By adding " 'max_count' => 10 " at heap creation time, you can limit the number of elements tracked in the heap. As new elements are added, inferior elements past the top ten will be dropped. That will reduce the amount of time needed to add elements and improve the efficiency of the heap solution. Of course then you don't have a heap full of values, but instead only the top ten, which may limit the datastructure's usefulness later in the script if the heap is needed again.

Good move - that modification convinces me. Although in that case, the underlying algorithm we now have seems too simple to bother with the overheads of a heap module (update: because a hash is a special sort of heap!). The following algorithm uses the bare bones to deliver the top-n into %SortaHeapy, without using any sorting (code updated):

$NumOfPortsToGet = 10;
local $loaded = 0;
my %SortaHeapy = ();
for my $key ( keys %Stats ) {
    ($key eq "UnauthOrigin") or SortaHeapy( $key );
}

sub SortaHeapy{
    my $key = shift;
    # if mini-heap not full just load it in
    if ( $loaded < $NumOfPortsToGet ) {
        $SortAHeapy{ $key } = $Stats{ $key };
        $loaded++
        return;
    }

    # otherwise do the degenerate heap sort/replace
    for my $hkey ( keys %SortaHeapy ) {
        if ( $SortaHeapy{ $hkey } < $Stats{ $key } ) {
            delete $SortaHeapy{ $hkey }; # replace
            SortaHeapy{ $hkey }; # but iterate the victim
            return
        }
    }
}
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