How to achieve the apparent goal of the math of the new edition


General Discussion


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The new edition is trying very hard to flatten the curve on dice rolling - both in terms of players having bonuses so high that their bonus to the roll is higher than the DC and players whose bonuses are so low that they refuse to try. This flattening is most apparent with skills, but applies to all d20s - attacks, saves, skills. But it's also creating a situation where what it's doing is either preventing players from trying to invest in certain things (i.e. I've seen hyper-focused characters with cracked out low-use Knowledge skills (nobility, geography, etc), fighters with massive Perform(Dance), and I've also seen "generalist" characters with basically the same bonus to all skill checks of the same attribute) while putting up an illusion of investment.

The changes in player-side computation of the math, combined with the way DCs scale, it looks like the goal is to create a system where the result is based on the result of the die roll itself and not the result of the check (die roll + bonus). Including a bonus at all is merely a pretense. So, let's drop the pretense and make the goal of the mechanics more transparent.

You have three Proficiencies: Proficiency A means a 5 or higher on the d20 is a success, Proficiency B means a 10 or higher on the d20 is a success, and Proficiency C means a 15 or higher is a success.

Using the PF1 framework for the classes,
Paladin gets ProfA in attack rolls, Will saves, and Fort saves; ProfC in Reflex saves
Rogue gets ProfB in attack rolls; ProfA in Reflex saves; ProfB in Fort and Will saves
Wizard gets ProfC in attack rolls; ProfA in Will saves; ProfB in Fort and Reflex saves
And skills get ProfA in a number of skills based on class (2+Int for Paladin and Wizard, 8+Int for Rogue), but you can trade one ProfA for two ProfB (a 10 Int Rogue could have 8 ProfA skills, or 7 ProfA skills and 2 ProfB skills, or 6 ProfA skills and 4 ProfB skills, or etc). All of the other skills (the "non-invested" skills) get ProfC.


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I don't think this is a fair assessment. A base success rate of 50% is certainly a goal, but the narrowed bonuses are because of the critical rules. Since rolling over by 10 is now a critical, giving someone too large of a bonus starts affecting critical rates. For example, if True Strike were ported over directly, it would equate to fighters being able to crit on nearly 95% of attack rolls, or on 100% of attacks they land. (I don't feel like doing the math for especially the third strike, but I suspect it's still an incredibly high number) Hence, it was nerfed to just letting you roll twice and take the better result. (Which I think is equivalent to a +4 bonus)

I don't think the extremely tight math is actually a design goal, so much as it's the by-product of a different design feature.


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"Flattening" is the wrong term. Pathfinder 2nd Edition steepened the curve on dice rolling. As RazarTuk explained, this is from the new +10 critical success rules. To compensate for the steeper curve, the Paizo designers are narrowing the range. This forum has been calling this tightening, as in "tight math."

Let's compare a PF1 attack roll to a PF2 attack roll. A character hits on a 9 or higher, a 60% chance, and then goes up a level and gains an additional +1 to hit. For a PF1 character, still battling the same kind of opponents, that raises the chance of hitting from 12 chances out of 20 to 13 chances out of 20, a 8.33% improvement. Damage is not changed, so that does not factor in. Critical hits are a fixed 10% chance, so that does not factor in. A 8.33% improvement in hitting is an 8.33% improvement in damage per attack.

In constrast, the same hitting on a 9 or higher in PF2 is a 50% chance of a regular hit and a 10% chance of double damage on a critical hit. The additional +1 to hit from leveling up can be viewed as improving 12/20 to 13/20, but really we need to separate regular hits and critical hits. Regular hits are unchanged, still 10 out of 20. Critical hits have gone up from 2 out of 20 to 3 out of 20. To combine them, we treat each critical hit as worth 2 regular hits, because they do double damage. The net improvement is from (10 + 2*2)/20 to (10 + 2*3)/20, a 14.29% improvement. That is 71% more improvement in rate of damage compared to PF1. The curve is steeper.

