Introduction
Understanding the number scale and how the resolution mechanic works is central to mastering any tabletop RPG. Pathfinder 2e is no different. For players of most d20-based games, including D&D, Pathfinder 2e’s degrees of success can introduce some complications. But when we look under the covers, what we find is actually pretty straightforward.
Table of Contents
Success, etc.
Pathfinder 2e, evolving from its roots in D&D, uses a d20 roll to represent randomness and unpredictability when attempting something challenging. Unlike D&D or PF1, PF2 uses “degrees of success”. Understanding the math behind degrees of success and how that maps to your d20 rolls can offer helpful insights when considering the value of different bonuses and penalties.
The possibility of critical success and critical failure further complicates this concept because a +1 bonus is more than just a 5% larger chance of success.
Consider a roll on which we succeed on an 11. In that case we get a critical failure on a 1, a failure on a 2 through 10, a success on an 11 through 19, and a critical success on a 20. We have a 50% chance of some sort of success and a 50% chance of some sort of failure.
Note that failure and success both account for 9 possible die rolls, while critical success and critical failure are only possibly on a natural 1/natural 20 because those rolls artificially alter your degree of success.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | (11) | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | (20) |
Now give your roll a +1 bonus, so instead of succeeding on an 11, you succeed on a 10. In this case, a natural 20 would beat the DC by 10 and would be a critical success. However, this doesn’t feel different because the outcome of a natural 20 is the same. The only practical change here is that a die roll of 10 is now a success.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | (10) | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | (20) |
This is somewhat misleading, and I chose to use this example specifically because this one case is misleading. It’s very easy to look a this case and say “+1 increases my odds of success by 5% and nothing more,” which undervalues the effect of that +1 bonus.
Consider another example: A character will commonly have an ability score of 18 in their Key Ability Score, and will hopefully be Trained in some skills attached to that ability score. Being Trained in something gives you a proficiency bonus of your level + 2, so a 1st-level character will often have a +7 bonus to skills to which they are well suited. As an example, a wizard with 18 Intelligence who is trained in both Arcana and Crafting will have a +7 bonus to use those two skills.
With that bonus in mind, consider the Level-Based DC’s table. A level 1 DC is 15. With a +7 bonus, you succeed on a roll of 8.
With that target roll set, we can consider the spread on the d20. A natural 1 remains a critical failure. 2 through 7 remain a failure. 8 through 18 are our success range. 18, 19, and 20 all get us more than 10 points over the DC, so those results give us a critical success.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | (8) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | (18) | (19) | (20) |
The value of +1
Continuing the example of a level 1 wizard, above, the impact of a single +1 bonus is much more apparent and interesting. Our critical success range now goes as low as 17, giving us a 4 in 20 (20%) chance to critically succeed. Our success range also moves down to 7 through 16, shrinking our failure range to just 2 through 6. A natural 1 remains a critical failure, but a critical success is now three times as likely.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | (8) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | (18) | (19) | (20) |
| 1 | 2 | 3 | 4 | 5 | 6 | (7) | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | (17) | (18) | (19) | (20) |
The +1 bonus changed the outcome of rolling a 7 and of rolling an 18, which means that there is a 1 in 10 (10%) chance of a +1 bonus improving your degree of success. It’s not a massive difference, but it will make a difference over time.
If you’re not convinced, next time you play count every time someone fails a roll by 1 or falls short of a critical success by 1 during the session.
Extreme Values
In unusual situations, such as players attacking a high-level monster or a player facing a horde of low-level monsters, your chances of success might be so high or your chances of failure might be so low that one of the degrees of success is outright impossible.
For example: Jo the level 1 champion finds themselves face to face with a lich, the inevitable big bad for their campaign. Jo decides to try their luck and attacks. They have a +7 attack bonus with their longsword, while the lich has an AC of 31. Jo needs to roll a 24 on the die to succeed on their attack roll. You will note that this is physically impossible.
A roll of 20 would still be a failure for Jo, but a natural 20 increases your degree of success by 1. In this case, since a 20 would be a failure, Jo can still succeed on a natural 20. However, their failure range runs from 15 to 20, and everything below that is a critical failure. A critical success is entirely impossible for Jo in this case.
Advancement
In D&D 5e there’s a clear curve where the game expects players to increase their primary ability score at levels 4 and 8, and then any increase in DC’s occurs to coincide with levels 4 and 8 or a level at which Proficiency Bonus improves.
Pathfinder 2e is no different, though the math is buried much more thoroughly.
