In the minds of those who watched them win the 1970 World Cup, Mário Zagallo’s Brazil still represents the fulfilment of all the seldom-kept promises of international football. The mere mention of their star players – Pelé, Jairzinho, Roberto Rivelino, Carlos Alberto – conjures images of suave magic under the Mexican sun. But there was one player, a little less celebrated, without whom their triumph would have been much harder to achieve.

Eduardo Gonçalves de Andrade, known as Tostão, was a 23-year-old centre-forward who had appeared fleetingly in Brazil’s 1966 campaign in England while still a teenager. Four years later he arrived with Zagallo’s squad having just recovered from a serious operation on a detached retina.

Some observers were beguiled by the way he looked so little like a Brazilian footballer, or indeed any sort of professional footballer at all. Pale in complexion, his hair already receding, he stood no more than 5ft 7in and better resembled the doctor he would eventually become. His physical slightness turned out to be deceptive – he was as tough as he needed to be – and his play was fundamental to the collective freedom with which the team attacked their opponents. Functioning as a false 9, he floated around the more charismatic presence of Pelé, finding space and linking play with uncanny perception.

It would certainly be useful if Sterling could end his England drought. But there is a more important job to be done.

He scored only two of Brazil’s 19 goals in their six matches, both of them in the 4-2 win over Peru in the quarter-finals, which might not seem much of a return for a centre-forward. But his assists came in profusion, never more spectacularly than in the group match against England, when he lost possession on the edge of the opposition’s penalty area, chased to regain it, exchanged passes with Paulo César, fended off Alan Ball, nutmegged Bobby Moore, hustled past Tommy Wright and then, counter-intuitively, turned back away from goal in order to spoon an exquisite ball to Pelé, who transfixed Brian Labone and drew Terry Cooper before sliding the ball sideways for the incoming Jairzinho to shoot home and decide the match.

It was Tostão’s deftness and vision that came to mind when a 5ft 7in forward swivelled on Jesse Lingard’s pass just outside the Panama area a fortnight ago and flicked a return at the most cunning of angles, inviting his teammate to score the third and most beautiful of England’s six goals. Raheem Sterling’s touch was instant and intuitive, his decision-making ego-free. It was exactly what Gareth Southgate had hoped for when he chose the Manchester City man as the key to unpicking defences.

Tostão’s importance to Brazil turned out to have nothing to do with his goalscoring ability, and neither does Sterling’s role in the England team. It would certainly be useful if the man who scored 23 goals for Manchester City last season could end an international drought stretching back to October 2015 – the emphasis placed on that barren spell clearly weighs on his mind whenever a chance to score presents itself – but there is a more important job to be done.

Tostão (left) and Pelé celebrate Brazil’s fourth goal in the 1970 World Cup semi-final. Photograph: Popperfoto/Getty Images

Southgate may well be the first England manager since Sir Alf Ramsey to decide on a system and then choose his players to fit the pattern. Others have struggled with fitting prominent figures into the starting lineup and allowed their presence to determine the tactical approach.

His modest coaching background has allowed him to develop his theory of the game away from the most intense public scrutiny. His early failure at Middlesbrough was followed by a period as the FA’s head of coaching and then as the manager of England Under-21s, where he could formulate his ideas and work on them with players amenable to tactical guidance.

He soon settled on his basic requirements. He needed a goalkeeper with accurate distribution. He looked for a back three capable of playing the ball between each other with confidence, sucking their opponents towards them before releasing the midfield, and willing to do that over and over again with great patience. He required wing-backs prepared to hold their stations, stretching the play laterally. He wanted responsibility in midfield and diligence and flexibility in the forward roles, including one player whose pace and nose for an opportunity would stretch the play vertically and keep the opposition on the back foot.

To achieve this he needed to be rigorous in his selection policy. Those who fitted the template were preferred over those with bigger reputations who had different skills or might feel they had earned the right to express themselves by straying from the prescribed pattern. And when he had the right player, he was prepared to defend him.

Southgate took big risks on Kyle Walker (out of position), John Stones (out of form) and Harry Maguire (low on experience) because he believed in their ability to do exactly what he wanted. The same is true of Sterling, who may not be a Tostão in terms of footballing refinement but whose personal repertoire of finding positions at speed, of occupying defenders and of smuggling the ball to a teammate makes him a vital cog in the machine, even when not everything into which he puts his unflagging energy comes off as he would wish.

The players can see for themselves Southgate’s approach is working, which helps to explain the healthy absence of moans leaked via the agents of those omitted from the starting lineup. Like Clive Woodward in 2003, the manager has convinced every member of the squad by word and deed that they have an important part to play. He has no time to waste changing the minds of those back home who fail to see the point of Raheem Sterling.