What is the "tight-math paradigm"?

[Lord Fyre]

What does the term "tight math" mean?

I see the term being thrown around, but the people using it appear to believe that everyone understands what they are saying. I don't. :(

[Ediwir]

Basically because of how the P2 system works, any small bonus, even just a +1, is a very valuable bonus to have at any level, while in P1 a +1 was just something you'd throw in and barely feel.

This is because of how the 4-degree success works and because of how consistent checks and DC progress. Even considering how you are not actually meant to face your own level in difficulty every time (try fighting a Troll with a lv5 fighter in Path1 and tell me it's easy, I dare you), altering your values by 1 point can change the entire feel of an encounter.

With a +1, you succeed more, crit more, and fail less. And when you fail, it's less severe.
With a +2, this is even more true.
The higher you go, your successes likely do not change, but you gain more crits instead.

So, if any small variation can have powerful consequences, the game's math has to lead characters to a tight range of modifiers, to keep the result comparable.

[NorthernDruid]

3.Finder in general has pretty few checks on how high a bonus you can get on a given level.

There's no max cap to how high a bonus you can stack and a solid bonus is usually something like +3-5.

Similarily, there's quite a few damage bonuses that stack multiplicatively in one way or another.

As such, it's very hard to predict or estimate how high spell DCs, how high skill/save/attack bonuses or how much damage, a PC is likely to have given their general build description.

3.Finder's math is very wide in it's span, and very loose in terms of what it let's the players do.

Tight math in this case, refers to more controlled scope of not only how high you can go, but what the overall span is.

It's not just limiting what you can stack together and what bonus range you'll be in though, it's also about normalizing things like AC vs to-hit so you don't end up with a non-martial, a secondary martial and a tank with ACs of 18, 27 and 36 respectively, and a general monster balance around +30.

In short, it's about creating consistency in what is achievable and therefore estimatably expectable.

At least that's what I get out of the term.

[ikarinokami]

PF2 is basically designed that all things being equal every check should be 50/50 regardlness of level against a same level opponent or check. and so the game has been designed that this is result. to do this you have to maintain very "tight" controls on the math of the game.

so "tight" in this case simultaneously refers to a few things.

1. tight refers to the fact that the game wants to mantain that 50/50 success rate

2. tight refers to that you have to keep tight controls on bonuses to maintain that 50/50 success rate

3. it also refers to how easy it is to throw off the game giving someone extra +1 because of how tight the math is in the game

[Zman0]

Generally its a reference to expected ranges of values and controls on those ranges. P2 has very tight controls on misclenaeous modifers, the range of those modifiers, the levels they happen with etc, where as something like P1 has much more available modifiers and much higher potential ranges.

For instance, look at attack modifier in P2 vs P1. In P2 we have Proficiency + Ability. So, you're looking at a +0 to +7 for Ability, effectively -2-+3 for Proficiency, and +20 for level, +5 Item. In P1 we have BAB varying from +10-+20, we have ability modifiers that can be pushed far higher with things like +8 ability and huge racial bonuses, we even have things like static +1 Weapon Focus etc in addition to +5 Item. We have tons of other random bonuses. In P1 the bonuses from spells etc are much greater.

So, when you're looking at the total range of modifiers you would encounter the math is much tighter in expected attack modifiers in P2 than in P1. The same exists for skills.

Another way the math is tighter is that Monsters are no longer built the same way, now they have progression tiers of competency meaning many any monster of a given CR will have a best skill of the same modifier, the attack modifiers are all within a couple points, same for perception, AC, etc. Instead of them varying wildly based on the interaction of their base abilities and good saves etc. Essentially this tightens Monsters closer to the average or expected or appropriate values for a monster of that level. It makes monsters perform more as expected with fewer wild swings.

In P1 the math wasn't very tight. You could end up with extraordinarily high modifiers for skills. In P2, the maximum skill value is +15 +level 20 for a maximum of +35, in P1 you could see something like a +50 in a skill.

[MerlinCross]

Tight enough to make everything feel the same. So you need to look for any bonus what so ever to feel like you're progressing.

The guides are going to be something to see after release.

[N N 959]

When I use the term "paradigm," I'm referring to the philosophy of designing the game around a predetermined range of outcomes. In order for the game to adhere to the paradigm, Paizo has to have stricter rules about how good a benefit can be and where a benefit can apply. As others have suggested, Paizo wants to know the range of rolls for a PC at any given level. As this seems to permeate all aspects of the game, for me, it has the effect of making the game feel constricted and contrived.

Think of it like Paizo changing a d6 to only have the numbers 1, 2, 2, 3, 3, 4.

[Mathmuse]

To us mathematicians, tight math means the case where a greater-than-or-equal-to inequality is at the equal-to extreme. It can also mean a rigorously proven teorem. That is not what it means here.

