liverpool John Moores University), to provide the answer in 1976. Midfielders worked hardest, covering 9.8km during a match. Strikers and full backs came next (8.4km and 8.2km), then central defenders at 7.8km. Even the goalkeeper managed 4km.

In today's high-tempo game these distances have increased by 30 per cent, as the graphic below shows, and midfielders such as Steven Gerrard and Frank Lampard will run distances approaching 13km over 90 minutes.

Studies of players' movement profiles are also revealing. In the average game, players execute more than 1,000 sequences such as sprints, tackles, headers, throws, rests etc. Switches in movements occur every five to six seconds, and sprints are made every 90 seconds. Players rest, on average, for three seconds every two minutes, but most surprising of all, only 2 per cent of the distance players run in a match involves contact with the ball. Football is a game played largely off the ball, which is why television, with its restricted camera perspectives, often gives a false impression of the play.

Research like this has had a profound effect on football physiology, and fitness training especially. The energy cost of 90 minutes of football amounts to about 66 per cent of the daily calorific intake of the average male. Carbohydrates in the diet (pasta, potatoes, bread) produce glycogen, the fuel that drives this prodigious effort. This is "burned" in combination with the oxygen we breathe and transmitted in the bloodstream to the active muscle groups. For footballers, glycogen replenishment is vital as reserves in the liver and muscles are often almost completely drained after a game. The body's potential for glycogen uptake peaks in the first few hours after hard exercise, which is why carbohydrate drinks are so popular. But a balanced diet is the key and if players follow nutritionists' advice, complete recovery is possible in 24 hours.

Conditions will be perfect in Germany this summer; no altitude problems as in Mexico in 1970 and 1986, nor the humidity of the 2002 tournament in Korea and Japan. But fitness will still be the priority as the competition unwinds, with fast recovery after hard games assured by good diet coupled with the careful resting and rotation of players in the squad.

2. Up for the game: mental toughness

No demanding physical task can be accomplished without a corresponding level of physiological and metal alertness, a state known as "arousal" in the psychology of sport. Playing performance and arousal are closely related and, generally, performance improves as arousal increases. This graphic shows, however, that a point is reached at which performance peaks and then begins to decline. Why this happens is not difficult to explain. The highest technical skills in football demand great precision; forcing the skill introduces errors, and the harder players push things, the more likely they are to fail. Sometimes this failure is catastrophic. Instead of declining steadily, performance crash-dives when athletes appreciate the enormity of the task and their inability to generate output at the required level. Something of this kind occurred to Paula Radcliffe when she broke down in Athens in the 2004 Olympic Marathon.

So getting to the performance peak is important, but the problem for coaches is that players differ; some, the most anxious, reach peak arousal quickly, whereas others require more motivation. Keeping arousal at the optimum level can also be a problem as the game ebbs and flows, and is especially important for psychologically intimidating events such as the penalty shoot-out. So how do players lift themselves and what techniques do they use to suppress anxiety and restore focus during the game's critical events?

Various forms of calming techniques are available, ranging from controlled breathing to progressive muscle relaxation. These are especially good for so-called somatic anxiety (soma=the body) and help to reduce muscle tension, heart rate and rapid breathing. Its counterpart, cognitive anxiety, is associated with negative or threatening thoughts about impending competition and can be relieved by a powerful technique called "imagery". Many players prepare by running through a kind of "mental movie" where, because the images are divorced from actual competition, inadequacy or failure simply do not enter the equation.

To be effective, all of these remedies must be capable of quick application during the twists and turns of actual matches, so it is often the players themselves who must self-administer the remedy when concentration wavers.

Mental toughness is paramount; plenty of players at the World Cup will set out to destabilise opponents, from defenders who engage in petty, niggling fouls to provoke retaliations and sendings-off, to goalkeepers who psyche out attackers in penalty shoot-outs by outrageous (but perfectly legal) rubber-legged displays on the goal line.

3. All about the system: the great 4-4-2 question

Deciding which formation to play will not be a headache for Sven Goran Eriksson, who rarely departs from his favourite 4-4-2. More adventurous coaches such as José Mourinho of Chelsea relish the attacking flair of 4-3-3, whereas Bolton's Sam Allardyce favours (and claims to have invented) the more defensively-minded 4-5-1.

There are only two simple but very important criteria; the formation must be good at winning possession of the ball, and using it to score goals. Analysts divide the pitch into imaginary thirds along its length; the defending, middle and attacking thirds. Controlling the play is important in all zones, but especially in the attacking third. Research shows that in internationals only 13 per cent of the possession is won here, but this leads to 66 per cent of all goals.

Passing is the means by which possession is retained, so key questions are: 1) How many unique passes can a formation generate; and 2) How much of this possession is delivered to the attacking third?

The graphic shows two of the most popular systems played in today's game, 4-4-2 and 4-3-3. How many unique passes are there in each? To log them, we record how many team-mates there are within a specific radius of the player passing the ball. Passes above 40 metres (44 yards) have been excluded.

The 4-4-2 formation has 66 possible passing combinations, compared with 56 in a 4-3-3. These are not the total number of passes in a game; that often exceeds 650 per side. The sequences are repeatedly cycled, some forwards, some backwards, some involving exchanges between midfielders, strikers or defenders themselves. The interesting point is that 4-4-2 (66) is the richest in terms of passing options (and hence in terms of retaining possession) for the popular formations. It can be compared with 4-2-4 (54), 4-3-3 (56) and 4-5-1 (62).

