Why is a value carried by position along an axis read more accurately than the same value carried by mark area?

## The channel is the reader's instrument A **visual channel** is a property of a drawn mark — position along an axis, length, area, colour, marker shape — that a column's values can be carried by, and **binding** a column to a channel is the statement that the channel varies with that column. The part people skip is that the channels are not interchangeable. Each one is a different instrument in the reader's hands, and they differ by a lot in how precisely a number can be recovered from them. Two mechanisms explain most of the gap: - **Some channels are read against a reference, others are not.** Position along an axis comes with ticks and a shared baseline, so the reader is effectively measuring. Area has no ruler next to it; the reader compares one mark against another from memory. - **Some channels are perceived non-linearly.** Doubling a mark's area does not look twice as much. Judgments of area, angle and colour intensity compress, so large differences read smaller than they are — and the compression varies between readers. ## A working ordering From most precisely decoded to least, for a numeric value: 1. **Position along a common axis** — the reader measures against a shared reference. 2. **Length from a common baseline** — nearly as good, because the marks start together. 3. **Length without a common baseline, and angle** — the comparison is still geometric but the reference is gone. 4. **Area** — ordering usually survives, ratio does not. 5. **Colour intensity, then colour hue** — coarse; a reader can say "more" and rarely "how much more". 6. **Marker shape** — carries no magnitude at all, only distinctness. This is a tendency, not a law: it describes typical readers on typical comparisons, and the gaps between neighbouring steps are smaller than the gap between the top and the bottom. | channel | what a reader can do with it | what it costs | |---|---|---| | Position on a shared axis | Recover the value; compare any two marks | Only two such channels exist in a flat picture | | Length from a common baseline | Compare values reliably | Needs the baseline, and marks must be adjacent enough to compare | | Area | Rank marks, sense rough magnitude | Ratios are underestimated and unreliable | | Colour | Rank coarsely, spot extremes | Needs a guide; small differences vanish | | Marker shape | Tell categories apart | No magnitude whatsoever | ## What follows for the binding The scarce resource is accuracy, and there is very little of it to allocate: - A flat picture has **two position channels**. Everything past the second variable is being demoted to an estimated channel, whether or not the author noticed. - So the real question at binding time is **which comparison the reader must get right**. Put that one on position. The variables that only need "roughly bigger" or "which group is this" can go on area, colour or shape. - **Adding a channel is not free.** Each extra binding adds a guide to read and a mapping to hold in mind, and the channels interfere with each other — a small mark in a pale colour is harder to judge on either dimension than a large one in a strong colour. - **Redundant bindings are sometimes right.** Carrying the same column on both position and colour buys nothing in precision but makes a group findable at a glance; it costs a channel, which is fine when you have one spare and not fine when you do not. ## What this does not say It does not say that area and colour are wrong. They are correct wherever the reader's task is ranking, grouping or spotting an extreme, and they are the only way to get a third or fourth variable into a flat picture at all. What the ordering says is narrower and more useful: **if a reader has to recover or compare numbers, the channel you chose sets the ceiling on how well they can.** No amount of styling raises that ceiling. It also does not say that precision is always what you want. A chart whose job is "is this unusual?" is served fine by a coarse channel, and forcing that comparison onto position can crowd out the one that actually needed it. ## What an interviewer is listening for Three things. That you know the channels differ as instruments and can rank the main ones roughly. That you can state the consequence in terms of the reader — *this reader will be able to recover that number and only rank this one*. And that you allocate deliberately: naming the comparison that needs accuracy and saying out loud which variables you are demoting, rather than binding columns to channels in the order they happened to occur to you.