The tight math in Pathfinder 2nd Edition means that the designers are trying to control the numbers themselves rather than giving the players many options to control them. For example, instead of a skill point system where the players decide on the skill bonuses for their characters, the PF2 skills receive a fixed +1 per level. Sometimes, the design allows an extra +1, such as improving a skill proficiency from trained (+0) to expert (+1), but the next improvement, master (+2), was allowed only for signature skills (that rule was recently dropped).

Ediwir wrote:

Basically because of how the P2 system works, any small bonus, even just a +1, is a very valuable bonus to have at any level, while in P1 a +1 was just something you'd throw in and barely feel.

This is because of how the 4-degree success works and because of how consistent checks and DC progress. Even considering how you are not actually meant to face your own level in difficulty every time (try fighting a Troll with a lv5 fighter in Path1 and tell me it's easy, I dare you), altering your values by 1 point can change the entire feel of an encounter.

With a +1, you succeed more, crit more, and fail less. And when you fail, it's less severe.
With a +2, this is even more true.
The higher you go, your successes likely do not change, but you gain more crits instead.

So, if any small variation can have powerful consequences, the game's math has to lead characters to a tight range of modifiers, to keep the result comparable.

The critical success is one factor that amplifies the effect of an additional +1 to a roll. Another factor is multiple attacks at 1st level. A Strength 18 paladin has trained proficiency with martial weapons, for a +5 to attacks at 1st level. Against a hobgoblin soldier, AC 15, he has a 55% chance of hitting on the first attack, 50% normal and 5% critical, and a 30% chance of hitting on the second attack, 25% normal and 5% critical, and a 5% chance of hitting on the 3rd attack, all of it critical. That sums to 0.75 regular hits and 0.15 critical hits per round, dealing as much damage as 1.05 regular hits. A Strength 18 fighter, in contrast has expert proficiency with martial weapons, for a +6 to attacks at 1st level. That gives 0.5 regular hits and 0.1 critical hits on the first attack, 0.3 regular hits and 0.05 critical hits on the second attack, and 0.05 regular hits and 0.05 critical hits. The total is 0.85 regular hits and 0.2 critical hits in a round, as much damage as 1.25 regular hits. 1.25/1.05 = 1.19, so that +1 from expert means 19% more damage.

A 1st-level fighter in Pathfinder first edition, limited to one attack per round and no way to increase the number of critical hits, would need a +2 to hit for the same improvement.

However, if the hobgoblin soldier raises his shield to raise his AC to 17, the numbers change. Or if the fighter performs a non-attack action such as Stride, the numbers change. The 19% improvement was an extreme case and a +1 more often gives only a 10% improvement, the equivalent of a +1 in Pathfinder 1st Edition. Likewise, a skill check or a saving throw that has no dramatic effect on a critical success or critical failure finds a +1 equally ordinary. The tight math can be boring.

[Lord Fyre]

Mathmuse wrote:

The tight math can be boring.

Or, have we just become spoiled?

[Lyee]

Nah, I don't think anyone's spoiled. Tight math is just very dull. It's easy to be the best-possible at something, and that... isn't even very impressive. Every thievery-loving character is going to be equally mediocre at thievery, and that's really not fun.

[Tarik Blackhands]

I'm personally of the mind that yes, a lot of people here are very spoiled by PF1.

You hear a lot of folks being frankly insulted that you can't fenagle ways to nail CR+2 monsters on 3+ or breeze by equivalent level skill checks checks on the same d20 roll if not better.

In other words, people unironically enjoyed being Angel Summoner and take exception to Paizo making the adjustments to clarify that the BMX Bandit is meant to be the norm.

[Alaryth]

That's true. But there is a great difference between "assure succes on a 2 versus same level", and "the best you can arrive is to succes on a 9 versus same level, and that with total optimization".
A character with proper optimization on their specialty should have succes on a 6 or around that number. If the difference between total optimization and zero optimization is succes on a 10 versus succes on a 13, the game begins to resamble doing coinflip on all rolls.

[GM Rednal]

I think what people are saying is "Pathfinder is a game of heroic fantasy, and it can be difficult to feel heroic if characters are too similar and you can't become too good at anything". As a roleplaying game, Pathfinder is also about telling a story - and most people seem to prefer being able to create characters that fulfill their story.

[NemisCassander]

I think Alaryth has hit upon a very easy way for Paizo to poll their playtesters. Consider the question:

"What do you believe is the number that an optimized character should need to roll (on a d20) to succeed against an equal-level challenge?"

"Similarly, what do you believe is the number that an un-optimized but decently skilled character should need to roll (on a d20) to succeed against the same challenge?"

Or, alternatively,

"What should be the marginal difference in the required roll conferred by optimization?"

Because, right now, Paizo's own answer to the first question seems to be, "9 or 10, depending on the level", and "11 or 12, depending on the level," to the second question.

And I am fairly sure that the marginal difference being seen does not appear to be enough in many players' minds to connote 'optimality'.

[Tamago]

Tarik Blackhands wrote:

In other words, people unironically enjoyed being Angel Summoner and take exception to Paizo making the adjustments to clarify that the BMX Bandit is meant to be the norm.

