A bar chart's vertical axis starts at 92 rather than 0, and two bars whose values differ by 4% look three times apart — why?

## What a bar's length is carrying A **mark** — the thing actually drawn for each row or each group, a point, a bar, a line, a tile — carries a column's values through a **visual channel**, a property of the mark such as position along an axis, length, area or colour. A bar's channel is **length**: the distance from the baseline to the bar's end. A reader recovers the number by seeing how long the bar is, and that length, measured in data units, is exactly `value - baseline`. Put the baseline at zero and the length equals the value, so the ratio of two lengths is the ratio of two values. Put it at 92 and the arithmetic changes with nothing on the page announcing it. A row worth 94 draws a bar two units long; a row worth 98 draws one six units long. The values differ by roughly four percent; the lengths differ by two hundred percent. The picture asserts the second thing, at a glance, and the tick labels reading 92, 94, 96, 98 are the only trace of the first. The distortion is not a fixed penalty either. It grows without bound as the baseline creeps toward the data: at a baseline of 93.9 the same two rows draw bars 0.1 and 4.1 units long, a forty-to-one picture of a four-percent gap. ## Which marks this breaks, and which it merely zooms | mark | channel carrying the value | what a non-zero baseline does | |---|---|---| | bar, or a filled area under a line | length measured from the baseline | breaks the encoding: every ratio read off the page is false, and the error grows as the baseline approaches the data | | point | vertical position | zooms the frame: every value is still recoverable by reading it against the ticks | | line joining points | position, with slope read as a rate | zooms, and inflates apparent steepness, so a reader over-reads how fast the quantity is moving | The rule worth carrying away is about the channel rather than about charts in general. **A channel read from the baseline needs the baseline at zero; a channel read against the ticks needs the ticks actually read.** Both popular slogans are wrong. "Every axis must start at zero" wastes the page on a series that lives between 94 and 98. "Truncation is fine if it is labelled" excuses the one case a label cannot repair, because a length is read at a glance and a tick label is read deliberately. ## The default is not something you can assume Designs genuinely differ here. Some extend the scale that maps values to length — the rule turning values into positions and lengths, together with the axis that lets a reader read them back — so that it includes zero whenever the mark is a length mark, unless the author overrides it. Others fit every axis to the values they were handed and will truncate a bar without comment. A third possibility is an author who set the limits deliberately and had a good reason. **The finished picture records none of this.** The same image comes out of all three paths. So "the tool would have started at zero if it mattered" is not an argument; it is a guess about which design produced the file. ## Reading one honestly, in three steps 1. Read the **lowest tick** before you read any bar. That is the baseline, and it is the whole story. 2. Convert two bars back to values by adding the baseline to each length, then form the ratio of the values. 3. Compare that ratio with the ratio the lengths suggested. The distance between those two numbers is the amount the chart is overstating. ## Drawing one honestly - Put the baseline at zero and accept that a four-percent difference looks like four percent. Very often that is the finding, and the chart is doing its job by saying so. - Where the interesting variation really is small against the level, change **what is drawn** rather than where the axis starts: draw the difference from a reference value, or the change from one period to the next. The length then encodes a quantity whose zero is meaningful, and the axis can start at zero honestly. - Where both the level and the fine resolution matter, move to a channel read against ticks — points, or points joined by a line — and state the limits plainly beside the chart. - A break drawn through the bars does not repair the encoding. The surviving lengths are still proportional to value minus baseline; the break warns only the fraction of readers who notice it. - Do not rely on a tick label to undo a length. ## What it does not fix The baseline is only one of the things an axis setting quietly decides. The same limits also govern which rows appear at all: a value outside them has no mark inside the drawn region, and the page says nothing about how many went missing. One line of configuration can therefore make a chart dishonest about proportion and about completeness at the same time, and neither shows up until someone compares the axis against the column it came from.