No, statistics is a perfect measurement of chance. Its just that chance includes variance around a prediction.
so in you mind if I play a fighter with +8 to hit and 1d8+9 damage, and you play a fighter with +8 to hit and 1d8+9 damage after 1 fight we will be equaly effective...
or can that variance you mentioned matter?
what if I play a fighter that has +8 to hit and 1d8+9 damage and roll, 18, 17, 16, 16, 19, 20, 15, 17, 20, 14, 18, 12
and you play a fighter that has +9 to hit and 2d6(brutal 1)+12 damage, but roll 1, 7, 5, 4, 9, 14, 12, 17, 11, 1, 9, 13, 7
if you need a 12 to hit, and I need a 13 to hit you would hit 4 times with no crits, and I hit 9 times pluse 2 crits...
so if I roll my 9 damage rolls ad get 10,10, 14, 15, 17, 16, 11, 10, 13 then my two cirts I do 17 and 17
Your 4 hits are for 20, 19, 23, and 24...
over the cource of the fighte I did mutch more damage, but you have tghe higher DPR...notice the impact you made on the game is not equal tot he statistics...
edit: DPR only works in theory, in real games with all the modfires and tactics, and dice varraints there is far more going on then those statistics show...so again WotC does not subscribe to the same theory of character design the Char op board does...it does not make them bad builds...