Just to play Devil's Advocate for a moment...

What's wrong with wanting to play Angel Summoner? Since this is a fantasy anyway, I like being able to really shine on something.

There is a place for a grim & gritty roleplaying game, but that's definitely not what Pathfinder is now.

[Matthew Downie]

Example of the loose-math paradigm: a high level PF1 PC could have an AC of 40 (if they bought +5 armor, shield, ring of protection, amulet of natural armor) or they could have an AC of 25 (if they didn't).

So what attack bonus is needed for a level-appropriate enemy against those guys? To avoid the risk of the monster flailing around ineffectually against the AC 40 PC, we should probably give it at least +30 to hit. But at that point the guy with AC 25 is so far behind the curve that even if he somehow gains a +7 bonus to AC it will make zero difference to his chances; the monster will hit him on a 2 either way.

[Bjørn Røyrvik]

Tarik Blackhands wrote:

I'm personally of the mind that yes, a lot of people here are very spoiled by PF1.

You hear a lot of folks being frankly insulted that you can't fenagle ways to nail CR+2 monsters on 3+ or breeze by equivalent level skill checks checks on the same d20 roll if not better.

In other words, people unironically enjoyed being Angel Summoner and take exception to Paizo making the adjustments to clarify that the BMX Bandit is meant to be the norm.

Yes, how dare they like being able to feel powerful or competent!?! They should sit down and shut up and play the game that doesn't allow them to play what they want because it's the new thing and the Right Way To Do It and their preferences are badwrongfun!

[GM Reaper]

Lord Fyre wrote:

Or, have we just become spoiled?

FAR TOO LONG HAVE WE ENDURED THE WHIMPERING OF SPOILED CHILDREN YEARNING TO FEEL IN CONTROL, TO HAVE FUN. BUT FEAR NOT, SOON WE SHALL TAKE AWAY THEIR TOYS, CRUSH THEIR FRAGILE DREAMS BENEATH OUR FEET AND MOCK THEIR LAMENTATIONS.

[Lyee]

I like the situation in Matthew's post: If someone in PF1 invested nothing into AC, then I would expect the high level monster to hit them on a 2. By this level, I'm okay with 'invested but barely anything' to not make a difference against the tough monsters that challenge the AC of 'full investment'. I am happy with the situation described in Matthew's post, that you have a wide variety of possible AC values. Some (25-32) will provide a variety of defenses against mooks and debuffed enemies, while other parts of the range (33-43) will provide a variety of defenses against challenging or buffed foes, or while you are debuffed.

[Vic Ferrari]

Matthew Downie wrote:

Example of the loose-math paradigm: a high level PF1 PC could have an AC of 40 (if they bought +5 armor, shield, ring of protection, amulet of natural armor) or they could have an AC of 25 (if they didn't).

42, with the shield, right (44 with tower)?

I agree, the problem in 3rd Ed/PF1 stems from BAB scaling so rapidly, and AC, not scaling at all, just equipment, money, magic (as you have shown). So it creates a weird race, imbalance.

[Mathmuse]

NemisCassander wrote:

I think Alaryth has hit upon a very easy way for Paizo to poll their playtesters. Consider the question:

"What do you believe is the number that an optimized character should need to roll (on a d20) to succeed against an equal-level challenge?"

"Similarly, what do you believe is the number that an un-optimized but decently skilled character should need to roll (on a d20) to succeed against the same challenge?"

Or, alternatively,

"What should be the marginal difference in the required roll conferred by optimization?"

Because, right now, Paizo's own answer to the first question seems to be, "9 or 10, depending on the level", and "11 or 12, depending on the level," to the second question.

And I am fairly sure that the marginal difference being seen does not appear to be enough in many players' minds to connote 'optimality'.

Despite my love of numbers, my answer to NemisCassander's question is not a number. A character, even an optimized one, should need more than a single d20 roll to succeed against an equal-level challenge. A single roll is an attack or a skill check, not a challenge.

Suppose a high-skill rogue wants to break into a 3rd-floor room to steal some plot-critical papers. He could sneak past the guards in the corridor and unlock the door. He could climb the outside of the building. He could climb an adjacent building and jump over. I expect several rolls for watching for guards, sneaking past guards, climbing, jumping, and opening locked doors or windows. That is a challenge.

Even in a single round of combat, I want to hear the wizard say, "My vast knowledge tell me that species is immune to my Fireballs. Fortunately, I also prepared Lightning Bolt."

Instead of a character always being 55% successful at everything, I want my character to be good at some things, bad at others, and repeatedly forced to figure out how to use the good thing in a bad situation. When I played a bloodrager who loved to charge into battle swinging her saber, she also carried a loaded pistol for when a saber was the wrong weapon.

What do I believe is the number that an optimized character should need to roll (on a d20) to succeed against a level-appropriate challenging skill check? Sometimes 4 and other times 15.

