One of Alexis Sánchez's school teachers in the small town of Tocopilla, in the dry and dusty north of Chile, recalls the time she asked the children to bring in pictures of their heroes in homemade frames. The kids were young and there were cartoon characters among the photos. Winnie the Pooh was there, Mickey Mouse too. Sánchez brought a picture of himself.

No one would ever describe Sánchez as cocky, but self-belief has been a vital part of his armoury. Tocopilla, population 24,000, nicknamed Devil's Corner, has declined since industry departedbut the pollution has been slower to head out with it. "Don't worry," he would tell his mum, a cleaner who in the summer travelled over 50 miles a day to sell fish, "I'm going to be a footballer." His father had departed, hardly known by his son, and as for Sánchez, he washed cars at the gates of the cemetery.

Nicknamed Ardilla, meaning Squirrel, he was the quickest up trees to recover the ball. Had Sánchez not been a footballer, he might still be there. But he is a footballer and he always was, playing barefooted in rough, uneven streets in his town. He never gave the ball to anyone but he promised, one day, to give them more than that. "I'll buy you a house and you a car," he would tell his friends.

He did not do that exactly, but he did pay for football pitches to be built in the town and every time he returns he brings boots and balls. Thus the favour is returned: the first boots Sánchez owned were given to him by the town's mayor, a football fan who could not help but be drawn to this kid just like everyone else. Undernourished, skinny still, not the powerful athlete he is now, but quick, electric in his movement, different.

Sánchez recalled that pair of Reeboks in an interview with El País: "I was like a dog with two tails," he said.

At 10, Sánchez had been to Rancagua to one of the academies run by Santiago side Universidad Católica, but soon returned home. Not for long. At 16, he made his first division debut with nearby Cobreloa and he was 17 when Udinese signed him, twice loaning him to Colo-Colo, back in Santiago. Buenos Aires was another loan stop, with River Plate, where he won the clausura, and then after three years as a regular at Udinese he signed for Barcelona for an initial €26m, rising a further €11.5m, in 2011.

By then he was already the Niño Maravilla, the boy wonder; central to the national team under Marcelo Bielsa and named the Italian league's best player. He had scored 12 and provided 11 assists in his final season there. But when he declared himself a jugadorazo, a great player, in March 2013 during his second season in Catalonia, what he had said was taken down and used against him.

The jugadoraso, written with an 's' to reflect an accent which team-mates admitted they could rarely understand, almost became a sniggering nickname.

His first season, aged 22, had been reasonable. He scored 12 goals in 25 league games and 15 in 31 starts overall, including one in el clásico. But the second was different. By Christmas, he had got just three goals, but none in the league. With every miss and every poor pass, the muttering grew louder; there were occasional whistles. At times it was bad enough to produce pity. Or laughter. He just could not get it right.

Confidence seemed to have deserted him. Perhaps declaring himself a jugadoraso, "one of the best in the world", was his way of motivating himself – he did something similar to Mauricio Isla during the World Cup this summer, publicly haranguing his doubting international team-mate during a press conference in Belo Horizonte to convince him that he was one of the best in the world – but it did not immediately work.

Tito Vilanova, the Barça coach, praised Sánchez's effort, which did not always convince. "He's trying" is rarely a winning argument. Others at Barcelona tried to convince Sánchez of his worth privately, while publicly team-mates talked up his contribution. They were right: his movement, work-rate, strength and intelligence, largely unnoticed by fans who had come to embrace players of touch and technique, did indeed facilitate the role of others, particularly Leo Messi.

But Barcelona were struggling and on one level he was the right player at the wrong club: when Pep Guardiola had first talked so highly of his qualities, they were not the typical Barcelona qualities. From a selfish perspective, a role on the right rather than mobile off the front, probably did not suit him either. He improved, scoring six in the last eight games of 2012-13, but the club's president, Sandro Rosell, wanted to sell. The sporting directorate argued the contrary, insisting that no one offered what Sánchez did.

There were still doubts, his style not always fitting the finesse the Camp Nou were accustomed to, but Sánchez responded with 19 league goals last year, including a lovely lob against Real Madrid. In a more direct style under Gerardo Martino, he was often the team's best performer. Yet as one of the few "sellable" players able to raise a significant fee, with Luis Suárez signing and with Neymar, Messi and the Uruguayan all happiest occupying the positions that Sánchez most enjoys, his time was over.

He may not have always been to everyone's taste, but there was appreciation now – from some at least. And he could have gone off to Arsenal a hero. On the final day, a brilliant, thumping shot momentarily looked like making Barcelona the league champions until Diego Godín equalised to give Atlético Madrid the prize.

So Sánchez could not claim the title, or a permanent place at Barcelona, but he had at least reclaimed his title. Last season, it was his supporters, those that lauded him before and who came to cheer him now, who pointedly referred to him as the jugadoraso. The squirrel from Tocopilla really was a great player after all.