To unbury the math, we can look at the skill proficiency bonus progression, the Level-Based DC’s table and the Armor Class and Strike Attack Bonus tables in the Gamemastery Guide’s rules for creating monsters. Comparing the progressions of these values and the Automatic Bonus Progression variant reveals exactly when the game expects players to start adding bonuses in various places.
Progression for Maximized Skills Using Key Ability Score
| Level | Max Skill Proficiency Bonus | Max Ability Modifier | Max Item Bonus | Total Bonus | DC | Succeed on roll of # | Automatic Bonus Benefit |
|---|---|---|---|---|---|---|---|
| 1 | +3 | +4 | – | +7 | 15 | 8 | |
| 2 | +4 | +4 | – | 16 | 8 | ||
| 3 | +7 | +4 | +1 | 18 | 6 | Skill Potency (one at +1) | |
| 4 | +8 | +4 | +1 | 19 | 6 | ||
| 5 | +9 | +4 | +1 | 20 | 6 | ||
| 6 | +10 | +4 | +1 | 22 | 7 | Skill potency (two at +1 each) | |
| 7 | +13 | +4 | +1 | 23 | 5 | ||
| 8 | +14 | +4 | +1 | 24 | 5 | ||
| 9 | +15 | +5 | +2 | 26 | 4 | Skill potency (one at +2, one at +1) | |
| 10 | +16 | +5 | +2 | 27 | 4 | 20 Key Ability Score | |
| 11 | +17 | +5 | +2 | 28 | 4 | ||
| 12 | +18 | +5 | +2 | 30 | 5 | ||
| 13 | +19 | +5 | +2 | 31 | 5 | Skill potency (two at +2 each, one at +1) | |
| 14 | +20 | +5 | +2 | 32 | 5 | ||
| 15 | +23 | +5 | +2 | 34 | 4 | Skill potency (three at +2 each, one at +1) | |
| 16 | +24 | +5 | +2 | 35 | 4 | ||
| 17 | +25 | +6 | +3 | 36 | 2 | Ability apex Skill potency (one at +3, two at +2 each, two at +1 each) | |
| 18 | +26 | +6 | +3 | 38 | 3 | ||
| 19 | +27 | +6 | +3 | 39 | 3 | ||
| 20 | +28 | +7 | +3 | 40 | 2 | skill potency (two at +3 each, two at +2 each, two at +1 each)22 Key Ability Score |
From the table above, we can see that for our absolute favorite skill (the one we increase first and which is tied to our Key Ability Score) starts out with a better than even chance of success and mostly gets easier over time, occasionally getting harder by 1 at a few levels.
The majority of your skills won’t be this good. You may not have item bonuses for most of your skills, and your relevant ability modifier may be much lower than your Key Ability Score. But the DC for success is no higher than 12 + your max proficiency bonus at that level. With ability score modifiers and item bonuses, you can easily reduce that so that even your lower skills succeed much of the time.
Unfortunately that means that Assurance won’t work on DCs appropriate for your level (I dig into that more in our Practical Guide to Assurance).
Armor Class
Next, let’s examine the players’ AC. There are a lot of variables to consider when looking at AC because you need to factor in proficiencies, Dexterity, and what armor a character is wearing. The table below is intentionally simplified, adding only your level to the base 10 AC and comparing that to the attack bonus of a monster of the same level according to the Strike Attack Bonus table in the monster creation rules.
| Lvl | Monster Strike Bonus (Moderate) | 10 + Level | Hits you on roll of # | Automatic Bonus Benefit |
|---|---|---|---|---|
| 1 | +7 | 11 | 4 | |
| 2 | +9 | 12 | 3 | |
| 3 | +10 | 13 | 3 | |
| 4 | +12 | 14 | 2 | |
| 5 | +13 | 15 | 2 | Defense potency +1 |
| 6 | +15 | 16 | 1 | |
| 7 | +16 | 17 | 1 | |
| 8 | +18 | 18 | 0 | |
| 9 | +19 | 19 | 0 | |
| 10 | +21 | 20 | -1 | |
| 11 | +22 | 21 | -1 | Defense potency +2 |
| 12 | +24 | 22 | -2 | |
| 13 | +25 | 23 | -2 | |
| 14 | +27 | 24 | -3 | |
| 15 | +28 | 25 | -3 | |
| 16 | +30 | 26 | -3 | |
| 17 | +31 | 27 | -4 | |
| 18 | +33 | 28 | -5 | Defense potency +3 |
| 19 | +34 | 29 | -5 | |
| 20 | +36 | 30 | -6 |
Now, that all looks super confusing and scary. An enemy hitting you on a -6 is clearly insane, and even hitting on a 4 at level 1 is terrifying.
