Editors' pick: Originally published Aug. 4.

There are three big reasons why we claim Social Security earlier than we should - and at least one of them is plain wrong. Maybe a second is also off kilter. That means literally millions of us every year are claiming Social Security at an age that is guaranteed to give us less of a payoff than we deserve.

The math is a slap in the face. If your Social Security payoff at the full retirement age of 66 is $1,000, it drops to $750 if claimed at 62, the earliest possible age. It climbs to $1,320 if not claimed until age 70, after which delay reaps no reward.

Take it at 70 if you have waited that long, because that is the best deal you will get.

Every dollar counts, because the evidence mounts that many seniors are scraping by on very lean incomes, and the average retiree household income is $32,000, according to the Transamerica Center for Retirement Studies.

In 2013, according to the Social Security Administration, 48% of women claimed benefits at 62. 42% of men did likewise. The Full Retirement Age -- 66 for the current crop - was when 27% of women and 34% of men claimed benefits. Maybe 4% of woman and 2% of men wait until age 70 to collect.

What's wrong with our math?

There also is a lot of buyer's remorse, according to a recent poll conducted for the Nationwide Retirement Institute which found that 23% would change when they collected retirement benefits to a later age, and 24% said their benefits were less than they had expected.

So why do many of us claim too early? Here are the reasons why we collect earlier than we perhaps should.

We have no faith in the Social Security system, said Evan Beach, with Campbell Wealth Management in Alexandria, Va. He elaborated: "A really bleak picture of the health of Social Security is painted by the media. Undoubtedly, the system will face strain as 10,000 boomers turn 65 every day."

But the reality, said multiple experts, is that it is very difficult to envision an implosion of the Social Security system any time soon. That would be catastrophic to millions of seniors and the impacts on the economy would be severe.

Furthermore, simple tweaks to the system - perhaps raising the earliest claim age to 64 and moving Full Retirement Age to 68 would add years to the system's solvency.

Experts insist Social Security just is unlikely to fail outright - so if fear of failure is why you are thinking of claiming, stop right there.

Reason two: Many retirees fear they won't live long enough to get what they paid into Social Security back out. Some advisors say this is wrongheaded. Said Marcus Dickerson of Gulf Coast Social Security Strategies: "I tell my clients that if they die early, they'll be dead, and they won't care. The real risk is in not dying on time and living longer than their financial resources can sustain them. Social Security is the best guaranteed, cost-of-living adjusted income stream available today, including any annuity that can be purchased in the private sector." Remember that when a spouse dies, the smaller of the two benefits stops. Delaying Social Security until age 70 provides the surviving spouse with the highest possible monthly income -- up to 76% more than the age 62 benefit, plus cost-of-living adjustments (COLAs) -- which for a lot of people, can be the difference between living comfortably and having to reduce their lifestyle as they age.

Understand: there is some mathematical logic in claiming early. Delay claiming until age 70 and to equal the money that would have been collected by claiming at 62, you have to live until around 80. But probably you will. A man turning 62 today will live until 83.7 according to the Social Security Administration. A woman will live until 86.3. Of course those are averages. Personal medical history and family life expectancy need to be factored into the math. But for many of us, delaying until 70 is the smart bet.

A third - and excellent - reason many people take Social Security early is "they need the money," said Richard Stieglitz, a CPA with Anchin, Block & Anchin LLP Accountants and Advisors. There just is no arguing with that.

If you need the cash, take Social Security as soon as you can and damn the math.

But if you can wait, wait. "There's a huge benefit in waiting," said Social Security expert Matt Carey.

This article is commentary by an independent contributor. At the time of publication, the author held TK positions in the stocks mentioned.