Function bollingerPercentB

Bollinger %B — where the price sits inside its own bollinger channel, as a fraction of the channel's width:

percentB = (price − lower) / (upper − lower)
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1 is a price on the upper band, 0 on the lower, 0.5 on the centre; above 1 or below 0 is a price outside its bands. Appends one column, default 'percentB'.

Not ×100. StockCharts and TradingView both draw %B as a decimal with 0 and 1 as the reference lines, and the whole reading is "is it above 1 / below 0", which the decimal form states directly. The % in the name is the indicator's, not a unit. (This is the opposite choice from bollingerBandwidth's ×100, and for the same reason: match the chart a caller is comparing against, per study.)

One column, read twice — deliberately

The price in the numerator and the price the bands are built from are the same column. That is the definition (%B places a series inside its own bands) and it is what makes the flat-window case a genuine 0/0 rather than something over zero. A caller who wants one series placed inside another's bands has bollinger plus arithmetic; an option for it here would be a second indicator wearing this one's name.

The flat window is undefined, and here that IS a 0/0

When σ = 0 the denominator 2·stdDev·σ is zero — and so is the numerator, because a flat window's price is its own mean. A genuine 0/0: the price could be said to sit anywhere in a channel of no width, so it sits nowhere. undefined.

This is the opposite answer from bollingerBandwidth's 0 on the same window, and the pair is the clearest illustration of the rule the package applies: ask whether the numerator is forced to zero independently of the denominator. BandWidth's is (it is 2·stdDev·σ itself); %B's is only zero because the window is flat, which is the same fact as the denominator being zero. bollinger itself draws the degenerate band there (upper = lower = middle, [PND-BBFLAT]) — a band of no width is a real thing to draw, but the price's position in it is not a real thing to report.

Edges

• Warm-up is period − 1 rows, and — as with bollingerBandwidth — it does not compose with the source's when run over another study's output. Length-preserving.
• Scale- AND shift-INVARIANT: numerator and denominator are both differences of prices in the same units, so a common multiplier cancels in the ratio and a common offset cancels in the numerator. Unlike bollingerBandwidth, which is only the first of the two — pinned by property tests on both studies, because the difference between them is exactly the mistake a reader would make.
• Unbounded. There is no clamp: a price far outside its bands reads well above 1 or below 0, which is the signal.
• A gap costs exactly its own bar. The window statistics skip a missing cell (see bollingerBandwidth, which therefore loses nothing), but the numerator reads the bar's own price, so the gap bar has no position and the next one does. Measured and pinned in study-missing-cells.test.ts.
• On every bar where bollinger emits bands with width, percentB equals (price − bbLower)/(bbUpper − bbLower); pinned by a test against the shipped study. The flat window is the one exception: the bands are drawn there (degenerate) and %B is undefined.