It’s going to take more than a strong stock market to fix America’s broken self-directed retirement finance model.

From the grim first quarter of 2009, when the closely watched Dow Jones industrial average hit lows around 6,500, the market has roared all the way back to prerecession levels and then on to new highs, with the Dow closing last week above 15,000.

It should be time for retirement savers to celebrate. But for millions of American workers who don’t even have retirement accounts, a strong stock market doesn’t matter. And for millions more, it won’t be enough to make a big difference in their lives.

More than a quarter of American workers are not confident about saving enough money for retirement, according to a survey published this spring by the Employee Benefit Research Institute (EBRI), the highest level in the 23 years that it has tracked retirement savings. Only about 13 percent said that they are very confident.

Workers, the EBRI speculated, are starting to figure out just how big of a hole many of them are in.

It’s actually surprising, given the data, that it was only 28 percent who said they are “not at all confident” about having a comfortable retirement. Nearly one-third of workers said they have less than $1,000 in savings or investments and well over half have less than $25,000.

EBRI tracks millions of 401(k) accounts, too, and only 7.5 percent of them at the end of 2011 held more than $200,000. More than 40 percent of accounts had less than $10,000.

The average 2011 year-end account balance of people in their 50s and who have been in a plan for 20 years, folks hopefully on their final lap before retirement, was about $176,000. Recent EBRI estimates suggest that this group, on average, saw account balances grow from January 2012 through May 1 by more than 25 percent, pushing their account balances to about $220,000.

That may sound like a lot, but there’s plenty of advice offered by personal finance writers that the safe target is retirement savings of at least 10 or 12 times an annual salary. Retiring with a $220,000 retirement savings account suggests living the lifestyle of someone who makes just over $20,000 a year.

Fidelity Investments, the global fund manager, has noted that lots of workers have a retirement plan at work as well as an individual retirement account from rollovers of accounts from a former employer’s plan, and it found that the age group of 55 to 59 had combined accounts worth about $329,000 at the end of 2012. Better than $220,000 but still well short of what many people hope to have entering retirement.

Fidelity has an upbeat tone to its communications about retirement, and John Sweeney, a Fidelity executive vice president, said “the good news is that the vast majority of 401(k) investors stayed the course” through the last downturn.

What’s implied in marketing materials from firms like Fidelity or in personal finance columns is that if you are nowhere near being on track to quit work with 10 or 12 times your salary salted away, the problem is you.

You didn’t start saving soon enough. You didn’t save enough from each check. You made poor investment choices. You cashed out when changing jobs. You took out loans from plans to pay for your kids’ college tuition. You took distributions rather than tough out a short-term financial crisis.

Kevin O’Laughlin, a financial planner with Affiance Financial in St. Louis Park and a board member of the Financial Planning Association of Minnesota, said the strong stock recovery from 2009 has helped investors understand the value of patience, but “even with that warm and fuzzy, people are still making significant behavior mistakes.”

When read in the black-and-white of a newspaper, that looks cold. Trust me when I say that over several telephone conversations, O’Laughlin comes across as precisely the kind of sensible financial adviser I would introduce to friends.

O’Laughlin and Fidelity’s Sweeney work in the world as it is. And they are right, too, if 401(k)-type accounts are what most of us have to fund retirement. It does matter if you start saving when you are young. It does matter that you spend less and save 10 or 15 percent of your income rather than 3 percent. It does matter that you invest enough in stocks and remain patient, to get enough growth to stay ahead of inflation.

But if a poor result happens to a few people, it’s a failure of those individuals. No argument there. If it happens to millions, it’s a failure of national policy.

Given how many have proved that do-it-yourself retirement saving doesn’t work, for most workers some sort of pension that takes the saving and investment decisions out of their hands would be a lot better. A beefed-up Social Security system, which is a sort of defined-benefit plan for all workers, may be better.

And let’s set aside completely the question of why an economy robust enough to produce a 15,000 Dow Jones industrial average can’t seem to produce enough jobs that fund the basics of a good life.

A 15,000 Dow clearly beats 6,500 for 401(k) investors, but the director of communications for EBRI, Stephen Blakely, almost didn’t see the point of my asking about the impact of a record stock market on the overall picture of American retirement finance.

“As our retirement confidence survey shows,” he responded, “a very large percentage of American workers have very little in savings, let alone investments.” 612-673-4302