When Bayern Munich celebrated their domestic double on 18 May, one player was not present at the party thrown for club members and sponsors. Mario Mandzukic, the scorer of 26 goals for the German champions last season, had already packed his bags and headed some 350 miles south-east to Croatia. “It was his decision,” Karl-Heinz Rummenigge, Bayern’s chief executive, said. “I’m a little sorry because of that, but it’s done now and cannot be changed. I suppose his departure fits the pattern of what was happening over the last few weeks.”

Mandzukic had been told by the Bayern coach, Pep Guardiola, that he was not needed for the German Cup final in Berlin – Bayern’s last game of the season – so saw no reason to stay in Bavaria any longer. But even though there were still a few days left before the start of Croatia’s preparations for the World Cup, he was not idle. He had something important to do.

On the morning of 19 May, the player turned up in his home town of Slavonski Brod, bringing with him three vans loaded with supplies and other humanitarian aid, all of which he paid for. The surrounding area was affected by the worst floods in living memory: around 15,000 people have been evacuated from their homes and people – locals, policemen, firemen, the army and the volunteers who came from all over the country – worked night and day repairing dams and building improvised water barriers, as well as rescuing people and animals.

That was the Mario Mandzukic most people do not know: a caring, generous and down-to-earth individual who wanted to lead by a positive example. Those who only see him on the pitch know him by his stage persona: this incredibly competitive, snappish and possibly slightly mad striker. And while at Bayern he has learned to restrain his temper and keep his cool for the most part, he can still be a danger to everyone around him when he wears the Croatia shirt.

Having opened the scoring against Iceland in the return leg of the World Cup qualifying play-off back in November, he got sent off only 11 minutes later for recklessly planting his studs into an opponent’s thigh at full speed, almost on the halfway line. That incident cost him a one-match ban and resulted in him missing the tournament opener against Brazil.

Now, though, he is back for Wednesday’s tie against Cameroon and his return is one of the main reasons for optimism in the Croatia camp before the game that is likely to go a long way towards deciding whether they stay beyond the group stage.

Despite a decent performance against Brazil, the Vatreni lost their first game, with the coach, Niko Kovac, and his players fuming about officiating in that match. As soon as they put that behind them and began to focus on the next opponent, the atmosphere in the team was shaken by media back in Croatia publishing photos of several players relaxing in the nude by the pool in their training base. In turn, players declared a media silence: they are refusing to speak to the press until further notice.

Mandzukic was not among the players in those pictures, but his name is on everyone’s lips.

His replacement, Hull City’s Nikica Jelavic, did not have the best of games against the Seleçao – arguably his best move was missing the ball, which instead hit Marcelo, surprising the Brazil left-back who scored a shocking own goal. Now with their star striker back, Croatia are hoping they can get some goals of their own and beat Cameroon. After all the praise of their display in the first match, for them the World Cup really starts now.

With a convincing win over Volker Finke’s side they would get very close to the second round, probably needing only a point in their last game – provided, of course, that Brazil beat Mexico; otherwise, they could be set for an early return home.

And Mandzukic is someone they rely on: not only as a focal point of their attacks and the most likely scorer but – more so than is the case with Bayern – one of the hardest workers on the pitch.

He stretches the defences with constant movement and seemingly endless stamina, opening space for others to come from behind or cut inside from the wing; his pressing on the ball has proven decisive on a number of previous occasions and he is, of course, one of the best strikers in the world when it comes to aerial power. So even if he does not score himself, his presence could be key for the team’s chances. A little madness is a fair price to pay for that.

In the past, Mandzukic’s extremely competitive nature often got him into trouble. At Dinamo Zagreb, he publicly stated he had no motivation to play against the “village teams” of the Croatian League. He was unhappy with the mediocrity of Wolfsburg where he was sold to and he has only really enjoyed his time at Bayern, where he helped win the European Cup in 2013, scoring a goal in the Wembley final against Borussia Dortmund.

However, Guardiola’s ideas and the imminent arrival of Robert Lewandowski have left him disillusioned. He was willing to fight for his place in the team, but has come to realise it is a battle he cannot win. “Let’s be honest, I can’t play to my strengths under Guardiola’s style – no matter how hard I try,” Mandzukic finally said to Sportske novosti, Zagreb’s sports daily, a couple of weeks ago. “I realised that after the games with Real Madrid in the Champions League. It’s best for both parties that we go our separate ways.”

And so, with Mandzukic adding he had already spoken to Rummenigge about his desire to leave the club and declined an offer for a contract extension, his fate finally looks sealed. He is leaving and Bayern will let him go for a right price, but no one yet knows where he will end up: the striker has been linked to a number of clubs in England, Spain and Italy.

If his character is anything to go by, he is likely to pick a club where he will be the undoubted first choice and have a chance of winning trophies. In Croatia, Arsenal are being mentioned more often than any other potential suitor and now that Arsène Wenger has won something again, is it finally time for him to bring in a world-class striker?