The Variable Advantage of Advantage

[Cuddlebot5000]

Roll Required - The minimum number that needs to show up on your d20 in order for you to hit/save/etc. For example, this number would equal the target's AC minus your to-hit bonus when considering attack rolls. Please note that this chart does not take into account the automatic failure of a 1 for attack rolls.
Chance to Hit - The likelihood that a number will be rolled that grants you success.
Chance to Hit (Advantage) - The likelihood that you will succeed when rolling with advantage.
Chance to Hit (Disadvantage) - The likelihood that you will succeed when rolling with disadvantage.
Swing - The change in the likelihood of success. For instance if you need a roll of 11 or higher to hit then you are 50% more likely to succeed when rolling with advantage and you lose 50% of your success likelihood when rolling with disadvantage.
Gain/Loss- The flat percentage that you will gain/lose when rolling with Advantage/Disadvantage, respectively. To continue the example of needing an 11 or higher to hit - a Gain/Loss of 25% means that your 50% likelihood of success changes to a 25% with disadvantage and to a 75% with advantage.
Equivalence - The average value that Advantage/Disadvantage has in terms of +/- To-Hit.



Roll Required
Chance to Hit
CtH (Advantage)
CtH (Disadvantage)
Swing
Gain/Loss
Equivalence


1
100%
100%
100%
0%
0.00%
n/a


2
95%
99.75%
90.25%
5%
4.75%
0.95


3
90%
99.00%
81.00%
10%
9.00%
1.80


4
85%
97.75%
72.25%
15%
12.75%
2.55


5
80%
96.00%
64.00%
20%
16.00%
3.20


6
75%
93.75%
56.25%
25%
18.75%
3.75


7
70%
91.00%
49.00%
30%
21.00%
4.20


8
65%
87.75%
42.25%
35%
22.75%
4.55


9
60%
84.00%
36.00%
40%
24.00%
4.80


10
55%
79.75%
30.25%
45%
24.75%
4.95


11
50%
75.00%
25.00%
50%
25.00%
5.00


12
45%
69.75%
20.25%
55%
24.75%
4.95


13
40%
64.00%
16.00%
60%
24.00%
4.80


14
35%
57.75%
12.25%
65%
22.75%
4.55


15
30%
51.00%
9.00%
70%
21.00%
4.20


16
25%
43.75%
6.25%
75%
18.75%
3.75


17
20%
36.00%
4.00%
80%
16.00%
3.20


18
15%
27.75%
2.25%
85%
12.75%
2.55


19
10%
19.00%
1.00%
90%
9.00%
1.80


20
5%
9.75%
0.25%
95%
4.75%
0.95

[Desamir]

Thanks for charting this.

Some obvious conclusions:


Flat % gain/loss should be ignored. All it tells you is the equivalent one-die hit number.
Swing % is the important number, functioning as a flat multiplier to your success.
Advantage gains value linearly as your hit chance decreases.
60% swing means your DPR increases by 60% with advantage.

[Douche]

1 wouldn't be 100% hit chance.. What if you have a negative modifier?

[Oramac]

Good info! Thanks!!

Looks like the TL;DR would be, the higher the AC you need to hit, the more advantageous Advantage becomes (and vice versa).

[Flashy]

1 wouldn't be 100% hit chance.. What if you have a negative modifier?

Then you would require some other number to hit, rather than a 1.

[Douche]

Then you would require some other number to hit, rather than a 1.

Oh... Right. I was trying to be smarmy but now I look dumb, hahaha. If you have a -2 modifier then you'd need a 3, lol. You got me, dawg :smallbiggrin:

[JohnDoe]

A roll of 1 is an automatic failure. A 20 is an automatic hit.

Modifiers definitely change things up, especially when considering classes and creatures.

Proficiency also has to be taken into account.

[Tanarii]

The 1 to 20 on the chart are target numbers AFTER all modifiers are included. In other words, if it's AC 18, and you have +11 to hit including all modifiers, the line you use is the line for '7'.

