Two standard deviations set each band’s distance from the moving average. They do not give your next trade a 95% chance of success. The confusion starts when a familiar statistic becomes a promise about a changing market.
This Read the Reaction lesson follows one warning from John Bollinger, then tests the distinction with an original calculation. The question is what a band can measure—not whether a particular chart looks convincing.
Start with the creator’s warning
In his account of the bands’ development, Bollinger recalls working with options and technical analysis after becoming active full-time in 1980. He sought widths that adapted to changing volatility. That is a technical-analysis tool from traditional markets, not a complete mechanical crypto strategy.
His fourteenth published rule explicitly cautions against inferring statistical properties merely because the calculation uses standard deviation. Applying that warning here does not attribute this exercise, a crypto recommendation or a performance claim to him.
Where the 95% idea comes from
For a normally distributed variable, approximately 95.45% of its probability lies within two population standard deviations of its population mean. NIST’s reference table states that mathematical result. It depends on the distribution and its parameters; a chart setting of “2” does not establish them.
A rolling average and rolling standard deviation are calculated from a finite, changing window. They are not known parameters of a stable normal distribution for the next price. Calculating dispersion does not prove normality. Adjacent 20-bar windows also share 19 observations, so a long sequence of readings is not automatically independent evidence.
A confidence interval for a mean addresses uncertainty about that mean, as NIST explains. A prediction interval addresses future observations and needs its own assumptions and calculation. NIST’s prediction-limit method accounts for estimating parameters from a sample. Neither label attaches automatically to trading bands.
Calculate the width before interpreting it
For this exercise, use the traditional construction described by Bollinger: a 20-period simple moving average, plus and minus twice the population-form standard deviation of the same closing prices. “Population-form” specifies the divisor here; it does not claim that 20 prices represent the entire market.
The average is the sum of 20 closes divided by 20. For standard deviation, subtract that average from each close, square the differences, sum them, divide by 20 rather than 19, then take the square root. The result has the same price units as the closes. We are measuring price levels, not percentage returns.
Imagine one fictional spot market’s completed one-hour closes, in USD per token. Closes 1–20 alternate 98, 102, 98, 102, continuing for ten pairs. All values are invented; this is arithmetic, not market data or a backtest.
At close 20, the average is 100. Every squared deviation is 4, so the standard deviation is √(80 ÷ 20) = 2. The lower and upper bands are 96 and 104. All 20 input closes fall within that one final interval. That 100% retrospective containment does not supply the next close’s probability—or measure each historical close against its own contemporaneous band.
Freeze the band, then reveal the next close
Before close 21 arrives, record the 96–104 interval. Now reveal an invented close of 104.50. It is above the frozen upper boundary because 104.50 > 104.00.
Next update the rolling calculation: remove the oldest 98 and add 104.50. The new window contains nine 98s, ten 102s and one 104.50. Its mean is 100.325; its variance is 4.706875 USD² per token².
| Measure | Close 20 | Close 21 |
|---|---|---|
| Mean | 100.000 | 100.325 |
| Standard deviation | 2.000 | 2.170 |
| Lower band | 96.000 | 95.986 |
| Upper band | 104.000 | 104.664 |
The same 104.50 is inside the updated bands. Nothing reversed: the observation helped change its own comparison interval. The close-20 bands remain unchanged at close 20; this is a new window, not a rewrite of the old one.
Both comparisons are legitimate if labeled. Only the frozen interval was available before close 21. One outcome cannot estimate a reliable coverage rate, and this constructed case proves no trading edge.
Keep three questions in separate records
A repeatable review distinguishes:
- Contemporaneous containment: does each completed close lie within the bands calculated including that close? Count boundary equality as inside and exclude warm-up bars without a full window.
- Next-close coverage: does the following close lie within bands frozen at the preceding close? Keep the one-bar horizon fixed. A close inside says nothing about intrabar excursions.
- Trade outcome: what did specified entries, exits and position sizes earn after costs? Neither containment count provides those orders or their fills.
Record venue, instrument, candle boundaries, price source, settings and exact sample dates. Count all eligible cases, not just attractive screenshots. Keep later evaluation data separate from data used to choose settings; overlapping windows and changing conditions limit what a raw percentage establishes. Our backtest guide explains why result definitions and coverage matter.
Use the bands for the question they answer
A band locates price relative to its recent window. It cannot establish which headline caused a move or predict the next announcement. The news-versus-technical lesson separates a catalyst from its observed reaction.
Before writing “95%,” name the event, horizon, calculation and evidence supporting that number. Without them, retain the band reading as a description and keep the probability claim out of the trade plan.
Educational only, not financial advice. All numerical market examples are hypothetical; no band setting guarantees containment or profit.