Thus, a +2 in PF2 (29% improvement) is slightly better than a +3 in PF1 (25% improvement), so PF2 out to give out +2s where PF1 gave out +3s.

As for The FlyingPhoton's system, +1 does not make a difference in that. It is purely by class. Paladins could dump strength and dexterity and still get the same rate of hitting.


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The math is supposed to make a character/creature that is 2 levels higher be twice as powerful, judging from the XP values in the monster manual. If things are equal level the chance to hit is 55% for an expected damage of 60%. Bonuses increase by about 1.5 per level. Two levels higher gives a +3 bonus for 70% chance to hit, so expected damage of 90%. Two levels lower is -3, so 40% chance to hit, for 45% expected damage. You do 50% more damage and take 25% less with a two level difference, for a relative contribution of (90 /60)/(45/60) = (90/45) = 2

So over 20 levels you have a bonus of 20 from level, 5 from item bonus, and the rest from ability score increases and proficiency increases to get about 1.5 per level.

But they don't need to do this, they could remove item bonuses and ability score increase, and have proficiency increases as actually increasing your effectiveness. This would make make bonuses increase by 1 per level, so doubling in power every three levels instead of every two, but still at a consistent rate.


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Okay, so, it's fun to say that everything's a coinflip and investment doesn't matter.

But if you're expert, +5 attribute, and +3 item to a skill, you're at +10 compared to someone with just +3 in the attribute, no training, no item. That's a big difference (and they could be as low as -1 in the attribute, you could be legendary with a +5 item and +7 attribute, etc). This very-achivable +10 changes results by an entire category: their failures are your successes, their successes your critical successes, etc. This is noticable and not an issue.

The issue comes from published numbers. Notably, the bestiary and 10-2. They give invested characters a 50/50 chance, or close to it, for on-level challenges, often impossible for uninvested characters.

So yeah, investing matters and affects the math. Unfortunately, investing brings you up to baseline competence for your level, and everyone else is a complete failure at it. The math works very well for under-leveled challenges. The on-level numbers are the issue. They've acknowledged this already for the bestiary, and I wouldn't be surprised to see 10-2 numbers lower in the final print.


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TheFlyingPhoton wrote:
You have three Proficiencies: Proficiency A means a 5 or higher on the d20 is a success, Proficiency B means a 10 or higher on the d20 is a success, and Proficiency C means a 15 or higher is a success.

The only problem is that the differences are too noticeable, and it doesn't account for the all-important treadmill.

Switch the numbers to 9/11/13, plus or minus level difference if you're dealing with other creatures, and you've got an accurate sans-pretense translation of the math.

Mathmuse wrote:
As for The FlyingPhoton's system, +1 does not make a difference in that. It is purely by class. Paladins could dump strength and dexterity and still get the same rate of hitting.

Easy. Cut ability scores. After all, the design strongly encourages, and largely assumes, very little ability score variation where it matters.


Lyee wrote:
Okay, so, it's fun to say that everything's a coinflip and investment doesn't matter.

That's usually a reference to equal-level challenges, which is not uncommon to encounter.


Vic Ferrari wrote:
Lyee wrote:
Okay, so, it's fun to say that everything's a coinflip and investment doesn't matter.
That's usually a reference to equal-level challenges, which is not uncommon to encounter.

Not uncommon, but the suggestion of a coinflip makes it apply regardless of the difficulty of what you're trying to do, which counters the other thing the math of the system is obviously trying to do: steeply scale with relative level.


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Vic Ferrari wrote:
Lyee wrote:
Okay, so, it's fun to say that everything's a coinflip and investment doesn't matter.
That's usually a reference to equal-level challenges, which is not uncommon to encounter.

Did you read the rest of my post?

I then went on to talk about that. That investment does matter, it just matters in bringing you up to par, and that the challenges appear to be set incorrectly.

I am not sure what you are trying to say in your post. I know most challenges are on-level. I have acknowledged what I feel is the issue there (DCs too high) and argued against a different percieved issue presented in the thread (that arguement that investment doesn't change the math - it does change it. It just brings it from 10% success to 60%, and that's terrible.)


