All of the die rolls are somewhat on the high side, and not at all what actually rolling three six-sided dice would produce.

I don't really see how they come out high on average - all that happens is that they come out fairly evenly spread over the entire range, whereas you get more of a bell-curve of probability with 3x6-sided...

In terms of "fine tuning", you should really turn some of that into loops. You're doing pretty much the same thing over and over again:

foreach (qw/Strength Intelligence Wisdom Dexterity
             Constitution Charisma/) {
  printf "%-15s", $_;
  for (1 .. 6) {
    printf "%2d\t", int(rand(6)) + int(rand(6)) + int(rand(6)) + 3;
  }
  print "\n";
}
[download]

Or:

printf "%s\t%s\n", $_,
  join "\t", 
   map { int(rand(6)) + int(rand(6)) + int(rand(6)) + 3 } (1 .. 6)
    for (qw/Str Int Wis Dex Con Chr/);
[download]

Tony