[Matthew Downie]

Lyee wrote:

I am happy with the situation described in Matthew's post, that you have a wide variety of possible AC values. Some (25-32) will provide a variety of defenses against mooks and debuffed enemies, while other parts of the range (33-43) will provide a variety of defenses against challenging or buffed foes, or while you are debuffed.

The problem is, if we throw in Tower Shield, Mithral, Dexterity bonus, Insight bonus, Luck bonus, Combat Expertise, Haste, etc, then even boss enemies aren't able to land a single hit. It can make things frustrating for the GM and boring for the player.

A little bit of tightening is a good idea.

[Alaryth]

Matthew Downie example is totally right, and certainly a serious problem for PF1. Saving throws is another glaring case.
But there should be some happy medium between a difference bonus on dice at level 20 of about 35, making the dice totally unnecessary and preparing adventures a nightmare, and the current situation on PF2Playtest of 5-6 points of difference outside corner cases, making the perceived competence of the character near disappear.
On my humble opinion, Paizo is right see that kind of situations on PF1 as a problem, but they have totally overcompensate, so the Playtest have the opposite problem.

[Moro]

There will always be a large percentage of people who dislike added restrictions, no matter the situation, and this sort of shortening of the math ranges usable by PCs can definitely be viewed in that light.

This holds true even when it comes to removing the illusion of choice rather than meaningful choice.

[necromental]

Mathmuse wrote:

Instead of a character always being 55% successful at everything, I want my character to be good at some things, bad at others, and repeatedly forced to figure out how to use the good thing in a bad situation. When I played a bloodrager who loved to charge into battle swinging her saber, she also carried a loaded pistol for when a saber was the wrong weapon.

This. So much this.

[MrAptronym]

With everyone now stating their support or opposition for the idea, I'll lead by saying that I for one am a big fan of tightening the math. I think how 'tight' exactly is for sure a question for the playtest to determine. I think when we discuss the math though, we should also mention that the math of how you succeed on checks is not the only form of advancement or advantage.

Along with the tighter math, there is seems to me to be an aim in v2 to focus progression on giving a character who specializes more options. You may not have the supreme numeric advantage on the tasks you specialize in, but you will be able to use that thing in more nuanced ways for better results.

[D@rK-SePHiRoTH-]

It means you are not allowed to break the game by minmaxing numbers

[Unicore]

Alaryth wrote:

Matthew Downie example is totally right, and certainly a serious problem for PF1. Saving throws is another glaring case.

But there should be some happy medium between a difference bonus on dice at level 20 of about 35, making the dice totally unnecessary and preparing adventures a nightmare, and the current situation on PF2Playtest of 5-6 points of difference outside corner cases, making the perceived competence of the character near disappear.
On my humble opinion, Paizo is right see that kind of situations on PF1 as a problem, but they have totally overcompensate, so the Playtest have the opposite problem.

The difference in PF2 at higher levels is going to be in the 10-15 range not the 5-6 points.

I think one aspect of this issue that the developers are actually paying attention to with their carefully crafted surveys, that is really difficult to theory craft with hypothetical situations, is that the numbers are mostly feeling off in the lower character range, especially from what they were in PF1. Because in PF1 it was pretty easy to hit that +10-15 separation range by level 5 to 7 with actual optimization, which are levels that people are pretty accustom to actually reaching in play and feeling like their character had basically achieved legendary status in their area of expertise.

[NemisCassander]

Mathmuse wrote:

NemisCassander wrote:

I think Alaryth has hit upon a very easy way for Paizo to poll their playtesters. Consider the question:

"What do you believe is the number that an optimized character should need to roll (on a d20) to succeed against an equal-level challenge?"

"Similarly, what do you believe is the number that an un-optimized but decently skilled character should need to roll (on a d20) to succeed against the same challenge?"

Or, alternatively,

"What should be the marginal difference in the required roll conferred by optimization?"

Because, right now, Paizo's own answer to the first question seems to be, "9 or 10, depending on the level", and "11 or 12, depending on the level," to the second question.

And I am fairly sure that the marginal difference being seen does not appear to be enough in many players' minds to connote 'optimality'.

Despite my love of numbers, my answer to NemisCassander's question is not a number. A character, even an optimized one, should need more than a single d20 roll to succeed against an equal-level challenge. A single roll is an attack or a skill check, not a challenge.

Suppose a high-skill rogue wants to break into a 3rd-floor room to steal some plot-critical papers. He could sneak past the guards in the corridor and unlock the door. He could climb the outside of the building. He could climb an adjacent building and jump over. I expect several rolls for watching for guards, sneaking past guards, climbing, jumping, and opening locked doors or windows. That is a challenge.

Even in a single round of combat, I want to hear the wizard say, "My vast knowledge tell me that species is immune to my Fireballs. Fortunately, I also prepared Lightning Bolt."

Instead of a character always being 55% successful at everything, I want my character to be good at some things, bad at others, and repeatedly forced to figure out how to use the good thing in a bad situation. When I played a bloodrager who loved to charge into battle swinging her saber, she...

I was more looking for a single instance/roll; e.g., an attack roll.

