The 18-to-1 gap that a zigzag closed to 1.6

Dark navy board slide, masthead “Five Boroughs Pest & Wildlife · Service-line review · Board pack, Q1 2026”, headlined “Rodent is not the whole business — four more lines are right behind it”. A subhead reads: citywide demand, measured the only way it can be measured — every pest complaint New Yorkers made to 311 in 2025, as logged by the Health Department; one complete year, one agency, one unit, a service request; nothing sampled, nothing weighted, nothing set aside. Filling most of the slide, under the label “311 service requests · NYC Health Department pest complaint types · calendar year 2025”, is a five-bar column chart. The y-axis is labelled 0, 500, 1,000, 1,500 and 2,000, and then, immediately above the 2,000 tick, 30,000, 31,000 and 32,000 — the stretch between 2,000 and 30,000 is replaced by a horizontal band of double zigzag lines running the full width of the plot and through the axis itself. A gold bar for Rodent (rat and mouse sightings, signs, and conditions) is labelled 31,312; it climbs to the top of the lower band, is interrupted by the zigzag, and resumes above it, standing just short of the top of the chart. Four blue bars follow: Pigeon waste (unsanitary pigeon condition) at 1,756, standing a little over half the rodent bar’s height; Standing water (mosquito breeding conditions) at 1,275; Bees & wasps (harbouring bees or wasps) at 548; and Mosquitoes (large number of mosquitoes) at 334. Down the right-hand side, a gold-bordered card reads 1.6× over the line “The rodent line’s lead over pigeon waste, read straight off this chart”. A card headed “Demand by service line · 2025” lists Rodent 31,312, Pigeon waste & odour 1,756, Standing water 1,275, Bees & wasps 548, Mosquitoes 334. A gold card headed “Read-out for the board” says rodent leads but this is not the runaway the trade press describes, that pigeon waste sits just behind it, that standing water and bees are within reach, that mosquito — a seasonal line the firm does not staff at all — is on the same chart as the rest, and recommends two mosquito technicians and a dedicated pigeon crew for FY27. A final card headed “Seasonality” gives 86 rodent complaints per day all year, 1.6 mosquito complaints per day in season, and 0 mosquito complaints between November and March. Three ticked boxes run along the bottom: “Zero-based axis. The scale starts at 0. No truncation, no log scale, no second axis anywhere on this chart”, “Nothing cherry-picked. One complete calendar year, and every complaint type the Health Department files as a pest”, and “One unit throughout. Every bar is the same thing — one service request, logged by one agency, counted once”. A footnote records that the counts were computed by us from NYC 311 Service Requests from 2020 to Present, NYC Open Data dataset erm2-nwe9, queried 21 August 2026, for complaints created between 1 January and 31 December 2025 with responding agency DOHMH, notes that Rodent bundles rat sightings, mouse sightings, signs of rodents and conditions attracting rodents, and states that the slide is a demonstration drawn by us in the manner of a board pack and has never been published anywhere. — Showing the misleading chart

The same five numbers on a cream background, kicked “The same five numbers · measured off the drawing · NYC 311 pest complaints · 2025” and headlined “The zigzag closed an 18-to-1 gap to 1.6.” A subhead explains that the axis really does start at zero and really does end above its tallest bar, but that in between it deletes 28,000 complaints — everything from 2,000 to 30,000 — into one thin band of squiggle, and that measuring what it drew gives a rodent bar 1.6 times the pigeon bar and 8.6 times the mosquito bar, against counts of 17.8 and 93.7. On the left, a panel headed “All five complaint types · one zero-based axis · 0 to 32,000 service requests” draws horizontal bars: Rodent 31,312, running nearly the full width and annotated inside the bar “8.0× the other four put together”; Pigeon waste 1,756, annotated “5.6% of the rodent bar”; Standing water 1,275; Bees & wasps 548; and Mosquitoes 334, annotated “1.1% of the rodent bar” and barely visible against the axis. Below it, a second panel headed “The other four · their own zero-based axis · 0 to 2,000 — rodent left out, because it is 31,312 and 15.7 times off this panel” draws the same four smaller types at a readable scale: pigeon waste 1,756, standing water 1,275, bees and wasps 548, and mosquitoes 334, annotated “pigeon waste is 5.3× this”. Below that, a strip headed “Move the break up or down the page and the same five numbers draw a different answer — rodent against mosquitoes, as the picture shows it” holds four small charts, each with a gold rodent bar and a blue mosquito bar. The first, with the break low on the page and 0–2,000 given 89% of the plot height, is labelled 7.0 : 1. The second, the placement the slide used, with 0–2,000 given 68% of the height, is labelled 8.6 : 1. The third, with the break high and 0–2,000 squeezed into 34%, is labelled 15.2 : 1. The fourth has no break at all — one zero-based axis from 0 to 32,000 — and is labelled in gold 93.7 : 1, its mosquito bar a hairline. Five cards run down the right. “Two knobs, not one” records that the break removes 28,000 complaints of scale and leaves the halves running at different rates: below it 1,000 complaints get 350 pixels of the published image, above it 165, so the top of the chart is compressed 2.1× against the bottom. “Where you put it is what you get” notes that the same five counts draw rodent at 7.0×, 8.6× or 15.2× the mosquito bar, none of them 93.7, while a zero-based axis gives 93.7 every time. “It is not a truncated axis” explains that a truncated axis chops the bottom off and admits it by starting at 94.6, whereas a break keeps the zero, keeps the top and takes the middle, so the chart passes the check most readers know and the lengths stop being proportional anyway. “What the slide got right” lists a zero-based axis, one complete calendar year, one agency, one unit, every category shown and numbers printed on every bar — six things right, and the zigzag enough on its own. “The check that catches it” says to find the break, read the tick immediately below and the tick immediately above it and subtract, which here gives 28,000 against a whole lower half worth 2,000, and that when the missing stretch is bigger than everything drawn beneath it, no length on the chart means anything. A gold-ruled callout at the foot reads “The break is not empty space. It is the finding,” and notes that the swallowed stretch is 89% of the very number the chart was drawn to show, that rodent complaints ran at 86 a day every day of the year, and that mosquito complaints ran at 1.6 a day across the seven months they happen at all and at none between November and March. A footnote gives the NYC Open Data source, dataset and query date, lists all five counts, records that the rodent total was checked independently against the same year broken out by borough, explains that the quoted bar lengths were set in the drawing itself and confirmed by measuring the published image, and says both drawings are our own. — Showing the misleading chart

