The key thing to understand is that map returns a list.

If you do not need a list returned, (which is the case in your example),use for.

Update:Style suggestion:
Your second loop is better written as

while (my ($k,$v) = each %byFile ) {
        print "$k\t=>$v\n";
}
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This is more idiomatic, uses less memory, and is faster than your loop.