Roberto Martínez still lives on the outskirts of Wigan, his dormitory village on the edge of the Lancashire plain proving as convenient a base for managing Belgium as it was for his previous jobs at Wigan Athletic and Everton.

It is already becoming easy to forget that the man who sent Brazil home early from Russia was practically run out of town while in his last Premier League post; certainly by the end of the 2015-16 season there were not too many Everton supporters sorry to see him go. It is quite a neat trick using a World Cup to reinvent yourself without actually changing very much, though that is exactly what Gareth Southgate has also managed to do with England.

Should Belgium and England end up facing each other on Sunday, an almost laughable prospect when the tournament started but a very real possibility now, the similarities between the managers will be difficult to ignore. Both were in charge of teams relegated from the Premier League for a start, which whatever his other faults was not a charge that could be levelled at Sam Allardyce.

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Martínez will always have that rather splendid FA Cup final win of 2013 with Wigan on his CV, though he and Southgate seemed to have their managerial limitations exposed when tasked with taking Everton and Middlesbrough forward. Southgate claims his best work was done at Boro, Martínez can look back at one encouraging season after promising to take Everton into the Champions League, but the inescapable reality is that no Premier League club was beating a path to either manager’s door once they became available.

Both in slightly different ways were considered too open and naive for the sharp-elbowed Premier League. Martínez because he placed too much emphasis on possession and paid too little attention to defence, Southgate because no one could imagine him raising his voice in the dressing room or resorting to scrapping tactics when the need arose.

Those perceptions have changed now the pair have reached the World Cup semi-finals, yet the managers in question have stayed the same. Southgate is being lauded for the very politeness and honesty that seemed to undermine him at club level – people are even saying his guileless decent-bloke persona would make a refreshing change to the political landscape – while Martínez has found himself in charge of some of the best attacking players on the planet.

A suspicion of defensive frailty remains – not too many teams in the knockout stage would have found themselves having to come back from two goals down against Japan – though Martínez does not appear too worried about it. What do you do when you are blessed with attacking players of the quality of Eden Hazard, Kevin De Bruyne and Romelu Lukaku? Appoint Thierry Henry as your assistant of course.

So have Bob and Gary just got lucky, or does international football suit some managers in a way club football does not? A bit of both is the probable answer. Anyone in the world would consider themselves lucky to be in charge of the present England and Belgium squads.

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Southgate might have been promoted by default but he found it easy to make a natural break with the past and let some emerging young talent come through. Belgium have had a winning team on paper for some years and Martínez was by no means an obvious candidate for the opportunity to release that potential on the pitch but even those who still choose to regard him as a smooth-talking chancer will have to admit that putting out Brazil represents significant improvement.

It may well be the case also that tournament football, because it is intense and short term, suits some managers better than the season-long slog at club level. At national level a manager does not have the responsibility of sourcing players or spending the club’s money either, and anyone familiar with Martínez’s wildly inconsistent forays into the transfer market will understand that is sometimes a relief.

Yet though it might be true Southgate and Martínez are managing to make the most of promising situations, like Chris Coleman harnessing team spirit and riding a wave of national fervour with Wales at Euro 2016, it should not be assumed their success shows anyone can do it.

Southgate in particular has changed the way England play. It was his preference to select Harry Maguire, play with a back three and move Kyle Walker in from full-back, and all three bold decisions have been vindicated. Jesse Lingard might not even have made some managers’ squads, yet Southgate has turned him into a key member of the team. Southgate stood behind Jordan Pickford when the goalkeeper drew some criticism in the group stage and it is fair to say that call also went well.

Martínez managed to think on his feet when Belgium went behind against Japan, something he did not always seem capable of doing at club level, and effectively turned the game with the introduction of Marouane Fellaini and Nacer Chadli. That reconstructed midfield remained in place for the Brazil game, where Martínez also deserved credit for devising a shape to bring the best out of his three most potent attackers. He played Lukaku and Hazard up front but not central, with De Bruyne allowed to come through the middle as the forward tip of a midfield diamond. Lukaku’s strength and De Bruyne’s deadly finishing were both seen to good effect in Belgium’s second goal against Brazil, as classically executed a counterattack as you will see at this tournament.

How the story ends remains to be seen, though it will end, in just less than a week. By that time either Bob or Gary could be striding the world like a colossus, installed as national manager on a more or less permanent basis like Joachim Löw, or they could be tormenting themselves by recalling what happened to Coleman after Wales, when he was obliged to try to prove himself all over again at Sunderland.

Right now, however, club football and relegation concerns must seem a world away. Reaching a World Cup semi-final is already an outstanding achievement but there could be so much more to come.