All facets must share the same scale to be comparable

What it is

Small-multiple comparison is cross-panel comparison, and it holds under one precondition only: every panel uses the same numeric scale. Once each panel auto-fits its own data range (the charting library default), a "full height" in one panel may be half in another — shape comparison distorts wholesale, and the "differences" readers see mix real differences with scale differences, inseparably. A shared scale is not an optional polish but the qualification condition for small multiples as a comparison tool.

Why it happens

The perceptual act of cross-panel comparison "carries a panel's shape to another panel under one ruler": with a shared scale the transfer is faithful; without one, readers transfer as if faithful, and the error equals the conversion gap between the two scales. Auto-fitting is also insidious: each panel looks "correct" alone, the damage erupts only in comparison, and single-panel inspection never finds it. The one legitimate use of free scales is shape-similarity comparison (removing magnitude to compare waveforms) — a specially declared analytical purpose, never a default.

Where it stops holding

When groups span orders of magnitude, a shared range flattens the small groups — and the right move is not unshackling each panel's scale but fixing the units first: log axes, indices (each group as a percentage of a base period), or per-group normalized shape plots, explicitly declaring the forfeited absolute comparison. Count facets share the y-axis count range; time facets share the time window and spacing. Ticks and gridlines must also agree, or the "aligned reference lines" between panels are themselves misaligned.

Applying it

• Turn off per-panel auto-fitting in facet rendering; compute one unified range and tick set over the full data; make shared scale the template default.
• For wide magnitudes, switch to log axes or indexed facets and caption "comparing relative change."
• Verification: the same value should render at the same height in any two panels; check with a data point present in two panels — different heights mean scales were not shared.

Related

• Same group: U2.15.1 Small multiples replace overlay with repeated like-for-like panels · U2.15.3 Facet order should carry information, not alphabetical habit · U2.15.4 Too many facets shrink panels below readability · U2.15.5 Small multiples compare shapes, not precise values
• Nearby: U1.11.3 Only charts sharing a scale can be compared on magnitude · U3.03.1 Log scales suit cross-magnitude data but demand logarithmic literacy
• Search terms: shared scale · faceted scales · free scales · small multiples