Indicator library · Regime

Efficiency Ratio, Direction Over Noise

Where price ended up, divided by how far it travelled to get there. Almost everything else on this site reads the endpoints; this reads the path, which is why adaptive indicators are built on top of it.

The calculation

ER = |close − close n bars ago| ÷ Σ|close − previous close| over the same n bars.

The numerator is the direction: the net distance from one end of the window to the other. The denominator is the volatility in Kaufman’s sense, the total ground covered, bar by bar, regardless of sign. Divide one by the other and the result is confined between 0 and 1 without any need for normalisation, because both terms are distances in the same units.

A reading of 1 means every bar in the window moved the same way: the price went from A to B without a single step backward. A reading near 0 means the instrument travelled a long way and arrived where it started. Nothing about either statement involves the price level, the instrument’s volatility or the direction of the move.

The same net move made two waysThe upper panel shows a price series that advances in a straight line for fifteen bars and then zig-zags upward for fifteen more, ending at a similar height. The lower panel shows the efficiency ratio, which sits close to one during the straight advance and falls to about a fifth of that during the zig-zag, even though the net progress over each stretch is comparable.CLOSE0.60.2ER 100.12chop beginsThe same net move made two waysThe upper panel shows a price series that advances in a straight line for fifteen bars and then zig-zags upward for fifteen more, ending at a similar height. The lower panel shows the efficiency ratio, which sits close to one during the straight advance and falls to about a fifth of that during the zig-zag, even though the net progress over each stretch is comparable.CLOSE0.60.2ER 100.12chop begins
Fig. 1: schematicComputed at build time. The first half advances 7.5 points in a straight line and the ratio reads 1; the second half advances 2 points by zig-zagging and reads 0.118. Comparable progress, a difference of roughly 8× in efficiency, and no other measure on this site would separate the two stretches, because the endpoints are almost the same.

Why the path matters

Every momentum measure in this library reads two endpoints. The rate of change subtracts a close from a close; RSI aggregates changes but discards their order; a moving average summarises levels. All of them report the two stretches in the figure above as broadly similar, because both went up by a similar amount over a similar number of bars.

They are not similar to trade. A straight advance can be held with a distant stop and rewards patience; a zig-zag to the same place stops out any reasonable trailing rule several times on the way. The efficiency ratio is the cheapest available statement of that difference, and it is the reason it appears as a component in adaptive indicators rather than as a chart people watch.

What uses it

Where the ratio does its work
UseHow
Adaptive averagesKAMA sets its own smoothing constant from the ratio: fast while movement is efficient, slow while it is noise.
Regime filtersApply trend rules only above a threshold, mean-reversion rules only below it, the same job ADX is usually given.
Position sizingAn inefficient market implies more adverse excursion for the same net move, which argues for a smaller position.
System diagnosticsSplitting a backtest's results by the ratio at entry shows whether an edge came from trending periods or from everything.

The last row is the least discussed and the most useful. A trend system tested over a decade reports one number; the same results split by whether the efficiency ratio was above or below 0.4 at entry frequently show that the whole edge came from a third of the sample, which is a statement about when the system works rather than whether it does.

Reading it on its own

Plotted by itself the ratio is a regime description and very little else, which is why it is rarely the chart anyone watches. Two habits make it useful without over-reading it.

Compare it with its own recent range rather than with a fixed level. An instrument whose ratio has run between 0.15 and 0.35 all quarter is telling you something when it reaches 0.5, even though 0.5 is not a high reading in the abstract. And read the direction of the ratio, not only its level: efficiency rising from a low base describes a market that has started to make progress, which is a different statement from efficiency that has been high for weeks.

Where it misleads

Known failure modes
SituationWhat goes wrong
Read as directionalThe numerator is an absolute value. A clean collapse scores as high as a clean advance.
Windows mixedA ratio over ten bars and over a hundred are different measurements. Thresholds do not transfer between them.
GapsAn overnight gap enters the numerator and the denominator as one large step, so a gap-and-drift stretch scores as highly efficient.
Very quiet marketsWhen the denominator is tiny, small rounding in the closes moves the ratio sharply. A liquidity floor helps more than a longer window.
Confused with related measuresThe vertical horizontal filter and the choppiness index answer the same question differently; their thresholds are not interchangeable.
Unadjusted pricesA split adds one enormous step to both terms, and the ratio it produces describes a corporate action.

What volume adds

The ratio measures the shape of the path and knows nothing about who made it. An efficient advance on expanding volume describes a market where size kept arriving on one side; an equally efficient advance on the thinnest sessions of the quarter describes a book with nothing in the way, which is efficient for exactly as long as that remains true.

The pairing is worth the second glance for a specific reason. The failure mode of any regime filter is that the regime changes before the filter notices, and thinning volume underneath an efficient advance is one of the few early indications available that the condition producing the efficiency is being withdrawn.

Frequently asked questions

How is the efficiency ratio calculated?

Divide the net change over n bars by the sum of the absolute bar-to-bar changes over the same n bars. The numerator is where price ended up; the denominator is how far it travelled to get there. The result runs from 0 to 1: one means every bar moved in the same direction, and a value near zero means the instrument covered a great deal of ground and arrived almost nowhere.

What does it actually measure?

How much of the movement was useful. Perry Kaufman called it efficiency for a reason borrowed from mechanics: the ratio of output to effort. Two stretches can have an identical net move and completely different ratios, and the difference is the path, one advanced in a straight line, the other zig-zagged to the same place. Nothing else on this site measures the path rather than the endpoints.

Is it the same as the vertical horizontal filter or the choppiness index?

They belong to the same family and are computed differently. The vertical horizontal filter divides the range of the window by the sum of absolute changes; the choppiness index compares the sum of true ranges with the window’s total range and puts the result on a logarithmic scale. All three ask whether movement was directional or noisy, and none of them is a transformation of the others, so quoting a threshold from one on another is an error.

Does it say anything about direction?

Nothing, because the numerator is an absolute value. A clean advance and a clean collapse both produce a ratio near one. That is deliberate and it is what makes the measure usable as an input to something else: it answers "was this movement efficient", and whatever uses it supplies the direction separately.

What lookback should I use?

Ten is Kaufman’s own for the adaptive average built on this, and the choice sets what "recently" means rather than tuning a quality. A short window reports the character of the last week and swings between extremes; a long one describes a quarter and rarely reaches either end. The number belongs to the horizon of the decision, and stating it matters because a ratio of 0.3 over ten bars and over a hundred are not comparable readings.

What counts as a high or low reading?

Above roughly 0.6 the movement has been strongly directional; below about 0.2 it has been almost entirely noise. Those are descriptive rather than statistical, and they hold up better across instruments than most thresholds on this site, because the ratio is already normalised by construction, dividing distance by distance, so it does not carry the instrument’s price level or volatility with it.

What is it used for?

Mostly as an input. Kaufman’s adaptive moving average uses it to set its own smoothing constant, so the average is fast when movement is efficient and slow when it is not. More generally it is a regime filter: apply trend rules only while the ratio is high, mean-reversion rules only while it is low. Read on its own it is a description of the recent path and rarely enough to act on.

How does it differ from ADX?

Both answer "is this trending" and they measure different things to get there. ADX compares directional movement with the true range through three layers of smoothing, so it is late and steady. The efficiency ratio is a single unsmoothed division over a window, so it responds immediately and is noisier. On the same data they agree about regimes and disagree about turns, and the efficiency ratio is by far the cheaper of the two to compute or to explain.