The 9.17% drawn 2.17 times longer than the other 9.17%

Dark navy dashboard slide, masthead “Structures asset desk · national bridge inventory” on the left and “Share of a fleet rated poor · by owner · 2025” on the right, headlined “Thirteen owners, one ring each.” Beneath the headline sits a bordered chip reading “Demonstration · drawn by us from published figures”. A standfirst says every figure is the Federal Highway Administration’s own 2025 National Bridge Inventory summary — the share of each owner’s bridges whose lowest condition rating puts them in Poor; that all 623,810 bridges in the thirteen named owner classes are on the chart with nothing dropped, smoothed or rescaled; that the angular axis is linear, zero-based, evenly ticked and gridded with every value printed beside its own bar; that the rings are in the order the source lists the owner classes, which is the order of NBI Item 22; and that FHWA publishes these figures as a table while the rings are ours. The main panel, headed “Bridges rated poor, by owner · 2025” and subtitled “One ring per owner class · angle = share rated Poor · linear angular axis, 0–35% over 330°, gridded every 5 points · rings in NBI Item 22 order”, is a radial bar chart: thirteen concentric gold arcs on faint navy tracks, each starting at twelve o’clock and running clockwise, with dashed grey spokes marking every five points from 0% at the top round to 35%. The category labels are stacked at twelve o’clock, innermost at the bottom: State 4.4%, County 9.2%, Town 10.5%, City 6.5%, State Park 10.1%, Local Park 12.3%, Other State Agency 9.2%, Other Local Agency 7.2%, Private 6.5%, Railroad 33.1%, State Toll 2.5%, Local Toll 0.6%, Federal/Tribal 7.6%. The picture is dominated by Railroad, on the tenth ring, running almost all the way round; Federal/Tribal sweeps only a fifth of a turn but, on the outermost ring, draws the second-longest bar on the page. State, on the innermost ring, is a short stub near the middle, and County, on the second, is a little over a quarter-turn. A “How to read” note in the lower-left corner says each ring is one owner class, that the further round its arc travels the larger the share of that owner’s bridges rated Poor, and that every arc starts at the top and runs clockwise on the same angular scale. A caption reads “Published figures as reported · every named owner class · one angular scale throughout”. Two columns of cards run down the right. “The four long arcs” prints “4 of 13 owner classes” in large type and says that after Railroad, four classes draw the longest bars on the chart — Federal/Tribal, Local Park, Other State Agency and Other Local Agency — while State and County, on the two innermost rings, are among the shortest. “Read-out for the desk” says railroad-owned structures are the outlier at 33.1% Poor against a national 6.7%, that below that the weight of the chart sits with those four classes, none of them a state DOT or a county road department, that the two largest owners sit in the quiet centre of the picture, and recommends holding the state and county inspection cycle where it is and moving the supplementary allocation to the four long arcs, where the ink is. “Every value on the chart” tabulates all thirteen rings with their owner class, share Poor, number Poor and total bridges, from State (4.40%, 12,799 of 290,912) to Federal/Tribal (7.56%, 859 of 11,363). “The ring order” explains that the rings run outward in the order the source lists the owner classes — State, County, Town, City, and so on out to Federal/Tribal — that the chart adds nothing to it, and that Item 22 is a codebook field whose federal codes are rolled into the single Federal/Tribal row on the outermost ring, the rings inheriting that order because it is the order the rows arrived in. “How a bridge is rated” explains that inspectors score the deck, superstructure and substructure from 0 to 9 — for a culvert, its culvert rating — and that the lowest of those sets the classification — 7–9 Good, 5–6 Fair, 0–4 Poor — and that Poor does not mean unsafe. “What a full turn is worth” says the angular axis runs from 0% to 35% across 330° of arc, so one percentage point is 9.43° on every ring. “Who owns what” notes that State (290,912 bridges) and County (226,268) hold more than four-fifths of the inventory, while the four classes above hold 14,090 between them, or 2.3% of the structures on the chart. “Why a share and not a count” says the owner classes hold wildly different numbers of structures, from 146 to 290,912, so a count of Poor bridges would rank the large owners first whatever condition they were in — the share answers how likely, not how many. “The national picture” gives 41,685 of 624,193 bridges rated Poor, 6.7% of the inventory, with 309,729 Fair and 272,779 Good. “Basis of measurement” credits the Federal Highway Administration, National Bridge Inventory, “Bridge Condition by Owner 2025”, table dated 15 June 2025 and page updated 23 June, totals for all states, DC, Guam, Puerto Rico and the U.S. Virgin Islands, notes that Guam did not submit data for 2025, and says the thirteen named owner classes are shown while the residual rows — Other (13 bridges), Unknown (370) and Null (0) — are left out and named, being 0.06% of the inventory, retrieved 10 September 2026. A method line runs along the foot: published figures as reported; every named owner class; linear angular axis, zero-based, gridded; every value printed; nothing smoothed, dropped or rescaled. A footnote credits the source, says all thirteen values are as published, and states that FHWA publishes them as a table while this slide is a demonstration drawn by us in the manner of an asset-management dashboard — the desk, the read-out and the recommendation are invented, and every figure behind them is real. — Showing the misleading chart

