you've got multiple errors. also use an auto increment primary key id to refer to specify rows unless you're searching for something. so "WHERE Name='$playername'" would be "WHERE Id = '$id'".
$sql="UPDATE player_stats SET Name='$Name', Number='$Number', Avg='$Avg', G='$G', AB='$AB', R='$R', BB='$BB', H='$H', 2B='$twoB', 3B='$threeB', HR='$HR', RBI='$RBI', SB='$SB' WHERE Name='$playername'";
$result = mysql_query($sql);