Axis crimes

The padded axis

The frame is the size of the unit. The data is the size of the data.

a.k.a. the 0-to-100 axis · full-scale deflection · scaled to the unit · the spec-sheet scale · axis headroom · dead space · the flattened axis · the over-ranged axis · the empty frame

The truncated axis raises the floor and makes a small difference enormous. This one is the same decision taken at the other end of the scale, and it makes a large difference invisible: the baseline is honest, the ticks are even, nothing is broken or clipped, and the top of the axis was chosen from the unit rather than from the numbers. A percentage runs to a hundred, so the axis runs to a hundred. A score runs to ten, a rating to five, a dial to whatever the face was printed with, a meter to its full-scale deflection. The data then lands in the first few per cent of the frame, and everything above it is a wall of empty box. What makes this one slippery is that the arithmetic is untouched. Bars from zero keep their ratios exactly: a model that fails twenty-eight times as often really is drawn twenty-eight times as tall, and anybody who measures the ink with a ruler gets the right answer. But nobody measures the ink. The eye reads each mark against the frame and against its neighbours, and when the whole field is a row of stubs along the floor, a twenty-eight-fold range arrives as a handful of pixels — below the size at which two lengths can be told apart by looking at them, which is where comparison actually happens. The conclusion the picture delivers is that nothing here is adrift, the variation is noise, the choice does not matter; and that conclusion was written by the empty space rather than by the data. It is most at home wherever the interesting quantity is rare — failure rates, fraud rates, defect rates, error rates, anything counted in parts per something — because rare things live near the bottom of their unit by definition, and the tool that drew the chart has no way of knowing that the bottom is where the whole story is. Four neighbours are worth telling it apart from, and the closest in outcome is the bar with no true zero, which produces the same wall of identical bars and takes the same cure — a dot plot and a unit people act in. The difference is where the damage is. There a constant sits inside every bar, so the ratios between them are wrong and subtracting the origin fixes it; here the ratios are exactly right and merely too small to see, so nothing needs recomputing and only the frame moves. The other three are about the frame as well. The clipped axis puts the ceiling below the data and flattens what pokes through; this one puts the ceiling far above it and flattens everything. The auto-ranged axis takes both ends from the data every time it is drawn, so every window is equally dramatic; this is the same abdication running the other way, and between the two of them sits the honest thing nobody did, which is to choose the bounds once, from the question. And the truncated axis is its mirror: raising the floor manufactures drama, padding the ceiling erases it, which is why the padded axis tends to turn up in charts that want a reassuring answer rather than an alarming one.

How to spot it

Read the axis maximum first and ask where the number came from. If it is a property of the unit — 100%, 1.0, 10, five stars, the top of the dial — rather than a number anything in the data goes near, the frame was settled before the data was looked at.
Measure the dead space. What share of the plot sits above the tallest mark? Past about four fifths empty, the chart is mostly frame, and whatever it is being used to claim is a claim about the frame.
A caption that says the field is uniform, flat, or all much of a muchness, printed beside a table whose largest value is several times its smallest. A ratio the eye cannot see is still a ratio; check it in the numbers rather than in the picture.
Rates of rare events on a percentage axis: drive failures, payment fraud, defects, cancellations, infections, adverse events. The rarer the thing, the smaller the part of the frame it can ever occupy, and the more the picture says nothing is happening.
Fixed-range furniture that came with the tool: a 0-to-100 progress bar, a five-star average, a 0-to-10 score, a gauge inherited from an instrument panel. Nobody chose these maxima for this data; they were in the box.
A legitimate zoom that looks like a crime. If the only way to see the data is to bring the top of the axis down, look at the mark before you object: bars in a frame that no longer starts at zero are the truncated axis, and dots in the same frame are not.
A conversion nobody performed. Small percentages usually have a natural unit on the other side of a multiplication — per thousand, per year, per shift, drives replaced, hours of work — and its absence is a good sign the chart was drawn in the unit the tool had rather than the unit the decision is in.

The fix

Set the top of the axis from the question, not from the unit, and then say where you set it. A frame ranged to a little above the largest value in the data, with the bound printed in the caption, gives the comparison back at once and costs a reader nothing but one line of reading. The part that trips people is the rule they learned first: bars start at zero, always. That rule is about the mark, not about the frame, and it is the reason the cure here is not to raise the floor. A bar encodes a length, so it needs the zero and it needs the full range beneath it; a dot encodes a position, which is all a ranged frame can honestly carry. Change the mark and the zoom stops being a lie: a dot plot, a strip plot, a range-framed line will all sit happily in a window that runs from nought to seven per cent, and none of them is making a promise about length that the frame cannot keep. Then do the multiplication the percentage was hiding. Almost every small rate has a unit on the other side of it that people act in — failures per thousand drives a year, cancellations per hundred trains, one in every forty orders, an engineer-day a week — and printing that figure beside the chart does more for a reader than any amount of redrawing. Put the uncertainty on the marks while you are there, because a rate computed from four hundred units and one from forty thousand are different kinds of number and a ranged frame is where that difference finally becomes visible. Keep the full scale where the full scale is genuinely the subject — a battery, a quota, a share of a vote, anything whose hundred is a real destination — and where you need both, draw both: the whole unit once, and an inset at the size of the data, which is the small-multiple answer to the same problem. And do not overcorrect into the opposite failure. An axis refitted to whatever is on screen each time is the auto-ranged axis, and it destroys comparability just as thoroughly; the fix for a frame chosen without looking is a frame chosen on purpose, held still, and written down.

