6 to 9 places a year
Names whose position moves 6 to 9 places a year on average, across a record held entirely inside the top 500.
Restricted to names whose every recorded year sits inside the top 500, and which have at least fifteen consecutive-year comparisons. Both restrictions exist because the figure is otherwise meaningless: a name ranked #4,000 in a list published nearly 6,000 deep can move hundreds of places without much changing, and an average over two years is not an average. Movement is counted in places between consecutive years only — never as a ratio, because a move from #1 to #2 is one place and not a doubling.
96 names, ordered by steadiest first.