But that tells us how much of a gap we need to close. The additional proficiency bonus on top of your level, your armor’s item bonus to AC, and your Dexterity need to be up to the task. There’s a ton of variation here because PF2 allows so much build versatility, but we can use some very simple examples to learn some things.
We’ll look at a wizard with 14 Dexterity in no armor, a rogue who is maxing their Dexterity in light armor (switching to gradually light armor or explorer’s clothing when appropriate), a barbarian in medium armor with enough Dexterity to fill out the Dex Cap, and a fighter with 12 Dexterity starting in chain mail before upgrading to half plate and finally full plate. The Champion will be +2 AC better than the fighter for big chunks of the level range, but that doesn’t add any additional learning to the table
| Lvl | Monster Strike Bonus (Moderate) | Wizard | Hit # | Rogue | Hit # | Barbarian | Hit # | Fighter | Hit # | Note |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | +7 | 15 | 8 | 18 | 11 | 18 | 11 | 17 | 10 | Fighter in chain mail |
| 2 | +9 | 16 | 7 | 19 | 10 | 19 | 19 | 10 | Fighter in half plate | |
| 3 | +10 | 17 | 7 | 20 | 10 | 20 | 10 | 21 | 11 | Fighter in full plate |
| 4 | +12 | 18 | 6 | 21 | 9 | 21 | 9 | 22 | 10 | |
| 5 | +13 | 20 | 7 | 23 | 10 | 23 | 10 | 25 | 12 | Defense potency +1 |
| 6 | +15 | 21 | 6 | 24 | 9 | 24 | 9 | 26 | 11 | |
| 7 | +16 | 22 | 6 | 25 | 9 | 25 | 9 | 27 | 11 | |
| 8 | +18 | 23 | 5 | 26 | 8 | 26 | 8 | 28 | 10 | |
| 9 | +19 | 24 | 5 | 27 | 8 | 27 | 8 | 29 | 10 | |
| 10 | +21 | 25 | 4 | 28 | 7 | 28 | 7 | 30 | 9 | |
| 11 | +22 | 27 | 5 | 30 | 8 | 30 | 8 | 34 | 12 | Defense potency +2 |
| 12 | +24 | 28 | 6 | 33 | 9 | 33 | 9 | 35 | 11 | |
| 13 | +25 | 31 | 6 | 34 | 9 | 34 | 9 | 36 | 11 | |
| 14 | +27 | 32 | 5 | 35 | 8 | 35 | 8 | 37 | 10 | |
| 15 | +28 | 33 | 5 | 36 | 8 | 36 | 8 | 38 | 10 | |
| 16 | +30 | 34 | 4 | 37 | 7 | 37 | 7 | 39 | 9 | |
| 17 | +31 | 35 | 4 | 38 | 7 | 38 | 7 | 42 | 11 | |
| 18 | +33 | 37 | 4 | 40 | 7 | 40 | 7 | 43 | 10 | Defense potency +3 |
| 19 | +34 | 38 | 4 | 43 | 9 | 43 | 9 | 44 | 10 | |
| 20 | +36 | 39 | 3 | 44 | 8 | 44 | 8 | 45 | 9 |
Looking at that scale is scary. There’s a lot of single-digit hit numbers.
Unarmored wizards are never better protected than they are at level 1, so strongly consider boosting your Dexterity at every 5th level. It’s not like you need to boost Strength or Charisma.
Light armor and medium armor have effectively the same AC, provided that you fill out the Dex Cap on your armor. Heavy armor comes out ahead by 1.
Regardless of what armor you’re wearingeapon, enemies matching your level with a moderate bonus to their strikes (the monster creation rules have a 4-tier scale and moderate is tier 2 of 4) will never need more than a 12 to hit you. Other bonuses (circumstance and status) are going to be very impactful, especially because a hit number below 11 means a growing likelihood of enemies scoring a critical hit.
Attacking
I’ve spent the past chunk of text scaring you, so it’s time to go on the offensive. Let’s look at player attack bonuses compared to enemies with moderate AC according to the Armor Class table in the monster creation rules.
To represent spellcasters, we’ll use the proficiency advancement rate for a typical full caster (cloistered cleric, druid, wizard, etc.) assuming that you’re maximizing your Key Ability Score at every opportunity. For weapon users, we’ll use the Barbarian’s proficiency with simple/martial weapons since the vast majority of weapon-using characters will advance at this rate, and we’ll again assume that you’re maximizing your Key Ability Score.
