Two Standard Deviations Does Not Mean 95 Percent — Bollinger’s Own Rules Say About 90, and a Band Tag Is Not a Signal

The bands are drawn two standard deviations out, and the normal-distribution figure attached to two sigma is about 95 percent. John Bollinger's own published rules tell you not to make that inference. Rule 14 — “Make no statistical assumptions based on the use of the standard deviation calculation in the construction of the bands.” “The distribution of security prices is non-normal and the typical sample size in most deployments of Bollinger Bands is too small for statistical significance.”^[2]

And he gives the number he actually observes, in a parenthesis: “(In practice we typically find 90%, not 95%, of the data inside Bollinger Bands with the default parameters)”^[2]

That is the originator's practical observation, not a theorem — the rules page describes itself as “The rules below covering the use of Bollinger Bands were assembled in response to questions often asked by users and our experience over 30 years of using the bands.” This page reports the figure as his; it does not verify it.^[2]

The most common way the indicator is described is the one its author rejects. Rule 6 — “Tags of the bands are just that, tags not signals. A tag of the upper Bollinger Band is NOT in-and-of-itself a sell signal. A tag of the lower Bollinger Band is NOT in-and-of-itself a buy signal.”^[2]

Rule 7 gives the reason — “In trending markets price can, and does, walk up the upper Bollinger Band and down the lower Bollinger Band.” And rule 8 inverts the usual reading of a breach altogether: “Closes outside the Bollinger Bands are initially continuation signals, not reversal signals.”^[2]

Source 1 records that traders read tags in opposite directions. Source 2 is the author saying the tag by itself is neither reading. His rule 22 sets the scope of the whole tool — “Bollinger Bands do not provide continuous advice; rather they help identify setups where the odds may be in your favor.”^[1][2]

Rule 9 — “The default parameters of 20 periods for the moving average and standard deviation calculations, and two standard deviations for the width of the bands are just that, defaults.” “The actual parameters needed for any given market/task may be different.”^[2]

But the two parameters are not independent. Rule 11 gives the adjustment with numbers — “If the average is lengthened the number of standard deviations needs to be increased; from 2 at 20 periods, to 2.1 at 50 periods. Likewise, if the average is shortened the number of standard deviations should be reduced; from 2 at 20 periods, to 1.9 at 10 periods.”^[2]

Rule 10 constrains what the middle line is for — “The average deployed as the middle Bollinger Band should not be the best one for crossovers. Rather, it should be descriptive of the intermediate-term trend.” — and source 3 repeats it: “Bollinger Bands work best when the middle band is chosen to reflect the intermediate-term trend, so that trend information is combined with relative price level data.”^[2]

On the average type, rule 12 — “Traditional Bollinger Bands are based upon a simple moving average. This is because a simple average is used in the standard deviation calculation and we wish to be logically consistent.” — and rule 13 — “Exponential averages must be used for BOTH the middle band and in the calculation of standard deviation.” This matches the encyclopedia footnote already cited above; the two sources agree here.^[2]

One more definition that is often quoted loosely: “BandWidth tells us how wide the Bollinger Bands are. The raw width is normalized using the middle band. Using the default parameters BandWidth is four times the coefficient of variation.”^[2]

Source 3 is Bollinger's own history of the tool. “The earliest example of trading bands that I have been able to uncover comes from Wilfrid Ledoux in 1960.” He lists what came before: “In the early '70s percentage bands became very popular, though we have no idea who created them.” and “Percentage bands are fixed, they do not adapt to changing market conditions; Donchian bands use recent highs and lows and Keltner bands use Average True Range as adaptive mechanisms.”^[3]

The stated motive is not statistical elegance but removing the analyst's hand: “The problem with that approach was that percentage bands needed to be adjusted over time to keep them germane to the price structure and the adjustment process let emotions into the analytical process.” — “If you were bullish, you had a natural tendency to draw the bands so they presented a bullish picture, if you were bearish the natural result was a picture with a bearish bias.”^[3]

And the premise that made it possible was new at the time — “At that time volatility was thought to be a static quantity, a property of a security”, which he says he stopped believing after watching a volatility column change in a spreadsheet.^[3]

The sigma question this page opened with is settled by the author directly: “We use the population calculation for standard deviation”. And the defaults — “The defaults today are the same as they were 35 years ago, 20 periods for the moving average with the bands set at plus and minus two standard deviations of the same data used for the average.”^[3]

The name was unplanned: asked live on air what he called the lines, “so I blurted out the alliteratively obvious choice: “Bollinger Bands.””^[3]