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Every pest complaint New Yorkers made to 311 in 2025, on one axis that starts at zero, ends above its tallest bar, and quietly deletes the 28,000 complaints in between. Rodent complaints outnumber pigeon complaints 17.8 to 1; the chart draws the rodent bar 1.6 times the pigeon bar. Slide the break up or down the page and the same five numbers draw 7.0, 8.6 or 15.2 — never 93.7.

311 Service Requests from 2020 to Present — NYC Open Data, dataset erm2-nwe9; pest complaint types with responding agency DOHMH, calendar year 2025, retrieved 21 August 2026, 2025Added August 21, 2026

01The claim

Rodent is not the whole business. Here is citywide demand for pest work, measured the only way anybody can measure it: every pest complaint New Yorkers made to 311 in 2025, exactly as the Health Department logged it. One complete calendar year, one agency, one unit — a service request — and every complaint type the department files as a pest, all five of them on a single chart. Nothing sampled, nothing weighted, nothing set aside, and the number printed on top of every bar. The axis starts at zero, as an axis under bars must. And read it and the trade-press story falls apart. Rodent leads, certainly, but it is not the runaway everyone describes: pigeon waste sits just behind it at 1.6 times back, standing water and bees are within reach, and mosquito — a seasonal line the firm does not staff at all — is on the same chart as the rest. The recommendation to the board follows: two mosquito technicians and a dedicated pigeon crew for FY27.

02The trick

Every count on the slide is right, the year is complete, the unit never changes, and the axis really does start at zero. It also stops at 2,000, resumes at 30,000, and marks the 28,000 complaints it dropped in between with a band of zigzag most people read as tidying-up. That band is the whole chart. A bar makes one promise — that its length is proportional to its value — and the promise cannot survive a hole in the scale, because the lengths on either side of the hole are no longer counting the same thing. Measure the drawing and the damage is exact. The rodent bar stands 1,006 pixels above the baseline in the published image; the pigeon bar stands 615. That is 1.6 to 1, for counts of 31,312 and 1,756, which are 17.8 to 1. Against the mosquito bar’s 117 pixels the rodent bar draws 8.6 to 1, for a true ratio of 93.7 to 1. There is a second knob in the same zigzag, and it is the one people miss: the two halves do not run at the same rate. Below the break, 1,000 complaints are worth 350 pixels of this image; above it, 165. The top of the chart is compressed 2.1 times against the bottom, so even within the rodent bar the ink is not one currency. And the ratio the reader takes away is not a fact about the data at all — it is a layout choice. Give the lower band most of the page and the same five counts draw rodent at 7.0 times the mosquito bar; put the break where this slide put it and they draw 8.6; push it high and they draw 15.2. Not one of those is 93.7. The uncomfortable part is how much the slide gets right on the way past. Zero-based axis, whole year, one agency, one unit, every category present, every number printed — six checks a careful reader would run, all six passed. Being a break rather than a truncation is exactly what lets it through: truncation chops the bottom off and confesses by starting at 94.6, while a break keeps the zero and the top and takes only the middle, which is where the difference happened to live. (The slide is our own demonstration, drawn in the manner of a board pack. The complaint counts are real, taken from the city’s open data.)

03The fix

Draw it on one zero-based axis and the picture is dull in the way findings often are: the rodent bar runs the length of the panel and the other four are slivers against it — 5.6% of it, 4.1%, 1.8%, 1.1% — because rodent complaints outnumber the other four put together by exactly eight to one. There is only one pest complaint in New York City, and it has a tail. That is the sentence the break was inserted to avoid printing, and it is the one the board needed. Then, if the small lines genuinely deserve reading, give them a second panel at their own zero-based scale rather than a gap in the first one, and say on it how far off the panel the big one sits — here, 31,312, or 15.7 times the panel’s own ceiling. Two axes plainly labelled beat one axis quietly interrupted: the reader can see precisely where the comparison stops, and inside each panel a length means something again. The second panel is where the real business intelligence turns up, incidentally, since at that scale pigeon waste is visibly 5.3 times mosquito, which the broken chart could not show either. The check that catches this in the wild takes about five seconds and needs no arithmetic beyond a subtraction. Find the break, read the tick immediately below it and the tick immediately above it, and take one from the other. Here that is 28,000 — against a lower half that covers 2,000 in total, and against a tallest bar of 31,312, of which the missing stretch is 89%. When more scale is absent than present, nothing on the page is proportional to anything and the only honest way to read the chart is off the labels, which is to say off a table wearing a chart’s clothes. Worth knowing, too, when the break is merely a nuisance rather than a lie: a line or a dot plot encodes position rather than length, so a clearly marked gap in one of those does less harm. Under bars there is no version that works. And the seasonality the slide waves at is its own small lesson in reading the numbers rather than the shapes — 334 mosquito complaints in a year is 1.6 a day across April to October and exactly none from November to March, against 86 rodent complaints a day, every day, all year.