It was only Muhamed Besic’s third start of the season but if he was anxious he hid it well. Standing in the tunnel before the Capital One Cup semi-final first leg against Manchester City, he yawned. He went on to produce his best performance in an Everton shirt, a cultured scrapper buzzing around the more sedentary solidity of Gareth Barry.

It is easy to be carried along by Roberto Martínez’s ebullience – although not so easy as not to raise an eyebrow when he describes Barry as one the great players in English history – but the match provided much for Everton fans to be optimistic about, and nothing more than Besic’s performance.

Among Everton players, only Barry touched the ball more than the 23-year-old. Most impressive, perhaps, was his calmness in the closing minutes as Everton, particularly after being reduced to 10 men by the late injury to Seamus Coleman, denied City the ball by keeping possession. The Goodison Park crowd, as it showed in its reaction to John Stones’s Cruyff turns against Tottenham in the previous game on Sunday, has little patience for overindulgence, but Besic, forever delaying a pass until a gap appeared, won applause. It was an odd 10 minutes against a City side producing yet another slightly lackadaisical performance but Besic’s movement and use of the ball in that spell spoke of a profound footballing intelligence.

The passing, though, was only part of it. Besic also made six tackles – five more than anyone else who started the game for Everton – and an interception. He was aggressive and mobile. All but one of his tackles were made in a line about 30 yards from his own goal, while his passing was spread across the pitch but particularly towards the right, where he linked up with Gerard Deulofeu.

Besic started the 3-1 win over Chelsea in September but was forced off after nine minutes with a hamstring injury. He had made only two substitute appearances before his start on Wednesday, although the second of those had been highly encouraging. It had arguably been his introduction in Sunday’s 1-1 draw with Tottenham that turned the match Everton’s way in the second half. After that game Martínez described him as “a contagious footballer” and it was notable he was the first to approach Stones as the crowd barracked him after his Cruyff turns. He is certainly not shy.

Nor is he, it is fair to say, an easy character. When he was 14 he was banned by the youth side for which he played in Berlin, shrugged and told his father that it didn’t matter, he’d still become the best player in the world. Or at least that is how the story goes: it has been repeated so frequently in the Bosnian media it has become gospel, although it is not entirely clear either which team he was playing for at the time or the precise reason for being banned. It may be it is an anecdote longer on emotional truth than facts: this is the type of thing a 14-year-old Besic should have done.

In 2012, by which time he had joined Hamburg, Besic rowed on the pitch with his coach Thorsten Fink, who ended up grabbing him by the throat. Besic left for Ferencvaros soon afterwards. Then in September last year he was sent off in Bosnia’s World Cup qualifying win over Andorra, having reacted to a heavy challenge by throwing his chewing gum into the face of an opponent (although not, as it turned out, the one who had fouled him).

Born in Berlin of Bosnian parents, Besic was a surprise selection for Bosnia’s opening game of the 2014 World Cup, in which they lost 2-1 to Argentina. His performance then meant he went overnight in Bosnia from being almost unknown to being hailed as the future of their football, while anybody who heard Martínez’s punditry on the game would have been aware how highly he rated the midfielder. He signed him later in the summer for £4m.

“Mo has got a very natural balance about knowing that he can be strong and aggressive but in the same way he’s a technical player on the ball,” Martínez said after Besic’s first friendly for Everton. “He’ll have that power to cope with the physicality of the league but also he has the comfort on the ball – in his long pass and short pass.”

It is that range of abilities, the combination of ball-playing and ball-winning that so stood out against City. One full game and a substitute appearance represent limited evidence but the signs are extremely positive. Besic probably won’t fulfil the boast he supposedly made at 14 but he could turn out to be an extremely valuable player for Everton – and then there is a decent chance his manager at least will describe him as the best player in the world.