Iron's Spells 'n Spellbooks structure rarity
How structure placement works
Minecraft places most structures on a grid. The world is split into square regions of spacing chunks, and each region gets exactly one candidate spot, somewhere in its first spacing minus separation chunks. So a structure with spacing 34 has one chance every 544 blocks in each direction, and two of them can never be closer than about separation chunks. Structures that share a group take turns at the same spots: each candidate picks one of them by weight, skipping those that do not fit the biome there, which is why a heavy-weight structure in a big group still turns up often.
The count within your search radius assumes every candidate lands in a suitable biome. Real numbers are lower for structures tied to rare biomes, and a candidate can also fail on awkward terrain. Click a column heading to sort; tick the box to compare with vanilla structures.