How to determine the average value of a debuff?

[SangoProduction]

So, assume that someone is rolling an attack, and would only hit on a 15, because reasons.
Then assume you hit them with Shaken. -2 to attack.

So, many who look at the debuff would go "That's a 10% reduced chance to hit." Because of the 20 sides he could roll on a die.
...But I've seen other people going like "He only hits on 6 numbers, and you removed 2 of them. That's a 33% reduced chance to be hit."

If we were to say they were more equal, and the attack hits on an 11+, then the debuff would still be a 20% added miss chance....which is significantly better than 10%. Almost twice as good, even!

They are both right.
However, which one is more generally useful for truly determining how effective buffs and debuffs are?

[Maat Mons]

That's a 10% reduced chance to hit.

The technically accurate thing to say would be "that's a 10 percentage point reduction," but people are often sloppy with terminology.

[SangoProduction]

The technically accurate thing to say would be "that's a 10 percentage point reduction," but people are often sloppy with terminology.


https://www.youtube.com/watch?v=hou0lU8WMgo

[grarrrg]

However, which one is more generally useful for truly determining how effective buffs and debuffs are?

Key word is "generally".
"Generally" the only reliable number in a "-2 to hit" is the "-2" part. So percentage-wise you err towards the -10%, because that's the only number that means anything in a vacuum.

[Kayblis]

The thing is, most of the time you'll be fighting in an environment in which you need 6~12 to hit, because of averages and the fact that attack bonuses scale faster than AC bonuses. When comparing debuffs, usually the amount of the penalty(-2 for Shaken, -3/-3 indirect for Exhausted, etc) is enough to determine the worth of it. One thing is certain though, any debuff after the first has its value raised by a lot, because the gains are cumulative. It's really hard to lose when you've pushed a -7 to-hit onto your enemy, and the action cost of debuffing hard usually is more effective than the lower cost of one debuff, assuming you can apply many debuffs consistently.

Do keep in mind that, in a numbers game, buffing and debuffing are two sides of the same coin. Buffing has the advantages of not failing on a save and not depending on the immunities of your enemies. You can't Exhaust an elemental, but Haste still works just fine.

[Madsamurai]

So, many who look at the debuff would go "That's a 10% reduced chance to hit." Because of the 20 sides he could roll on a die.

Correct.


...But I've seen other people going like "He only hits on 6 numbers, and you removed 2 of them. That's a 33% reduced chance to be hit."

Not quite correct.

A -2 penalty reduces your chance to hit by 10% but it reduces the number of hits you will score by ~33%. Which of these is more important to you depends on what you are measuring. The first option allows you to compare debuffs without knowing anything about the target. I.E. -2 is less powerful then -3. The second option can be rephrased as "It will reduce the enemy's damage output by 33%." I think that is more useful for projecting the outcome of specific fights.

[Maat Mons]

Correct. ... Not quite correct.

You've got it backwards. The first example is a percentage point difference (https://en.wikipedia.org/wiki/Percentage_point). The second example is a percentage difference (https://en.wikipedia.org/wiki/Percentage#Percentage_increase_and_decrease).

[Unavenger]

There's a 10% chance that the target rolls a result which would have been a hit, but is not. So if they deal 2d6+3 points of damage on a successful hit, then you've reduced their average damage by 1 dpr - though if you have 4 hit points, that may not be a helpful way of looking at it. You could also ask yourself how much it increases your longevity by, in which case you probably want to be looking at the relative risk decrease, rather than the absolute risk increase - it reduces the chance that you'll be knocked flat by a third, so you're going to last one and a half times as long (the inverse of the remaining two thirds) on average - where it would previously take them three and a third rounds, it will now take them five on average, which means that it's worth hitting them with shaken using your action, assuming they have no chance to save.

-tl;dr It depends what you're using the probability for.

[Troacctid]

Well of course what you really want to do is calculate the enemy's expected damage per round weighted against the probability of hitting your AC and then compare the figures to determine the total amount of damage saved over N rounds.

For example, if I, a 1st level cleric with 18 AC, cast cause fear (DC 14) against a bugbear (http://www.d20srd.org/srd/monsters/bugbear.htm), its expected damage in the following round goes from 2.6 down to 0.78, a 70% reduction, but an absolute savings of less than 2 points. Pulling the same trick against an ogre (http://www.d20srd.org/srd/monsters/ogre.htm) reduces its expected damage next round from 8.8 down to 2.88, again about a 70% reduction, this time an absolute savings of about 6 points. If our cause fear lasts 3 rounds on a failed save, we end up saving an additional estimated 3.12 damage against the bugbear, and an additional 10.56 damage against the ogre.