Implementations disagree on one detail that changes every number on the chart: whether the standard deviation divides by n or by n-1. The source settles it in a footnote: "Since Bollinger Bands use the population method of calculating standard deviation, the proper divisor for the sigma calculation is n, not n - 1."^[1]

This is not a rounding difference. The sample form (n-1) divides by a smaller number, so it produces a larger sigma and therefore wider bands for the same prices. Wider bands mean a touch of the lower band is registered later, or not at all — so two charts of the same instrument can disagree about whether a signal occurred. This page does not compute the size of that gap for any particular window; it records which divisor the definition specifies.^[1]

A second footnote covers a related trap. If the simple moving average is changed to an exponential or weighted moving average, "it must be changed for both the calculation of the middle band and the calculation of standard deviation." Switching only the centre line to an EMA and leaving the sigma on a simple average is a mismatch the source explicitly warns against.^[1]

The bands are three lines. The middle is an N-period moving average; the upper is MA + Kσ and the lower MA - Kσ, where σ is an N-period standard deviation. The method was propounded by John Bollinger in the 1980s, and he registered "Bollinger Bands" as a U.S. trademark in 2011.^[1]

"Typical values for N and K are 20 days and 2, respectively." The default centre line is a simple moving average, with exponential averages "a common second choice", and "usually the same period is used for both the middle band and the calculation of standard deviation." 20 and 2 are described as typical, not as derived optima — the article calls them two parameters "chosen independently by the user."^[1]

Two derived measures come up constantly and are worth stating exactly. %b = (last - lowerBB) / (upperBB - lowerBB), which "equals 1 at the upper band and 0 at the lower band" — so values above 1 or below 0 mean price is outside the bands. Bandwidth normalises the width of the bands over time. %b is a position measure; bandwidth is a width measure. They answer different questions.^[1]

The stated aim is modest. "The purpose of Bollinger Bands is to provide a relative definition of high and low prices of a market. By definition, prices are high at the upper band and low at the lower band." That is a definition, not a prediction — it says where price sits relative to recent volatility, not where it goes next.^[1]

Traders read it in opposite directions, and the source says so. "Some traders buy when price touches the lower Bollinger Band and exit when price touches the moving average" — mean reversion. "Other traders buy when price breaks above the upper Bollinger Band or sell when price falls below the lower" — breakout. These are contradictory rules drawn from the same lines, and the article presents both without choosing.^[1]

On width: "When the bands lie close together, a period of low volatility is indicated", and "as the bands expand, an increase in price action/market volatility is indicated." Options traders reportedly sell options when the bands are historically far apart and buy when they are close together, expecting volatility to revert. Narrow bands describe present quiet; they do not date the move that follows.^[1]

The article has an Effectiveness section, and it does not read as promotion. "Various studies of the effectiveness of the Bollinger Band strategy have been performed with mixed results." Lento et al. (2007), analysing trades "spanning a decade from 1995 onwards" across markets including the Dow Jones and forex, "found no evidence of consistent performance over the standard 'buy and hold' approach."^[1]

The same study found the opposite rule worked better. The authors "did, however, find that a simple reversal of the strategy ('contrarian Bollinger Band') produced positive returns in a variety of markets." A separate study of the Chinese market reported "significant positive returns on buy trades generated by the contrarian version" of several rules including the Bollinger Band rule, "after accounting for transaction costs of 0.50%."^[1]

This page does not adjudicate those results and carries no backtest figures of its own. It records that the reference source itself publishes findings of no consistent advantage over buy-and-hold, alongside findings that the reversed rule performed better. Whether any Bollinger Band rule produces a profit is not addressed here.^[1]

This page now rests on three sources: an encyclopedia article and two pages written by the indicator's originator. Bollinger's book was not consulted, nor were the effectiveness studies the encyclopedia cites.^[1][2][3]

Sources 2 and 3 are the author describing his own tool. That makes them first-hand for what the tool is and what he intends by it — and not independent evidence that it works. The 90-percent figure is his practical observation with default parameters, not a measured statistic this page verified, and the rules are his guidance, not an industry standard.^[2][3]

Not established: how much the n versus n-1 choice moves the bands for a given window; which charting platforms use which divisor; whether any reading of the bands is profitable. No backtest figures of this page's own appear anywhere on it.^[1][2][3]

Retrieved 2026-09-28. Both originator pages HTTP 200 and read in full (74 and 64 lines); 28 quotations from them were each searched for in the fetched text before publication.^[2][3]