# D&D 5EHow much does initiative add to damage output?

#### Sword of Spirit

##### Legend
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

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

#### Nagol

##### Unimportant
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.

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#### crashtestdummy

##### First Post
...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

##### 41st lv DM
That sounds like alot of pointless work.

##### (they/them)
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

##### Legend
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

##### First Post
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

##### First Post
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...)

#### BoldItalic

##### First Post
Going first every round is 27% more fun.

##### (they/them)
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...)

Wouldn't you also need to divide it by 5 because the example uses +5 vs 0?

So, assuming the 6.5% number is correct it would be 1.3%/number of rounds.

So somewhere over 1/3% per +1.

#### crashtestdummy

##### First Post
Bid's method of calculation (which gave the +6.5% for a +5 initiative difference) is more accurate than my initial simple +5% per +1, but it still needs to be divided by the average number of rounds of combat if you want to calculate the effect on overall DPR, which is the original request.

If there is an average of 3 rounds per combat, then that +6.5% chance of going first means that the average DPR will go up by 6.5/3 = 2.17% because there will be 2 rounds where all parties have their DPR and one round where only the winner of initiative has their DPR.

#### UngeheuerLich

##### Legend
Overall it may be 6.25% if you use damaging attacks only. If it is a fireball against a horde of low level creatures it may be a lot more. A hold person against few higher level creatures is also a lot more So high initiative is especially good for casters and against them. Against othe wepon users who damage more steadily it is not too important.
(although a sharpshooter may kill one or two creatures before they even act and thus reduci g incoming damage a lot. Maybe you should value high initiative as a damage prevention tool rather than an increase damage tool.

#### FormerlyHemlock

##### Hero
d20+10 > d20: 86% of the time
d20+5 > d20: 70% of the time
d20+4 > d20: 66% of the time
d20+3 > d20: 62% of the time
d20+2 > d20: 57% of the time
d20+1 > d20: 53% of the time
d20+0 > d20: 48% of the time
d20-1 > d20: 43% of the time
d20-2 > d20: 38% of the time
d20-3 > d20: 34% of the time
d20-4 > d20: 30% of the time
d20-5 > d20: 26% of the time
d20-10 > d20: 11% of the time

Interestingly, each +1 of initiative seems to be about a +4% chance of going first, at least when bonuses are small. Diminishing returns over +5.

##### (they/them)
Bid's method of calculation (which gave the +6.5% for a +5 initiative difference) is more accurate than my initial simple +5% per +1, but it still needs to be divided by the average number of rounds of combat if you want to calculate the effect on overall DPR, which is the original request.

If there is an average of 3 rounds per combat, then that +6.5% chance of going first means that the average DPR will go up by 6.5/3 = 2.17% because there will be 2 rounds where all parties have their DPR and one round where only the winner of initiative has their DPR.

You still need to divide the 2.17% by 5 because it is for +1 not +5. And I would argue that the average amount of rounds in combat is closer to 3.5.

Even still you end up with around .4% increase per +1 which sounds about right. That is a lot lower than 5%.

#### CapnZapp

##### Legend
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.
Okay so let's assume you get to act one round more roughly every other fight if you win initiative.

Each +1 bonus to Initiative equivalent to 1/20th of a round's worth of damage output.

At around level five or so, let's say a PC does 20 damage/round on average to put a nice round number on it. (Feel free to replace "level five" with "level eight" or whatever; that's not the point)

+1 to initiative then means +1 damage (per fight, not per round).

Then we halve that (you gain the benefit one fight out of two): half a point per plus.

#### CapnZapp

##### Legend
The best I can suggest is that each +1 to initiative will result in a +5% higher damage output
Or 1/20th

#### CapnZapp

##### Legend
Unless your comparing against another player.
Of course we're comparing between players.

The entire reason for minmaxing is to select a character build that performs better than other character builds.

#### Rhenny

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.

Yes. Winning initiative will alter the ratio of damage done to damage taken. It is about survivability/quick strike rather than pure damage output.

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