[Desamir]

A roll of 1 is an automatic failure. A 20 is an automatic hit.

Modifiers definitely change things up, especially when considering classes and creatures.

Proficiency also has to be taken into account.

This is explained in OP's first paragraph:


Roll Required - The minimum number that needs to show up on your d20 in order for you to hit/save/etc. For example, this number would equal the target's AC minus your to-hit bonus when considering attack rolls. Please note that this chart does not take into account the automatic failure of a 1 for attack rolls.

[Cuddlebot5000]

Thanks for charting this.

Some obvious conclusions:


Flat % gain/loss should be ignored. All it tells you is the equivalent one-die hit number.
Swing % is the important number, functioning as a flat multiplier to your success.
Advantage gains value linearly as your hit chance decreases.
60% swing means your DPR increases by 60% with advantage.


Thanks for the analysis! I included the Gain/Loss column to show that just because the percentage changes the most at an 11 needed to hit you're not getting as much value out of that higher percentage as you would be at higher numbers needed. Also, I find it cool (NERD) that the Gain/Loss is the same for a 2 as it is for 20, yet the difference in the benefit they provide you could not be greater.

[endur]

Thanks for charting this.

Some obvious conclusions:


Flat % gain/loss should be ignored. All it tells you is the equivalent one-die hit number.
Swing % is the important number, functioning as a flat multiplier to your success.
Advantage gains value linearly as your hit chance decreases.
60% swing means your DPR increases by 60% with advantage.


Actually, Flat % is more important than swing. If you have an option of advantage or a +X, then you will want to compare flat % to the +X.

Swing tells you the result of advantage, but it doesn't help you compare advantage to something else (as the something else will also likely increase the swing).

[gullveig]

Looks like the TL;DR would be, the higher the AC you need to hit, the more advantageous Advantage becomes (and vice versa).

I think not. You gain the most of Advantage when you need a roll of 10.

Also, considering a +1 bonus to a roll equals to a +5% extra chance in the roll then the Advantage system gives you a bonus roughly between +1 to +5.

The chart proved me that it is a good mechanic. It gives you a big advantage when you are at 50/50% chance of success/failure bot not so much when you already have a big chance of success or failure.

[Tanarii]

I think not. You gain the most of Advantage when you need a roll of 10.That depends what you are looking at.

If you want to know your biggest DPR increase as a value, it's (I believe) at a 10. That's the Gain/Loss column.

If you want to know the biggest percentage (ie relative) increase in DPR, it's at a 20 to hit. That's the Swing column.

Which is more important? Depends what you want to know.

[Cuddlebot5000]

That depends what you are looking at.

If you want to know your biggest DPR increase as a value, it's (I believe) at a 10. That's the Gain/Loss column.

If you want to know the biggest percentage (ie relative) increase in DPR, it's at a 20 to hit. That's the Swing column.

Which is more important? Depends what you want to know.

This exactly. I have also updated the chart with another column called equivalence that gives you the average value of the advantage/disadvantage in plus/minus to-hit terms.

[Desamir]

Actually, Flat % is more important than swing. If you have an option of advantage or a +X, then you will want to compare flat % to the +X.

Swing tells you the result of advantage, but it doesn't help you compare advantage to something else (as the something else will also likely increase the swing).

Interesting point. Do you have an example of a situation where you need to choose between advantage and +X?


I think not. You gain the most of Advantage when you need a roll of 10.

Also, considering a +1 bonus to a roll equals to a +5% extra chance in the roll then the Advantage system gives you a bonus roughly between +1 to +5.

The chart proved me that it is a good mechanic. It gives you a big advantage when you are at 50/50% chance of success/failure bot not so much when you already have a big chance of success or failure.

This is incorrect. You gain the most of advantage when you need a roll of 20, when it increases your chance of success by 100%. If you have a DPR of x and hit on a 11, your DPR with advantage is 1.5x. If you have a DPR of y and hit on a 20, your DPR with advantage is 2y.

