As both a player who has a Hexblade char, and as a DM that likes to sprinkle in NPC's that are based on player stats (yes, I know the pitfalls in that), I like to optimize damage.
To that end, I am trying to see what does more Expected Value damage (don't want to fool with any potential maximums) for a 12th level pure Hexblade.
Now, Hexblades are all about tradeoffs, like what Conc spell to use, or what Bonus Action to use on a turn. To that end, I have come up with 3 situations.
a. Hexblade has Shadow of Moil up, and firing at a distance with EB. Assume that Agonizing Blast, Hexblade's Curse are also both functional. Assume the target does not have any way to get past the Heavy Obscurement due to SofM, and the 3 EB attacks are at Advantage, at a +9 to hit, with an expected value of 5.5+5+4 = 14.5 per successful strike.
b. As above, but instead of EB, the Hexblade is going to engage in melee, at a +10 to hit, and Lifedrinker functional, so d8 + 15 = 19.5 per successful strike. However, there is the potential for a 6d8 Eldritch Smite to be used with a Crit. And S of M does D8 damage to any successful attacks against me. For the sake of argument, assume keeping up Conc is not an issue.
c. A range attack again, but instead of S of M up, it would be Hex, so an additional 3.5 damage per successful hit with EB = 18 HP, but not at Advantage.
I am thinking this is one messy speadsheet, that naturally has to take into account the AC of the target. Assume an AC of 21, and a fight lasting 4 turns, with the Conc spell up 1st round, and Hexblade's Curse up 2nd round.
Now, it is simple enough math for scenario a and b to assume Advantage gives me a +5 to hit, and calculate chance of hit * expected damage = "a number". But that does not take into account the chance of Crit'ing on a 19 or 20. (obviously 10% without Advantage, I think 19.1% with Advantage)
Given that you don’t have to confirm crits in 5E, it’s not very complex unless you want to include ACs you can only miss with a 1 or hit with a crit (those values aren’t really interesting, so just ignore them). You want to multiply the chance of success with the average result of a success, do the same for a critical success, and add the results. Advantage just doubles your chance of success. To hit AC 16 with a +14 to hit, 1 in 20 rolls fails, 18 in 20 succeed normally, 1 in 20 crits. To hit AC 10 with a +5 to hit, 4 in 20 fail, 15 in 20 succeed normally, 1 in 20 crits. To hit AC 23 with a +7 to hit, 15 in 20 fail, 4 in 20 succeed normally, 1 in 20 crits. Generally, (20 - AC + attack bonus) in 20 succeed normally and 1 in 20 crits. This only breaks down if the difference between AC and attack bonus is 1 or lower (because a 1 autofails) or the AC is too high to hit on anything but a crit (you get a negative number). Make it easy on yourself and disregard the extremes.
So: 1) if you crit on a 20, your expected total damage result is ((20 - AC + attack bonus)/20) x (average normal damage) + (average crit damage/20). If you have Advantage, multiply by 2. 2) if you crit on 19-20, your expected total damage result is ((19 - AC + attack bonus)/20) x (average normal damage) + (average crit damage/10). Again, multiply by 2 if you have Advantage.
Do this for every separate attack roll in a given situation, add everything up, and you can compare.
Well, I hope I didn’t make any mistakes anyway. I’m sure I’ll get corrected if I did. :p
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As both a player who has a Hexblade char, and as a DM that likes to sprinkle in NPC's that are based on player stats (yes, I know the pitfalls in that), I like to optimize damage.
To that end, I am trying to see what does more Expected Value damage (don't want to fool with any potential maximums) for a 12th level pure Hexblade.
Now, Hexblades are all about tradeoffs, like what Conc spell to use, or what Bonus Action to use on a turn. To that end, I have come up with 3 situations.
a. Hexblade has Shadow of Moil up, and firing at a distance with EB. Assume that Agonizing Blast, Hexblade's Curse are also both functional. Assume the target does not have any way to get past the Heavy Obscurement due to SofM, and the 3 EB attacks are at Advantage, at a +9 to hit, with an expected value of 5.5+5+4 = 14.5 per successful strike.
b. As above, but instead of EB, the Hexblade is going to engage in melee, at a +10 to hit, and Lifedrinker functional, so d8 + 15 = 19.5 per successful strike. However, there is the potential for a 6d8 Eldritch Smite to be used with a Crit. And S of M does D8 damage to any successful attacks against me. For the sake of argument, assume keeping up Conc is not an issue.
c. A range attack again, but instead of S of M up, it would be Hex, so an additional 3.5 damage per successful hit with EB = 18 HP, but not at Advantage.
I am thinking this is one messy speadsheet, that naturally has to take into account the AC of the target. Assume an AC of 21, and a fight lasting 4 turns, with the Conc spell up 1st round, and Hexblade's Curse up 2nd round.
Now, it is simple enough math for scenario a and b to assume Advantage gives me a +5 to hit, and calculate chance of hit * expected damage = "a number". But that does not take into account the chance of Crit'ing on a 19 or 20. (obviously 10% without Advantage, I think 19.1% with Advantage)
How should I create such a speadsheet?
Given that you don’t have to confirm crits in 5E, it’s not very complex unless you want to include ACs you can only miss with a 1 or hit with a crit (those values aren’t really interesting, so just ignore them). You want to multiply the chance of success with the average result of a success, do the same for a critical success, and add the results. Advantage just doubles your chance of success.
To hit AC 16 with a +14 to hit, 1 in 20 rolls fails, 18 in 20 succeed normally, 1 in 20 crits. To hit AC 10 with a +5 to hit, 4 in 20 fail, 15 in 20 succeed normally, 1 in 20 crits. To hit AC 23 with a +7 to hit, 15 in 20 fail, 4 in 20 succeed normally, 1 in 20 crits. Generally, (20 - AC + attack bonus) in 20 succeed normally and 1 in 20 crits. This only breaks down if the difference between AC and attack bonus is 1 or lower (because a 1 autofails) or the AC is too high to hit on anything but a crit (you get a negative number). Make it easy on yourself and disregard the extremes.
So:
1) if you crit on a 20, your expected total damage result is ((20 - AC + attack bonus)/20) x (average normal damage) + (average crit damage/20). If you have Advantage, multiply by 2.
2) if you crit on 19-20, your expected total damage result is ((19 - AC + attack bonus)/20) x (average normal damage) + (average crit damage/10). Again, multiply by 2 if you have Advantage.
Do this for every separate attack roll in a given situation, add everything up, and you can compare.
Well, I hope I didn’t make any mistakes anyway. I’m sure I’ll get corrected if I did. :p
Want to start playing but don't have anyone to play with? You can try these options: [link].