Hey everyone, I know the tighter maths and associated stats have been covered here quite a bit, but I cannot for the life of me surface the relevant threads. Is anyone able to summarise this for me or point me to a past discussion?
I'm trying to get a measure on how much a +1 influences success rates. My initial interpretation was that against a matched DC it affected three potential faces (CF->F, F->S, S->CS), ie 15% of your rolls would be positively impacted. But I realise now that (I think) it's not possible to have a situation where all three faces are relevant without a 20 and 1 being present (thus two impacted faces becoming redundant anyway).
So in what scenarios does that +1 have affect 0%, 5%, 10%, 15% of your rolls? I also know there was a theoretical 'DPR' % increase floating around, can someone break down that maths for me please?
FWIW I'm trying to get a better touchstone on it for the purpose of creating custom items/effects, and want to be careful about numerical effects.
Thanks!
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In most practical scenarios, it will affect 10% of rolls*. If it's only affecting 5% of rolls, you were looking at more than a 50% chance to crit or crit fail to begin with.
*This assumes that the crit fail or the crit success is different from a regular fail or crit. Changing your third attack's crit fail into a regular fail is only rarely relevant.
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Assuming you crit on a 19...
and you do 10 damage (just to use a round number)
40% change to miss = 0
50% * 10 damage hit = 5
10% * 20 damage crit = 2
=7 average damage.
=+1 gives..
35% change to miss = 0
50% * 10 damage hit = 5
15% * 20 damage crit = 3
=8 average damage.
=14% more damage.
The next +1 gives...
30% chance to miss = 0
50% * 10 damage hit = 5
20% * 20 damage crit = 4
= 9 average damage.
= 12.5% more damage.
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I made some graphs a while back that show this and some other things. the graphs are here, you can make your own too with the tool.
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I made some graphs a while back that show this and some other things. the graphs are here, you can make your own too with the tool.
Yoooo this is exactly the data I was looking for, thanks for your work!
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In most practical scenarios, it will affect 10% of rolls*. If it's only affecting 5% of rolls, you were looking at more than a 50% chance to crit or crit fail to begin with.
*This assumes that the crit fail or the crit success is different from a regular fail or crit. Changing your third attack's crit fail into a regular fail is only rarely relevant.
If you succeed on a natural 11, a +1 doesn't change your critical chances either. Whether you need a 10 or 11, you only critically succeed on a natural 20 and only critically fail on a natural 1. On any other number, it will change your success chance and one of the two.
So it's usually 10%, but there are some occasions when it's 5%. Slightly less than 10% overall.
Much of this depends on the crit outcomes, whether they're significant.
Do crit successes double? Do crit fails set you back or even make you drop your weapon? And so on.
Back in the playtest days, one of the devs shared a climbing example w/ a +3 bonus, which back then seemed pretty average to us PF1 veterans. Turns out that even with both sample creatures having a reasonable chance of success, the one w/ +3 would almost certainly succeed at climbing away from a pursuer (due to bursts from crit successes) while the other climber was quite likely to get caught. (So if you ever build a climb-chase, be careful when tuning that DC.)
He also shared the math on +3 attack difference. Assuming a crittable foe and nothing special like Fatal or Crit Specializations, the average damage went up by just over 50%, so I've been using the rule of thumb that each +1 makes you about 1/6 more effective (again, assuming crit successes and/or crit failures matter).
So a Fighter 1 w/ 18 Str does about 50% more damage than a Warpriest 1 w/ 16 Str using a generic Strike. As bonuses accumulate, the difference gets more extreme, so that a good rule of thumb for non-martials doing martial things is you're primary attack is about as good as a martial's secondary attack (partly due to martials accumulating more damage bonuses too). Which is fine since casters can cast as their primary role & Strike too, which is pretty strong.
Martials get a proficiency bump at 5th, I think because it's where the casters can get bumped to an 18 Str/Dex and catch up (kinda).
The small differences are similarly powerful on defense if your lower AC is giving your enemies a better chance to hit. A Champion's AC makes him quite tougher than the Barb w/ more hit points.
I think this is why nearly all monsters have very high attack w/ medium damage (rather than medium attack w/ higher damage like a Barbarian). That way battles are less swingy if unforeseen attack bonuses/AC penalties occur. This also means bonuses & penalties mean more to Barbs!
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Another thing to consider is the time that it takes to hit the average numbers.
PF2e has more of a character's damage potential tied up in dice than PF1e. So when considering hit averages and its impact on damage values you also have to consider over what period of time. This is especially important as how much the average damage is boosted varies quite a bit depending on the target DCs.
A +1 is more stably impactful in PF2e, and has a greater impact the more likely you were to hit something in the first place. But isn't something that will turn the game upside down and make or break every combat you enter.
Otherwise my barbarian and his terrible dice luck would be doing significantly better than the alchemist and sorcerer.
Dice entropy matters :).
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How strong is a +1?An equally relevant question is how fun is a +1?
How much fun is +$1?
If it's pouring rain and $1 more means you can buy a bus ticket home instead of walking, that dollar is a lot of fun.
It's the same here. If a +1 turns your hit into a crit, which triggers Fatal or a cool crit specialization on your weapon, then +1 is a lot of fun.
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How strong is a +1?An equally relevant question is how fun is a +1?
I'm not sure how relevant a question this is. Getting +1 on things is seldom something you give up a narrative or 'cool' ability for. It tends to come baked in, or instead of another +1 at a different thing. So...how fun it is just never becomes relevant.
How fun the game is, that's super relevant (and, IMO, the game is pretty fun), but how fun an individual +1 is just seldom comes up as a meaningful concern.
