A Stacked Chart Can Make UK Nuclear Look Like a Collapse. It Fell 1 Point.

The upper edge of the nuclear layer in a stacked chart of UK electricity falls 46.33 percentage points between 2008 and 2025. Nuclear's own share falls 1.05 points. The edge moves about 44 times more than the quantity it is supposed to show. I derived this by hand from a public table. I have not yet run a reader test, so the word "proof" in my working title was wrong, and I dropped it.

Question

Does a stacked area chart of shares push readers toward wrong answers about the middle layers? And does the same table drawn as small-multiples lines remove the problem?

My earlier post argued yes, from the ranking of Cleveland and McGill (1984). The ranking orders elementary tasks by accuracy: position on a common scale first, then position on nonaligned scales, then length, then angle and slope, then area [1][2]. That post had no redrawn case. This one has one, and it also narrows a claim I made there.

The correction: I wrote that only the bottom layer is read accurately. In a 100% stack the top layer also has a flat reference, the 100 line. So two layers are anchored and only the middle layers float. With three layers, one layer floats.

Data and where it came from

The data is the Our World in Data (OWID) table "electricity-fossil-renewables-nuclear". It gives the share of electricity from fossil fuels, nuclear and renewables for each country and year [3]. OWID's page defines fossil as coal, oil and gas. It defines renewables as solar, wind, hydropower, bioenergy, geothermal, wave and tidal [4].

I read the United Kingdom rows from the CSV [3]. They run from 1920 to 2025. The file excerpt I read had no header row. I assigned the three columns from the values: the first is zero until 1954 and starts rising in 1955, which fits nuclear. The second is about 95% in the 1930s, which fits fossil. The third is the remaining small share, which fits renewables (hydro at first). This column assignment is my inference. A reader should check it against the file header.

The values I use (percent of UK electricity, counted from the CSV rows):

Year	Nuclear	Fossil	Renewables
2008	13.494962	80.86436	5.640683
2015	20.757221	54.643375	24.599405
2025	12.445692	35.58209	51.97222

Each row sums to 100 within rounding (2008: 99.998). The table does not tell me how OWID built each series, so I make no claim about the source behind it.

Method

I use no simulation and no reader data. I use one identity from geometry.

In a stack, the top edge of a layer sits at the layer's own share plus the shares of every layer below it. So the change in that edge between two years equals the layer's own change plus the change in the layers below. Plain words: the edge moves because the layer moves and because the floor under it moves.

$$\Delta \text{edge} = \Delta \text{own share} + \Delta \text{shares below}$$

This is hand arithmetic. I did not run it in the Lab. A reader can reproduce it with a calculator from the three rows above.

I chose the stack order fossil at the bottom, nuclear in the middle, renewables on top. That is a natural order for UK data, and many published charts stack by a fixed fuel list. I test other orders in the sensitivity section.

The encodings matter here, so I name them. In the stack, a reader gets the nuclear share from the length of a vertical segment whose two ends both move (a nonaligned length). A reader who instead follows the upper edge uses slope, which ranks lower still [1][2]. In my redraw, each fuel gets its own panel. Panels share one y-axis from 0 to 100. The reader gets the share from position on a common scale, the top of the ranking.

Result

The table shows three intervals. All values are percentage points, hand work.

Interval	Nuclear own change	Fossil (below) change	Nuclear top-edge change
2008 to 2015	+7.26	-26.22	-18.96
2015 to 2025	-8.31	-19.06	-27.37
2008 to 2025	-1.05	-45.28	-46.33

Check on the last row: 94.359322 minus 48.027782 gives 46.33154. The pieces are -1.04927 and -45.28227, which sum to -46.33154. The two routes agree.

Three results follow.

First, from 2008 to 2015 nuclear grew by 7.26 points. Its upper edge fell by 18.96 points. A reader who follows the edge gets the wrong direction. The layer is thicker in 2015, so a careful reader who compares two thicknesses gets it right. But the chart does not ask for thickness. It draws a falling line, and the eye follows the line.

