wickra/docs/wiki/indicators/volume/Indicator-EaseOfMovement.md

EaseOfMovement

Ease of Movement (EOM) — Richard Arms' measure of how far price travels per unit of volume, averaged over a window.

Quick reference

Field	Value
Family	Volume
Sub-category	Oscillators
Input type	Candle (uses high, low, volume)
Output type	f64
Output range	unbounded around zero (scaled by divisor)
Default parameters	period = 14, divisor = 1e8 (Python)
Warmup period	period + 1
Interpretation	Light-volume moves push it away from zero; sign tracks direction.

Formula

distance_t = (high_t + low_t)/2 − (high_{t−1} + low_{t−1})/2
EMV_t      = distance_t · (high_t − low_t) · divisor / volume_t
EOM_t      = SMA(EMV, period)_t

Arms' question is how easily did price move? A bar whose midpoint jumped a long way on a wide range but light volume gets a large EMV; a bar that needed heavy volume to budge gets a small one. The divisor is a pure output-scaling constant — the conventional 1e8 keeps EMV readable for typical share volumes; smaller markets want a smaller divisor. The window SMA smooths the noisy per-bar EMV into a tradeable line.

Parameters

• period — the SMA averaging window (Python default 14).
• divisor — the volume-scaling constant (Python default 1e8). Rust exposes EaseOfMovement::new(period) for the 1e8 default and EaseOfMovement::with_divisor(period, divisor) for an explicit value.

Inputs / Outputs

From crates/wickra-core/src/indicators/ease_of_movement.rs:

impl Indicator for EaseOfMovement {
    type Input = Candle;
    type Output = f64;
    // update(&mut self, input: Candle) -> Option<f64>
}

EaseOfMovement is a candle-input indicator that reads high, low and volume. In Python the streaming update accepts a 6-tuple or a dict; the batch helper takes high, low, volume numpy arrays. Node and WASM expose update(high, low, volume) and the matching batch.

Warmup

EaseOfMovement::new(14).warmup_period() == 15. The first candle only seeds the previous midpoint, so the first EMV appears on candle 2 and the first averaged value on candle period + 1.

Edge cases

• Zero-volume bar. Contributes EMV = 0 instead of dividing by zero (zero_volume_contributes_zero pins this).
• Zero-range bar. high == low makes the (high − low) factor zero, so EMV = 0.
• Constant series. Unchanging midpoints give zero distance, so EOM stays at 0.0 (constant_series_yields_zero pins this).
• Reset. eom.reset() clears the previous midpoint and the SMA window.

Examples

Rust

use wickra::{BatchExt, Candle, Indicator, EaseOfMovement};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // EOM(period = 1, divisor = 1): one EMV value is its own average.
    let mut eom = EaseOfMovement::with_divisor(1, 1.0)?;
    let out = eom.batch(&[
        Candle::new(9.0, 10.0, 8.0, 9.0, 50.0, 0)?,      // seeds the previous midpoint (9)
        Candle::new(12.0, 14.0, 10.0, 12.0, 100.0, 1)?,  // mid 12, distance 3, range 4
    ]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, Some(0.12)]

Bar 2: EMV = distance · range · divisor / volume = 3 · 4 · 1 / 100 = 0.12. This matches the reference_values test in crates/wickra-core/src/indicators/ease_of_movement.rs.

Python

import numpy as np
import wickra as ta

eom = ta.EaseOfMovement(1, 1.0)
high = np.array([10.0, 14.0])
low = np.array([8.0, 10.0])
volume = np.array([50.0, 100.0])
print(eom.batch(high, low, volume))

Output:

[ nan 0.12]

Node

const ta = require('wickra');
const eom = new ta.EaseOfMovement(1, 1.0);
console.log(eom.batch([10, 14], [8, 10], [50, 100]));

Output:

[ NaN, 0.12 ]

Interpretation

EOM crossing above zero says price is drifting up without needing much volume — an easy, low-resistance advance; below zero is the same for a decline. A reading hovering near zero means volume is heavy relative to the distance covered, i.e. price is grinding. The sign tracks direction; the distance from zero tracks how freely the move is happening.

Common pitfalls

• Reading the raw magnitude. It depends entirely on the divisor you chose — only the sign and relative size are portable.
• Feeding it scalar prices. It needs high, low and volume.

References

Richard W. Arms Jr.'s Ease of Movement; the box-ratio formulation here matches the standard definition.

See also

• Indicator-ForceIndex.md — a different price-change-vs-volume gauge.
• Indicator-ChaikinMoneyFlow.md — bounded money-flow balance.
• Indicators-Overview.md — the full taxonomy.