[ericgrau]

So, assume that someone is rolling an attack, and would only hit on a 15, because reasons.
Then assume you hit them with Shaken. -2 to attack.

So, many who look at the debuff would go "That's a 10% reduced chance to hit." Because of the 20 sides he could roll on a die.
...But I've seen other people going like "He only hits on 6 numbers, and you removed 2 of them. That's a 33% reduced chance to be hit."

If we were to say they were more equal, and the attack hits on an 11+, then the debuff would still be a 20% added miss chance....which is significantly better than 10%. Almost twice as good, even!

They are both right.
However, which one is more generally useful for truly determining how effective buffs and debuffs are?
The actual damage is reduced by 33% or 20% so that one. However...

For the guy who only hits on a 15, is that his best form of attack? Can he switch? Also remember you're only reducing the damage of 1 creature, not all of them, and that his CR is usually less than the PC's level. And also compare to dead enemies that deal -100% damage, and that a damaging effect stacks with an ally's damage, while a debuff usually does not stack with an ally's effort. And often it only takes 2-3 rounds to outright kill a foe, 1 round with help from all(y/ies).

So reducing his damage by even 33% in a round is pretty meh. Tagging multiple enemies with shaken OTOH is pretty good.

This is why one of my favorite core cleric spells is prayer. +1 to all ally rolls, +1 to ally damage, -1 to same on all enemies. Often you're getting around 8 10ish%s (d20 rolls) and 8 5ish%s (damage) in a single round. Once your allies kill the foes the -1s are redundant with the +1s that helped the killing, so it's not actually as good as taking out 120% of a foe. But it is pretty close to the value of dropping a baddy with a single action. At low level I like bless too. Even though it's not even half as good, low level core or limited book clerics don't have a lot of great options. Plenty of ok options like bless or swinging a mace, sure.

[Selion]

In Pathfinder there is a table of average monster stats by CR. I don't know if there is something similar in d&d3. 5, but you just have to use the average value of AC corresponding to your level and calculate the damage reduction on it

[Madsamurai]

You've got it backwards. The first example is a percentage point difference. The second example is a percentage difference.

I mean, you are right that one is a "percentage point" difference and the other is a "percentage difference" but I was not talking about the math terms, but what they mean with regard to the OP's question.

[grarrrg]

In Pathfinder there is a table of average monster stats by CR. I don't know if there is something similar in d&d3. 5, but you just have to use the average value of AC corresponding to your level and calculate the damage reduction on it

Yes, but no.
You also have to figure out how likely you are to want to debuff a given monster.

That goblin that only hits you on an 18 or better? A -2 drops his actually by 67%! ... but it's a goblin. You aren't going to waste it here.

The massive scary dragon that can hit you on 3 or better? Barely above the default gain of 10%... But you're much more likely to want the debuff anyway.

[upho]

The absolute numbers won't tell you much of an ability's practical usefulness, other than in a strict comparison to another ability decreasing the same enemy value in a comparable manner (ie -3 to hit is better than -2 to hit if all other things are equal, which they rarely are). IOW, it doesn't matter much whether you talk about a 10% percentage point or a ~33 percentage difference without more detailed info about for example the "average" (=mean) and "typical" (=mode) values of the enemies you expect to fight in your game.

And speaking of the "in a comparable manner", do keep in mind that in practice only the total net results relative the investment and action costs matter. Meaning say an ability triggered by every melee attack (not hit) you make which gives the typical targeted opponent a 30% chance to save against a -2 to hit debuff is normally much better than an ability which grants a -4 debuff but also requires you to hit with a special standard action melee attack (even if you hit with a 95% probability).

Also keep in mind that - especially in a more challenging game requiring the players/PCs to fight as a team and plan their tactics - reliability in itself often has great actual value, and that most probability comparisons you find (such as DPR) don't take this value into account. In other words, an ability which gives you say a 10% chance per round of taking an average enemy out of combat is typically far less useful than say an ability which gives you a 90% chance of reducing the same enemy's most important combat statistics by 10% per round. This is btw one of the two major reasons why for example weapons with high crit multipliers are typically a lot less useful than the related DPR numbers imply during nearly all levels for a vast majority of builds (the other being that overkill damage numbers are wasted), and why things like the related abundant ammunition (https://www.d20pfsrd.com/magic/all-spells/a/abundant-ammunition/) + named bullet (http://www.d20pfsrd.com/magic/all-spells/n/named-bullet/) combo or the boar's charge (https://www.d20pfsrd.com/classes/core-classes/barbarian/rage-powers/paizo-rage-powers/boar-s-charge) rage power are typically even more powerful in a real game than they may initially appear.

