HIgh score not up to scratch

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Any help Here:

At the moment this shows a USERNAME-COMPETITION and POINTS for a user with 
the highest points out of many competitions.

The USERS also have a second points field (acc_margin) where lower score is 
better.
So my problem is that i need to show the highest scoring user (by points) 
then if there is another user with the exact same points then the user with 
the lowest (acc_margin) is shown.

<?php
     for ($x=1; $x<=$no_comps; $x++) {
    $max_query[$x] = mysql_result(mysql_query("SELECT MAX(points) as Num 
FROM leaderboard WHERE comp_id = $comp_ids[$x]"),0);
    //get name
    $query4 = @mysql_query("SELECT username FROM leaderboard WHERE points = 
" . number_format($max_query[$x],0) . " AND comp_id = $comp_ids[$x]");
    $result4 = @mysql_fetch_array($query4);
    $leader[$x] = $result4['username'];
    //get comp name
    $query5 = @mysql_query("SELECT name FROM comps WHERE id = 
$comp_ids[$x]");
    $result5 = @mysql_fetch_array($query5);
    $comp[$x] = $result5['name'];
    echo "<tr class=tdb1><td>" . $leader[$x] . "</td><td>" . $comp[$x] . 
"</td><td align=center>" . number_format($max_query[$x],0) . "</td></tr>";
   }
    ?>

HERE IS THE TABLE:

      Field Type Null Default
      id   int(11) No
      user_id   int(11) No  0
      comp_id   int(11) No  0
      username   text No
      points   int(11) No  0
      amt   float No  0
      margin   int(11) No  0
      acc_margin   int(11) No  0





****************************
I had a similar question earlier that i was helped with but i cant seem make 
it work here:
(here it is)

SELECT * FROM leaderboard WHERE comp_id = $comp_id ORDER by points DESC, 
acc_margin ASC
*******************************

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