Suppose a disk track contains n sectors, its free space percentage is p, and the free space is randomly distributed. The average number of sectors the disk head must skip before arriving at any free sector is:
Appendix A.1 shows a proof of (1) and extends it for situations where the file system block size does not equal the size of the smallest addressable disk unit.
Formula
(1) is roughly the ratio between occupied
sectors and free ones. This is a promising result for the eager
writing approach because, for example, even at a relatively high
utilization of 80%, we can expect to incur only a four-sector
rotational delay to locate a free sector. For today's disks, this
translates to less than 100 
. In six to seven years, this
delay should improve by another order of magnitude because it scales
with platter bandwidth. In contrast, it
is difficult for an update-in-place system to avoid at least a
half-rotation delay. Today, this is, at best, 3 ms,
and it improves slowly. This difference is
the fundamental reason why eager writing can outperform
update-in-place.