Tip: For PF, I suggest you compare your numbers to this spreadsheet (https://docs.google.com/spreadsheets/d/1E2-s8weiulPoBQjdI05LBzOUToyoZIdSsLKxHAvf8F8/edit?usp=sharing), which includes most of the actual average values of more than 3080 opponents published by Paizo (and a few third party publications like Tome of Horrors). You can also use this this simpler version (https://docs.google.com/spreadsheets/d/1BQS6uZh7_bpp3RSwOVfuYd_Eg-4iXlHXTXeWVKksihY/edit?usp=sharing) with target numbers mostly based on the monster creation target numbers (explained in this article (https://rpgwillikers.wordpress.com/2015/09/29/bench-pressing-character-creation-by-the-numbers/)), although this of course is of greater use only if you mostly fight monsters rather than NPCs.

(I think it would be a valuable lesson for players, DMs and especially developers/homebrewers to take a careful look at for example average CMD numbers and saves in both these spreadsheets, as they'll tell you quite a lot about for example how viable for example the common ability DC of "10 + half level + secondary/tertiary stat score mod" is, especially for an ability which also requires you to succeed on other die rolls before the save even comes into question. So yeah, this confirms for example that Fort is on average indeed quite a bit higher than other saves, and that Stunning Fist does indeed suck, albeit less than basically all other comparable abilities since its DC actually can be improved beyond the generic +2 granted by Ability Focus or ability score increases. And on the other hand, a few unfortunately very rare abilities, like a barb's Str-based Savage Dirty Trick (https://www.d20pfsrd.com/classes/core-classes/barbarian/rage-powers/paizo-rage-powers/savage-dirty-trick-ex) DC, can actually be kept very competitive throughout all levels with just some moderate optimization.)


The thing is, most of the time you'll be fighting in an environment in which you need 6~12 to hit, because of averages and the fact that attack bonuses scale faster than AC bonuses. When comparing debuffs, usually the amount of the penalty(-2 for Shaken, -3/-3 indirect for Exhausted, etc) is enough to determine the worth of it. One thing is certain though, any debuff after the first has its value raised by a lot, because the gains are cumulative. It's really hard to lose when you've pushed a -7 to-hit onto your enemy, and the action cost of debuffing hard usually is more effective than the lower cost of one debuff, assuming you can apply many debuffs consistently.This. (With a few notable exceptions, such as the Cornugon Smash (https://www.d20pfsrd.com/feats/combat-feats/cornugon-smash-combat/) and Soulless Gaze (https://www.d20pfsrd.com/feats/damnation-feats/soulless-gaze-damnation/) combo which instead relies on quickly piling on debuffs of other combat parameters for less relative investment and action cost, and does so effectively enough to easily break at least low-op games...)


Do keep in mind that, in a numbers game, buffing and debuffing are two sides of the same coin. Buffing has the advantages of not failing on a save and not depending on the immunities of your enemies. You can't Exhaust an elemental, but Haste still works just fine.And this. Although this is of course highly dependent on many other factors. For example, most martial builds will find it far more beneficial to invest in debuff simply because they don't have access to any buff abilities resulting in equally beneficial value changes in relation to the action and investment costs.

[Selion]

Yes, but no.
You also have to figure out how likely you are to want to debuff a given monster.

That goblin that only hits you on an 18 or better? A -2 drops his actually by 67%! ... but it's a goblin. You aren't going to waste it here.

The massive scary dragon that can hit you on 3 or better? Barely above the default gain of 10%... But you're much more likely to want the debuff anyway.

Yes, but the average enemy you encounter is about your level, without a further knowledge the most likely guess is estimating monsters in a 1-2 level range of CR from yours.

[grarrrg]

Yes, but the average enemy you encounter is about your level, without a further knowledge the most likely guess is estimating monsters in a 1-2 level range of CR from yours.

The examples may be extreme, but the point is the same.
You aren't going to use it on something with low damage output. So taking an average of monsters isn't representative.