It was a risky bet from the start.

Since 2011, Paris Saint-Germain has been owned by Qatar Sports Investments, a portfolio of sports properties controlled by the Qatari government. Its stated objective was to become a global juggernaut, dominating not just France but conquering Europe by winning a Champions League title. The unstated implication was always that in its rivalry with other Gulf states like Abu Dhabi, owners of similarly upwardly mobile Manchester City since 2008, PSG would allow Qatar to keep up with its neighbors while burnishing its brand through sports.

The Qataris have since spent hundreds of millions of euros trying to get there. Neymar alone has cost them roughly half a billion. And there was widespread speculation that he was signed as much for his abundant ability as to send a message that the nation’s spending power remained undiminished in spite of the economic blockade that hit Qatar about two months before the transfer.

Yet whereas City has been a resounding success as Abu Dhabi’s sporting vanity project, PSG isn’t that yet for Qatar. Certainly, the club is more successful than it’s ever been, and its value and revenues have skyrocketed. Income is now over half a billion euros a season, the sixth-most in the world, according to Deloitte. And the club’s overall value is well on its way to reaching a billion dollars — presently standing at $841 million, it has the 11th-highest valuation in the world, per Forbes.

City has won the Premier League twice — and seems a lock for a third title — while lifting the FA Cup once and the League Cup three times in almost a decade under its new ownership. Yet in six full seasons since QSI’s takeover, PSG has won Ligue 1 four times, the Coupe de la Ligue four times and the Coupe de France three times — twice doing the domestic treble.

In Europe, they’re not far apart. PSG made four straight Champions League quarterfinals, before stranding in the round of 16 last season and against Real Madrid on Tuesday. City took longer to reach the big dance and didn’t survive the group stage until its third try. The last three seasons, it has been eliminated in the round of 16, semifinals and round of 16 again, respectively. This year, the quarterfinals are assured for City after a 4-0 away win against FC Basel in the first leg of the round of 16.

So what sets the two clubs so far apart, when neither team was really a powerhouse in their league before their big buyout?

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PSG was one of the more popular clubs in France, by dint of being from the populous capital, but had won the league just twice in its history. City had last won the league 1968 and the FA Cup in 1969. Yet in order for City to accrue the sort of glory it was expected to as a return on its investment, domestic success sufficed.

The Premier League is hard to win, no matter how much money you throw at it. Some of the richest clubs in the world play there, reducing money to a necessity for competitiveness, rather than a differentiator. France is different. After Olympique Lyon’s seven straight titles at the beginning of the century, it was essentially a free-for-all. Before PSG strung together four straight titles from 2013 through 2016, five different clubs won it in five years — six in six, if you count PSG.

A hefty injection of cash would do the trick. But like a team dominating Portugal, the Netherlands or Scotland, or any other respected league outside of the Big Four of England, Spain, Italy and Germany, domestic trophies alone don’t quite move the needle. For City, English silverware was enough. But PSG would need to win something in Europe. To justify the outlay. And to yield the kind of PR and prestige return on investment Qatar expected.

PSG was built for Europe; not for France. One of its technical directors, the since-departed Leonardo, actually said so out loud.

But winning in Europe is a rare thing even for the greatest of dynasties. The much-admired and adored FC Barcelona has won it just once in the last half-dozen seasons. Because a single bounce, let alone a bad night, can derail an entire campaign. Legacy, then, comes to depend on a handful of moments over the course of half a decade. It’s a perilous approach.

And it’s one that’s not worked out for PSG. In 2013, it ran into Barca in the quarterfinals and went out on away goals. In 2014, it suffered the same fate against Chelsea. In 2015, it ran into the Barca buzz-saw again and in 2016, City won out by a single goal. Last year, PSG somehow blew a 4-0 first leg lead against… yes, Barca.

Unfortunate draws; aggregate ties lost on away goals; late collapses: they’ve conspired to prevent a European breakthrough for PSG.

And this season was no different. In the first leg against Real Madrid, the three-time winners in just four years — speaking of bad draws — PSG was the better team in the first half. Were it not for a pair of deflections, the Parisians might have gone into halftime with a 2-0 lead in Madrid. Instead, a series of fortuitous plays buoyed a Real turnaround and a 3-1 win.

Things looked bleak for the return leg. Yet PSG was again the stronger side in the opening act on Tuesday, without the injured Neymar no less. A pair of strong saves by young PSG goalkeeper Alphonse Areola stemmed the tide when Real did break through.

But a single, savvy Real attack early in the second half, resulting in a Cristiano “Who else?” Ronaldo goal, doomed PSG’s would-be comeback. When a frustrated Marco Verratti was sent off with a second yellow, reducing the embattled Unai Emery’s home team to 10 men, things looked hopeless. A deflected header trickling in off a bump from Edinson Cavani, bringing PSG within two goals of extra time, was perhaps the prelude to a miracle. But then an enormous deflection on Casemiro’s shot from a broken attack put Real 2-1 ahead again.

A single moment. A bad bounce. Three weeks after PSG was more deserving of a win than the two-goal loss it got. And now it was all over again. With a humiliating 5-2 aggregate scoreline no less.

For all the club’s growth and its long strides, PSG is no closer to its larger objective. It has gone all-in on a long-shot gamble. And those rarely pay out.

Leander Schaerlaeckens is a Yahoo Sports soccer columnist and a sports communication lecturer at Marist College. Follow him on Twitter @LeanderAlphabet.