Free in Marca: your very own poster of José Mourinho. If anyone needed proof that Real Madrid's coach is unique, here it was. By the end of last season, the country's best-selling newspaper could hardly bare to look at Manuel Pellegrini, let alone produce a poster of him. Much the same could be said of the men who preceded Pellegrini, from Carlos Queiroz to Mariano García Remón, Vanderlei Luxemburgo to José Antonio Camacho. Coaches, as the former Madrid manager Juande Ramos said this week, "are useful to have around – as someone to burn".

Mourinho is different; Mourinho is someone to pin on your wall, an idol. And because Mourinho is different, everything about this Real Madrid is different too. For the first time, the superstar is on the bench. Mesut Ozil claims he joined Madrid to work with "the best coach in the world". No one ever said that about Juan Ramón López Caro. The club's president, Florentino Pérez, has certainly never said this about any of his coaches before: "This year's galáctico is Mourinho."

On the morning Mourinho officially signed, he was taken round the stadium, finishing up before the trophy that obsesses Madrid. "When we got to the last European Cup [which Madrid won in 2002], Pérez said he missed it," Mourinho revealed. "I said: 'I only won my last one 10 days ago and I already miss it.' We both want the same thing. Madrid have an incredible history in the European Cup and an incredible negative history in recent years."

He could not have summed it up better. In the competition that defines them, they have not won a knockout tie in six attempts. By their own measure, the biggest club of all are not a big club at all. They went three years without a trophy of any kind at the end of Pérez's last presidential reign and, despite spending €258m (£212m), ended his comeback season empty-handed. Meanwhile, Mourinho achieved with Internazionale what Madrid so desperately want to achieve: he won the European Cup and he defeated Barcelona.

That is why Madrid invested almost €100m (£82m) in paying off Pellegrini and signing Mourinho and his staff. Talk of beautiful football, occasional gripes by the very few dissenters are largely a red herring. Nothing else matters: Madrid must win, they must be a European force. Forget former talk of fantasy, when he announced Mourinho's arrival Pérez said simply, and quite accurately: "Madrid's identity is winning."

No one guarantees results like Mourinho. Madrid bought the best players in the world, now the best coach – and everything that comes with him. A change of model, a shift in the balance of power. There have been no superstar signings, no bombastic presentations, and the first thing the director general Jorge Valdano did when he presented Mourinho was to offer a very public apology for having once likened some of Mourinho's football to "shit on a stick". A boss begging forgiveness from his employee; a coach on top. This time, the manager manages. In return for one thing: success.

"What's beautiful, beautiful, beautiful isn't working for Real Madrid," Mourinho said. "What's beautiful, beautiful, beautiful is winning for them."

As Madrid's season gets under way in Mallorca, the question is, will he? On Madrid's terms, that is. Pellegrini insisted that his successor would have to get 100 points and considerably more than 100 goals. As one first-teamer puts it: "We weren't the problem, Barcelona were." And the truth is that, despite Barcelona's internal disputes, economic crisis and short squad, despite a media campaign that appears to be trying to get Mourinho beatified, despite the obvious enthusiasm for his methods from players and staff, there is less optimism now than the day the Portuguese arrived.

Even Mourinho has been cautious, realistic. He has been strikingly downbeat, noting that Madrid have had a "difficult pre-season", warning that there will be "problems" if the club cannot sign an additional striker and Karim Benzema or Gonzalo Higuaín suffer injury, admitting that he does not have a traditional "leader", and underlining Barcelona's continuity and clarity. Madrid, by contrast, still need time and Mourinho claims he has none. Madrid, he says, are not yet ready.

The European draw – Milan, Ajax and Auxerre – is tough, but even a not-ready Madrid should be too good for the rest of the Spanish league: last season they finished 25 points clear of now-weakened Valencia, who were third, and 33 points above Sevilla. They do not face Barcelona until late November. Early in their Champions League campaign, Inter were resoundingly beaten by Barcelona last year. No one recalls that now.

Yet the air of caution blowing through the Bernabéu has raised an uncomfortable question: what if Madrid still don't win anything? Even with the world's best coach. Even with a model founded wholly on success. If Mourinho fails like Queiroz, Camacho, García Remón, Luxemburgo, López Caro and Pellegrini did, where does that leave the club, the project? Then where do they go? Will they be patient? Will they be allowed to be? Will the fans? Will the media?

Beneath the intense excitement surrounding Mourinho's appointment, the conviction that here, at last, is a coach worthy of the galácticos, a special one for a special club, there is a disquieting realisation, an apprehension. In signing Mourinho, Madrid could be betting everything on a solitary hand. Still, at least it is a hell of a hand.