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Willpower, apparently, can be bought.

The chance to win or lose $20 a month enticed dieters in a yearlong study to drop an average of nine pounds – four times more weight than others who were not offered dough to pass up the doughnuts.

Many employers, insurers and Internet programs dangle dollars to try to change bad habits like smoking or not exercising, but most studies have found this doesn’t work very well or for very long.

The new study, done with Mayo Clinic employees, was the longest test yet of financial incentives for weight loss. Doctors think it succeeded because it had a mix of carrots and sticks – penalties for not losing weight, multiple ways to earn cash for succeeding, and a chance to recoup lost money if you fell off the “diet wagon” and later repented.

Incentives are “not like training wheels where people learn healthy habits and then will continue them on their own.” You have to keep them up for them to work, said one study leader, Dr. Steve Driver of Mayo in Rochester, Minn.

If you’re looking to set up a system like this at work or among friends, the key is to make it self-sustaining, Driver said. The Mayo one did that by having people who didn’t lose weight put penalties into a fund that paid rewards to those who did.

It’s also a good idea to make people pony up in advance. One woman flew into a tizzy when she stepped on a scale at a weigh-in and was told she’d have to pay.

“She headed for the door” but later came back and paid, Driver said. “People in Minnesota are pretty honest.”

Mayo paid for the diet study, which involved 100 obese employees at the Mayo Clinic but was not a workplace wellness program. Half were given weight-loss counseling, monthly weigh-ins and a three-month gym membership. The others had those things plus financial incentives.

The aim was to lose four pounds a month up to a goal that depended on their starting weight. If they failed, they paid $20 into a kitty. If they succeeded, they got a voucher to collect $20 when the study ended. Part of the kitty was used to pay the rewards. The rest was put into a lottery that anyone could win, whether they made their weight-loss goals or not.

“People saw that if they stuck with it, they had a chance at winning more than they had lost,” Driver said.

Participants in the financial incentives group also earned $10 a month and lottery “tickets” for coming to monthly weigh-ins and texting their weights to study leaders each week, said Dr. Don Hensrud, preventive medicine chief at Mayo. So people could have lost as much as $240 or won as much as $360, plus what built up in the lottery fund.

After a year, 27 of the 50 financial incentive participants came out ahead moneywise. About 62 percent of them completed the study versus 26 percent of the other group. The incentives group lost a little more than nine pounds on average, compared to 2.3 pounds for the others.

The results are promising, but people may need to lose more than nine pounds to make a big difference in health, said Dr. Kevin Volpp, director of the University of Pennsylvania’s Center for Health Incentives and Behavioral Economics.

“There’s been an explosion of interest in this,” Volpp said, adding 86 percent of large employers now provide similar incentive programs.

The cash was a big motivator for one study participant – Audrey Traun, 29, a lab training specialist who dropped 40 pounds, from 215 pounds to 175.

“I was impressed. I didn’t think I was quite capable of that,” said Traun, who lives in Kellogg, Minn. As the study went on, though, the cash became less important, and “it was actually more motivating to see my progress – pounds lost and how my clothes were fitting,” she said.

Traun used the nearly $400 she earned in the study on a family vacation.AP Medical Writer Maria Cheng in London contributed to this report.