The same thirteen owner classes on a cream background, kicked “The same thirteen owners · the same published figures · one straight axis” and “Share of a fleet rated poor · by owner · 2025”, headlined “The 9.17% drawn 2.17 times longer than the other 9.17%.” A standfirst says nothing on the dashboard was truncated, smoothed or rescaled — its angular axis really does start at zero, it is evenly gridded, and all thirteen values are printed on it; that what sets the picture is that a bar bent into a circle is a length that has been multiplied by its radius, and the radius is the ring, which was handed out by the order of the source table; that County and Other State Agency have the same share of their bridges in Poor condition, 9.17% and 9.17%, and the dashboard draws one of them 2.17 times longer than the other because one got ring 2 and the other ring 7; and that straightened out against one ruler, eleven of the thirteen bars change places. The main panel, headed “The same thirteen owners, drawn to one ruler” and subtitled “Share of each owner’s bridges rated Poor · same figures, sorted worst to best · zero-based linear axis, evenly ticked, one common baseline · counts printed beside each bar”, is a horizontal bar chart on an axis running 0% to 35% in even steps of 5. Railroad leads at 33.14% (169 of 510), then Local Park 12.33% (18 of 146), Town 10.50% (3,257 of 31,025), State Park 10.15% (125 of 1,232), then two highlighted bars of visibly identical length — Other State Agency in orange-red at 9.17% (85 of 927) and County in blue at 9.17% (20,740 of 226,268) — followed by Federal/Tribal 7.56% (859 of 11,363), Other Local Agency 7.19% (119 of 1,654), Private 6.52% (26 of 399), City 6.47% (3,232 of 49,932), State 4.40% (12,799 of 290,912), State Toll 2.46% (193 of 7,858) and Local Toll 0.63% (10 of 1,584). A caption reads “Same numbers, one axis, no radius · every bar starts and is read in the same place”. Five cards run down the right. “The two 9.17%s” carries a small diagram: on the left, the two arcs as the rings drew them — a short blue quarter-circle inside a much longer orange-red one, both sweeping 86.4° from the same twelve o’clock line, labelled “As the rings drew them · 86.4° each”; on the right, the same two values as equal-length horizontal bars against a single baseline, labelled “Against one baseline · the same length”. A table beneath gives County 9.17%, ring 2, radius 196, arc drawn 296, and Other State Agency 9.17%, ring 7, radius 426, arc drawn 643, and a line notes that 20,740 of 226,268 is 9.166%, 85 of 927 is 9.169%, both arcs sweep 86.4°, and one is 2.17 times the length of the other — exactly 426 ÷ 196, the ratio of the two radii. “What the ring was worth” tabulates all thirteen owners with their share Poor, their rank by rate, their rank by ink and their arc length: Railroad 33.14% ranks 1 and 1 at 3,076; Local Park 12.33% ranks 2 by rate and 3 by ink at 771; Town 10.50% ranks 3 and 8 at 418; State Park 10.15% ranks 4 and 6 at 558; Other State Agency 9.17% ranks 5 and 4 at 643; County 9.17% ranks 6 and 10 at 296; Federal/Tribal 7.56% ranks 7 by rate and 2 by ink at 873; Other Local Agency 7.19% ranks 8 and 5 at 559; Private 6.52% ranks 9 and 7 at 555; City 6.47% ranks 10 and 9 at 307; State 4.40% ranks 11 and 12 at 109; State Toll 2.46% ranks 12 and 11 at 247; Local Toll 0.63% ranks 13 and 13 at 68. A note says the arc is in the chart’s own units, radius times angle, that eleven of the thirteen bars are in the wrong place, that the two that are not are the extremes, which had nowhere to go, and that ranks 5–7 sit within 1% of each other so should be read as arithmetic rather than as something the eye could settle. “The exchange rate nobody printed” says the outermost ring has a radius of 702 and the innermost 150, so a degree at the edge is worth 4.68 times a degree at the middle; that Federal/Tribal has the seventh-worst rate of thirteen and the second-longest bar, and State is eleventh-worst and draws less ink than State Toll, which is twelfth; and that inside any one ring the arcs are exactly right — it is the comparison between rings, the entire reason the thirteen were put in one picture, that belongs to the seating plan. “What to draw instead” says one zero-based axis, one baseline, sorted by the values, and that where the circle is genuinely wanted a dot on each ring beats an arc, because a dot marks an angular position and position is all a shared angular axis can honestly carry. “And the thing neither chart carries” says rates are the right question for condition but counts run the other way: County’s 9.17% is 20,740 bridges, just under half of every Poor bridge in the country, while the identical 9.17% is 85. Five notes run along the foot: the same thirteen published figures; one zero-based linear axis; one common baseline; sorted by the values; counts printed beside the rates. A closing footnote credits the source and states that FHWA publishes these figures as a table, that both drawings are ours, that the desk, the read-out and the recommendation on the first are invented, and that every figure behind them is real. — Showing the misleading chart

