As a follow-on to last week's single-sided discussion, here's a clearer illustration of the fact that most companies are working within relatively tight constraints, cassette-wise, subject to their strengths and preferences. As we look at ten, eleven, twelve, and even thirteen speed cassettes, we can see that every cassette of a given cog count falls more or less in a line. More range = larger average steps; More cogs = smaller average steps.
That makes sense: the average step in a cassette should be pretty close to the range divided by the number of cogs. The average doesn't tell the whole story, of course, and can mask different approaches. If the goal is consistent steps across the cogs, then standard deviation (a measure of the variation within the set) is a good shorthand for how well this is being achieved. In the plot above, the size of each point is tied to the cassette's standard deviation. Smaller points represent more consistent steps while larger suggest more variety.
If all gears are used equally, consistent steps may be a good target. But designers may want to place larger steps in little-used areas (like the highest or lowest gears). That means leaves smaller steps for the bulk of any given ride with a handful of "hail Mary" cogs for the steepest climbs (or worst bonks).
This can most clearly be seen in 3T's 11-speed "Overdrive" and "Bailout" cassettes. Both share a 356% 9-32t range but the Overdrive model puts its biggest step at the high end (one extra-tall gear for long, steep descents) and the Bailout, which would be my pick on paper, saves the big steps for low gears. SRAM's Eagle cassette (called out for its use in AXS "Mullet" gravel builds) has a bit of a hammock profile, with larger steps at the extremes and smaller steps mid-block.
There are also some examples here of cassettes whose progression is almost certain to feel odd- see if you can spot the abrupt changes in step size from a couple of lesser-known brands.
Fun to think about? For some of us, yes. But truth be told, I'll take an imperfect ride on any one of our J.Guillem bikes over a perfect spreadsheet any day.