*shrug* If your answer remains 'somewhere between 4 and 15', I feel we are going to have the current system in the final product which I, for one, will never run or play.

[GM Rednal]

*Glances in* 7 is a good 'success' number for a normally-built, non-optimized (or worse, min-maxed) character trying to be reasonably good at something. At that point, you will succeed about 70% of the time. Failure is still a possibility, but you'll succeed a bit more than twice as often as you fail, and that seems to be a pretty sweet spot.

[Mathmuse]

MrAptronym wrote:

Along with the tighter math, there is seems to me to be an aim in v2 to focus progression on giving a character who specializes more options. You may not have the supreme numeric advantage on the tasks you specialize in, but you will be able to use that thing in more nuanced ways for better results.

I listed the 174 feats in the PF1 Core Rulebook to see where they ended up in the Pathfinder Playtest Rulebook. The cross correlation was a daunting task and I set it aside for now, but it meant that I read all 174 feats and compared them to PF2 rules.

I was surprised how many PF1 feats simply changed a number, usually by a fixed increase. Of the first five feats, only Alignment Channel let the character do something new, channel energy affecting outsiders based on their alignment. For the other four, Acrobatic gives a +2 bonus on Acrobatics and Fly checks, Agile Maneuvers swaps Dex bonus for Str bonus when calculating CMB, Alertness gives a +2 bonus on Perception and Sense Motive checks, and Animal Affinity gives a +2 bonus on Handle Animal and Ride checks.

PF2 covers most of these with the skill increase given at 3rd level and every 2 levels after that. And it originally limited it from -2 to +1 for untrained to trained and from +1 to +2 for trained to expert for non-signature skills. I suspect part of the reason that people are complaining that feats feel so limited in PF2 is the conversion of half of them to skill increases so that the players failed to spot them when reading feats. Since the numerical increases act through the proficiency system, they are constrained by the tight math of the proficiency system.

(An irony is that my main use of bland feats such as Animal Affinity was with 1st-level NPCs to give them reasonable skills in their professional role. PF2 requires 3rd level or 2nd-level rogue for the same effect, so my townsfolk NPCs will suffer. I might create a homebrew Expert class that increases a skill or two to expert at 1st level in place of a class feat.)

Thus, the PF2 feats have to change more than a number. A 1st-level cleric in PF2 could learn Communal Healing that heals the cleric while she heals others, or Emblazon Symbol to free up a hand, or Holy Castigation for the same effect as Alignment Channel. A few change the size or number of dice, such as Deadly Simplicity and Healing Hands, so they are essentially numerical, but the numerical feats are fewer.

[Mathmuse]

NemisCassander wrote:

Mathmuse wrote:

What do I believe is the number that an optimized character should need to roll (on a d20) to succeed against a level-appropriate challenging skill check? Sometimes 4 and other times 15.

*shrug* If your answer remains 'somewhere between 4 and 15', I feel we are going to have the current system in the final product which I, for one, will never run or play.

That wasn't my answer. I want 4 or 15, not anything inbetween. I want optimized characters to have clear strengths and weaknesses.

I am busy crunching numbers on ways to loosen the tight math while keeping the advantages of the tight math. The underlying math is almost at college level: The Mind-Boggling Math of Exponential Leveling. Figuring out how to tweak the math to alter the effects is more difficult than college-level math. Fortunately, the statements of Jason Bulmahn and Mark Seifter show that they understand it.

[Mark Seifter]

Mathmuse wrote:

I was surprised how many PF1 feats simply changed a number, usually by a fixed increase. Of the first five feats, only Alignment Channel let the character do something new, channel energy affecting outsiders based on their alignment. For the other four, Acrobatic gives a +2 bonus on Acrobatics and Fly checks, Agile Maneuvers swaps Dex bonus for Str bonus when calculating CMB, Alertness gives a +2 bonus on Perception and Sense Motive checks, and Animal Affinity gives a +2 bonus on Handle Animal and Ride checks.

This was also something that I didn't expect when I went in for an initial analysis for Starfinder feats. We were tight on page count throughout that process, and we had estimates of how long the feats section would be based on PF1, but the number of pages that dropped off from things as simple as when I consolidated all the +2/+2 skill feats that had been padding out the PF1 CRB to Skill Synergy were substantial and far more than I expected. Everyone was happy to finally get some extra pages back for once!

[rknop]

...you did an analysis of Starfinder feats, and "Barricade" made it through?

*boggle*

[Mark Seifter]

rknop wrote:

...you did an analysis of Starfinder feats, and "Barricade" made it through?

*boggle*

I did an initial analysis of Starfinder feats that laid the groundwork for that chapter, in a way similar to Mathmuse described of looking through PF1 feats, and this led to my creating the majority of the feats in there. However, many of the feats that let you do specific skillsy stuff like Veiled Threat, Medical Expert, Fast Talk, Barricade, Antagonize, Amplified Glitch, and others were added later on; every section of a project like Starfinder (or PF2) is a huge team effort!

