I think we’ve been looking at Social Security retirement benefits all wrong. In the long-running debate about when to take Social Security — as early as age 62 or as late as age 70 — the focus has been on timing your claim to get the most money, in total, out of the social safety net.

This is a circular argument that will never be fully decided until the Social Security recipient in question dies. So let’s shift the focus from the question “How do we get the most out of Social Security?” to “How do we get Social Security when we need it most?”

Simply put, you’re more likely to run out of money at the end of retirement than at the beginning.

Behavioral science explains why we are all so prone to preferring money today over tomorrow. It’s called “hyperbolic discounting,” and behavioral economists plead that we meaningfully overvalue money now, unfairly discounting money later.

But the risk of making less money in your early retirement years is dwarfed in comparison to the risks of longevity and inflation in the latter stages of retirement. And the probability you will outlive your money meaningfully decreases if you wait to take Social Security.

Prove it!

Let me show you through an example that, while hypothetical, is no doubt close to reality for many.

We’ll consider three couples, the Earlies, the Fullers and the Laters. Each couple:

  • Retires with $1 million in tax-deferred retirement savings.
  • Has an identical 50 percent equity, 50 percent fixed-income portfolio.
  • Has a pretax retirement income need of $90,000 per year.
  • Will supplement their Social Security income with the retirement savings necessary to fulfill their income needs.
  • Includes one household member who will receive the maximum in Social Security benefits and one who will receive 50 percent of the maximum.

The only difference is that the Earlies retire and begin taking Social Security retirement benefits at 62, the Fullers at 67 and the Laters at 70.

This hypothetical case study is designed to result in an academic probability that each couple will not run out of money, and applies more than 3,000 iterations of randomized historical market returns for the respective retirees’ portfolio allocations.

Then, we show the likelihood that each couple will have at least one dollar left in retirement savings at the end of four different time periods — 20, 25, 30 and 35 years into retirement.

Therefore, if you see a result of 47 percent in the 25-year column of the table below, it means the couple represented still had at least one dollar left in their retirement savings at the end of that period in nearly half of the thousands of iterations run. In other words, that couple had a 47 percent chance of not running out of money 25 years into retirement. Statistically, a probability of 85 percent or better is favorable.

The findings

What did we find? If you die early enough — within 20 years of your retirement date — you have a reasonably good chance to outlive your money regardless of when you take Social Security. The Earlies hit the golf course fully five years before the Fullers, but it’s not clear that they’ve suffered for it at the 20-year mark.

At 25 years, however, there’s a greater than 50 percent chance the Earlies have run out of money and now must ask their kids to pay their greens fees. At 30 years their probability of solvency has dropped to 30 percent, and at 35 years they’re likely relying on their reduced Social Security benefit for all of their income.

Why do the Earlies fail? Because in order to meet their income needs with a reduced Social Security benefit, they put too much pressure on their portfolio to pick up the tab. They were forced to take an effective withdrawal rate of 5.62 percent in their first year of retirement.

How do the Fullers look? Pretty good. Buoyed by a Full Retirement Age (FRA) Social Security benefit and beginning with a reasonable 4 percent effective rate of withdrawal from their portfolio, at 20 and 25 years into retirement, they’re in the 90 percent-plus range. But if they plan on seeing their faces on a Smucker’s jar, their probability of success declines to 67 percent when they’re 35 years into retirement.

As you’d guess, the Laters are solid. Because of their increased Social Security benefit, they require only a 3.26 percent portfolio withdrawal rate in year one. Statistically, they ride off into the sunset and should have the funds to test the boundaries of science in their pursuit of longevity.

If you suspect you’ll die early — and have lineal or medical justification for that belief — you might justify taking Social Security as early as you can (although a lesser-earning spouse could still benefit from your higher benefit when you’re gone). And please forgive the inherent insensitivity in this analysis, which presumes the Earlies, Fullers and Laters all have a choice in taking their benefits at various points in time. Many retirees don’t, and if you need to retire and take early Social Security for any number of valid reasons, of course you should do just that.

But if you hope to have a longer retirement — 30 or 35 years, especially — your chances of not outliving your retirement savings improve greatly if you delay Social Security. Waiting is like purchasing longevity and inflation insurance for what will hopefully be a long and prosperous retirement.

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By Tim Maurer, Director Personal Finance, The BAM Alliance

This commentary originally appeared January 1 on CNBC.com