I am intrigued. I've been thinking about this problem today, but I can't think of an efficient relational implementation in current DBs. How would you do this? I came up with the following:

1) On get_rank() do a count(*) where score < users_score;

2) Store row_number() over() [...] order by score in a lookup table and refresh every so often. Use this for get_rank() lookups.

The problem I have is that you either have to calculate the rank on read using a linear-time count() or on write which means updating n/2 rows on average with their new position.

edited formatting