Length encodings must start at zero

What it is

Bars, areas, and blocks — encodings that carry value in length or area — are read proportionally: "this bar is twice as long, so the value is twice as large." That reading holds only with a zero baseline — length proportional to value is what makes proportions meaningful. Move the baseline to a non-zero value and length carries "value minus offset," while readers keep reading proportionally, so every comparison they utter is wrong. The zero baseline is not a convention but the mathematical precondition of length encoding: without it the encoding does not exist. This leaf is the encoding-level rule governing every chart that uses length — bars, histograms, areas, lollipops, bullet charts — not just the bar-chart family.

Why it happens

The perceptual contract of length encoding is a shared origin: two bars leaving the same baseline is what lets their length difference be read as a value difference. A truncated baseline quietly rewrites the contract to "measure from the offset," but the reader's habit is unchanged (years of bar-chart training cemented proportional reading), producing systematic amplification: the value difference unchanged, the visible difference multiplied (amplification = data range / visible range). Area encoding suffers worse — area scales with the square of edge, so truncation error multiplies again. This is why "a little truncation is harmless" fails: the offset enters by multiplication, not addition.

Where it stops holding

The rule binds only length/area encodings; position encodings (vertical placement of points and lines) do not depend on an origin and may be legitimately truncated (next leaf). Diverging bars take a meaningful midpoint as zero (positive/negative, target) — that defines zero at the centre of symmetry rather than truncating. Percentages are naturally bounded (0–100): start at 0 and done. Interval scales without a true zero (Celsius-like) should not be length-encoded for comparison at all. Bars on a log axis are a special case — zero does not exist logarithmically, which is why bars do not belong on log axes.

Applying it

• Audit library defaults: some tools auto-tighten the range "for looks"; bar charts must pin the zero baseline explicitly.
• Review rule: any length/area-encoded mark with axis start ≠ 0 goes back; exceptions (diverging zero) must state their zero definition.
• Verification: pick two bars; readers' reported length ratio should equal the true value ratio; if not, check the baseline first, then the scale type.

Related

• Same group: U3.01.2 Position encodings tolerate truncation when clearly marked · U3.01.3 Axis truncation is the most common misleading device
• Nearby: U2.02.2 The baseline must start at zero · U2.04.1 Only the bottom series of a stacked chart owns the common baseline · U3.02.4 Length encodings crossing the break lose all comparability
• Search terms: zero baseline · length encoding · truncated axis · bar chart