Updating a table field with a consecutive number

Let's suppose I have a table like this one but without data in the Position
field:
----------------------------------------------------------------
Date Score Position
----------------------------------------------------------------
Jan. 2, 2011 1000 1
Jan. 2, 2011 999 2
Jan. 3, 2011 1000 1
Jan. 3, 2011 999 2
Jan. 3, 2011 998 3
Jan. 4, 2011 1000 1
Jan. 4, 2011 999 2
Jan. 4, 2011 998 3
Jan. 4, 2011 997 4

As you can see, the records are order by date and each date has a score and,
depending on the score, a position is assign from 1 to n. I suppose I need
to traverse the table ordered by date and score (one record at a time) and
UPDATE the position field starting with 1 until the date changes. At this
point, I would start from position 1 again until the next date change and so
on. At least this is what I imagine I can do. I will appreciate any advice
about a way of achieving my objective.

Respectfully,
Jorge Maldonado