如何在基于分数的mysql数据库的RANK列中保存排名（从sql查询中找到）？

Question

I have made a simple php form where user can insert their name and score which is stores to mysql database.

when user submit the form their inputs are inserted to a table names SCORES to NAME and SCORE column in database. There is one more coloumn names RANK.

Now i want to make search page in php to find the score and rank(based on score) by name.

I have sql query to find rank but it do not store rank to the database permanently.

SET @rnk=0;
SET @rank=0;
SET @curscore=0;
SELECT score,NAME,rank 
FROM (SELECT AA.*,BB.ID,
        (@rnk:=@rnk+1) rnk,
        (@rank:=IF(@curscore=score,@rank,@rnk)) rank,
        (@curscore:=score) newscore
      FROM (SELECT * 
            FROM (SELECT COUNT(1) scorecount,score 
                  FROM scores
                  GROUP BY score) AAA
            ORDER BY score DESC) AA 
      LEFT JOIN scores BB USING (score)) A;

Can i do something to store rank into database so i can find from search page and one thing more that score shoud be refreshed if new records inserted to database..??