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Looking at some basic number crunching: One of the two effects of the Elemental Adept feat (PHB, p. 166) is that treats 1s as 2s when rolling damage, for a chosen element.
What is the average damage increase from Elemental Adept for a few signature spells/elements?
Alternatively, the perfect answer can provide a formula for calculating this damage increase, based on the number of dice rolled and the size of the dice.
Ok, the easiest thing to do is to figure out the per die increase in damage. This is easy to calculate.
d4 increase of .25 per die (1/4)
(2+2+3+4)/4 = 2.75
d6 increase of .16 per die (1/6)
(2+2+3+4+5+6)/6 = 3.66
d8 increase of .125 per die (1/8)
(2+2+3+4+5+6+7+8)/8 = 4.625
d10 increase of .1 per die (1/10)
(2+2+3+4+5+6+7+8+9+10)/10 = 5.6
d12 increase of .083 per die (1/12)
(2+2+3+4+5+6+7+8+9+10+11+12)/12 = 6.58
To get the average per spell, multiply the increase by the number of dice rolled. So if you're using say, Fireball, and have elemental adept - fire, the average increase is .16*8 or 1.33 DPR (and really it's less because you have to factor accuracy in, probably about .75 times that depending on your DC and the target's Dex save).
Its worth noting that this only changes the average, and not the median or maximum. It simply skews the curve a bit towards the high side rather than having a symmetric distribution.
