“We are Real Madrid,” Marcelo said boldly after Real Madrid had – just – held off Juventus’s fightback in the quarter-final. The reference was clear: they were not Barcelona, not the sort of team to go giving away three-goal leads as their great rivals had against Roma the previous night, not the sort of side who countenanced failure. Whether that is arrogance or a necessary mindset for winning probably depends on perspective, but what is true of that Madrid is that their most obvious quality is simply that they win. Inexplicably at times, but remorselessly.

Madrid are only the fourth side to have been European champions three times in a row. Only they themselves, between 1956 and 1960, have had a run of sustained success better than the four Champions Leagues they have won in the past five years. That suggests they are one of the greatest teams in history and yet it really doesn’t feel like it.

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Perhaps the issue is one of proximity, that being so close means their flaws stand out and time will provide the perspective that allows their achievements properly to be measured. And yet there was no such issue with Pep Guardiola’s Barcelona, whose 2011 triumph confirmed the greatness they had touched in 2009 and come so close to repeating in 2010.

“In 10 years I don’t think anybody will speak about how we lost,” Jürgen Klopp said on Saturday night, and perhaps that is the real issue with perspective. There is an assumption that a club that keeps winning must be great and the precise details fade away. Saturday’s success, after all, was the result of a bizarre concatenation of freakish circumstance: a brilliant overhead kick, two hideous goalkeeping errors and an injury to the opposition’s best player.

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But what’s really bizarre is how frequently similar circumstances have occurred this season. Sven Ulreich’s mistake that ultimately settled the semi-final against Bayern seemed like an error for the ages. A game and a half later, it was battling to stay on the podium for worst mistake made against Real Madrid by a goalkeeper in the Champions League this season. Add in penalties given and not given, against Juve and Bayern, and it’s pretty clear that a lot of key moments have fallen Madrid’s way this season. Whether you think that is a matter of luck or of the winning mentality of which Marcelo spoke probably depends on who you support.

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The dissonance comes when Madrid’s Champions League record is compared to their record in the domestic league. In those last five seasons they have won the domestic title only once. That makes little sense: how can a team that dominates in Europe not dominate at home?

And yet none of those other sides who won three titles in a row also won their domestic league in each of those three seasons. Madrid’s five in-a-row champions of the late 50s won the league only twice in that spell. Ajax won only two between 1971 and 1973. Bayern won only one between 1974 and 1976 – and finished as low as 10th in the Bundesliga in 1975. Perhaps this is simply the smoothing effect of time: Bayern, certainly, could easily have lost the 1975 final against Leeds and the 1976 final against St-Étienne.

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In a sense, of course, this is, anyway, not comparing like with like. The competition is very different now to when those previous three three-time champions were contesting it. Then, limited to champions, it was harder to get into, but with only five rounds could be won with a couple of good performances. Now for the superclubs – with access to the last 16 and often the last eight all but guaranteed – the issue is peaking at the right time and having the decisiveness to win those key games in the spring.

And greatness, anyway, perhaps is about more than mere trophies. As Arrigo Sacchi has always been very keen to point out, what matters in football, what is remembered, is not necessarily what is done, but what is done well. The Ajax of 1971-73, the Internazionale of 1964-65, the Barcelona of 2009-11, Sacchi’s Milan of 1989-90, they all took the game in new directions. They innovated, created new styles. They stood for something (and while that may have included a cynicism akin to Sergio Ramos’s, it certainly did not involve two of their biggest stars using their post-match interviews to agitate for moves).

It’s not clear what exactly Madrid stand for. No philosophy, certainly, beyond having the money to sign lots of very good players. But they have that vital ruthlessness and in Zinedine Zidane a coach who, for all the doubts about him, has a habit of making decisive substitutions. Does that make them great? Perhaps in one sense it does, and such matters are probably necessarily subjective. But beyond the highly efficient accumulation of silverware, it would be hard to argue this Madrid have changed the game. They are, though, indisputably Real Madrid.