The Bollinger Bands indicator, created by financial analysis master John Bollinger, is fundamentally based on the statistical theory of normal distribution. This indicator cleverly integrates the short-term fluctuations of the financial market with long-term patterns, showcasing the essential characteristics of price movements around a central value.

The normal distribution theory states that data typically exhibits a regular distribution around the mean. Specifically, about 68% of the data falls within one standard deviation of the mean, 95% of the data is within two standard deviations of the mean, and 99.7% of the data is distributed within three standard deviations of the mean. Bollinger Bands are based on this principle, treating price fluctuations as random variables that follow a normal distribution, thereby constructing dynamic boundaries for price volatility.

Through extensive empirical research, Bollinger discovered that a 20-day moving average as the middle band (mean), combined with two standard deviations above and below, can most accurately reflect the normal price fluctuation range. This means that approximately 95% of price data will fall within this range, and fluctuations beyond this range can be considered abnormal. This is also the theoretical basis for using Bollinger Bands to assess market overbought and oversold conditions.

A notable feature of the Bollinger Bands is its dynamic adjustment capability. It can automatically adjust its bandwidth according to changes in the market environment: when the market is calm, price fluctuations are small, and the bandwidth narrows; whereas during periods of significant market volatility, the bandwidth expands accordingly. This adaptability allows the Bollinger Bands to maintain its effectiveness under different market conditions.

Overall, Bollinger Bands provide investors with an intuitive and scientific tool by applying statistical principles to financial market analysis, helping them better understand and predict market trends.