The part that's being misconstrued here is the value of +attack. A +1 when you can only hit on a 20 is much more valuable than a +1 when you hit on an 11. Even though advantage gives the equivalent of +5 when you hit on an 11, it actually provides less of a DPR increase than a +1 when you hit on a 20. Think about it--in the former case, you increase your hit chance by 50%; in the latter case, you double it.

EDIT: OP, it looks like you swapped the Gain/Loss and Swing columns on me! :eek:

EDIT2: OP fixed it, all good.

[Tanarii]

Your biggest DPR increase as a value and as a percentage will be at a 20 to hit. In both cases, you want to know your Swing.But the value of gained DPR is highest at 10, not at 20. Because that's calculated by GAIN * (ATTACK AVG DMG), and thus greatest at 10. Whereas percent DPR increase is calculated by (SWING + 1), which is greatest at 20.

Edit: swapped GAIN & SWING per the OPs edit in post below. And I see you cut out the thing I quoted. We both got thrown off by that table edit I think. ;)

[Cuddlebot5000]

EDIT: OP, it looks like you swapped the Gain/Loss and Swing columns on me! :eek:

Thanks for the catch! I copy/pasted from my excel doc and just remade the table when I added the new column. Forgot that I still needed to switch the names, my bad! I corrected it :smallsmile:

[Desamir]

But the value of gained DPR is highest at 10, not at 20. Because that's calculated by GAIN * (ATTACK AVG DMG), and thus greatest at 10. Whereas percent DPR increase is calculated by (SWING + 1), which is greatest at 20.

Edit: swapped GAIN & SWING per the OPs edit in post below. And I see you cut out the thing I quoted. We both got thrown off by that table edit I think. ;)

Yep, I wanted to make sure I had the terminology right before posting, so I removed it. Now that it's fixed:

That's an interesting way of looking at it, I'll have to think about that some more.

[djreynolds]

Put this in the guide section, very good stuff.

[ShikomeKidoMi]

Yep, I wanted to make sure I had the terminology right before posting, so I removed it. Now that it's fixed: That's an interesting way of looking at it, I'll have to think about that some more.

Look at it this way: You're arguing at which point advantage provides the largest relative damage increase and he's discussing at which point it causes the largest absolute increase.

Large relative gains to small numbers aren't as good as smaller percentage gains to much bigger numbers. If you double the number one, you still only have 2 (an increase of 1). If you add 25 percent to the number 10 you have 12.75 (an increase of 2.75).

Or to put it really simple terms, if someone asks you to pull a coin out of your pocket and they'll give you a penny if you pull out a penny or two and a half (somehow) pennies if you have a dime, the second one makes you more money, if you're lucky enough to have a dime.

[SilverCBFox]

Look at it this way: You're arguing at which point advantage provides the largest relative damage increase and he's discussing at which point it causes the largest absolute increase.

Large relative gains to small numbers aren't as good as smaller percentage gains to much bigger numbers. If you double the number one, you still only have 2 (an increase of 1). If you add 25 percent to the number 10 you have 12.75 (an increase of 2.75).

Or to put it really simple terms, if someone asks you to pull a coin out of your pocket and they'll give you a penny if you pull out a penny or two and a half (somehow) pennies if you have a dime, the second one makes you more money, if you're lucky enough to have a dime.

But what if you look at it from the perspective of the action economy in dnd - when you grant advantage when someone has to roll a 20 to hit you are almost giving them two attacks for one (95%) since it is not common that two 20s will be rolled at once but for a roll of 11 or more needed you are only effectively giving them another attack every other attack (50%)

[Walnut]

If I need a 20 to hit a creature, then advantage will nearly double your damage output and the creature will live half as long and have that many fewer attacks to use against you. While if I need an 11 my damage will only increase by 50%, only cutting monster life by a third.

Of course that doesn't take into the entire party. Against low AC opponents, damage from attack roll sources likely constitute a larger percentage of the party damage, so advantage will give a small multiplier to a large percentage of the damage. Against a high AC target more of the damage comes from save based sources or auto damage like magic missile, so advantage with give a large multiplier to a smaller percentage of the party damage.

