Amid all the changes underway with retirement, from disappearing pensions to shrinking matches on company 401(k) plans, one thing – so far – has remained constant: Social Security.

Among those age 65 and over, more than half of married couples and 74 percent of those who are not married depend on Social Security for at least half of their income, according to the Social Security Administration.

But are Americans leaving Social Security money on the table? And could the Social Security statement provide more information that would help them make better choices?

"It probably could do more," said Eleanor Blayney, consumer advocate at the Certified Financial Planner Board of Standards, which oversees certified planners. The agency does provide various benefit calculators online, she said, but unless you are single and your financial history is simple, "the claiming strategy is not really straightforward."

Considering the number of people who claim benefits early, Blayney may be onto something. In 2014, about 36 percent of men and 41 percent of women who turned 62 claimed Social Security at that age. And while that early claiming rate is well below what it was 30 years ago, many Social Security experts say it is still too high.

Why? Well, waiting to claim at age 70 gives you a monthly benefit that is as much as 76 percent higher. For example, if your benefit at the current full retirement age of 66 is $1,000 but you opt to claim at 62, it would be reduced to $750. If instead you wait until age 70, it would be $1,320, a nice increase. Even so, less than 2 percent of men and 3 percent of women wait that long.

Some people believe they will not live long enough for the higher benefit to offset the years they delay claiming. However, an analysis published in 2015 by JPMorgan Asset Management found that by age 80, even those who waited to claim at age 70 would have received at least as much as if they had claimed earlier. In addition, it said that 62 percent of men and 72 percent of women age 65 will live to age 80 or beyond.

Then there is the possibility that people claiming benefits early may feel they need to get the money right away. Yet a 2015 working paper published by the National Bureau of Economic Research found that roughly a third of Social Security beneficiaries who claim before their full retirement age have enough money in IRA accounts to cover at least two years of benefits, and roughly one-fourth have enough to cover four years of benefits. These people may have personal health situations that make them want to claim benefits early, but from a numbers perspective it may not be necessary.

Some experts say the Social Security Administration could persuade more people to delay claiming benefits if it presented a better picture of personal finances and retirement.

"A comprehensive retirement planning framework would show workers that pushing back their retirement age does more than raise their monthly Social Security benefit. It also reduces the savings they need at retirement, as the higher monthly benefit reduces the income they need from savings; and it shortens the length of time their savings need to provide that income, " research economist Steven Sass of Boston College's Center for Retirement Research wrote in a 2015 brief.

Sass found that while people do value the information they receive in Social Security statements, it does not necessarily lead them to change their behavior. In fact, 2 in 3 working Americans give themselves a grade of "C" on retirement readiness.

The Social Security Administration mails out paper statements — generally only once every five years — starting when you turn 25. Online statements are available anytime, but if you sign up for those, you will stop receiving paper statements.

Claiming benefits "gets really complicated when you have people such as a widow or widower" who may be able to claim spousal benefits, said Webster Phillips, a senior policy analyst at the National Committee to Preserve Social Security and Medicare. "You can lose a lot of money by making the wrong choice."

Although he said the agency does not advise people what to do, if you file online, you may be even more on your own than interacting with a real person at a Social Security field office.

The statement you now receive may actually "undersell" the benefit of waiting to claim because of how it forecasts a future beneficiary's earnings, Blayney explained.

"Your benefits are computed on 35 years of earnings," she said. "Say in those final years, 62 to 70, you are making some good money. It's very possible that it will add a new data point to your earnings history," and your benefits will increase even more than the Social Security tables project.

The current system, Blayney said, "could bias people to take the money and run because they are not seeing an even bigger benefit at 70 or even at 66."

The Social Security Administration could also help people by finding a way to link related benefits statements, Blayney said. That way, someone looking into when to claim could compare the different amounts they could receive based on, say, their own earnings, their spouse's, or their ex-spouse's.

For those willing to do some research, there is useful information available about effective Social Security claiming strategies. The agency itself does provide extensive online information for retirement planning, and offers tips on applying for Medicare. There is also some updated information on claiming strategies that are being phased out, which may have special relevance for married couples. For people with simple work and marital histories, that may be plenty.

But with more than half of all workers in a recent study reporting that they have less than $25,000 saved for retirement, Social Security benefits stand to be at least as important in the future as they have been in the past. And that means every bit of added information can help.