D&D 5E How much does initiative add to damage output?

[Sword of Spirit]

Since most combats don't end at the formal end of a round, higher initiative means you'll not only go first in the first round, but over the course of your adventuring career you will end up with many more attacks than someone with less initiative, so you'll end up putting out more damage.

How can we mathematically conceptualize this? What do we need to know (or what assumptions should we define) to be able to determine about how often you are going to get an additional attack per each point of initiative bonus (and hence, what percentage each point of initiative bonus adds to your damage output)?

Since math isn't really my thing, I ask for the wisdom of those who like math more than I.

 

[Whirlingdervish]

over the long run it won't as initiative is a random thing you will lose initiative as often as you win it.

 

[Nagol]

over the long run it won't as initiative is a random thing you will lose initiative as often as you win it.

Comparatively higher bonuses will tend to go first more frequently. That said, it will be a subtle effect that probably is modest in value.

 

[Rhenny]

Although, depending on the foes, and the level of the PC involved, it could be substantial. 3 attacks with great weapon master, a high level fireball or a disintegrate that overcomes a save, could end a fight before it really begins. I'm not a math guy either, but I bet you could do a number of situational calculations that show how valuable a high initiative becomes.

That barbarian feature that grants advantage on initiative, or the bonus a bard gets (can't remember what it's called now and I can't get to my books) can make higher initiative rolls more reliable.

 

[crashtestdummy]

...the bonus a bard gets (can't remember what it's called now and I can't get to my books) ...

Jack of All Trades -- adds half proficiency (round down) to initiative (amongst other things).

Because that's +1 to +3 and initiative is a D20, that means it increases the chance of winning initiative by 5-15%, depending on level, assuming everything else is static. Since everything else is not static, it becomes very difficult to determine the impact.

Statistically, winning initiative will make a difference, as postulated, but calculating the amount of difference would be a nightmare because there are so many variables. The best I can suggest is that each +1 to initiative will result in a +5% higher damage output in the long run, because you're 5% more likely to get a blow/spell in on the final round of combat. However, that's over the long run and I wouldn't expect to see that in reality except of a very long period of play.

 

[ccs]

That sounds like alot of pointless work.

 

[ad_hoc]

Statistically, winning initiative will make a difference, as postulated, but calculating the amount of difference would be a nightmare because there are so many variables. The best I can suggest is that each +1 to initiative will result in a +5% higher damage output in the long run, because you're 5% more likely to get a blow/spell in on the final round of combat. However, that's over the long run and I wouldn't expect to see that in reality except of a very long period of play.

That seems too high to me.

I think initiative is overrated in general.

Probably the easiest calculation would be with an Assassin because Assassinate relies on winning initiative.

You could calculate how much damage you gain from getting advantage and how much you gain from auto-criting when you have surprise.

 

[mellored]

Winning inititive does not make you deal more damage, it males you take less. You still need to hit them the same number of times b but they will have one less round to hit you back. Unless your comparing against another player.

Inititive is a contest, and thus not a flat 5%. It's value changes depending on how far apart you are. That said, 4% is probably a good estimate.

Also, I'll estate 4 rounds per battle . So saving you 25% health if you win.

Giving a rough estimate of 1% more health per inititive. Though obviously it matters more to some classes then others.

 

[bid]

How can we mathematically conceptualize this?

Player A and creature B both roll for initiative. After a few rounds, player A will kill creature B.
- A wins initiative = A B A B A B A
- B wins initiative = B A B A B A B A

If it takes 4 attacks to kill B, going first means A will defend 3 times instead of 4. With no bonus, A will defend 3.5 times on average, at best that's 3/3.5 = 0.86... something like +14%


If you do the 20x20 grid for both initiative rolls, each will go first 190/400. With a +5 bonus, one will have 190+20+19+18+17+16/400 of going first while the other will have 190-19-18-17-16-15/400. Or 280 vs 105, or 3.27 defenses.

Equation: (105/(105+280) + 3) / 3.5 = 0.935

That's about +6.5% bonus. {close enough to mellored back-of-the-envelope calculations, nice}


That also means that a S&B Dex20 fighter will do about 106.5% of the damage of a S&B Str20/Dex10 fighter. Melee wasting a turn to reach the target has a much bigger impact, something around +25%.

I don't think it's worth considering.

 

[crashtestdummy]

That seems too high to me.

You're correct -- it's too high. As bid has indicated, you need to divide that by the average number of rounds per combat, because that percentage increase only applies to the last round of combat. That is, the person who wins initiative gets in one extra round of attack over the person who loses initiative (or the fellow adventurer whose initiative is after the person who kills the opponent).

Anyone know what the average number of rounds per combat is?

(I did say it was complicated...)