Lyee wrote:
Vic Ferrari wrote:
Lyee wrote:
Okay, so, it's fun to say that everything's a coinflip and investment doesn't matter.
That's usually a reference to equal-level challenges, which is not uncommon to encounter.

Did you read the rest of my post?

I then went on to talk about that. That investment does matter, it just matters in bringing you up to par, and that the challenges appear to be set incorrectly.

I am not sure what you are trying to say in your post. I know most challenges are on-level. I have acknowledged what I feel is the issue there (DCs too high) and argued against a different percieved issue presented in the thread (that arguement that investment doesn't change the math - it does change it. It just brings it from 10% success to 60%, and that's terrible.)

I am pretty much with you on this one. I find the scales have tipped too far the other way.

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I would tune on-level challenges such that an invested character succeeds on a ~5 on the d20, which, yes, does mean that they crit on a 15. Make sure crit success effects can occur with that frequency without being disruptive, and now you have characters who actually feel good at the things they're supposed to be good at.

I'd also replace table 10-2 with a formula, and then make sure to time ability increases and suggested item availability to go with the formula.


Pathfinder Adventure Path, Rulebook Subscriber
ryric wrote:

I would tune on-level challenges such that an invested character succeeds on a ~5 on the d20, which, yes, does mean that they crit on a 15. Make sure crit success effects can occur with that frequency without being disruptive, and now you have characters who actually feel good at the things they're supposed to be good at.

I'd also replace table 10-2 with a formula, and then make sure to time ability increases and suggested item availability to go with the formula.

The problem with that is every character is going to be "invested" in combat. So I think that math works with skills since skill checks come up way less often so it makes sense that you should be able to pass skill checks that you invested in often. But combat I just don't agree. Only missing on a 4 or lower just isn't a challenging fight in my eyes.


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Lyee wrote:

Okay, so, it's fun to say that everything's a coinflip and investment doesn't matter.

But if you're expert, +5 attribute, and +3 item to a skill, you're at +10 compared to someone with just +3 in the attribute, no training, no item. That's a big difference (and they could be as low as -1 in the attribute, you could be legendary with a +5 item and +7 attribute, etc). This very-achivable +10 changes results by an entire category: their failures are your successes, their successes your critical successes, etc. This is noticable and not an issue.

The issue comes from published numbers. Notably, the bestiary and 10-2. They give invested characters a 50/50 chance, or close to it, for on-level challenges, often impossible for uninvested characters.

So yeah, investing matters and affects the math. Unfortunately, investing brings you up to baseline competence for your level, and everyone else is a complete failure at it. The math works very well for under-leveled challenges. The on-level numbers are the issue. They've acknowledged this already for the bestiary, and I wouldn't be surprised to see 10-2 numbers lower in the final print.

That's not really a fair comparison. You're talking about two optimizers here: one that tries to be good, and one that actively tries to be bad. But... players who see issue with the system aren't commenting on the gap between Untrained and Expert. They're commenting on the gap between fully optimized and casually doing the thing.

Let's look at a fair comparison, and do it at a few levels.

Level 1. Checking into an unnamed skill. The best character will be Trained and have an 18. That's a +5. The "not really trying at all" character will have a 14 in a stat and also be trained. They're at +3. 10% better success rate isn't "no difference," but in gameplay both characters will be rolling and hoping for the die to favor them.

Level 5. The best character still only has a 19, but he's now bumped up to Expert. He has a +10. The "not really trying at all" hasn't pushed proficiency, but did take a stat bump. They're riding at +8. So... still 10% difference.

Level 10. The best character finally gets to 20 and he gets the +1 item. He's also pushed to Master proficiency. They've got a +18. Meanwhile the "not really trying at all" character pushed their stat to an 18. They're running in with a +14. Now a 20% difference in success rates.

Level 15. Best goes to 21 in a stat and Legendary proficiency. They have +24. "Not trying" goes to 19 in stat, remains at only Trained. They've got a 19. 25% difference.

