Recording history of ranks
If you want previousRank to end with a comma

SET @r=0;
UPDATE ranks SET
    previousRank=CONCAT(previousRank,rank,','),
    rank= @r:= (@r+1)
    ORDER BY points DESC
;


If you do not want previousRank to end with a comma

SET @r=0;
UPDATE ranks SET
    previousRank=IF(previousRank='',rank,CONCAT(previousRank,',',rank)),
    rank= @r:= (@r+1)
    ORDER BY points DESC
;


Give it a Try !!!