Mechanism and definition
A chart can display price using either a linear or logarithmic scale.
- Linear scale: the chart’s vertical (or horizontal) distance changes in proportion to the absolute change in the value. If the price increases by the same amount each step, those steps look the same size.
- Logarithmic (log) scale: the chart’s distance changes in proportion to the percentage (ratio) change. If the price grows by the same percentage each step, those steps look the same size.
This distinction matters because chart interpretation often treats distance as meaning. With linear scales, distance reflects absolute movement; with log scales, distance reflects relative movement. That difference is the core mechanic behind most practical limitations.
Evidence and concrete example with clear assumptions
Assume a price starts at 100.
- Move A: from 100 to 110 is a +10 absolute change and a +10% relative change.
- Move B: from 200 to 210 is also +10 absolute change, but only +5% relative change.
On a linear scale, Move A and Move B take up the same vertical distance because both are +10 in value.
On a logarithmic scale, Move A and Move B take up different distances because the relative (percentage) changes differ (+10% versus +5%).
So, even if two moves look comparable under one scale, they can represent different kinds of “effort” under the other. This is not a flaw in the scale; it is a mismatch between what the scale visualizes and what your interpretation assumes.
Main limitations and failure modes
1) The wrong measurement interpretation
A common failure mode is assuming that chart distance represents the same concept under both scales. Under linear scaling, distance is tied to absolute differences; under log scaling, it is tied to relative changes. If a reader implicitly expects distance to always reflect “how big the move is,” they may draw incorrect conclusions.
2) Hidden assumptions about reference points
Log charts reflect ratios, so the choice of what part of the data is treated as the reference range affects how the plot “spreads out” over time. If you compare segments that start and end at different baseline levels, the apparent balance between moves can shift.
Because the baseline can be chosen by the charting setup and the time window you select, your conclusions may depend on those choices rather than on an underlying, scale-invariant property.
3) Variable relationships over time
Historical relationships between visual features (such as repeated-looking distances, slopes, or gaps) are not guaranteed to persist. Markets do not follow a stable rule that ensures that what looks similar on one scale today will map to the same meaning tomorrow.
Even without using any real-time data, it’s reasonable to expect that volatility conditions, liquidity, and the distribution of returns can change. When the underlying return behavior changes, the practical value of interpreting either scale as revealing stable structure can drop.
4) Costs and execution are not shown by scale
A scale choice changes the picture of price movement, but it does not incorporate trading costs, execution quality, or other frictions. Two setups that look consistent in chart space can produce different outcomes in practice if spreads, commissions, or execution timing differ. This creates uncertainty that visualization alone cannot resolve.
5) Reduced intuition for some users
Log scaling can be less intuitive if you mainly think in absolute terms. For example, many people naturally compare “how many units did it move,” which aligns with linear intuition. If you interpret log charts as if they were linear, the mismatch can produce systematic misreads.
Verification and what to check next
To independently verify what you understand about the limitation, focus on the assumptions behind your interpretation:
- Clarify whether your comparison is about absolute changes or relative (percentage) changes.
- Check how the chart behaves when prices double (ratios) versus when they add the same amount (absolute steps).
- Compare the same time window in both scales and ask what changes in your interpretation, not just what changes visually.
- Treat any historical “repeatability” as uncertain: different future conditions may not preserve the same mapping between chart shape and real movement.