Some of those fans decided to make a direct appeal to Van Wagenen.

“Hire Girardi and bring back the black jerseys,” wrote a fan named Dan Healy when he sent Van Wagenen money via Venmo on Oct. 17, a week before Girardi was hired by the Philadelphia Phillies.

“Sign Rendon,” Robbie Rose wrote on Dec. 11, the same day Rendon reached a seven-year, $245 million deal with the Los Angeles Angels — over $100 million more than the largest contract the Mets have ever given to a player.

Rose, 19, a Queens native, was watching the news at the State University of New York College at Cortland when he saw that the Yankees, the Mets’ crosstown rivals who spend quite differently, had lavished a record nine-year, $324 million free-agent contract on the star pitcher Gerrit Cole. Rose was tired of hearing from his roommates, who are Yankees fans, about how their team had once again nabbed a top player with a big check.

So Rose had an idea. He was inspired by other fans who had requested money on Venmo from players who made a big mistake that cost their team a win, or who had sent money to an opposing player whose mistake led to victory for their favorite team. During the N.F.L. playoffs in 2019, for example, Philadelphia Eagles fans sent Chicago Bears kicker Cody Parkey money on Venmo after he missed a potential game-winning field goal.

Rose sent Van Wagenen $1.

“I didn’t even know if it was him, but it’s not a common name,” he said, adding later: “It was just a lighthearted joke. I just wanted him to make a signing.”

Van Wagenen did dole out several free-agent contracts this winter worth a total of just over $24 million — including ones for pitchers Michael Wacha, Rick Porcello and Dellin Betances. But all were short-term deals for players who didn’t excite the fan base the way Rendon or Cole would have. The new players might help the Mets contend for a playoff spot this season, but it won’t be because of the money Rose or Wilton sent.