A max(anything) will only return one value (unless combined with GROUP BY or the like).

So you can just

$sth_max_score->execute();
# no loop here:
my @max_score = $sth_max_score->fetchrow_array();
# now $max_score[0] holds your desired value
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There's a prettier solution:

$sth->execute();
$sth->bind_columns(\my $max);
$sth->fetch;
# $max holds the value here
[download]