[John Mechalas]

Mathmuse wrote:

That wasn't my answer. I want 4 or 15, not anything inbetween. I want optimized characters to have clear strengths and weaknesses.

If I am following you correctly, you are thinking in terms of outcomes and not individual die rolls. I happen to agree with that philosophy. PF2, to me, feels laser-focused on individual rolls.

For example, by the rules, a successful Acrobatics (climb) check means you move 5 feet up or down. So to climb a 20' wall, you need 4 acrobatics checks, any of which can result in a critical failure which means you fall.

For those not as familiar with math as mathmuse is :) what's the outcome? If you could only critically fail on natural 1 then you have a 5% chance of falling per check. But when you put multiple checks in a row the odds of a fall being the outcome increase, significantly. Mathematically, the probability that, among several trials, we get at least one of a specific type of event, is:

P(at least one) = 1 - P(none)

To get P(none), you multiply the probabilities for each trial together, because each trial is independent of the other. So, P(none) is .95 for one trial, but for four trials it becomes .8145. To climb your wall, you need at least 4 checks, and the probability of a fall jumps to 18.55%(!) Now consider that you actually don't succeed half the time...Unless you get critical successes (which are as likely as falls), you are looking at more than 4 die rolls to climb the wall. Let's make it 6. Now your probability of falling jumps to just over 26%(!)

This is the problem with focusing in individual die rolls as the outcomes, instead of the encounter as an outcome. The more dice rolls involved, the more likely you are to hit a terminating failure.

I would ask NemisCassander's question differently: given a level-appropriate challenge (with multiple tasks/rolls involved), what percentage of the time should PC's succeed (where a failure means retreat, regroup, try something else, or at the extreme, a PC death occurs, etc.)? Followed closely by, how many of the party's total resources should be expended?

PF1 seemed to shoot for a high number to the first, and 1/3 to the second. In practice, thanks to splat book explosion, my gut tells me that players were in the 90% range to the first, and much less than 1/3 to the second.

[NemisCassander]

Mathmuse wrote:

NemisCassander wrote:

Mathmuse wrote:

What do I believe is the number that an optimized character should need to roll (on a d20) to succeed against a level-appropriate challenging skill check? Sometimes 4 and other times 15.

*shrug* If your answer remains 'somewhere between 4 and 15', I feel we are going to have the current system in the final product which I, for one, will never run or play.

That wasn't my answer. I want 4 or 15, not anything inbetween. I want optimized characters to have clear strengths and weaknesses.

I am busy crunching numbers on ways to loosen the tight math while keeping the advantages of the tight math. The underlying math is almost at college level: The Mind-Boggling Math of Exponential Leveling. Figuring out how to tweak the math to alter the effects is more difficult than college-level math. Fortunately, the statements of Jason Bulmahn and Mark Seifter show that they understand it.

Ah, so your answer is 4. Got it.

(Specifically, I am asking for what you think the roll needs to be for an optimized character to succeed at what they optimized, not a general number.)

I agree with you on 'giving characters clear strengths and weaknesses', but it does not appear that PF2E agrees with this. And I have some sympathy; high-level balance gets wacky. However, many examples of this in PF1E--such as the oft-maligned 'high-level saving throw conundrum'--has already been dealt with by nerfing spells into the ground. Basically, anything that was concerning on failing a saving throw in PF1E or 3.5 now needs a crit fail... which means that I could have a +5 difference in my saves without much of an issue. It's a big boggling.

[Leedwashere]

I like tighter math than PF1 offered. I've experienced supposedly threatening monsters faffing about for their turns. When this happens for monsters too weak to actually be a threat it doesn't bother me, but later on in every campaign it became extremely difficult to hit anyone in the party that put effort into defense. When only bosses can hit at all, that becomes a little frustrating.

But I do feel that the math in PF2 has gone a little too far the other way, and feels like it's been tightened enough to strangle the fun.

I've always set my own expectation benchmarks at the number 7. Rolling 6 or lower, I've noticed, feels like "dang I rolled bad" but failing on a 9 or 10 feels different. It starts to feel more like "dang, I suck." Succeeding on a 7 or 8 (firmly between "I can't roll" and "I suck") is where one feels like they're actually kind of awesome. It should not be easy to hit that benchmark, and the game's math should not expect it, but it should be possible with effort. 7, in my opinion, is the extreme of excellence.

[Pandora's]

One thing people are overlooking is that there are some abilities in the playtest that greatly modify your success rate without saying "+4" on the can. The Rogue's Sneak Savant feat is a good example. It doesn't give you a static modifier, because it isn't meant to increase your critical success rate. Instead, it says you only fail on a critical failure. If you had, for example, a 30% chance to succeed at a Sneak action before, that feat gives you an 80% chance instead. That's a whopping effective +10 bonus. It's possible that abilities like this are underutilized, but nothing about tighter math means that abilities can't dramatically affect success rates.

