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| #1Et_tuAug 26, 2014 18:32:35 | Excel sheet with data and comments:
Earlier in the week I made another thread about this and after reciving some constructive criticism I have re-done these calculations, factoring in hit chance and advantage. I have determined that the difference between the two is minimal with a difference in damage only hovering around 2, even though in certain situations the greataxe can do 11 more damage on average that the 2d6 weapons and I will argue why that situation will never happen.
First I calculated the averages of the sets of die rolled for normal attacks and all forms of brutal critical up to x4 brutal critical (level 17 barbarian half-orc). I then calulated the ratio of crits normal attacks for hit chances ranging from 100% to 5%. The equation used here was "(n-1)/n for normal attacks" and "1/n for crits", where "n= number of results on a d20 that result in a hit." The ratio for crit with advantage were calculated via 2dnD1 (2dn drop lowest) where n is the same as above and the ratio for a normal hit is "1-crit ratio".
From here the average damage for a given hit chance is "(Avg damage for normal hit)*(Ratio for normal hit at given hit chance)+(Avg Damage on crit)*(Ratio for crit hit at given hit chance)"
I then highlighted the sections where a certrain die combination did more damage. The tables furthest on the right are the difference in damage between 2d6 and 1d12 where a positive number is when the 2d6 weapon has the upper-hand and the magnitude of that upper-hand and a negative number is where the 1d12 weapon has the upper-hand and the magnitude of that upper-hand.
As you can see the 1d12 does significantly more at low hit chance and high brutal critical, but that advantage drops quickly. It is due to the speed at which this damage difference drops that I argue that the difference between the 1d12 and 2d6 is very small. On the "Character Analysis" tab in the bottom left of the spreadsheet you will see how I determined this.
I made a character assuming a starting str of 16 and that the player would max his str first using the +2 at levels 4 and 8. I then compared his hit chance through the levels against AC 13 and AC 22. The reason for these selections was that the AC 13 is the average AC from every monster released in the DM Basic Rules v0.1 and the AC 22 is the highest AC I have seen (red dragon) short of the Tarrasque (AC 25) which I will assume is an oddity not a norm. A higher AC favors the greataxe. I then put the damage differences for both the half orc barbarian and other barbarian at different levels and you will notice the largest difference is -1.91. Even if this character had left his str at 16 the difference would only be -2.55. From this I claim that unless you intentionally make a barbarian with low str the 1d12 and 1d6 weapons are comparable.
Whew. That's done. I am glad I can still play a barbarian with a maui and not fall far behind because of it. |