Smooth Is a Lie

Real lives don't compound in a smooth line. One-time windfalls and hits move the end point, and when they land can matter as much as how big they are.

Most retirement charts you've seen are smooth curves. Same deposit, same return, every year, sloping politely up and to the right. It's a fine way to teach compounding. It's a strange way to describe a life.

Actual incomes bounce, and the big bounces lean down. Karen Dynan, Douglas Elmendorf and Daniel Sichel found that household income volatility rose about 30% from 1971 to 2008, and the share of households whose income fell by half over two years went from about 7% in the early 1970s to more than 12% in the early 2000s.³ Looking at millions of Social Security earnings records, Fatih Guvenen and coauthors found that earnings changes show "negative skewness and very high kurtosis": most years move a little, every so often one moves a lot, and the big moves lean down: large drops are more common than large jumps.⁴

So this page keeps the smooth line and draws a second one next to it, the Jagged Curve, with eight of life's one-time events dropped in.

Figure 3.1. One Life, Two Lines

Start with the tool's defaults: 32 years old, $70,000 saved, $14,000 a year going in, growing at 7% a year after inflation. The smooth line reaches $2,744,010 at 67.^M Now turn on all eight one-time events, alternating good and bad, from 36 to 63. The jagged line ends at $2,587,662, which is $156,348 lower.^M

That gap isn't a surprise on its own. The four windfalls add up to $50,000 and the four curveballs to $98,000, so the eight events net to −$48,000. Losing money costs money. The surprise comes next.

Economists have a name for what the smooth line hides. In 1945, F. A. Hayek wrote that economists can forget "the constant small changes which make up the whole economic picture" because of a "preoccupation with statistical aggregates, which show a very much greater stability than the movements of the detail."⁵ That's his view, and he was writing about the economy as a whole, not one household. On this page the smooth line plays the aggregate and the jagged line plays the detail.

Figure 3.2. Same Events, Shuffled

The page has two buttons for this. Windfalls First puts the four good events at 36 to 48 and the four hits at 51 to 63. That pile ends at $2,809,184, which is $65,174 above the smooth line, even though the events still net to −$48,000.^M Curveballs First flips it: the hits land at 36 to 48, the good events after. That pile ends at $2,248,151, which is $495,859 below the smooth line.^M

Nothing about the events changed except when they happened. A dollar that leaves at 36 takes 31 years of compounding with it. A dollar that arrives at 63 only gets four. Early money, in or out, is the money that counts the most. That's the same arithmetic that makes the two levers on this site work, time and savings rate, just running in both directions.

Same idea, different variable. Market years have an order problem too. This page holds the return at a steady 7% so only life events move the line, but real markets have down years: in the S&P 500 from 1950 to 2025, about 2 in 10 calendar years were down before inflation, and closer to 3 in 10 after it.⁶ When a bad stretch lands matters most once money is coming out instead of going in. Four Isn't Fate shows that with Bad Years First.

Figure 3.3. Four Windfalls, Four Curveballs

These are teaching sizes, picked so a single event shows up on a 35-year chart. The real ones are usually smaller and much more frequent. In the Fed's 2025 household survey, 59% of adults had at least one major unexpected expense in the prior year, and car repair or replacement was the most common (30%). For car, home or appliance, and medical bills, the typical (median) cost was $1,000 to $1,999 among people who knew the amount.⁷ The same survey found 63% would cover a $400 expense with cash or its equivalent, and 55% had three months of rainy-day savings.⁸

Job loss is the one that can run long. In 2025 the typical (median) stretch of unemployment was 9.9 weeks, and the mean was 23.0 weeks. By August 2026 the median had risen to 11.4 weeks.⁹ The long tail is real: for men who lost long-held jobs in mass layoffs, Steven Davis and Till von Wachter found an average cost of 1.4 years of prior earnings when unemployment was below 6%, and 2.8 years when it was above 8%.¹⁰ Those are averages for that group, not what any one job loss costs, and they're not what the −$15,000 preset stands for.

The Gift is a placeholder, and it's kept small on purpose. It stands in for an inheritance, and most families haven't received one. In the 2019 Survey of Consumer Finances, 21.9% of families whose parents didn't have a college degree had received one, and 27.2% of those whose parents did. Among the families who had, the median was $76,200 and $92,700.¹ About half of inheritances are under $50,000, and those make up only about 5% of all inheritance dollars.² So a big gift is a real possibility for some people, not something to count on.

Hold the two button numbers side by side. Same person, same savings habit, same eight events, same total, and that total is negative. One order still ends above the smooth line, and the other ends almost half a million below it. The smooth line didn't lie about the math. It just left out the part where life happens on its own schedule.

What this is not

This isn't a prediction of anyone's life events, a claim that windfalls or hits are likely, or a suggestion about how to plan for them. The event sizes are teaching values, the orders are chosen to show the effect, and 7% is a historical teaching rate. Different events or ages can flip the result. Education, not advice.

Try it: Smooth Is a Lie. Add events, move them around, and watch the Jagged Curve answer.