The only case I can come up with is deciding to use buff spells (including playing a Bard), and in that case I'd argue that most of them either provide +1 to a large group (with five PCs, often taking two actions a piece that +1 is probably relevant every single round...even in much smaller groups it's probably relevant every two rounds or so), or come in lots bigger than +1 and last a whole fight, which again means they almost certainly matter at least once.
Success is generally fun, and so buffing is generally fun, IME.
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A +1 is fun 5% - 10% of the time. Which means you could go several encounters with it achieving zilch.How strong is a +1?An equally relevant question is how fun is a +1?How much fun is +$1?
If it's pouring rain and $1 more means you can buy a bus ticket home instead of walking, that dollar is a lot of fun.
It's the same here. If a +1 turns your hit into a crit, which triggers Fatal or a cool crit specialization on your weapon, then +1 is a lot of fun.
Much more often 10% than 5% in fact, considering -
* A +1 always either reduces the number of d20 die faces that results in a critical failure, or increases the number of die faces that earn you a critical success. This is inherent in the +/-10 scaling.
* Most skills have both a critical failure and a critical success effect.
* So do saves.
* While in the basic situation, attacks don't have critical failure effects, there are some exceptions, such as Press abilities that still do something on a failure, but not a critical failure; and some reactions that can be taken when an enemy critically fails to hit you.
So a +1 on skills or saves is more consistently valuable, but of course the value of a +1 should be seen based on how much success change it gets multiplied by the value of that success (or failure).
Another thing to note is that a +1 or -1 is not always just one +1/-1; if you make an enemy frightened just before all your allies get a turn, that's a lot more than if it's only for yourself.
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Another note on percentages; we tend to call all these percentages but actually we're talking about percentage points, i.e. the difference between two percentages.
If I have a 10% to crit someone and I get a +1 to hit, that's a 50% increase in my crit rate. If I had a 20% chance to crit someone and I get a +1, it's only a 25% increase in crit rate.
So a +1 should be valued in comparison to base rates and how much it changes them. For example, you're a fighter and have to climb a wall and below you is a lava river. (It happens all the time.) On a success you move, on a failure you're stuck (and take a bit of damage from the convection heat), on a critical failure you fall in. The convection heat is annoying but you can cope with that, but falling in will kill you. Let's say the DC is 20 (the Expert DC for a wall with small handholds and footholds) and you have an Athletics of +8. So you will critically fail if you roll a 1 or 2. There's not much you can do about rolling a 1, but if you got a +1 bonus, you'd merely fail on a 2 so you halve your chance of sudden fiery death.
But now let's consider the wizard who didn't go to the gym and has a +0. He's gonna die on a roll of 10 or less. A +1 would make him die on a 9 or less.
I'll argue that the +1 is not worth the same for these characters. For the wizard, even with a +1, he'd be crazy to try this. For the fighter, a one in 20 chance of death is still bad, although if he really had to go there, he could.
But let's say both characters have a hero point, and since you can spend those after hearing the results of a roll, that could be used to reroll on a critical failure. For the wizard the odds without hero point of surviving a climb attempt are 50%, with a +1 they're 55%, and with a hero point they become 75% and 79.75% respectively. Yay hero points. For the fighter the odds were 90% and 95%, and they become 99% and 99.75%
So that's interesting. A +1 and a hero point combined make a much bigger difference if your rolls weren't so hot to begin with, while they just squeeze out the last bits of uncertainty if you were already good.
So which is more valuable? If you have one +1 athletics potion, who should get it? That's an interesting choice... who do you like most?
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How strong is a +1?An equally relevant question is how fun is a +1?
Why derail the thread with your question instead of actually responding to the op?
How strong is a +1?An equally relevant question is how fun is a +1?
Understanding how big an impact that +1 has can make it more fun, if you let it.
Fun is subjective, as you know, which makes each individual their own gatekeeper to fun.
You have to let yourself have fun.
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How strong is a +1?An equally relevant question is how fun is a +1?
Not terribly. It's below the value to be immediately noticeable, but it's been proven above to have a positive impact. A +1 will rarely make or break a session, but they add up. Like I was telling my Bard player the other day, you might not notice your Inspire Courage's effect encounter to encounter, but by the time we're done Act 1 you'll probably be glad you spent your actions on it.
The biggest benefit of the bard is that it is +1 to multiple people (and much more at later levels). And if you have the free actions it is more impactful than a third attack ;)
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The biggest benefit of the bard is that it is +1 to multiple people (and much more at later levels). And if you have the free actions it is more impactful than a third attack ;)
Most definitely, but at level 1 and his first PF2 game I wanted to be upfront about how the math is tight enough to be under our perceptive thresholds in many cases.
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Very good considering the system. The bonuses are small because they (Paizo) KNOW that we will find a way to stack as many as possible. I remember there was someone who was talking about that around 4th level you can get hits reliably on a 2 or 3 (I don't remember exactly). All from stacking those +/- 1's and 2's. So while a +1 all by itself might not seem super appealing you instead should be looking into how many bonuses you can be pulling overall.
For instance if you have a Bard, Barbarian, and Rogue in your group.
Bard casts Inspire Courage for a +1. Barbarian uses Intimidate for a -1 from demoralize. and then the Rogue flanks with the Barbarian for an additional -2 to his AC. So that's a total of +4 (relatively) on your attack roll.
Now some people may argue that you need a specific party build to accomplish that but P2e has so much customization that AT LEAST one person in the party should be trying to debuff. So you can stack some stuff at least. It is a party game after all. Everyone should be working together.
I've made calculations on the impact of a +1 on your damage with a weapon with no special crit attribute, and it's between 9 and 16% in most classical situations for your first attack.
If you calculate it on both a first and a second attack then it's closer to 15%.
So, it's pretty big.
On basic saves, on the other hand, it's around 8% (but I haven't done a complete calculations on these ones, so I may be wrong).