Composition claims are about parts of a whole, and they are the messages that go wrong most often, because the whole is frequently not a whole.
When is a part-to-whole chart legitimate?
Three preconditions have to hold before any part-to-whole form is legitimate. Every value must be non-negative, because none of these forms can draw a negative part. The parts must be mutually exclusive and must together exhaust the total, or the reader will read a share that is not a share. And the total itself must mean something: revenue by segment sums to revenue, which is meaningful, while returns by sector sum to a number that means nothing at all.
That third one is where the opening pie died. Eight sector returns, two of them negative, added to 28.5, and the software treated 28.5 as a whole. Realty's 18.4% became 64.56% of that whole and drew as 232.42 degrees, a slice covering nearly two thirds of the circle for a sector carrying 5% of the index. The two negative sectors vanished. No rendering could have saved it, because the message was never a composition message in the first place.
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Which form fits your number of parts?
When the preconditions do hold, the form follows the part count and the period count.
Two or three parts in one period is a single stacked bar, and quite often it's a sentence instead. "Interest income is 71.4% of revenue and everything else is the remaining 28.6%" needs no chart at all.
Four or more parts in one period is a sorted horizontal bar of the shares, never a pie, with a long tail collapsed into an "other" row once the small parts stop earning their labels. Your reader now compares lengths on a common baseline, gets exact values from direct labels, and can rank the parts at a glance. A treemap is worth using only when a real hierarchy exists and you want to show both levels at once. Even then it comes with a warning. Area is read poorly, and a treemap's rectangles differ in both dimensions, so a reader can only reliably tell big from small.
Parts across a few periods, where the shares are the point, is a hundred-percent stacked bar with no more than five parts. Only the bottom band and the total have a common baseline. Every band above the first floats, so its changes are hard to read. Keep the series you care about at the bottom. Beyond five parts, switch to small multiples of share lines, one panel per part on a shared scale.
When should you use a waterfall?
A total decomposed into signed drivers is a waterfall, and this is the form most analysts under-use. Take a revenue bridge: 52.0 crore last year, 66.2 crore this year, and five drivers in between. New customers added 11.9, price and mix added 4.6, a new quick-commerce channel added 2.2, existing-customer volume lost 2.9 and discontinued products lost 1.6. The net is 14.2, which is 27.31% growth. A waterfall gives the picture that matters: gross additions of 18.7 against subtractions of 4.5, and a gross-to-net ratio of 1.32. It also carries the one fact that would never survive a stacked bar, which is that revenue from customers the company already had went backwards. A pie of this is impossible because two drivers are negative. A stacked bar of channel revenue for the two years is a legitimate chart that answers a different question and hides the decline entirely.
Why does a pie chart fail above three slices?
Now the pie, properly. The objection is about angle. Fashion has nothing to do with it. The eye recovers a quantity from an angle far less accurately than from a length on a common scale, and the error grows with the number of slices and shrinks as slices get closer in size. Take a bank's revenue split: interest income 71.4%, fee income 14.2%, treasury 8.1%, insurance distribution 4.3% and other 2.0%. Those draw as 257.04, 51.12, 29.16, 15.48 and 7.20 degrees. The two smallest slices differ by 8.28 degrees out of 360, which no reader resolves, and comparing them means travelling around the circle. On a bar chart you'd just look along a line. Three slices is the ceiling at which the form still works, and at three slices the answer is usually a sentence anyway. A legend makes it worse at any slice count, because it adds a lookup between the colour and the name.