“People are pretty much doing the opposite of what they should be doing,” said Matt Fellowes, founder and chief executive officer of United Income and co-author of the paper.

When to take Social Security is a key decision for America's elderly, for whom the program has become a critical safety net. About half of older Americans get most of their income from the program.

Unlike investments and other sources of retirement income, Social Security benefits are guaranteed to keep up with inflation and last for life. That's important when half of all 65-year-old American women can expect to live past age 86, according to Social Security estimates. The average life expectancy for U.S. men who are currently 65 is age 84.

The report is based on about 2,000 households that participated in a long-running University of Michigan study.

To calculate ideal filing years, United Income estimated retirees' spending and longevity and ran about 500,000 possible scenarios for each participant, including various market conditions, for a total of about 1.1 billion simulations.

Only 4% of U.S. retirees are waiting until age 70 to claim Social Security; some 57% should be doing so, the report calculated.

Meanwhile, more than 70% start taking checks before turning 64, a time when—ideally—only 6.5% of retirees should be cashing checks.

The lost income from these less-than-optimal decisions amounts to about $111,000 per household, the researchers estimate.

The United Income analysis finds little rhyme or reason in Americans' claiming decisions. If you're healthy and expect to live a long time, you should maximize benefits received late in life by delaying.

But the report finds that people don't do this: Those who ended up dying before 75 were just as likely to have claimed early as those who died after 85. (There is a way to claim benefits, then suspend them until later, but it's kind of complicated.)

Why are so many people getting it wrong?

Some retirees might not realize it, but by tapping Social Security at 62 or 63, they're locking in that lower benefit amount for the rest of their lives. Social Security's rules are also complicated, particularly for married people, and the ideal strategy isn't always obvious. Perhaps that's why four years ago, a 384-page book on Social Security-claiming strategies became an unexpected bestseller.

What about the theory that, in the end, you'll probably get the same amount, no matter what you do?

That's not true for most people, especially since people are living longer. Other retirement experts have done the math and determined that, assuming you're in reasonable health and can afford to wait, you should.

That's especially true for women, who are likelier to live longer. Then again, it's not true for people who might die earlier.

However, while most people are better off waiting until 70, about 43% of adults would actually be better off claiming benefits earlier than that, the report concludes. Primary breadwinners should be waiting until age 70 about twice as often as their spouses do.

“Rather than a simple rule of thumb about when to claim Social Security, the optimal decision varies broadly, both across and within households,” said Fellowes, a former Brookings Institution scholar.

Fellowes said the issue isn't a lack of financial literacy. Indeed, affluent and educated retirees are more likely to make a mistake than are poorer and less-educated ones.

Rather, the problem is that the ideal claiming decision can be very difficult psychologically. Balancing your savings with Social Security means, in effect, betting on when you are going to die.

So how does one achieve the necessary balance? The researchers say the best strategy requires dipping into savings in your 60s in order to guarantee a larger check later on.

By claiming at the right time, more than half of retirees would see incomes in their 70s and 80s rise by more than 25 percent. But they would need to have the psychological grit to sacrifice some savings early on—and retirees are often reluctant to watch those balances fall.

“Getting rid of their financial safety blanket is something that makes people really nervous,” Fellowes said.

And relying on financial advisers and wealth managers to tell you what to do may be a mistake—they might not have your best interests at heart. Very often, the ideal claiming decision would cause a clients' investment account balance to drop in the near term, squeezing a source of revenue for financial firms.

If everyone took benefits at the right time, the analysis concludes, the poverty rate among elderly Americans would drop from about 13% to 7%. Meanwhile, the wealthiest 25% of retirees would get an average 14% income boost over the rest of their lives, versus 6% for the poorest quarter of retirees.

If Americans were more clever about claiming Social Security, it would also cost the government more. Lawmakers already face a long-term funding gap for Social Security and Medicare. But Fellowes estimates that the cost might be offset a bit by higher tax revenue from Americans who work further into their 60s—assuming they can keep or find a job, given health issues and age discrimination by employers.

One way to solve the problem of retirees pulling the trigger too early, the researchers say, is legislation.

“Early claiming should be made an exception, and reserved for those who have a demonstrable need to claim benefits before the full retirement age,” the report concludes.

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