Wenger picked wrong club if he wanted to conquer Europe
Tony Barton has one, so too do Louis van Gaal, Guus Hiddink, Rafael Benitez and Roberto Di Matteo. Jose Mourinho, Sir Alex Ferguson and Jupp Heynckes are among those who have two. Bob Paisley and Carlo Ancelotti have three apiece.
For Arsene Wenger, 32 years into his august management career, the reality has been that he will probably never retire with a European Cup on his office shelf.
Can a manager of Wenger's vintage still be called great when he has not yet found a way to win the greatest prize in European club football?
Wenger has excelled at so much in his three decades in management and yet on Tuesday night he was put on the brink of another second-round elimination, this time by a rival manager 20 years his junior, in a khaki parka, with a Champions League title already to his name.
Alongside each other on the touchline, Wenger and Luis Enrique looked like two executives nurturing conflicting generational views on the appropriate attire for a company jolly. What must Wenger think when he considers Enrique's career?
Two previous league finishes to his name, seventh with Roma in 2012, ninth with Celta Vigo in 2014, then handed the controls of the most successful club of the age.
How many great teams does the itinerant modern super-coach create? And how many, would he concede in private, does he inherit?
How many times will Pep Guardiola, Ancelotti or Mourinho catch the wave at the right time in the life of a super-club and win another Champions League title?
There is coaching and then there is managing, and the victories of the past - the kind that Wenger has tried to achieve - are of a different hue altogether.
If Enrique wins a second Champions League this season, does that really put him on the same level as Ferguson, the great club-builder? Or Brian Clough, the man who fashioned Nottingham Forest's double European champions from the husk of second division strugglers?
If Zinedine Zidane were to win his first as a coach with Real Madrid this May does he compare to Sir Matt Busby?
The modern Champions League is a giant battle of super-club infrastructures, a war of the game's old money and its new fossil fuel fortunes; of vast global scouting network and the dead hand of technical directors harvesting talent in much the same way those seabed trawlers dredge for fish.
Everyone agrees the coach is important but his long-term influence can be hard to detect, and you know that at each of these clubs there is a document detailing the options for the day he is sacked.
On nights like Tuesday, it is worth remembering that Arsenal are different - for better, for worse.
They are still the club of their manager, with all his beliefs, his strengths, his neuroses and his weaknesses. The tendency is to dwell on the mistakes, and the stubbornness, but at times you have to remember that Wenger is the last of an old order of managers whose influence and job spec has been denuded.
He reached a final in 2006 but his best chance of a Champions League title with Arsenal was 12 years ago, when they were the best team in Europe and lost to Chelsea in the quarter-finals.
Since then the Frenchman has clung on to the dream of Arsenal's first triumph but if he really wanted to win it, he needed to do what most of the new generation do these days: pick a new club to fulfil his ambition.
With his stock high and well aware of the future conditions under the Emirates Stadium financing programme, Wenger was once the prize for every new owner or president.
In the summer of 2004, Florentino Perez tried to recruit Wenger during his first spell as Real Madrid president.
In the summer of 2006, the Madrid presidential candidate, Juan Miguel Villar Mir, met Wenger again with a view to him coming to Spain, but then failed to win the election.
Even long past Arsenal's millennial trophy-winning prime there was an open-door at the Qatari-era Paris Saint-Germain whose owners, the Al-Thani family, met Wenger in November 2012.
Wenger stayed, ever more the garden-shed inventor in football's corporate era, and over time many decided Arsenal were doing him a favour and not the other way around.
The debate over what was sacrificed in order that the Emirates Stadium could be built is at the heart of the past 10 years of Wenger's career.
What is undeniable is that the stadium was intended to establish Arsenal among the elite permanently but the changes that occurred in European football during that time have meant that they have fallen just short.
There will be those who cannot forgive Wenger his unwillingness to spend money on players at critical times, or point out that in recent years he has done so but to little effect.
Yet defeats like the one this week are the consequence of a decade of Barcelona superiority over Arsenal - in financial, sporting, reputational terms.
Every other modern coach has long since given up carrying the hopes of one club on their back and become individual brands-for-hire in an atomised game - it means less of the long-term responsibility but also fewer chances to leave a permanent legacy somewhere.
And so Wenger looks destined never to win the defining trophy of his profession, leaving him behind the likes of Joe Fagan, Emerich Jenei, the Romanian who guided Steaua Bucharest to an unlikely victory, and the Belgian Raymond Goethals, whose 1993 triumph came with the corrupted Marseille team and caused Wenger agony at Monaco.
It is a missing part of his career but there are ways he can rationalise it.