In the gallery

Dark navy slide kicked “Storage procurement desk · drive selection for the 2026 build” on the left and “Operator’s published annual failure rates · calendar year 2025” on the right. The headline reads “Nothing in this fleet fails. Buy on price.” A bordered gold chip beneath it reads “Demonstration · drawn by us from Backblaze’s published table”. The standfirst says every figure is the operator’s own published annual table for 2025 — 31 drive models, 344,196 drives, 115,638,676 drive days, 4,317 failures — that nothing is sampled, smoothed, indexed or rescaled and no model has been dropped, and that the axis is linear, evenly ticked every ten points, unbroken, starts at zero and runs the full range the unit can take, 0% to 100%, because the quantity is a percentage; the whole field lands between 0.22% and 6.30% around a fleet-wide figure of 1.36%. The main panel, “Annualised failure rate by drive model, 2025”, subtitled “Percent of drives failing per year · every model in the published annual table · linear percentage axis from 0 to 100, gridlines every ten points, nothing truncated, broken, clipped or logged”, is a column chart whose y-axis is labelled 0%, 10%, 20% and so on to 100%, with pale gridlines a hundred pixels apart across the whole height. Thirty-one blue columns are ranged along the very bottom of the frame in ascending order, from a barely visible sliver at the left to a slightly taller one at the right; the last column, the Toshiba MG08ACA16TEY, is drawn in gold and is the tallest thing on the chart. A gold leader line runs up from it to an annotation reading “The tallest column on the chart: 6.30%” above a second line, “63 pixels of the 1000 this plot is tall”. A dashed red-brown rule just above the baseline is labelled “Fleet-wide, 2025: 1.36%”. Along the right edge of the plot a tall square bracket spans everything above the data, labelled “93.7% of this frame holds no data”. Model numbers run vertically beneath the columns. Five cards fill the right-hand column. “The spread, in one figure” prints a large gold 6.08 beside “points, best to worst”, then explains that this is the distance between the best model, Seagate ST16000NM002J at 0.22%, and the worst, Toshiba MG08ACA16TEY at 6.30% — on a hundred-point axis, 6.1% of the plot height, or 61 pixels of 1000, with 22 of the 31 columns standing shorter than a fortieth of the frame. “What the pack concluded” says no model is visibly adrift from any other, the entire field is a flat line along the foot of the chart against a fleet figure of 1.36%, and reliability is not separating the vendors; its recommendation is to drop drive reliability from the scoring matrix for the 2026 build, award on price per terabyte, and revisit if any model ever clears 10%. “The table, as published” is a monospace extract with columns for model, drives, average age in months, failures and AFR: ST16000NM002J 466 drives, 35.9 months, 1 failure, 0.22%; WUH722626ALE6L4 1,201 drives, 2.5 months, 1 failure, 0.40%; ST12000NM000J 1,075 drives, 16.4 months, 4 failures, 0.42%; then “… 25 models between …”; then ST12000NM0007 1,038 drives, 72.9 months, 55 failures, 5.48%; ST10000NM0086 1,044 drives, 95.2 months, 57 failures, 5.66%; MG08ACA16TEY 5,197 drives, 47.5 months, 318 failures, 6.30%; and totals of 344,196 drives, 4,317 failures, 1.36%. A line under the extract notes that age is the published average age of the model’s drives in months and that the chart plots the last column only. “Nothing in the picture is bent” lists one quantity, one unit, one publisher, one twelve-month window, a linear axis that starts at zero and is ticked evenly to its maximum, every model in the annual table drawn at the same width, none dropped and nothing smoothed or rescaled, ending “Whatever is wrong with this slide, it is not the arithmetic and it is not the baseline.” “How the top of the axis was chosen” says the quantity is a percentage and a percentage runs from nought to a hundred, so the axis runs from nought to a hundred: nobody typed a maximum, nobody cropped anything, and the chart shows the whole of the scale the number is measured on. Footer chips read “Published figures, as reported”, “One unit, one publisher”, “Zero-based linear axis, evenly ticked”, “Every model in the table” and “Nothing smoothed, dropped or rescaled”, above a source line crediting Backblaze’s “Backblaze Drive Stats for 2025”, published 12 February 2026, giving the reporting period and the inclusion thresholds, noting that the 31 rows are as published and their drive counts sum to the 344,196 drives the report analysed, and stating that Backblaze publishes the figures as a table while the chart, the desk, the conclusion and the recommendation are ours and every number behind them is the operator’s own.

The 28-fold spread drawn in the bottom sixteenth of the frame

The padded axis