The efficiency ratio (ER) was introduced by Perry Kaufman as the engine of his adaptive moving average. It answers a simple question: of all the ground price covered, how much of it actually got anywhere?
The formula
Over a lookback of n bars:
- Net change = the absolute difference between the latest close and the close n bars ago.
- Path length = the sum of the absolute bar-to-bar close changes across the same window.
- Efficiency ratio = net change ÷ path length.
Because both parts are measured in the same units, the ratio is scale-free: it reads the same on Bitcoin at 70,000 and on a token at 0.50, and on a 3-day chart as on a monthly one.
Two extreme examples
- Price rises by 1 on each of ten bars. Net change is 10, path length is 10, so ER = 1.00 — perfectly direct travel.
- Price alternates +2, −2, +2, −2 for ten bars. Net change is 0, path length is 20, so ER = 0.00 — lots of movement, no progress.
Real markets sit in between, and the interesting signal is usually the change in the ratio: a trend that keeps its direction while its efficiency falls is covering more ground to get less far.
How MoonWire uses it
Our multi-timeframe reads compute ER over the last 10 closes on each timeframe and label trend strength from it: strong at 0.50 or above, moderate from 0.30, weak below 0.30. Direction comes separately from price versus its moving average, so a chart can be "up, weak" — rising, but inefficiently.
Two published readings show the range. On 4 August 2026 Bitcoin's 3-day trend flipped up on an ER of about 0.03, the least directional travel anywhere on that week's board. On 3 September 2026 Ethereum's 3-day ER fell to 0.60 — lower than the week before, but still in trending territory.
ER describes the path already taken. It does not say whether the next bars will be efficient.