Is it possible to be in love with a website? I think I'm in love with this website -> http://rumkin.com/reference/dnd/diestats.php
Try things like:
A) Testing the new DnD advantage/disadvantage system where you roll 2 d20 and keep the higher if you have advantage, or roll 2d20 and keep the lower if you have disadvantage.
* Advantage = type "2d20D1" (Average = 13.82)
* Neither = type "d20" (Average = 10.5)
* Disadvantage = type "2d20P1" (Average = 7.17)
B) Or test the RATM (roll and take middle) system where you roll 3 d20 and keep the middle value.
* RATM = type "3d20D1P1" (Average = 10.5 again, but with a much tighter standard deviation)