Balance of Power Indicator (BOP): Formula, Raw vs 14-Bar Signals and the Gap Problem

The Balance of Power (BOP) measures, bar by bar, how far the close finished from the open relative to the bar's full range. Igor Livshin presented it in Technical Analysis of Stocks & Commodities in August 2001 as a way to score bulls against bears by “assessing the ability of each to push price to an extreme level”. A bar that opens at its low and closes at its high scores +1; the reverse scores −1. The raw values are noisy, so the Traders' Tips code published with the article plots a 14-bar average.

How the Balance of Power is calculated

Livshin's article computes three rewards for each side, based on the open, on the close and on the move from open to close, each divided by the high-low range, and averages them. The Traders' Tips published with it pointed out that, “if you do the math”, the raw value “is actually equivalent to (Close-Open) / (High-Low)”. We checked the identity on our data: the three-reward version and the short formula give the same values.

Livshin wrote that he “deliberately developed BOP not to be a range-bound indicator, so it is as sensitive at extreme points as it is at other levels”. The value itself still cannot leave −1 to +1, as the simplified formula shows. In practice the 14-bar average stays well inside it: on daily Bitcoin from March 2025 to October 28, 2026, it ran between −0.301 (June 6, 2026) and +0.297 (October 9, 2025).

How traders read it

• Above zero: closes have been finishing above opens on average, read as buyers in control; below zero, sellers.
• Zero-line crosses of the average, as a change of side.
• Divergence: price making a new high while the BOP average makes a lower high, or the reverse (see divergence).

Raw BOP or the 14-bar average: how many signals?

We took the last 600 bars of three series to October 28, 2026 and counted the zero-line crosses from the 15th bar on, once the 14-bar average exists: 586 bars per series. The hourly Bitcoin window runs from October 4 to October 28, 2026; the daily windows start in March 2025 for Bitcoin and in June 2024 for the S&P 500 ETF. A bar with a value of exactly zero is skipped.

The raw value changes sign about every other bar, on every timeframe: it is the color of the candle, scaled. The 14-bar average cuts the crosses by about three quarters, still one every 7 to 8 hourly bars and about every 8 daily bars. Intraday, that is a cross every few hours on Bitcoin.

The gap problem

The BOP only sees the bar from its own open, as the left half of the schematic below shows. On a market that gaps, it can disagree with the day's change. In the same 586 daily bars of the S&P 500 ETF, the sign of the raw BOP was opposite to the sign of the close-to-close change on 114 of 585 day-to-day changes (19.5%; the one bar with a raw value of exactly zero is counted as not opposite), and on 57 of the 161 days that opened 0.5% or more away from the prior close.

On Bitcoin, which trades around the clock, each bar opens where the previous one closed, so the problem does not arise: in our series the sign of the raw BOP always matched the sign of the bar's change. The indicator reads very differently on a 24-hour market and on a market with a session gap.

Two indicators with the same name

Don Worden's TC2000 platform also has an indicator called Balance of Power, unrelated to Livshin's formula. Worden Brothers says that its formulation has never been published and is its intellectual property. Values you see under that name on TC2000 cannot be reproduced with the formula on this page.

Does it work?

No published test shows an edge for BOP crosses or divergences, and we did not test divergences here. Our bench measures chart patterns detected by rule against random entries, not indicators (see our methodology). The same close minus open over high minus low ratio is at the heart of the Relative Vigor Index, which smooths it differently. Indicators that weigh where the close falls in the range by volume include the accumulation/distribution line and Chaikin Money Flow. One way to filter BOP crosses by trend is a moving average or the MACD (our suggestion, untested). More tools are listed with the trend indicators.