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Assuming that at each cache level the bandwidth is independent of the amount of data moved, the speedup can be estimated as follows: s = time_old / time_new = (data_old * bandwidth_new) / (data_new * bandwidth_old) = (data_old / data_new) = (max_bytes_per_sector_old * num_sectors_old) / (max_bytes_per_sector_new * num_sectors_new) = (num_sectors_new * bytes_per_sector_new / bytes_per_sector_old) / num_sectors_new = bytes_per_sector_new / bytes_per_sector_old where we used that the "useful" amount of data moved, remains constant, i.e. bytes_per_sector_old * num_sectors_old = bytes_per_sector_new * num_sectors_new. Thus, the maximal speedup is s_max = max_bytes_per_sector / bytes_per_sector. Using that the maximal improvement = 1 - (1 / s_max), we get improvement_percent = (1 - bytes_per_sector / max_bytes_per_sector) * 100 At each cache level, the relevant amount of data is given by the sectors missed at its respective lower-level cache, introducing new factors of `cache_miss_rate`. 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