[Unicore]

I agree that the math might be a little tighter than it needs to be right now, but I think that it makes a lot of sense to run a really tight ship for the play test because it is inevitable that things are going to get loosened up in production and with the onslaught of supplemental material that a game like this is designed to incorporate.

I firmly believe that one of the major issues to resolve is that it is ok for the math around hitting an enemy with a physical attack to be tight, because everyone gets 3 actions which can be attacks, so if a character didn't attack multiple times, they probably did other things to feel effective in the turn. It makes no sense to me to have PCs generally able to hit on a 7+, but to have equal level opponents require a 12+ or better (which is often where the numbers were in PF1, or even more skewed). but we definitely don't want monsters having crit ranges in the 17+ very often so the math for attacking is good when it is tight.

Skills on the other hand, don't usually get 3 rolls to succeed, and that is where a lot of the frustration with the math being as tightly balanced as it is for attacks is coming from. Some of this is people having wildly different ideas about what skill checks can accomplish, or GMs pretty much using DCs or ideas from PF1 in play when they don't want to take the time to look up the new rules, but some of it is also that there are not enough skill feats and many of them are not working yet like players want them to (assurance, for example).

[Marc Radle]

It seems fair to say that the ‘tight math’ concept of Pathfinder 2E is more or less equivilant to D&D 5E’s ‘bounded accuracy’ concept

[rknop]

Mark Seifter wrote:

rknop wrote:

...you did an analysis of Starfinder feats, and "Barricade" made it through?

*boggle*

I did an initial analysis of Starfinder feats that laid the groundwork for that chapter, in a way similar to Mathmuse described of looking through PF1 feats, and this led to my creating the majority of the feats in there. However, many of the feats that let you do specific skillsy stuff like Veiled Threat, Medical Expert, Fast Talk, Barricade, Antagonize, Amplified Glitch, and others were added later on; every section of a project like Starfinder (or PF2) is a huge team effort!

Well, so, here's where this is relevant to the PF2E playtest.

Games like Pathfinder are very vulnerable to what one might call the "potion sponge" problem. New rules are coming out all the time (it eventually gets very overwhelming, frankly). Sometimes those are cool new classes, or new fun items. However, sometimes it's a new feat, or a new item, whose description suggests that something people have been doing all along wasn't actually possible, and you have to have a specific item or a feat to be able to do it. (It's worse when it's a feat, because that's a very limited resource.) The potion sponge in Advanced Race Guide suddenly made us all think that we weren't supposed to be able to drink potions under water, even though many of us had no problem with that beforehand.

Barricade, from Starfinder, is one of the worst examples of a feat gating what should just be something anybody might try. Quickly stacking a few loose objects to make some temporary cover that won't last very long is a creative action that you might expect a player in an RPG to try. But, now, it looks like you need a feat before you can do that. (What's next? Requiring a feat to suggest in the middle of combat that we could call a temporary truce?)

Perhaps at some level this is just what happens when you have a very rule-heavy game. There's a rule for so many things that if you don't find a rule for it, you should be prepared for a rule to come out in a later supplement that limits access to it. This is particularly true in a rule-heavy game like Pathfinder, where the rules aren't as systematic as something such as GURPS. New rules tend to be wholly new feats and classes that are haphazard based on what the topic of the new supplements are. If you don't like it, perhaps you should be playing FATE or something where rules for what you can try are far less specified.

However, I'm worried that the "feats and ability levels gate what you can try" model is so baked into PF2E that it's going to turn out to be more of an issue than it was with PF1E. Lots of the skill unlocks and such really are just bonuses to actions, which isn't a problem. But, tying lots of feats to skills mean that instead of just a list of new powers you can get, the rulebook becomes in part a list of all the things you can't try to do with a skill. There is a danger of Pathfinder 2 being "Pathfinder: the Potion Sponge Edition". New feats will inevitably come out. As much as I'd like to see the Player Companion and Campaign Setting lines become all setting information, with new mechanics limited to items (but no potion sponges), NPCs, monsters, the very occasional rare spell, and locations, I know that cool new powers for your character is what sells. So, we'll be showered with a constant stream of feats, just as we are in Pathfinder. How many of those new feats are going to be things that gate something that previously we thought we could just try? Hard to say, but the design of PF2E as it exists leans pretty heavily on that kind of thing.

[thorin001]

Marc Radle wrote:

It seems fair to say that the ‘tight math’ concept of Pathfinder 2E is more or less equivilant to D&D 5E’s ‘bounded accuracy’ concept

Very much so. They just used a lot of rules to disguise it.

[Vic Ferrari]

Marc Radle wrote:

It seems fair to say that the ‘tight math’ concept of Pathfinder 2E is more or less equivilant to D&D 5E’s ‘bounded accuracy’ concept

Doesn't seem fair, to me. You do not add your proficiency bonus -2 to everything, and many rolls are straight ability checks.

[Deadmanwalking]

thorin001 wrote:

Marc Radle wrote:

It seems fair to say that the ‘tight math’ concept of Pathfinder 2E is more or less equivilant to D&D 5E’s ‘bounded accuracy’ concept

Very much so. They just used a lot of rules to disguise it.