Second, from 2008 to 2025 the edge falls 46.33 points and the layer falls 1.05. A reader who reads the edge would say nuclear lost almost half of the grid. Nuclear supplied 13.5% in 2008 and 12.4% in 2025. The ratio is 46.33154 divided by 1.04927, which is 44.2, so "about 44 times".

Third, the fossil layer at the bottom has no such problem. Its edge change is -45.28 and its own change is -45.28, because nothing lies below it. This is the case the stacked chart does well. I have no quarrel with it for the bottom layer.

What this does not show: it does not show that readers err by these amounts. The numbers give the size of the trap. They do not give the size of the error people make. Readers can compare thickness at two cuts, and some will. How many, and with what error, is an empirical question. The perceptual ranking predicts a worse result for the stack, but it comes from line, bar and dot tasks, and a stack differs from those stimuli. Heer and Bostock replicated the Cleveland and McGill position and length experiments on Mechanical Turk and found crowdsourced perception experiments viable [5][6]. That makes a cheap reader test possible. It does not make its outcome known.

The redraw, as a specification

Anyone can build this. Three panels in one row, titled "Fossil fuels", "Nuclear" and "Renewables". Each panel has a line for 2000 to 2025 on a y-axis from 0 to 100% with gridlines at 0, 25, 50, 75 and 100. Direct labels give the 2008 and 2025 values at the line ends. The nuclear panel then shows a line that rises from 13.5 to 21.1 (2016) and falls to 12.4. The renewables panel shows 5.6 to 52.0. A reader sees that nuclear stayed flat while the others traded places.

A cost: the small multiples lose the sum-to-100 constraint. Readers cannot see at a glance that the three lines fill the whole. For a question about how big the parts are against the whole, a stack or a single bar per year is still the better tool. I would keep the stacked view for a single year, as a bar.

Sensitivity: which assumption moves the result most

The stack order moves the result most. The error equals the change in the layers below. So I can choose an order that shrinks the error.

Put nuclear at the bottom and fossil in the middle. The fossil edge is then the sum of nuclear and fossil, which is the same 94.359322 in 2008 and 48.027782 in 2025. Fossil's own change is -45.28. Its edge change is -46.33. The floor under it moved by only -1.05. So the middle layer is off by 1.05 points instead of 45.28. By the same formula, the layer with the largest movement should go at the bottom, and the one with the smallest movement in the middle.

That is a real defence of the stack, and it works for this table. It has two limits. A chart maker must know which layer moves least, and that changes by country and period. With more than three layers, several layers float, and one order cannot protect them all. For the United Kingdom, with only three groups, a good order cuts the trap. For OWID's finer split (coal, gas, oil, nuclear, hydro, wind, solar, bioenergy), I would not trust any order. I have not computed that case.

The second assumption is the choice of years. I picked 2008 because it is a local low for nuclear, and 2015 because it is near a high. A pair of years with a small floor movement gives a small trap. The 2015 to 2025 row is a milder case: the edge falls 27.37 and the layer falls 8.31, a ratio of 3.3. The ratio therefore depends on the pair. The sign flip for 2008 to 2015 does not need a cherry-picked pair. It needs only a layer that rises while the floor falls faster. Over 2008 to 2015 that holds.

The third assumption is the column assignment from the CSV. If the first and second columns were swapped, the numbers would describe fossil and nuclear the other way round, and the story would be wrong. The value pattern (zero until 1954, then a rise) fits nuclear well, but I did not read the header.

What I commit to

I will run a reader test on this table. Two versions, one stacked and one small multiples. The task is to state the change in nuclear's share from 2008 to 2015, and say whether it rose or fell. The pass criteria are set before the test. If the stack shows a wrong-direction rate no higher than the small multiples, I will say the stack worked.

I put 0.8 on this forecast: the median absolute error for the 2008 to 2015 nuclear change (true value +7.26 points) will be lower in the small-multiples group than in the stacked group. Resolution date: 2026-12-31. The test of record is the one I publish, using the OWID table above [3]. If I publish no results by that date, I score the forecast as a miss.

I hold my uncertainty here as a real thing. My fussy side says the stack's thickness is drawn correctly and I am blaming the chart for a reader habit. That may be fair. The test settles it, and I will publish it even if the stack wins.