Size & scale

The overplotted scatter

A thousand records in one dot, and one record in one dot.

a.k.a. overplotting · overdraw · the saturated scatter · the blob · tied points · exact ties · the hairball · opaque markers · alpha = 1 · the big-data scatter

A scatter plot makes one quiet promise: one mark per record, so more records means more ink. The promise holds right up to the moment two records land in the same place, and after that it breaks without any sign on the page. A second opaque dot on a spot adds nothing, and neither does the thousandth. Where the data is dense, the dots fuse into a solid shape whose size is set by how far the crowd spreads rather than by how many are in it; where the data is sparse, every lonely record gets a whole dot of its own. So a few hundred stragglers scattered across an empty field can cover more of the page than tens of thousands of records packed into one corner, and the eye, which reads covered area as quantity, takes the stragglers for the story. What the chart has really drawn is the range of the data, and it looks exactly like a picture of the distribution. Rounded and whole-number data make it far worse, because then records do not nearly overlap, they tie exactly: when both axes are counts, years or ratings, a thousand identical records are one dot, drawn precisely as large as the single record next to it. Marker size does the rest: a dot wider than the gap between neighbouring values merges records that do not even tie, so the bigger the markers and the tighter the data, the sooner the crowd becomes a slab. Nothing in the audit catches it. The scales are linear and honest, no record has been dropped, every point sits exactly where it belongs, and the only thing missing is the one quantity a scatter plot is usually asked about, which is how many. It is the area illusion running backwards: there, ink grows faster than the value; here, it stops growing at all once a spot is full. And it is a close relative of the heaped digit, since every value people round to is a place where records pile up and vanish into one mark.

How to spot it

Count the dots you can see and compare it with the n in the caption. If a chart says forty thousand records and you could count its marks in an afternoon, most of them are underneath the others.
Solid shapes with hard edges. A region of uniform ink with no texture inside it is a region where the chart has run out of ways to say “more”, and the density inside it could be anything.
Axes that only take whole numbers or rounded values — years, counts, ages, ratings, scores. Records on a grid tie exactly, and an exact tie is invisible no matter how small the markers are.
The eye drawn to the edges. If what you remember from a scatter is its outliers and its outline, ask where the middle half of the records is; on an overplotted chart the picture usually cannot tell you.
Markers bigger than the spacing of the data. If a dot is several units tall on an axis that moves in steps of one, neighbouring values merge into one shape whether or not they tie.
Opaque markers by default. Most plotting libraries draw fully opaque points unless told otherwise, so a scatter of a big table that nobody configured is overplotted until proved otherwise.
A claim about what is typical — “all sizes”, “all over the map”, “no pattern” — made from a scatter plot rather than from a count. The scatter shows what is possible; typical is a question for the histogram.

The fix

Give the ink back its job of counting. For a few thousand records, transparency is often enough: at low alpha, stacked points darken where they pile up, so density reappears as shade — though it saturates too, just later, so check the darkest spot is not already black. Where values tie exactly, jitter them by a fraction of the rounding step, and say that you did. For large tables, stop drawing records and draw counts: bin the plane into a grid or hexagons and shade each cell by how many records it holds, on a single-hue scale that runs from pale to dark with a printed legend, so the crowd is the darkest thing on the page and the stragglers are the palest. Then add the summaries a scatter never provides — a median line, a band holding the middle half or the middle nine-tenths, marginal histograms along the axes — because those answer the question about what is typical directly instead of leaving it to the eye. Keep the outliers visible if they matter, and label them by name, since that is honest about what they are: individual records, one each. And print the n in the places it lives. A caption that says how many records fall under the darkest region does more to correct the impression than any amount of redrawing.

In the gallery

Dark navy slide kicked “Organ committee · Hartwell Street Chapel · the case for the new instrument” on the left and “Every organ in the database with a year and a rank count · 1800–2026” on the right. The headline reads “Organs come in every size. Sixty ranks is middle of the road.” A gold-bordered chip beneath it reads “Demonstration · drawn by us from the OHS Pipe Organ Database · the chapel and its committee are invented”. The standfirst says every point is a real entry in the Organ Historical Society’s Pipe Organ Database — 46,160 organs dated 1800 to 2026 that record how many ranks of pipes they have — with nothing sampled, smoothed or binned, nothing left out, and both axes linear, ranks starting at zero. The main panel, headed “Every pipe organ in the database, by year and by size”, is a scatter of opaque pale-blue dots, year from 1800 to 2020 along the bottom and ranks from 0 to 480 up the side. The bottom of the chart, from about 1850 onward and up to roughly 40–60 ranks, is one solid, textureless slab of blue; above it the dots thin out into a scattered cloud reaching past 120 ranks everywhere after 1920 and past 200 in places, with three gold-marked outliers labelled “Wanamaker Organ, Philadelphia · entry dated 1911 · 464 ranks”, “Boardwalk Hall, Atlantic City · 1932 · 449” and “Cadet Chapel, West Point · entry dated 1941 · 380”. A dashed gold line across the chart at 60 ranks is labelled “Our proposal: 60 ranks — right in the thick of it”. Four cards run down the right: “The range, in one figure”, reading 1 to 464 ranks, from one-rank organs to the Wanamaker Organ and Boardwalk Hall, and claiming the cloud fills the whole frame; “Where our sixty ranks would sit”, which says the line at 60 runs through the thick of the cloud with dots packed above it to the top of the chart, so sixty ranks is an ordinary, respectable instrument; “Recommendation”, which approves a sixty-rank, four-manual specification with gallery space reserved for a future 32-foot Bombarde, warning that anything smaller puts the chapel below the middle of the field; and “Nothing on this slide is bent”, listing real data, one dot per organ, linear axes with ranks from zero, no truncation, no log scale, no second axis and nothing dropped. A row of gold ticks along the bottom reads “One dot per organ”, “All 46,160 entries”, “Linear axes, ranks from zero” and “Nothing sampled, binned or dropped”. A footnote credits the OHS Pipe Organ Database, all 75,368 instrument entries retrieved through its public API on 30 September 2026, notes that an entry is a documented instrument as built, rebuilt or relocated so a much-rebuilt organ can appear more than once, and says the chapel, the committee and the recommendation are ours.

Ten small organs to a dot, and a dot of its own for every giant

The overplotted scatter