What about attacking potential? The amount of possession in percentage terms that each formation delivers into the attacking third is easily determined: 4-2-4, 15 per cent; 4-3-3, 13 per cent; 4-4-2, 12 per cent; and 4-5-1, 8 per cent. This time, 4-2-4 comes out on top, but few teams risk this today because two midfielders are easily swamped in the modern game.

Eriksson's favourite, 4-4-2, is deservedly popular; good possession, attacking potential. But the ability to switch play as the game evolves is what often decides the result; in 2002, England failed to capitalise when Ronaldinho was sent off and they could make no impact against Brazil's 10 men when the game was there for the taking.

4. Set pieces: the game within the game

Set pieces - throw-ins, corners, free kicks and penalties - are a prolific source of goals in international football matches, and are frequently the deciding factor in closely contested games.

The free kick, the most spectacular of all, relies for its outcome on subtle aerodynamic effects, but it is the beauty of the spectacle that attracts even the most casual supporter. Expectations have been raised to unrealistic levels. A free kick or a penalty; what's the difference when elite players can do such magical things with the ball?

At the heart of every successful free kick is spin. Artists such as Thierry Henry strike the ball so that it spins about a vertical axis. Aerodynamic forces push the ball sideways; for a ball spinning anticlockwise, the movement will be right to left. Most elite free-kickers use sidespin but a few, like David Beckham, manage to inject a little topspin. When this happens, the aerodynamic force has a downward component, so the ball both swerves and dips. To achieve this, it must be struck with the foot ascending, a little like a racket in a topspin drive in tennis. This is very difficult to do with a ball on the ground.

If the striker gets it all right, a swerving free kick is virtually unstoppable. That's the catch: speed (60-70mph), spin (5-10 revolutions per second) and elevation (16-17 degrees) must all be precise. The ball then takes only nine-tenths of a second (900 milliseconds) to reach the net, but it's a split second packed with incident.

As the graphic shows, spin and velocity - in fact, everything that will decide the outcome - are determined by just 15 milliseconds of boot-on-ball contact. With attackers in the wall blocking the goalkeeper's view, the first he sees of the shot is 400 milliseconds later when the ball pops up over their heads. He can do nothing, however, until his brain processes the information during 200 milliseconds of reaction time. With 300 milliseconds of the drama left to play, the goalkeeper is only just beginning to move. This is not sufficient time to get across the goal for a well-hit shot. About 10 per cent of free kicks succeed in the English Premiership, rising to 15 per cent in international matches where elite players are involved.

England need an in-form Beckham and his dead-ball artistry, but he must learn restraint and leave some of the more routine deliveries to team-mates such as Gerrard and Lampard.

5. Crunch time: winning the penalty shoot-out

If free kicks are a good way to resolve close matches, penalties are the gold standard. The conversion rate for penalties in normal time is 80 per cent. This falls to 75 per cent in a shoot-out, as goalkeepers become better at anticipating the strikers' intentions. These are the kind of odds you'd bet your mortgage on. So why do strikers miss? And why do England fail so abjectly in shoot-outs?

Hitting a perfect penalty is not difficult. Research has shown that even the best keepers cannot cover every inch of the goal. However well they dive, there's an "unsaveable zone" that they cannot reach, as this graphic shows.

This is a very attractive target, 28 per cent of the goal area and easily within the capability of a professional footballer. The ball should be confidently struck into this zone - "place with pace". Full-blooded instep kicks are unnecessary; recall Chris Waddle's thundering miss against West Germany in 1990 and David Beckham's sky-er against Portugal in 2004. Again, the arithmetic is comforting. A ball hit at 60mph will take just over four-tenths of a second to reach the goal, and if it is well placed it will nestle in the net before the goalkeeper has completed his dive.

Notice what looks like an attractive target close to either post at ground level. Strikers should avoid these; goalkeepers are now adept at getting down quickly, and more penalties are being saved when they are hit low. Shots at about shoulder height invariably succeed if they are well directed.

The key to winning shoot-outs is practice. Coaches should know their players' penalty success rates. Penalties should be rehearsed, preferably after hard training to replicate the conditions. When players are selected for the shoot-out list, they should be ranked from weakest to strongest and shots taken in this order; research has shown this can increase the chances of winning considerably.

England are quite capable of going all the way this time, with world-class players and strength in depth. It would be good to see the demons of Germany, Argentina and Portugal exorcised in at least one penalty shoot-out success on the way to the final. What a psychological boost that would be for the team and supporters.

6. Did it cross the line? Technology's answer

So the team is fit, mentally tough and has the perfect formation. David Beckham is ready to take the free kicks, and the squad has rehearsed its penalties. What can go wrong? Sadly, a great deal. World Cups have been marred by inconsistent refereeing and gamesmanship. Then there is the current offside rule, so complex that coherent decisions are almost impossible.

One area of potential controversy could have been eliminated - the "disputed goal", where the ball crosses the goal line but returns into play. The problem for officials is the speed at which this happens; the ball can be in and out of the net in only 18 milliseconds.

The most famous disputed goal was Geoff Hurst's of 1966 (see below), but four decades later we are no better placed to resolve incidents of this kind. The solution was meant to be the "smart ball" carrying a microchip that transmits the ball's position continuously. A computer compares the ball's location with the known co-ordinates of the goal line, posts and bar, so deciding whether the ball is over the line is easy.

The technology, developed by a German consortium including the ball maker Adidas, was tested at the World Under-17 championships in Peru in September 2005. No detailed results of the trials have been published and,Fifa says, further testing is needed. Football history has a knack of repeating itself, and a high-profile goal-line incident is overdue.

Ken Bray's 'How to Score: Science and the Beautiful Game' is published by Granta, £10.99