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An asset-management dashboard we drew puts the thirteen owner classes of the American bridge inventory on thirteen concentric rings, one each, with the angle of every arc set by the share of that owner’s structures the inspectors rate Poor. Nothing about it is bent: the angular axis is linear and zero-based, gridded every five points, every value is printed beside its own bar, and all 623,810 bridges in the named classes are on the chart. But a bar bent into a circle is a length multiplied by its radius, and the radius is the ring — handed out here by the order the source table happens to list the owner classes in, which is the order of a codebook field. County and Other State Agency have the same share of their bridges in Poor condition, 9.166% and 9.169%; both arcs sweep the same 86.4°, and one is drawn 2.17 times the length of the other, which is exactly the ratio of their two radii. Straightened onto one axis, eleven of the thirteen bars change places.

Federal Highway Administration, National Bridge Inventory, “Bridge Condition by Owner 2025”: totals for all states, DC, Guam, Puerto Rico and the U.S. Virgin Islands, table dated 15 June 2025 and page updated 23 June (Guam did not submit data for 2025). Thirteen named owner classes, 623,810 bridges; the residual Other, Unknown and Null rows (383 bridges) are excluded. Shares, arc lengths and rankings ours. Retrieved 10 September 2026, 2025Added September 10, 2026

01The claim

Thirteen owner classes, thirteen rings, one number each. The figures are the Federal Highway Administration’s own 2025 National Bridge Inventory summary: the share of each owner’s structures whose lowest condition rating — deck, superstructure or substructure, scored 0 to 9 by an inspector, or for a culvert its culvert rating — falls in the Poor band. All 623,810 bridges in the thirteen named classes are on the chart. Nothing is dropped, smoothed, indexed or rescaled. The angular axis is linear and zero-based, running 0% to 35% across 330° of arc, so one percentage point is 9.43° on every ring; the gridlines are drawn every five points and every value is printed beside its own bar. Railroad-owned structures are the outlier at 33.1% Poor against a national 6.7%, and after them four classes draw the longest bars on the chart: Federal/Tribal, Local Park, Other State Agency and Other Local Agency. State and County, on the two innermost rings, are among the shortest. Read-out for the desk: the weight of the chart sits with those four, none of them a state DOT or a county road department; hold the state and county inspection cycle where it is and move the supplementary allocation to the four long arcs, where the ink is.

