Function balanceOfPower

Balance of Power (Igor Livshin) — how much of the bar's range the buyers or the sellers actually took:

bop = (close − open) / (high − low)
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The body over the range. +1 is a bar that opened on its low and closed on its high (buyers took the whole thing), −1 the mirror, 0 a bar that closed where it opened however far it ranged in between. Bounded [−1, +1] on real bars, because the body cannot exceed the range.

Appends one column, default 'bop'. Reads open, high, low and close, each named by an option defaulting to its DEFAULT_OHLCV name.

One indicator, two conventions — the raw form ships (F-AMBIG)

TA-Lib's BOP is the raw per-bar ratio above, with no smoothing at all; ChartIQ and several other packages draw it through a moving average, because the raw line is noisy enough to be hard to read. Both are in circulation and they are the same indicator, so this study ships the raw form by default — that is the one an oracle can pin bar-for-bar against TA-Lib — and exposes period to get the smoothed one:

balanceOfPower(bars);                              // TA-Lib BOP, exact
balanceOfPower(bars, { period: 14 });              // the smoothed form
balanceOfPower(bars, { period: 14, maType: 'ema' });
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maType is the shared MaType menu (spelled maType, not type, because the average is an ingredient here rather than the output — the keltner / envelope side of that split). It throws when passed without a period: an option that silently does nothing is worse than an error, and there is no sensible "smooth with an EMA but over no bars".

A flat bar is 0, not missing — and that is the algebra, not TA-Lib

high === low makes the denominator zero. It also makes the numerator exactly zero on any real bar: a bar with no range traded at one price, so its open and close are that price and close − open is 0. The value is therefore 0 — the limit from either side, and the honest reading (no side took anything, because there was nothing to take). This is the clvValues rule and the same argument #699 settled there, not a copy of TA-Lib's guard, though the two agree: TA-Lib returns 0.0 when high − low < 1e-8.

The one deliberate delta is that threshold. TA-Lib treats any range under 1e-8 as flat; this study tests range === 0 exactly, so a bar with a genuine but sub-1e-8 range reports the (large) ratio rather than 0. At the scale of real prices such a bar is a rounding artefact either way; the exact test is used because an epsilon that is right for dollars is wrong for a column of basis points, and the oracle asserts the fixture has no bar in the gap so the TA-Lib agreement is exact where it is claimed. A redirected open or close (pointed at a smoothed column, say) can put a non-zero body over a zero range; that reads 0 too, as clvValues does — a bar with no range has nowhere to place anything.

Edges

• No warm-up in the raw form: bar 0 is defined. With period, the warm-up is the chosen average's own over the derived array (period − 1 for the window types, later for the composed ones — see movingAverageValues).
• Scale- AND shift-invariant: the body and the range are both differences of prices, so a common multiplier cancels in the ratio and a common offset cancels in each difference. This is the rsi side of the scale pair, not the atr side — both pinned by property tests.
• A gap in any of the four inputs costs that bar in the raw form, plus whatever the chosen maType costs when smoothing (window types recover, the ema family skips, smma and kama propagate).
• The zero-range guard is at the output and therefore live: the division is the last thing that happens before withColumn in the raw form, and the guard is what stops ±Infinity reaching the carrying maTypes in the smoothed one.