"This is the worst day of my life," Bart Simpson complains at one point in the Simpsons movie.

"The worst day of your life so far," Homer gently corrects.

What's true for Bart is true for most of us younger than 50 or so, according to a new analysis of life satisfaction encompassing seven massive surveys and 1.3 million randomly sampled people from 51 countries.

Happiness, those surveys show, follow a generalized U-shape over the course of a life: People report high degrees of happiness in their late teens and early 20s. But as the years roll by, people become more and more miserable, hitting a nadir in life satisfaction sometime around the early 50s. Happiness rebounds from thereinto old age and retirement.

If you plot the age-happiness curves from all seven of those surveys on the same chart , the shapes of the curves, rather than any absolute value, are what's important. The surveys asked about happiness in different ways - some framed it in terms of "satisfaction," while others asked people to rate where they fell between "happy" and "unhappy." So the absolute values of each line aren't directly comparable.

Two things stand out: First, the curves all follow the same general U-shaped trajectory. Youth and old age are periods of relative happiness, while middle age is something of a rock bottom. Second, they generally agree that the bottom of that U hits some time in the early 50s.

These similarities are even more remarkable given the differences in the underlying surveys, which were administered in different countries. They include the General Social Survey (54,000 American respondents), the European Social Survey (316,000 respondents in 32 European countries), the Understanding Society survey (416,000 respondents in Great Britain) and others.

Researchers have been finding evidence of a U-shaped happiness curve for years now. It's even been observed among apes. The strength of this particular study is in demonstrating how consistent that curve is across a variety of different data sources.

Note that rock bottom in the chart above doesn't denote absolute misery - people in their 50s still generally rate their life satisfaction in the mid-to-high range, a 7 out of 10, for instance, or a 3.5 out of five. But that's substantially and significantly lower than how people in their late teens or early 20s rate their happiness. The difference between the two - happiness at youth and happiness at middle age - is roughly equivalent to the decline in well-being caused by getting divorced or losing a job, according to the analysis.

These trend lines are all adjusted for other factors known to affect happiness and life satisfaction, like income and health.

"There is much evidence," the paper's authors conclude, "that humans experience a midlife psychological 'low.'" The exact causes of this aren't entirely clear. One common explanation is that in wealthy countries like ours, middle age is a particularly stressful time. People in their late 40s and early 50s are often at the peak of their careers (will all the headaches that entails), and many are dealing with unruly adolescent children to boot.

There's also some disagreement about the universality of the U-shaped happiness curve. Researchers who have teased out country-level trends have found different variations on the curve, particularly among less wealthy nations. Other researchers have examined longitudinal data, which tracks the same individuals over time, and found evidence for flat or wavy happiness trajectories throughout a lifetime.

Still, the authors of this working paper argue that the evidence they've mustered is strong enough that "these kinds of plots of happiness and life satisfaction should be shown - with a discussion of appropriate caveats - to all young psychologists and economists."

For the rest of us under the age of 50, it may simply be enough to know that even if we're having a particularly bad day, statistically speaking things are going to get a lot worse before they get better.