• $s$ = odds of normal hit(for balance purposes) = 0.6
• $c$ = odds of a crit = 1/20 = 0.05
• $S$ = odds of a non-crit hit = 0.6-0.05 = 0.55
• $d$ = damage dice
• $a$ = ability score mod

Average damage of an attack. Accounting for crits

$$ x=c(2d+a)+S(d+a) $$

Per-attack damage added by Hew (costs a bonus action add): a crit with a heavy weapon will let you make an additional attack a bonus action

$$ c(x) $$

Turn this into a range. Assumes a (reasonable) attack roll ability score = [3,5] and uses heavy+melee weapon damage dice range = [5.5, 7]

$$ (0.05)(0.05(2(5.5)+3)+0.55(5.5+3)) = 0.26875 \\ (0.05)(0.05(2(7)+5)+0.55(7+5)) = 0.3775 $$

Per-attack Hew damage range: $0.279 - 0.378$ damage

• Note: this costs a bonus action on 1/20 turns, which is a negligible cost

Per-attack "Heavy Weapon Mastery" damage. Only added on a hit, unaffected by crits

$$ s(a) $$

Turn this into a range. Assumes a (reasonable) attack roll ability score = [3,5]

$$ 0.6(3) = 1.8 \\ 0.6(5) = 2 $$

Per-attack "Heavy Weapon Mastery" damage range. $1.8 - 2$ damage

Combine the two ranges for total damage range.

$$ 0.279+1.8=3.079 \\ 0.378+2=2.378 $$