As Stephen Hawking arrived on stage in the basement of the Savoy Hotel in London, Peter Crouch robot-danced on the screen behind, Chris Waddle skied a penalty, and a Prodigy soundtrack thundered a helpful reminder to the waiting journalists: "Exhale, exhale, exhale."

It was not an obvious environment for the Cambridge cosmologist, who as former Lucasian professor of mathematics held the position once occupied by Sir Isaac Newton. Hawking, a Fellow of the Royal Society, was here to tout some formulae he had drawn up for a bookmaker on England's chances of success at the World Cup in Brazil. If it were anyone else, the room probably would have been empty.

Hawking was approached on the understanding that a theoretical physicist might be marginally better qualified to make predictions than Paul the Octopus, the eight-armed oracle that rose to fame by correctly selecting all the winners through its eating habits during the 2010 World Cup. The German cephalopod died three months after the final whistle.

"Ever since the dawn of civilisation, people have not been content to see events as unconnected and inexplicable," Hawking began, before launching into his results. "They have craved understanding of the underlying order in the world. The World Cup is no different."

One aspect of England's scratchy record in World Cup penalty shoot-outs since they won the trophy in 1966 perhaps doesn't require a knowledge of high-level mathematics. "As we say in science," Hawking put it, "England couldn't hit a cow's arse with a banjo."

Scientists have a long, inglorious history of churning out often meaningless equations for sponsors. There are formulae for cups of tea, strawberries and cream, and the most depressing day of the year. All are commissioned by companies as PR stunts and their value ends there. They are overwhelmingly drawn up byscientists whose names are unknown to any Nobel committee.

Hawking, who may yet win a Nobel prize for noticing that black holes can evaporate, was asked by the Irish bookmaker, Paddy Power, to spend a month looking at England's World Cup performances and draw some conclusions. The company's spokesman, who happens to be named Paddy Power, said he had not expected the world-renowned scientist to agree. "We thought there was a 1% chance he'd say yes. But he did. I was totally surprised," said Power.

To work out the conditions that suited England's football players best, Hawking (or perhaps his students) analysed 45 World Cup matches the team had played since their last tournament win in 1966. They also analysed 204 penalties taken in penalty shoot-outs, a particular weakness for England.

Hawking said the factors affecting England's performance – though surely this applies to any team – can be broken down into five areas: environmental, physiological, psychological, political and tactical.

The team fared better when playing in stadiums less than 500 metres above sea level, the scientist said. Temperate climates helped too, with a five degree Celsius temperature rise more than halving England's win rate. "The game in Belo Horizonte against Costa Rica is the best of a bad bunch, with England's opener in Manaus against Italy the most difficult. The searing temperature and late kick-off are far from ideal," Hawking said.

On the psychological front, England have a better record wearing red than white shirts, perhaps because red can make players feel more confident and appear more aggressive, Hawking added. England normally play a 4-4-2 formation, but 4-3-3 has been slightly more successful in the past, with 58% of matches won. Under 4-4-2 England won 48% of matches.

England have taken part in three World Cup penalty shoot-outs since they were introduced in 1978, and lost every time. Hawking's tips for success may not be news to the England players. Placing the ball in the top left or top right corner of the net – more easily done with the side of the foot – is a winning strategy. But speed plays its part: "Get a runup of more than three steps. Give it some welly," the Professor added.

Neither the age of players, nor whether they were left or right-footed, seemed to make much difference. "But bald players and fair-haired players are more likely to score. The reason for this is unclear. This will remain one of science's great mysteries," Hawking said.

The scientist's report brings the statistics together into two multi-term equations intended to predict the team's future success, but from the start, Hawking sets the tone for how the work might be regarded. Opening the report, he writes: "It is widely accepted in the field, that a key factor of achieving World Cup champions status is winning matches."

He concluded that England need to wear red, play 4-3-3, kick off in the afternoon and avoid referees from South America to best succeed in Brazil

Power refused to divulge how much the bookmakers had paid Hawking, but the scientist said he split the fee between two charities, one devoted to saving children in Syria, and the other to motor neurone disease, the condition Hawking was diagnosed with as a student.

Jim Al-Khalili, a physicist at Surrey University, said the statistics were fun but he considered Hawking's equations "meaningless". He took particular issue with the formula for the perfect penalty.

"This is utterly pointless of course. As someone who played football several times a week, all year round, every year between the ages of 10 and 30 and who has stacked up hundreds of hours of penalty-taking practice, I can speak with some authority, if not international quality skill."

Penalty shots depended on natural ability, practice and psychology, Al-Khalili said. "It is the third of these that the England team has suffered a lack of over the years. Any professional footballer should be able to score from the penalty spot every time, but they don't when under pressure. England players have been psychologically less able to cope with this when compared with their German counterparts.

"None of these factors can be captured in an equation, even a computer code of the size of the most sophisticated climate models would fail to capture these factors with any level of reliability."

Hawking confessed he did not bet on sport and was not a fan of football. "Shouting at the television is not for me, but each to his own," he said. Pushed to name a favourite, he noted the home advantage for Brazil. "I'm sure they have enough quality to lift the World Cup for the sixth time," he said.