To further complicate things at a target roll of 18, bless is as good as advantage.

TL/DR: it will depend on the situation and the party composition how much advantage matters.

[bid]

If I need a 20 to hit a creature, then advantage will nearly double your damage output
Yeah, we really need an extra column [= CtH(advantage) / CtH] to show that DPR increase.

[Tanarii]

But what if you look at it from the perspective of the action economy in dnd - when you grant advantage when someone has to roll a 20 to hit you are almost giving them two attacks for one (95%) since it is not common that two 20s will be rolled at once but for a roll of 11 or more needed you are only effectively giving them another attack every other attack (50%)


If I need a 20 to hit a creature, then advantage will nearly double your damage output and the creature will live half as long and have that many fewer attacks to use against you. While if I need an 11 my damage will only increase by 50%, only cutting monster life by a third.its true that you're only gain a 50% round gain with a 10 to hit, and almost double with a 20 to hit. But you started off with needing 10 times more rounds more to kill the target.

To put it another way, if you need a 20 to hit, +1 to hit is better than advantage. At a ten to hit, advantage is like getting +5 to hit.

SWING is your relative gain, but that's relative to your base DPR ... which shrinks linearly as you go up the table. GAIN is relative to your base damage independent of hit chance, which is a fixed value,

[Desamir]

Look at it this way: You're arguing at which point advantage provides the largest relative damage increase and he's discussing at which point it causes the largest absolute increase.

Large relative gains to small numbers aren't as good as smaller percentage gains to much bigger numbers. If you double the number one, you still only have 2 (an increase of 1). If you add 25 percent to the number 10 you have 12.75 (an increase of 2.75).

Or to put it really simple terms, if someone asks you to pull a coin out of your pocket and they'll give you a penny if you pull out a penny or two and a half (somehow) pennies if you have a dime, the second one makes you more money, if you're lucky enough to have a dime.

Ultimately, the only stat that matters is Time To Kill. The faster you kill a monster, the fewer actions it can take, and thus the fewer of your resources it can deplete. Even though there will be a higher marginal gain of DPR on row 11, the marginal and relative improvement in TTK will always be smaller than on rows 12+. Ergo, Advantage is better with a lower base hit chance.

I don't disagree that your marginal DPR increase is higher at 11; my point is that it doesn't mean much as a metric. Relative DPR increase, on the other hand, directly ties to TTK.


Yeah, we really need an extra column [= CtH(advantage) / CtH] to show that DPR increase.

That's essentially the Swing column.

[Desamir]

its true that you're only gain a 50% round gain with a 10 to hit, and almost double with a 20 to hit. But you started off with needing 10 times more rounds more to kill the target.

Right. So getting advantage with a 20 to hit will reduce the monster's lifespan by a much greater absolute and relative value, when compared to getting advantage at 11 to hit.

[bid]

That's essentially the Swing column.
Oh, right. That's perfect thank you.

[Tanarii]

I don't disagree that your marginal DPR increase is higher at 11; my point is that it doesn't mean much as a metric. Relative DPR increase, on the other hand, directly ties to TTK.But moving your number up or down on the chart via direct bonus or penalty also affects your TTK.

More to the point, sometimes your base TTK is so poor that advantage increasing it is meaningless. It's great that advantage is 'better' in terms of TTK when you need a 18+ to hit. But that's still a fight you probably don't want to be in. Meanwhile it might be acceptable in a 16+, even though the swing (or relative DPR gain, or TTK decrease) is less.

Edit: By which I mean this:

Right. So getting advantage with a 20 to hit will reduce the monster's lifespan by a much greater absolute and relative value, when compared to getting advantage at 11 to hit.You're still probably going to die because the base TTK was 10x longer. So the TTK gain being more relatively or absolutely is moot.

(That's actually two arguments. The second one is a new 'moving the goalposts' argument and starts where I say more to the point. Just to be clear. :smallwink: )