Problem: When a query has a large limit (e.g. 1000) and there are multiple shards (e.g. 10), naively each shard must return the full 1000 results — totaling 10,000 scored points transferred and merged. This is wasteful since data is randomly distributed across auto-shards.
Instead of asking every shard for the full limit, ask each shard for a smaller limit computed via Poisson distribution statistics, then merge. This is safe because auto-sharding guarantees random, independent data distribution.
The strategy trades a small probability of slightly incomplete results for a large reduction in inter-shard data transfer, especially for high-limit queries across many shards. The 1.2x safety factor and the 99.9% Poisson threshold keep the error rate very low — comparable to inaccuracies already introduced by approximate vector indices like HNSW.
