Averages Lie — Box Plots Don't
"Year X was on average good for stocks." Statements like this sound reassuring — but they conceal the crucial question: how reliable was that pattern?
An average of +10% can come from 13 years at +15% and one year at -50%. The box plot shows you both at a glance: the typical return and how much it varies.
What Is a Box Plot?
A box plot — also called a whisker diagram — is a compact representation of the return distribution. It answers five questions at once:
- Median (middle line): the typical value — exactly half of all years lie above it, the other half below. More robust than the average because outliers barely affect it.
- Box (colored area): the interquartile range (IQR) — this is where the middle 50% of all values fall. A narrow box = consistent pattern. A wide box = high dispersion.
- Whiskers (dashed lines): the range of "normal" values, typically 1.5× the box width.
- Points outside: outliers — unusual exceptional years that fall outside the norm.
- Diamond/Triangle: in SeasonAlpha the mean — often close to the median, but with outliers it can diverge significantly.
The Dow Jones by Decade Digit
SeasonAlpha analyzes all years since 1896 and groups them by their final digit (x0 through x9). This creates cohorts: all "x5 years" (1925, 1935, 1945 ... 2015, 2025) are analyzed together.
The chart shows clear differences between the cohorts:
x5 years are historically the strongest. The median sits at around +20%, the box extends consistently into positive territory — and even the upside outlier (+60%) shows the power these years can unleash. 2025 belongs exactly to this cohort.
x0 and x1 years are the most dangerous. Both show outliers of -75% to -80% — those are the great crash years (1930, 1931). The median sits near zero, the box is wide: high risk, little reliability.
x3, x4, and x8 years show positive medians with wide dispersion — broadly friendly, but with large downside swings possible.
x9 years stand out with a noticeably narrow box: the middle 50% cluster tightly around the median. This means: a comparatively consistent, predictable pattern — even if the median is only moderately positive.
What Does This Tell You as an Investor?
Three insights that an average value alone cannot provide:
1. Median beats mean. For x0 and x1, the mean is pulled downward by the extreme crash years. The median is more telling: it shows what you can expect in a "normal" x0 year.
2. Wide box = more uncertainty. A positive median is nice — but if the box ranges from -30% to +40%, that is not a reliable pattern. x5 is convincing because both the box and the median are positive.
3. Outliers are not errors. They show you the worst-case scenario. Anyone who was invested in x1 years (2001, 2011, 2021) knows: the wide box and the downside outlier were no theory.
How to Use the Decade Cycle in SeasonAlpha
- Open the "Decade Cycle" page
- Enter a ticker in the sidebar (default:
^DJI) - Expand the "Return Distribution by Cohort (Box Plot)" section
- Hover over individual boxes: median, Q1, Q3, min, max are displayed
- Compare: what final digit does the current year have? What does the historical box look like?
The current year 2026 carries the final digit x6 — a cohort with a positive median, but a notable upside outlier (+60% in a single year). The box is medium-width: moderate reliability.
Conclusion: Distributions, Not Averages
Box plots are one of the most revealing tools in data analysis — especially in the stock market, where a single crash year can distort the average of an entire decade. They show you not only what happened historically, but how stable that pattern was.
For the current year 2026 (digit x6): the median is positive, dispersion is moderate. No reason for euphoria — but no warning signal either, unlike x0 or x1.
Analyze your current stock market year at seasonalpha.ai — the decade cycle is waiting for you.
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FAQ
What does the final digit mean in the decade cycle?
The final digit of a year (0–9) determines its cohort. All years with the digit 5 — that is 1925, 1935, 1945, and so on — are analyzed together. This produces a robust sample of roughly 13 years per cohort from 130 years of stock market history.
Why is the median better than the average?
The median is the middle value of a sorted series — it is barely influenced by outliers. A single crash like 1931 (-53%) pulls the average sharply downward but leaves the median largely unaffected. For seasonal patterns the median is therefore more meaningful.
What does a narrow box tell me?
A narrow box (small IQR) means that the middle 50% of annual returns are clustered closely together. The pattern is more consistent — you have a better idea of what to expect. A wide box signals high uncertainty, even if the median is positive.
Are x5 years really always good?
Historically yes — but "always" does not exist in the stock market. 2025 is statistically in a strong cohort, but the box plot also shows: there were x5 years with negative returns. Statistics provides probabilities, not guarantees.
For which markets does the decade cycle work?
SeasonAlpha shows the decade cycle for all available tickers — from the Dow Jones and S&P 500 to the DAX and Euro Stoxx, through to individual stocks and ETFs. The longer the data history, the more robust the conclusion.