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Write amplification is physical bytes written divided by logical bytes. A B-tree writes the log plus the page, plus each index. A levelled LSM rewrites data once per compaction level, so amplification grows roughly with level count — often ten times or more. This matters for SSD endurance and for provisioned IOPS, both of which are billed on physical writes.
Write amplification
B-tree ~ 2 + 0.5 x indexes; levelled LSM ~ 1 + 1.1 x levels + 0.4 x indexes; size-tiered ~ 1 + 0.5 x levels + 0.4 x indexes; physical = logical x factor
Each level is roughly ten times the previous one, and merging a level into the next rewrites the overlapping data. The trade is much better read amplification and space efficiency.
Size-tiered LSM has the lowest write amplification but the worst space and read amplification. Levelled is the usual default; tiered suits append-heavy time-series data.