Mr. Carter has done research on how to comport himself, including watching an instructional YouTube video by the former stockbroker who was the subject of the movie “The Wolf of Wall Street.” He believes the key is to come off as the alpha presence. “The one that asks the most questions is the one in control,” he said. “If they ask me questions — ‘How are you doing?’ — I’ll come back, ‘The question is how are you doing?’ This is my phone call, as much as I can make it.”

But on this day he repeatedly ran up against the limits of his powers. Even those who remained interested after 10 or 15 minutes of painstaking back-and-forth often demurred when Mr. Carter asked them for payment information. “This one guy was outside in a wheelchair,” Mr. Carter said of a caller who couldn’t produce his credit card. “He didn’t want to go in and get it. I said, ‘I’m fine waiting,’ but I can’t push him.”

These setbacks only seem to make Mr. Carter focus more. At one point, he made a swiping motion between his face and his headset with his index finger and middle finger. “They recommend that you keep the microphone two fingers away,” he said. “I’m always doing that — checking that it’s two fingers. I’ll do that for the rest of my life.”

It seemed, all in all, like a grueling way to make the slightly more than $30,000 that Mr. Carter estimates he takes in before taxes. “The good thing is he can take hours off,” Lori told me. “But then he can lose his spot. It’s always a fight for the top.”

I was reminded of the Alec Baldwin monologue from the movie “Glengarry Glen Ross,” except that the prize for having the most sales wouldn’t be a Cadillac, it would be a set of steak knives, because the Liveops analytics team had calculated that agents would give nearly as much effort for a prize worth a small fraction of the cost.

Of course, unlike the salesmen in that movie, the Liveops agents can’t really be fired — the third prize — because they weren’t employees to begin with.

A while later, Mr. Carter described a recent initiative in which agents were promised a bonus if 95 percent of their collective sales were paid up front. “I knew it wasn’t going to work as soon as they said it,” he told me, because a handful of agents with low paid rates could ruin everyone else’s chances.

“They did do a pullover sweatshirt for the top two,” he added, brightening. “I was second, so that’s coming.”