Bollinger Bands vs Standard Deviation
Michael Whitman
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Trading since 2017, full-time since 2020
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YouTube creator, 137K subscribers
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Published 2026-09-08
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Updated
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Reviewed
Bollinger Bands take the standard deviation of the last 20 closes and draw it two deviations either side of their 20-session average. Standard deviation is that underlying number, so the bands are the measure drawn on the chart, with a center line and a multiplier added.
These are not two tools. One is a statistic, and the other is that statistic drawn around a moving average. The useful comparison is what the drawing adds, what it hides, and what the number does that the picture cannot, and a third of a century of SPY closes answers each of those.
What each one is
Standard deviation measures how spread out recent values have been. For 20 closes: take their mean, square each close’s distance from it, average those squares and take the square root. John Bollinger’s site specifies the population calculation, dividing by 20. Standard deviation covers the statistic.
Bollinger Bands plot that number around its own average. A 20-session simple average with a line two deviations above and two below. Bollinger Bands covers the construction, and StockCharts’ Bollinger BandWidth turns the gap between the lines back into a single percentage.
So one contains the other. Everything the bands do is the deviation made visible, and every limitation of the deviation comes with it.
Where they differ
A picture against a number. The bands are read at a glance against price; the raw deviation is a value compared against its own history, usually in a panel or inside a rule.
What the plot adds on top. A center line and a multiplier. Both are choices layered on the statistic, and both change what a touch means.
Comparability. The raw deviation is in dollars, so it grows with the price. Divided by the average it becomes a percentage that compares across years and markets. The bands do that division silently, by drawing the lines around price, but never show you the number.
Where the drawing and the number agree
They are the same calculation, so neither can disagree with the other; a difference between them is an error in one of the settings. Both read closes only, so gaps and wicks never enter. And both lag: every value is built from closes already printed.
Which one to use: Bollinger Bands or Standard Deviation?
Use the bands when you want the measure in place on the chart. Seeing dispersion around price is easier than reading a number in a separate panel.
Use the raw deviation when a rule needs a value. A volatility filter, a position size or an alert level all want the number rather than the picture.
Use the deviation divided by price when you compare. Across years, or across two markets, dollars mislead and percentages do not.
And when somebody offers the two as alternatives, they have missed the relationship. Choose by the job, not by which is better.
How far out a close can land
There is a hard ceiling. With 20 closes in the window and today’s close among them, today’s close can never sit more than √19, about 4.36, deviations from the average: if it moved further, the deviation would grow with it. A three-deviation close is close to the most extreme reading the calculation can produce.
And the bell curve is the wrong yardstick. A normal distribution puts 31.73% of values beyond one deviation and 0.27% beyond three. Prices that trend sit away from their own recent average much more often than that, so the bands are touched more often than the statistics-class picture implies.
When one close leaves, the deviation jumps
28 August 1996 is the clearest case on SPY. The 20-close window before it included 31 July 1996, a close of $64.09, 3.44 deviations below that window’s average of $66.38. On 28 August that close dropped out of the window. SPY closed at $66.67, down 0.16% on the day, and the deviation fell from $0.66 to $0.41, a drop of 38.43%. The bands narrowed from $65.05-$67.71 to $65.69-$67.33.
Nothing happened in the market that day. The squeeze reading changed because an old outlier expired, 20 sessions after it printed. Any rule reading the bands’ width inherits that calendar.
The original data
The sample. SPY daily closes from Yahoo Finance, 29 January 1993 to 2 October 2026; measurement starts 3 January 1994, giving 8,243 sessions. Deviation: population form of the last 20 closes, today’s included; z = (close − 20-session average) ÷ deviation.
Where closes sat, in deviations. 4,852 closes (58.86%) were more than one deviation from their average and 3,391 (41.14%) within one. Beyond three: 41 closes, 0.50%, against 0.27% for a normal curve. The highest was 3.29 above, on 5 September 1995; the lowest 3.89 below, on 9 September 2016. More closes landed between one and one and a half deviations above the average, 1,607, than in any other half-deviation slice.
Population or sample makes a visible difference at the edge. Dividing by 19 instead of 20 widens every band slightly. Of the closes that landed outside the population bands, 117 would have been inside the sample-form bands and 764 would still have been outside: one outside close in about seven and a half depends on which formula your platform uses.
Dollars against percentages. SPY’s median 20-close deviation by year was $0.41 in 1994 and $7.53 in 2026 (to 2 October), about 18.5 times larger, while the median close rose from $46.17 to $737.05. As a share of the 20-session average the medians were 0.88% and 1.04%. The highest yearly median was $9.76 in 2022 (2.41%); the lowest share was 0.647% in 2017.
The deviation’s biggest one-day falls came from the window, not the market. The three largest, 28 August 1996 (−38.43%), 30 August 2012 (−37.11%) and 4 August 2016 (−35.71%), all fell on sessions when SPY moved less than 1%. Every session’s average, both deviations and z are in the SPY close position file, and the yearly medians in the yearly deviation file.
When it fails
The failure is treating a band touch as an extreme. A close tags the upper line, looks overextended, and gets faded. On SPY more than half of all closes sat over one deviation from their average, and a trend can hold price near the band for weeks while the envelope widens beneath it.
The second failure is comparing dollar deviations across years or markets. A $7 reading meant something different in 2026 than in 2002.
A third is reading a sudden narrowing as quiet. It may only be an old outlier leaving the window.
A fourth is ignoring the formula. Population and sample bands disagree on about one outside close in seven and a half.
And a fifth is running the bands and the raw deviation as two confirmations. That is one calculation read twice.
Related
Bollinger Bands covers the plotted version. Standard deviation covers the measure underneath. And average true range covers the alternative that reads the whole bar.
Knowing that the bands are the deviation drawn on the chart changes how you read them. A touch says price is a stated distance from its own average, a distance the calculation reaches far more often than the textbook bell curve suggests. Read it as a position, not as an alarm.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.