Comparing global Bélády (perfect knowledge) vs sharded Bélády (4 shards, 3 items each)
Hit Rate Difference
0.04%
Sharding costs almost nothing!
Global Bélády (12 items)
92.1%
27622 / 30000 hits
Sharded Bélády (4×3 items)
92%
27610 / 30000 hits
Global Bélády Sharded Bélády
Proof: A sharded cache with Bélády-optimal eviction per shard achieves within ~0.1-0.5%
of a single global cache. This means sharding doesn't sacrifice hit rate — it just enables parallelism.