Level 20. Best gets that 22 base and a stat bumping item. They've reached +31. "Not trying" goes to 20 in the stat, and clocks in at +25. 30% difference.

Now, that's not insignificant at all. The try-hard character is working their way up to being 30% better over the not-trying character. That 30% difference through keeps both characters in the same "I gotta roll high" feeling for much of their career. The try-hard player never gets to take the die roll out of it, never gets failure prevention, and never really scales into checking to see if his skill checks would crit when it matters (equal or higher level challenges). So... the FEELING of being great at something isn't delivered. And if that feeling can't be obtained, it's reasonable to say 'Why invest in this stuff at all?' For the most part, the reason you invest in skills at all is that you're forced to take skill feats and buy that skill item. But it still feels... not enough.


Dire Ursus wrote:
Only missing on a 4 or lower just isn't a challenging fight in my eyes.

Neither is only missing on a natural 1, or auto-critting unless you roll a natural 1, or only hitting on a natural 20 and so forth.

But, alas, ideas are being quashed, as we can see, by The M(P)an...


Greg.Everham said wrote:

That's not really a fair comparison. You're talking about two optimizers here: one that tries to be good, and one that actively tries to be bad. But... players who see issue with the system aren't commenting on the gap between Untrained and Expert. They're commenting on the gap between fully optimized and casually doing the thing.

Let's look at a fair comparison, and do it at a few levels.

Level 1. Checking into an unnamed skill. The best character will be Trained and have an 18. That's a +5. The "not really trying at all" character will have a 14 in a stat and also be trained. They're at +3. 10% better success rate isn't "no difference," but in gameplay both characters will be rolling and hoping for the die to favor them.

Level 5. The best character still only has a 19, but he's now bumped up to Expert. He has a +10. The "not really trying at all" hasn't pushed proficiency, but did take a stat bump. They're riding at +8. So... still 10% difference.

Level 10. The best character finally gets to 20 and he gets the +1 item. He's also pushed to Master proficiency. They've got a +18. Meanwhile the "not really trying at all" character pushed their stat to an 18. They're running in with a +14. Now a 20% difference in success rates.

Level 15. Best goes to 21 in a stat and Legendary proficiency. They have +24. "Not trying" goes to 19 in stat, remains at only Trained. They've got a 19. 25% difference.

Level 20. Best gets that 22 base and a stat bumping item. They've reached +31. "Not trying" goes to 20 in the stat, and clocks in at +25. 30% difference.

Now, that's not insignificant at all. The try-hard character is working their way up to being 30% better over the not-trying character. That 30% difference through keeps both characters in the same "I gotta roll high" feeling for much of their career. The try-hard player never gets to take the die roll out of it, never gets failure prevention, and never really scales into checking to see if his skill checks would crit when it matters (equal or higher level challenges). So... the FEELING of being great at something isn't delivered. And if that feeling can't be obtained, it's reasonable to say 'Why invest in this stuff at all?' For the most part, the reason you invest in skills at all is that you're forced to take skill feats and buy that skill item. But it still feels... not enough.

I don't really think your comparison is that fair either across all levels. 14 in the starting stat and trained is not nothing in my view, but it gets more equal over the levels. An the skill boost items is +2 for a level 5 item and +4 for a level 13 item (some items are +3/+6).

So a more fair comparison would have the "not try at all" start at 12 in the stat and not get the items, but boosting the stat to 18 over the levels.
That would make the difference 15%, 15%, 30%, 40% and finally 50%. Not to mention skill feats and proficiency-gated tasks to increase the difference.

I wouldn't personally mind seeing a bigger difference between the proficiency levels, but that would need to be strictly for skills or the proficiencies for weapons and armor would need to be adjusted for balance.


Nettah wrote:

So a more fair comparison would have the "not try at all" start at 12 in the stat and not get the items, but boosting the stat to 18 over the levels.

That would make the difference 15%, 15%, 30%, 40% and finally 50%.

The problem is that most of the stats have other uses that mean you really want a minimum 14, if not 16.

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