02The trick

Every number on that dashboard is right, the angular axis really is zero-based and gridded, and the picture still ranks the owners wrong — because the reader is not measuring the angle. A radial bar chart bends each bar into an arc on its own concentric ring, and the length of an arc is its radius times its angle. The angle is the data. The radius is the ring, and a ring is not data: it is a slot, handed out here by the order the source table lists the owner classes in, which is the order of NBI Item 22, a codebook field. So every bar on the chart has been multiplied by a constant that nobody chose on purpose and that appears nowhere on the page. The cleanest demonstration is a pair the data hands over ready-made. County has 20,740 of its 226,268 bridges in Poor condition, which is 9.166%. Other State Agency has 85 of 927, which is 9.169%. Those are the same number to three significant figures, and the chart draws both arcs sweeping the same 86.4° — but County landed on ring 2, at radius 196, and Other State Agency on ring 7, at radius 426, so one arc is 296 units long and the other 643. That is 2.17 times the ink for an identical value, and 2.17 is exactly 426 ÷ 196. Nothing else differs. Once that is visible the rest of the chart comes apart with it. Federal/Tribal has the seventh-worst rate of the thirteen and, on the outermost ring, the second-longest bar — 7.56% drawn 2.09 times longer than Town’s 10.50%. State, on the innermost ring, has the eleventh-worst rate and draws less ink than State Toll, which is twelfth, despite a rate 1.79 times as high. Sorted by ink, eleven of the thirteen bars are in the wrong place; the two that are not are Railroad and Local Toll, the extremes, which had nowhere to go. The exchange rate that does all this is the ratio of the outermost radius to the innermost, 702 to 150, so a degree at the edge is worth 4.68 times a degree at the middle — a multiplier the chart is not aware it is applying and therefore never prints. What makes it hard to catch is that nothing is exaggerated and no axis is bent. Inside any one ring the arcs are exactly proportional, and the ratios between two values on the same ring survive intact. It is only the comparison between rings that is invented by the layout — which is the entire reason the thirteen owners were put in one picture. And the two sanity checks a bar chart normally offers are both gone: there is no common baseline, since every arc begins at twelve o’clock on a different circle, and there is no common ruler at the far end, since every arc finishes at a different distance from the centre. (FHWA publishes these figures as a plain table; both drawings are ours, the desk, the read-out and the recommendation on the first are invented, and every figure behind them is real.)

03The fix

Unbend it. On the redraw the same thirteen numbers sit on one zero-based horizontal axis, sorted worst to best, every bar starting at the same baseline and ending against the same ruler — one length per number, with the radius taken out. The two 9.17%s become what they always were, two bars of identical length, and the ranking the desk needs is readable in a glance: Railroad alone at 33.14%, then Local Park, Town and State Park in the low tens, the two identical bars, and County’s 9.17% sitting four places higher than the rings put it. The redraw is not introducing drama; it is removing thirteen different multipliers that were standing between the reader and the data. Where the circle is genuinely wanted — and sometimes it is, for a quantity that really is cyclical — the honest version puts a dot on each ring rather than an arc, because a dot marks an angular position and position is all a shared angular axis can carry, with no length being multiplied by anything. And if a radial bar chart has to ship, draw the angular gridlines, print every value on its own arc, order the rings by the values so the flattery at least runs the same way as the data, and say in the caption what a full turn is worth. One thing the straightened chart still cannot do is answer the question the desk will ask next, and it is worth printing beside the rates rather than instead of them: these are shares, so they say how likely and not how many. County’s 9.17% is 20,740 bridges, just under half of every Poor structure in the country; the identical 9.17% next to it is 85.