Axis crimes

The rebased index

Every line passes through 100 on a date somebody chose.

a.k.a. rebasing · the base year · indexed to 100 · 2017 = 100 · the reference period · normalised series · the common baseline · index points

Indexing divides every series by its own value in one chosen period and multiplies by 100, which is why it is the standard cure for dual axes: two quantities of different size, in different units, end up on one honest ruler. The cure has a knob. Each series is divided by a different number, so moving the base multiplies each line by a constant of its own — one slides up, the other down — and the gap the reader carries away is a fact about the date in the divisor as much as about the data. The base is also the single point where the chart declares the series equal, so the crossing everybody reads off is a cell in a spreadsheet. And the reading inverts either side of it: to the right of the base the higher line has grown more since the base, while to the left the higher line is the one that grew less on the way to it.

How to spot it

Find the 100. Every line goes through it on the same date, and that date is the only thing on the chart that is not a measurement.
Ask where the base sits inside the window. A base in the middle means everything to its left is being read backwards, because there the higher line is the one that grew less.
Ask why that year. A trough for one series, a peak for another, a round number, “the last normal year” — each is a choice, and each moves every gap on the chart.
Redraw it in your head with the base moved to another year. If the ranking survives, it was in the data; if it flips, it was in the divisor.
Two lines that never cross except at the base. Basing at the extreme of the ratio between them puts one above the other in every period by construction, and it looks exactly like a durable lead.
A claim about size — bigger, larger, the leader — made from an index. An index has no level: every line passes through 100 at the base because it was divided by itself there, and nowhere on the chart is a quantity.
A gap quoted in “points”. Index points are not a unit of anything; they are the difference between two growth factors measured from a date the caption may not even name.
The base hiding in the axis title: “2017 = 100”, “Jan 2020 = 100”, “rebased”, “indexed”, “normalised”. Where no base is named at all it is usually the first period plotted, which quietly makes the choice of window a choice of base.

The fix

Choose the base for a reason you can state before you have seen the lines, then state it: put it in the caption the way you print a unit, and prefer the start of the window, because with the base at the first period every point is to its right and “above” means “grew more since the start” everywhere on the chart. The far edge is not the same thing, and is worth saying out loud because it looks equally tidy: a base at the last period puts the whole chart to its left, so every reading on it is inverted — the mid-window trap taken to completion. Where the base is doing work — a rebound measured from a trough, a comparison anchored on a year one series happened to have a bad one — draw the chart at two or three bases and let the reader see the knob; what barely moves between them is the finding. Better still, take the comparison off the index altogether. When the question is which one is pulling ahead, plot the ratio of the two series as a single line: rebasing either of them only multiplies that line by a constant, so its shape is the whole relationship and there is no base left to argue about. Keep the finding in words as well as in ink, because growth between two named dates is the one thing rebasing cannot touch — dividing two points on the same line cancels the base — so a sentence saying that one series rose 3.9% and the other fell 11.5% between two stated years survives every version of the picture, which is more than the picture can say for itself. And never let an index carry a claim about size. Every line passes through 100 at the base because it was divided by itself there, so there are no levels on the chart at all; if the reader needs to know which is bigger, that is a different chart with a real unit on its axis.

In the gallery

Dark navy briefing slide, masthead “Materials briefing · US industrial production · Plastics & rubber vs primary metal · Annual, 1997–2025 · Index 2011 = 100”, headlined “Plastics and rubber has not fallen below primary metal in any of these twenty-nine years”. A standfirst says the two series come from one publisher, one release and one unit — the Federal Reserve’s industrial production index for plastics and rubber products and for primary metal, annual averages of twelve seasonally adjusted months — that every complete calendar year since 1997 is plotted with nothing smoothed, nothing omitted, one axis and no second axis, and that both series are rebased to a common year, 2011 = 100, the second full year of the recovery from the 2009 trough, so that growth is comparable between them; in 2025 plastics stands at 103.92 and primary metal at 88.47, a lead of 15.5 points. The main panel, labelled “Industrial production · annual average · 1997–2025 · index 2011 = 100 · axis 70 to 130”, is a line chart with gridlines at 70, 80, 90, 100, 110, 120 and 130 and a dashed amber vertical rule at 2011 marked “Base 2011 = 100”. A blue line for plastics runs from about 111 in 1997, climbs into the low 120s through the 2000s, plunges to 90.5 in 2009, returns to 100 at the dashed rule and drifts along the 104–114 band thereafter, ending at 103.92. An amber line for primary metal starts near 105, falls into the low 90s by 2003, recovers to about 102 by 2008, drops to 76.0 in 2009, meets the blue line at 100 in 2011 and then runs below it for the rest of the chart, ending at 88.47. The two lines touch once and never cross. A table headed “The two series as drawn · 2011 = 100” lists 1997 110.87 and 104.93 with a lead of +5.94, 2003 119.31 and 91.88 with +27.43, 2009 90.48 and 75.97 with +14.51, 2011 100.00 and 100.00 with +0.00, 2017 110.79 and 89.79 with +21.00, 2020 105.28 and 77.76 with +27.52, and 2025 103.92 and 88.47 with +15.45, noting that the lead is plastics minus primary metal in index points on this base. A second table, “The lead, decade by decade”, gives 1997–2006 a mean lead of +19.1 points and plastics ahead in 10 of 10 years, 2007–2016 +9.9 and 9 of 10, and 2017–2025 +21.1 and 9 of 9. Down the right-hand side a card carries the figure “15.5 pts” over “Plastics’ lead over primary metal · 2025” and “Level in 2011, ahead in the other twenty-eight years”. A card headed “Read-out for the materials desk” says plastics and rubber is at or above primary metal in every year of the span, that the two touch once in 2011, and that the polymer line is the higher of the pair both before and after. A “Sourcing note” card says twenty-nine years of daylight is not a cycle and that capacity planning for moulded and cast parts should assume polymer keeps taking work the foundry used to have. A card headed “Why 2011 = 100” calls it the second full year of the recovery from the 2009 trough, by which point both industries had turned up and the collapse year itself was well clear of the comparison, a neutral post-recession baseline belonging to neither series. Further cards cover “One publisher, one unit”, “Why index at all” — two industries of different size cannot share a raw axis, so rebasing both to a common year retires the second axis and puts them on one ruler — “What we did not do”, which lists no second axis, no smoothing, no year dropped, no partial year included since 2026 is still running, and notes these are lines that encode position rather than length with the axis labelled 70 to 130, plus “Data quality” and “Basis of measurement”, naming FRED series IPG326S and IPG331S. Three ticked boxes run along the foot: “One axis, one unit”, “Every complete year plotted” and “Both series rebased to a common year”. A footnote gives the source and retrieval date and says the slide is a demonstration drawn by us in the manner of a materials briefing, that the desk, the read-out and the sourcing note are invented, and that every figure behind it is real.

The 30.5-point swing that came from moving the 100

The rebased index