Speed boost vs Damage boost

It can be difficult to figure out what is better when you have to choose between 30% more damage or 30% faster damage, what will give the most damage output?
Let’s compare.

When using melee at an attack speed of 1,5 attacks per second and a weapon that deals 1d6 +5  damage, we will have some random damage and some set damage, but the output in 10 seconds will always be between 90 and 165 damage before adding anything else.

Let’s add 30% more damage output, this is simply 90 x 1,3 = 117 and 165 x 1,3 = 214,5
Now let’s add 30% more speed instead, this gives us 1,95 attacks per second (or 0,507 seconds per attack) so in 10 seconds you will have 19,5 x 1d6+5 damage, giving a range of 117 to 214,5.

Critical hits, these influence damage output greatly. So let’s use a 2x multiplier to calculate this. 1d6 +5 x2 = 12 to 22

Now let’s add the Damage boost of 30%, that makes critical damage 15,6 to 28,6 so with heaven’s aligned giving only crits for the next 10 seconds that gives 234 to 429 damage output.

30% Attack Speed boost (19,5 attacks x 12 to 22 damage) will be dealing 234 to 429 damage.

So again we are getting the same numbers. Offcourse the chance to crit every hit is extremely small, a weapon normally has a 5% to 20% chance to critically hit. Let’s compare damage output by giving it a 5% chance.

If a weapon only crits when you roll a 20, that gives the Attack speed boost a 97,5% chance to roll a crit in 10 seconds, for the Damage boost there is a 75% chance to roll a crit in 10 seconds. However, if you were to do 100 attacks to reflect these percentages, 97,5 x 22 max damage would give 2145 total damage from the Attack Speed boost, 75 x 28,6 would give 2145 total damage from the Damage boost. (and yes you can’t do 0,5 attacks in reality but for  calculating this works better).

So for the raw damage it’s exactly the same, BUT the action boosts don’t account for other damage modifiers like Fire burst, doublestrike or properties you get from other items that help with damage or instakills.

Additional damage types vs raw damage. Since raw damage output is the same for both boosts, the real difference can be found in the dominant power of your weapon.

Cleave does not get affected by speed but does get affected by the damage boost, so in the 20 seconds an action boost lasts, you have 8 more attacks with 30% more damage, 4 x cleave will deal a total of 31 to 57, 4 x Great cleave will deal a total of 41 to 119 for a total of 72 to 176,

where Attack Speed boost will give 4x cleave damage of 24 to 44 with Great cleave dealing 32 to 92 for a total of 56 to 136, thus on a weapon with only raw damage the difference is 16 to 40 damage.

However, if the weapon has an additional weapon property on it like Holy Burst, dealing 2d6 Holy damage and at least 3d6 to critical damage, Attack speed bonus will grant 9 additional attacks in 20 seconds, this would give 18 to 54 extra damage even without critical hit. These numbers vary heavily per weapon.

Conclusion, your playstyle and the dominant power of your weapon should decide what you pick, does your weapon have mostly raw damage? or does your weapon/equipment have several additional types of damage?