The 30.5-point swing that came from moving the 100

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. — Showing the misleading chart

The same two series on a cream background, kicked “The same fifty-eight numbers · every base year in the window · US industrial production 1997–2025” and headlined “Move the 100 and a 15.5-point lead becomes a 15.1-point deficit.” A standfirst says nothing on the briefing was truncated, smoothed, cropped or given a second axis, that the two series are real and the same unit from the same release with every complete year plotted, and that what sets the whole picture is the one number that never appears on it: rebasing multiplies each series by a constant of its own, so moving the 100 slides one line up and the other down — at base 2011 plastics never falls below primary metal in any of the twenty-nine years, and at the Fed’s own 2017 = 100 the two cross eight times and metal finishes ahead. Two line charts sit side by side, each 1997–2025 on an axis running 70 to 130 with a dashed rule at its base year. The left, outlined in gold and labelled “Base 2011 = 100 · the briefing’s chart”, shows the navy plastics line above the gold metal line throughout, ending 103.92 against 88.47, captioned “Plastics never below, all 29 years. 2025 gap: plastics +15.45 points.” The right, labelled “Base 2017 = 100 · the published base”, shows the same two series tangled together, swapping places repeatedly, ending 93.80 against 98.53, captioned “The lines cross eight times, two by under a quarter-point. 2025 gap: primary metal +4.73 points.” Below them, a column chart headed “The 2025 gap under all 29 possible base years · index points” draws one column per candidate base year against a zero rule, positive columns above and negative below, with 2011 picked out in gold at +15.45 and 2020 in gold at −15.07; a caption notes that the highest is 2011, the lowest 2020, that the answer changes sign five times, and that the last column, base 2025, is zero because basing a chart at its own final year forces the lines to meet there. Beside it, a line chart headed “The one picture no base can move · plastics ÷ primary metal, 1997 = 100” traces the ratio of the two industries from 100 in 1997 up to about 123 in 2003, down to a circled low marked “2011 · lowest”, and up again to a circled high marked “2020 · highest” before ending near 111; its caption says rebasing either series only multiplies this line by a constant, so its shape is the relationship and its level is a label. A table headed “What survives rebasing · growth between two named dates” gives 1997 → 2025 as −6.3% for plastics and −15.7% for primary metal, with plastics holding up better; 1997 → 2011 as −9.8% and −4.7%, primary metal; 2011 → 2025 as +3.9% and −11.5%, plastics; and 2017 → 2025 as −6.2% and −1.5%, primary metal. Eight cards run down the right. “Where the 100 goes” says twenty-nine years sit inside this window and any of them can be the base, that the 2025 gap runs from plastics +15.45 at base 2011 to primary metal +15.07 at base 2020, a 30.5-point swing with no number touched. “The crossing is a date” says two indexed lines are forced equal at exactly one point, the base, because each was divided by itself there, that the point is a cell in a spreadsheet, and that every other place the lines meet is a coincidence. “Left of the base, above means behind” explains that right of the base the higher line has grown more since the base while left of it the higher line is the one that grew less on the way to it, and notes the briefing draws plastics above metal across 1997–2011, a stretch in which plastics fell 9.8% and primary metal fell 4.7%. “Why 2011 put plastics on top” says 2011 is the year the plastics-to-metal ratio was at its lowest in the window, and basing a chart at the ratio’s minimum puts one line at or above the other in every single year by construction rather than by finding. “An index has no level” says both lines pass through 100 at the base because each was divided by itself there — on this chart they start at 110.9 and 104.9 — so neither line is a size and “plastics is bigger than primary metal” was never on the chart. “What survives rebasing” says growth between any two dates on one line, because dividing two points on the same series cancels the base. “The remedy with a knob” notes that indexing is the standard fix for dual axes and a good one, since it retires the second scale, but that it carries a knob of its own and, unlike a second axis, does not look like one. “Basis of measurement” names the two FRED series and their definitions. A gold-ruled callout at the foot reads “An index chart’s crossing point is a date somebody typed, not a finding,” and advises putting the base at the start of the window, where no reading is inverted, warning that the far end is not the same thing because a base at the last period leaves the whole chart to its left, then naming the base in the caption the way you print a unit and choosing it for a reason you can state before seeing the lines, drawing the chart at two or three bases where the base is doing work, plotting the ratio when the question is which one is pulling ahead, and keeping the finding in words, since a sentence naming two dates and two percentages survives every rebasing there is. A footnote gives the source and retrieval date, lists published 2017=100 values for both series at 1997, 2011, 2017, 2020 and 2025, explains that the gap panel recomputes the 2025 reading for each of the twenty-nine base years and that 2026 is incomplete and excluded throughout, and says both drawings are ours, that the briefing, the desk and the sourcing note on the first are invented, and that every figure on both is real. — Showing the misleading chart

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A materials briefing on two American industries: the Federal Reserve’s production index for plastics and rubber products against the one for primary metal, twenty-nine complete years, one axis, no second scale, every year plotted and nothing smoothed. Both series are rebased to a common year, 2011 = 100, which is the standard cure for a second axis — and on that base the polymer line never once falls below the metal line, finishing 15.5 points clear. The base is the knob. Twenty-nine years sit inside the window and any of them can be the divisor; at 2020 = 100 the same fifty-eight numbers hand primary metal a 15.1-point lead instead, a swing of 30.5 points with nothing touched. 2011 is the year the ratio between the two industries was at its lowest, and basing there is what puts one line above the other in every year of the chart.