Not quite.

In PF2, accuracy is bounded within each level, but not between, say, 1st and 20th levels. This makes a huge difference from 5E, as it makes level differences much more meaningful. In 5E a 1st level character can hit a 20th level one fairly readily, and swarms of low level enemies are thus a real problem. In PF2, this is very much not the case and fighting foes more than 4 levels above you tends to be suicide even in large numbers.

It has similar effects in terms of on-level opposition, but that doesn't make it the same thing.

As to the main topic:

I think people here are equating tighter math and a low chance of success in a manner that is not necessarily true. Both are true of PF2 at the moment, but they are not actually linked. You can reduce every DC in the game by 5 and the math is equally tight, while chances of success increase drastically. After all, tight math has to do with there being a limited variance between PC chances, not what those chances are at the high end.

And a reduction of that sort is basically what I've been advocating in various threads (well, probably not dropping them all by 5, but dropping almost all of them all by 2 seems a definite possibility). I like the tight math, but think it's currently calibrated with a lower chance of success for PCs than is ideal. And changing this is very doable.

[Vic Ferrari]

Yeah, math tweaks like this are relatively easy, 5th Ed played around with the maths right up until the end (when they decided on Proficiency Bonus).

[Scythia]

Let's look at a lv 15 character. At 15, the DC for a level appropriate skill check is 35, basically 20+level. So, before we factor in ability mod and proficiency rank bonus the PC would have to roll a 20 on the die to succeed. Let's add in +6 for ability mod, say they really wanted to be good so they began with an 18, and used at least two of their ability bonuses on the stat (three wouldn't matter due to the minimization of increase after 18), and they have a potency item. This brings the needed roll to 14 or higher. Let's say they're legendary at the skill, so add in the 'legendary' +3. That brings the needed roll to 11 or higher. Literally doing everything they could to be good at a skill gives them slightly less than half a chance to succeed. Anyone who hadn't focused every bit of available resources on that skill would have an even worse chance. Additionally, 11 or higher means that the +10 = crit rule is effectively meaningless to the character.

Now, it's true that some skills have high quality tools that can add a bonus, and there are buff spells that can help, but applying those still only gets you to around 8 or higher (7 might be possible, but I haven't seen the stars align perfectly yet), which means it takes special tools and/or your allies buffing you to get to where you really ought to be on your own when you put so much character resources and effort into being really good at something.

[StratoNexus]

Deadmanwalking wrote:

I like the tight math, but think it's currently calibrated with a lower chance of success for PCs than is ideal. And changing this is very doable.

I agree. Keeping the variance smaller than PF1 is a good goal and while I would prefer a variance that is slightly larger (~4 points more) the current range can work for my games. An adjustment to the difficulties I think can make this system robust and fun as opposed to robust and a bit punititive.

Scythia wrote:

Let's look at a lv 15 character. At 15, the DC for a level appropriate skill check is 35, basically 20+level.

Scythia wrote:

Literally doing everything they could to be good at a skill gives them slightly less than half a chance to succeed. Anyone who hadn't focused every bit of available resources on that skill would have an even worse chance. Additionally, 11 or higher means that the +10 = crit rule is effectively meaningless to the character.

To be fair, 35, is the High difficulty, but I agree with your point. In my opinion, if you have focused on a skill to the extent that you have done everything you are able to improve it, then the Extreme difficulty (which would be 40 at level 15) is what should be 50/50.

[Scythia]

StratoNexus wrote:

Deadmanwalking wrote:

I like the tight math, but think it's currently calibrated with a lower chance of success for PCs than is ideal. And changing this is very doable.

I agree. Keeping the variance smaller than PF1 is a good goal and while I would prefer a variance that is slightly larger (~4 points more) the current range can work for my games. An adjustment to the difficulties I think can make this system robust and fun as opposed to robust and a bit punititive.

Scythia wrote:

Let's look at a lv 15 character. At 15, the DC for a level appropriate skill check is 35, basically 20+level.

Scythia wrote:

Literally doing everything they could to be good at a skill gives them slightly less than half a chance to succeed. Anyone who hadn't focused every bit of available resources on that skill would have an even worse chance. Additionally, 11 or higher means that the +10 = crit rule is effectively meaningless to the character.

To be fair, 35, is the High difficulty, but I agree with your point. In my opinion, if you have focused on a skill to the extent that you have done everything you are able to improve it, then the Extreme difficulty (which would be 40 at level 15) is what should be 50/50.

High is the category suggested for most checks.

[pjrogers]

Has there been any thought or discussion of a declining rates of return approach? For example, every skill modifier greater than twice the character's level only provides a 0.5 increase.

Say, you had a 5th level character with 5 ranks in Perception and an additional 10 points of ability mods, feats, etc.. Currently, that would be a +15, but the quick and dirty declining rates of return model I describe above would make that a +12 (10 unmodified because it's twice the character's level and then the remaining 5 halved to 2).