Size & scale

The free-scale small multiple

Six panels in one grid, six different rulers.

a.k.a. free y-axis · scales = "free_y" · independent axes · per-panel autoscaling · faceted chart · the trellis with six rulers · the sparkline grid · auto-fit axes

A small multiple works by holding everything constant except the data: same chart, same size, same years, same scale, repeated down the page, so that any difference the eye finds is a difference in the numbers. Fit each panel’s axis to its own series and the last of those constants quietly goes, while the picture looks exactly as it did. Every panel is now drawn to its own ruler, so a bar that reaches the top of one frame and a bar that reaches the top of the next are the same height and not the same quantity, and the comparison between panels — the only reason to put the panels in one frame — is invented by the layout. The panels are not individually wrong, which is what makes it hard to see: each is a correct chart of its own series, and the ratios inside a panel survive. It is the ratios across panels, the ones the grid is silently offering, that are a fact about the autoscaler.

How to spot it

Read the axis on every panel, not just the first one. If the top number changes from panel to panel, no two marks on the page are drawn to the same ruler.
Panels with no axis numbers at all — a sparkline row, a tile grid, a dashboard of little charts. Autoscaling is the default almost everywhere, so assume it happened until the page says otherwise.
Every panel’s biggest mark reaching the top of its frame. Real series rarely peak in the same year and never peak at the same size; an autoscaler makes them all peak at 100% of the frame.
The quietest series looking as busy as the loudest. A panel with nothing happening gets its wiggle stretched until it fills the frame, so noise arrives drawn at the same amplitude as signal.
Take one panel’s axis maximum and divide it by another’s. That number is how much more a pixel is worth in the first panel than the second, and it is the exchange rate the grid never printed.
Ask whether the axis was fitted to zero or to the data. Fitted to the data it is also a truncated axis, once per panel, and the two crimes compound.
The library default: ggplot2’s scales = "free_y", one chart object per series in a spreadsheet, most BI tools’ small-multiple widgets. Free scales are usually a setting nobody chose.

The fix

The shared scale is not a nicety of small multiples, it is the whole mechanism — so the first answer is one zero-based axis for the entire grid, drawn once at the edge. If that flattens five panels into a line along the bottom, the flattening is the finding, and it is a finding the free-scale version was hiding rather than solving. Then ask which question the grid is for. If it is about amount, keep the shared axis and let the giant be a giant. If it is about growth, index every series to a common base year and share that axis instead, printing each panel’s level in the corner so nobody mistakes a rate for a size; that is a different chart of the same data, and saying which one you are showing costs a line. Where a series genuinely lives orders of magnitude below the others, give it its own panel at its own scale and separate it visually — a rule, a gap, a heading that says the scale changes here — because at that point they are not a small multiple, they are several charts that happen to share a page, and the reader deserves to know which they are looking at. And if free scales are unavoidable, at minimum print each panel’s maximum large enough to read and repeat the unit on every panel, since the axis maximum is the exchange rate, and a grid that hides its exchange rates is asking to be read as a comparison it cannot support.

In the gallery

Dark navy board slide, masthead “Ridgeline Materials Group · Critical minerals desk · Supply briefing, FY27”, headlined “Six critical minerals, six years — and every one of them is at a record”. A subhead reads: world mine production for the six minerals on the FY27 qualification list, as published by the U.S. Geological Survey — one source, one unit, six full calendar years, every value printed on the slide; the six panels are identical, same chart, same size, same years, same order, and every one of them starts at zero; nothing is indexed, nothing is smoothed, nothing is set aside. Filling the left of the slide, under the label “World mine production · metric tons · USGS Mineral Commodity Summaries · 2019–2024”, is a three-by-two grid of six small column charts, each in its own bordered card. Every panel carries the mineral’s name at the top left, a growth multiple in gold at the top right, a one-line note on what is being counted, six blue columns for 2019 to 2024 with the last one picked out in gold, and two axis labels down the left edge: “0” at the baseline and the panel’s maximum at the top. The panels read: Natural graphite, ×1.45, natural graphite gross weight, axis to 1,600,000; Rare earths, ×1.77, rare-earth-oxide equivalent, axis to 390,000; Cobalt, ×2.01, cobalt content, axis to 290,000; Lithium, ×2.79, lithium content excluding U.S. production, axis to 240,000; Vanadium, ×1.15, vanadium content, axis to 105,000; Tantalum, ×1.14, tantalum content, axis to 2,100. In five of the six the gold 2024 column reaches the top of its frame; in vanadium it stops just short, a little below the 2021 column. All six panels show the same silhouette — flat or slightly lower in 2020, then a climb to the right. Below the grid sits a table headed “Metric tons, mine production” listing all thirty-six figures by year, with the 2024 column in gold: natural graphite 1,100,000, 1,100,000, 1,130,000, 1,300,000, 1,530,000, 1,600,000; rare earths 220,000, 240,000, 290,000, 300,000, 376,000, 390,000; cobalt 144,000, 140,000, 165,000, 190,000, 238,000, 290,000; lithium 86,000, 82,000, 107,000, 130,000, 204,000, 240,000; vanadium 86,800, 86,000, 105,000, 100,000, 104,000, 100,000; tantalum 1,850, 1,700, 1,840, 2,000, 2,040, 2,100. A caption under the table notes that the highlighted column is 2024, the last bar in every panel above, and that each panel is drawn on its own axis, printed at the panel’s top-left corner. Down the right-hand side, a gold-bordered card carries “6 / 6” over the line “Minerals finishing the window at or within 5% of their six-year high”. A gold card headed “Read-out for the board” argues that the ramp is broad-based, that every one of the six streams ends the window at its high with the same shape in every panel, that there is no single bottleneck and no laggard to write off because the whole basket is moving together, and recommends splitting the FY27 qualification budget evenly across all six streams on one reporting cadence. A card headed “Why six small panels” says that one chart per mineral, drawn identically, is the standard way to put several series in front of a board at once, because the design is held constant so that anything the eye picks up is a difference in the data. A card headed “Every number is on the slide” says the table carries all thirty-six figures and each panel prints its own axis, so nothing has to be taken on trust. A final card, “Basis of measurement”, gives source USGS Mineral Commodity Summaries, “World mine production and reserves”, world total (rounded); unit metric tons throughout; years 2019–2024, each as first published; coverage worldwide, all reporting countries. Three ticked boxes run along the bottom: “Every panel starts at zero. No truncation, no axis break, no log scale, no second axis anywhere on this slide”, “One source, one unit. Metric tons of mine production, from one publisher, for all six minerals and all six years”, and “Six identical panels. Same chart type, same dimensions, same six years in the same order, and each panel’s axis printed on it”. A footnote credits the USGS Mineral Commodity Summaries world mine production tables, notes that each year is taken from the edition in which it first appeared — 2019 and 2020 from MCS 2021, 2021 and 2022 from MCS 2023, 2023 and 2024 from MCS 2025 — that the 2020, 2022 and 2024 figures are USGS estimates, that rare earths are rare-earth-oxide equivalent and lithium is contained lithium excluding U.S. production, and states that the slide is a demonstration drawn by us in the manner of a sourcing briefing, has never been published anywhere, and that the production figures are real.

The pixel that is worth 5,333 tonnes in one panel and 7 in the next

The free-scale small multiple