Industrial production: plastics and rubber products (NAICS 326) and primary metal (NAICS 331), Board of Governors of the Federal Reserve System, G.17 release, via FRED series IPG326S and IPG331S — monthly, seasonally adjusted, Index 2017=100, averaged over the twelve months of each complete calendar year, 1997–2025, 2026Added September 2, 2026

01The claim

A materials briefing comparing two American manufacturing industries that make much the same kind of thing in two different substances: plastics and rubber products, which is where a moulding machine lives, and primary metal, which is where a foundry does. Both lines are the Federal Reserve’s industrial production index, a measure of real output, taken from one release, published in one unit, seasonally adjusted, and averaged over the twelve months of every complete calendar year from 1997 to 2025. Nothing is smoothed, no year is dropped, no partial year is admitted — 2026 is still running and is left out — and there is one axis and no second scale. Because two industries of different size cannot share a raw axis, both series are rebased to a common year: 2011 = 100, the second full year of the recovery from the 2009 trough, by which point both had turned up and the collapse year itself was well clear of the comparison, a neutral post-recession baseline belonging to neither. On that ruler plastics and rubber does not fall below primary metal in any of the twenty-nine years on the chart. The two touch once, in 2011, and the polymer line is the higher of the pair both before and after. The mean lead is 19.1 points across 1997–2006, 9.9 across 2007–2016 and 21.1 across 2017–2025, and in 2025 plastics stands at 103.92 against primary metal’s 88.47, a lead of 15.5 points. Read-out for the materials desk: twenty-nine years of daylight is not a cycle. Sourcing note: capacity planning for moulded and cast parts should assume polymer keeps taking work the foundry used to have.

02The trick

The base year is the knob, and it is the one number on the chart that is not a measurement. Indexing divides every series by its own value in one chosen period, which is exactly why it is the standard cure for dual axes — it retires the second scale and puts two different-sized quantities on one ruler. But 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 slides down, and the gap the reader carries away moves with them. Twenty-nine years sit inside this window and any of them could have been the divisor. At 2011 = 100 the 2025 reading is plastics 15.45 points clear; at the Federal Reserve’s own published base of 2017 = 100 it is primary metal 4.73 points clear and the two lines cross eight times instead of never; at 2020 = 100 it is primary metal 15.07 points clear. That is a swing of 30.5 points in the headline, across fifty-eight numbers none of which has been touched. What makes 2011 the useful pick is not that it is a bad year to choose — it is a perfectly defensible one, and the reason given for it on the slide is true — but that it happens to be the year the ratio between the two industries was at its lowest in the whole window. Base a chart at the minimum of the ratio and one line stands at or above the other in every single period, by construction rather than by finding, and the picture that produces looks exactly like a durable, decades-long lead. There is a second, quieter thing wrong with the reading, and it is the part worth taking away. The base is the one point where the chart declares the two series equal, so it is a crossing that means nothing, and the reading inverts on either side of it. To the right of the base, the higher line has genuinely grown more since the base. To the left, the higher line is the one that grew less on the way to it. The briefing draws plastics above metal for the whole of 1997–2011 — a stretch in which plastics fell 9.8% and primary metal fell 4.7%, so the line that looks ahead is the line that did worse. And no line on the chart is a level at all: each passes through 100 at the base because it was divided by itself there — on this chart they start at 110.87 and 104.93 — so “plastics is bigger than primary metal” was never a claim the picture could make. (Both drawings are ours; the briefing, the desk and the sourcing note are invented, and every figure behind them is real.)

03The fix

Put the base where it cannot invert anything, and say what it is. That means the start of the window, not simply an edge of it: with the base at the first period every year is to its right and “above” means “grew more since the start” everywhere on the chart, while a base at the last period puts the whole chart to its left and inverts all of it — the same trap as a base in the middle, only complete. Name the base in the caption the way you print a unit, and choose it for a reason you can state before you have seen the lines rather than after. Where the base is doing real 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 for themselves. Here that takes one panel: the same two series at 2011 = 100 and at 2017 = 100, side by side, one showing a lead that never lapses and the other showing eight crossings and the opposite winner. Then take the comparison off the index altogether, because there is a version of this chart the base cannot move. When the question is which of two series is pulling ahead, plot the ratio between them as a single line: rebasing either series only multiplies that line by a constant, so its shape is the entire relationship and there is nothing left to argue about. Drawn that way, the plastics-to-metal ratio rises hard through the early 2000s, collapses to its low in 2011 — the year the briefing chose as its base — recovers to a high in 2020 and eases back to about 111, still a tenth above where it started, which is a real and rather interesting shape, and not one that either indexed chart shows. Keep the finding in words as well as in ink. Growth between two named dates is the one thing rebasing cannot touch, since dividing two points on the same line cancels the base, so the same four rows hold in all twenty-nine versions of this chart: 1997 to 2025, plastics −6.3% and primary metal −15.7%; 1997 to 2011, plastics −9.8% and primary metal −4.7%; 2011 to 2025, plastics +3.9% and primary metal −11.5%; 2017 to 2025, plastics −6.2% and primary metal −1.5%. Read those and the honest story is neither of the ones the two pictures tell: over the full span the polymer industry has held up better, over the first half it did not, and both are below where they started. Finally, do not let an index carry a claim about size. Every line on one passes through 100 at the base because it was divided by itself there, so the chart has no levels on it anywhere; if a reader needs to know which industry is bigger, that is a different chart with a real unit on its axis. None of which is an argument against indexing — it remains the right answer to a second axis, and this exhibit is a demonstration of the cure rather than a case against it. It is an argument for treating the base the way we already treat a baseline, a bin edge and an axis maximum: as a decision, printed where the reader can see it.