How can I avoid the subquery for this query (SQL server 2005)?

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SQL-Server-2005

Select 
    FirstName, 
    MiddleName,
    LastName, 
    MatchType, 
    RunsScored
From (
        Select  
            s.Id, 
            a.FirstName, 
            a.MiddleName,
            a.LastName, 
            s.MatchType, 
            s.RunsScored, 
            Row_Number() Over(Partition By MatchType Order By RunsScored Desc) rn
        From 
            PlayersCareerBatting s Join PlayersBioDataNew a 
        On s.Id=a.Id

     ) x
Where rn=1

here is my code. for this code, i'm getting a query speed too slow. so i want to speed up the query. for that, i'm going to avoid the sub-query for that. pls help me how to avoid sub-query to run query faster.

What I have tried:

Select a.firstname, a.middlename, s.matchtype, Max(s.Runsscored) from PlayersCareerBatting  s Join PlayersBioDataNew a 
		On s.Id=a.Id group by s.matchtype,a.firstname, a.middlename

i tried this. but this showing all the rows, i want only the rows who got maximum in runsscored with their respective names.