If Disney gets it right, the smartband technology could ripple through the leisure industry to other parks or even zoos, museums and Las Vegas resorts. And there is an added element of pressure for Mr. Staggs. Disney is set to name a new chief executive in 2016, and he is one of several leading candidates. Successfully completing the project would be an important feather in his cap.

Image A guest uses a MagicBand at Disney’s Animal Kingdom Lodge in Orlando. Credit... Gregg Matthews for The New York Times

Mr. Staggs said that about three and a half million people had participated in tests of the new system, adding that the early feedback had been “fantastic.” Among the findings: Because guests no longer have to present paper tickets at turnstiles, the system has reduced the park entry time by 25 percent.

The technology allowed Disney to accommodate 3,000 additional daily guests at its Magic Kingdom park over Christmas. Mr. Staggs said use of the new FastPass reservation system has increased 40 percent over the old one, freeing people from standing in line and increasing the number of experiences they have there.

Still, investors have been keenly waiting for financial evidence that the $1 billion investment is paying off. Disney’s parks business has lately been a good one — operating profit climbed 17 percent last year, to $2.33 billion — but the company’s spending on the project has dented margins at its flagship property here. Underscoring its importance to the company, analysts have peppered Disney executives with questions about the system in recent conference calls.

“We have a positive view of the project, and technology this complex always takes longer than you expect to roll out,” said Michael Nathanson, an analyst at the research firm MoffettNathanson. “But we’re still trying to figure out how to measure the return on what is a rather large investment. That’s where the frustration is.”

Robert A. Iger, Disney’s chief executive, has encouraged patience. “This is still a very new product, so we are not even close to being able to quantify it,” he told analysts in February.