Playing to the cameras before the opening round, the men teased each other about their newfound fame, with Molinari saying, “I might not talk to him and give him a cold shoulder and see how he takes it.”

It was a joke that played off a longstanding friendship that predates their recent success. Fleetwood’s wife and manager, Claire Fleetwood, used to manage Molinari, and during their Ryder Cup campaign Tommy Fleetwood would describe Molinari as “one of my best friends, not just on tour, but in life.”

As the Dubai event approaches, Homer is working with the tournament sponsors, the shipping company DP World, to produce a promotional event built around Moliwood and the sponsor’s ownership of the ship Queen Elizabeth II.

Whatever form that takes, the frothy marketing stunts have a serious intent. Since Keith Pelley, a Canadian media executive, became chief executive of the European Tour in 2015, the organization has retooled for the social media era.

When the organizers talk about the selling points of a tour that has historically been financially and culturally secondary to the dominant PGA Tour, they are as likely to invoke the character and social diversity of its global venues and players, as they are its competitive credibility. The popular success of Fleetwood and Molinari represents a rare intersection of both.

And in a golf world where the PGA Tour represents the gold standard, Pelley and Homer know that legitimate claims for the European Tour’s viability as a stand-alone circuit needs sustained performances from its elite competitors. “It starts on the course,” Homer said.

Historically, that’s been a tough sell. Despite the vastly improved prize money that the Rolex Series has provided to important events on the European Tour, the top European players still plan their seasons around the PGA Tour. Players have complained about the travel strain of trying to reconcile PGA and European Tour commitments, and Rory McIlroy suggested last year that a world tour could be created by having the PGA Tour buy the European Tour.