Note that I’m intentionally omitting the Fighter, which will typically have +2 better proficiency at any given level. Also note that spellcasters don’t benefit from the Attack Potency benefit since spell attack bonuses aren’t increased by items.
| Lvl | Monster AC (Moderate) | Full Caster Spell Attack | Hit # | Barbarian | Hit # | Automatic Bonus Benefit |
|---|---|---|---|---|---|---|
| 1 | 15 | +7 | 8 | +7 | 8 | |
| 2 | 17 | +8 | 9 | +9 | 8 | Attack Potency +1 |
| 3 | 18 | +9 | 9 | +10 | 8 | |
| 4 | 20 | +10 | 10 | +11 | 9 | |
| 5 | 21 | +11 | 10 | +14 | 7 | Martials hit Expert |
| 6 | 23 | +12 | 11 | +15 | 8 | |
| 7 | 24 | +15 | 9 | +16 | 8 | Casters hit Expert |
| 8 | 26 | +16 | 10 | +17 | 9 | |
| 9 | 27 | +17 | 10 | +18 | 9 | |
| 10 | 29 | +19 | 10 | +21 | 7 | Attack potency +220 Key Ability Score |
| 11 | 30 | +20 | 10 | +22 | 8 | |
| 12 | 32 | +21 | 11 | +23 | 9 | |
| 13 | 33 | +22 | 11 | +26 | 7 | Martials hit Master |
| 14 | 35 | +23 | 12 | +27 | 8 | |
| 15 | 36 | +26 | 10 | +28 | 8 | Casters hit Master |
| 16 | 38 | +27 | 11 | +30 | 8 | Attack potency +3 |
| 17 | 39 | +29 | 10 | +32 | 7 | Ability apex |
| 18 | 41 | +30 | 11 | +33 | 8 | |
| 19 | 42 | +33 | 9 | +34 | 8 | Casters hit Legendary |
| 20 | 44 | +35 | 9 | +36 | 8 | 22 Key Ability Score |
This reveals some very interesting insights.
For spellcasters, it’ll never be easier to hit than it is at level 1. Once you get into high levels, it’s actually harder to hit than it was below level 10, so it’s likely better to rely on saving throws unless you have other bonuses to your attacks.
For martial characters, things stay roughly the same for the full level range, provided that you’re buying potency runes for your weapon. Martials have roughly a +2 bonus to hit compared to spellcasters across most of the level range, meaning that attacks are consistently more effective for martial characters.
The pattern of the hit numbers also reveals an interesting pattern: your hit number will get gradually more difficult over several levels before you get an improvement, then your hit number will drop by a couple points. This means that not only do you get the bonus to stay on track, but the game’s math is actually engineered so that your upgraded attack bonus actually feels like an improvement rather than just keeping you perfectly on pace with the monsters’ AC progression.
What about Multiple Attack Penalty?
Multiple Attack Penalties (MAP) are a major component of making tactical decisions in combat. Martial characters might rush to make as many attacks as possible, but the MAP intentionally makes additional attacks less effective.
Based on the insights gained above, let’s assume that a martial character will typically hit on a roll of 8 on the die.
| Attack # | Regular Attack Hit # | Hit % | Crit % | Agile Weapon Hit # | Hit % | Crit % |
|---|---|---|---|---|---|---|
| 1 | 8 | 65% | 15% | 8 | 65% | 15% |
| 2 | 13 | 40% | 5% | 12 | 45% | 5% |
| 3 | 18 | 15% | 5% | 16 | 25% | 5% |
To be succinct: You’re not going to hit with that third attack unless you’re using an agile weapon, and even then the odds are poor. Save your third Action for something more impactful.
What do I do with this information?
There are a lot of takeaways here.
- A +1 has a 10% chance to affect the outcome of a roll unless the die roll you need to succeed happens to be 11.
- Your best-case scenario with skills is very good. You can afford not to put expensive resources (expensive items for item bonuses) into your best skill.
- Enemies of your level are going to hit you most of the time. Many enemies will be below your level, but when they’re not you need to be cautious and look for AC bonuses.
- Casters will rarely have better than 50/50 odds to hit spell attacks, so saving throws are likely more effective.
- Martial characters will hit on an 8 through most of the level range, meaning that you can expect to crit on 18+. Fighters have another +2 to hit on top of that, so a fighter using a simple or martial weapon might crit as much as 1 out of every 4 strikes (25% of the time, ignoring Multiple Attack Penalty).
- Multiple Attack Penalties are no joke. Unless you’re using an Agile weapon, you’re unlikely to hit enemies of your level with your third attack, and even then the odds are poor. Critting beyond your first attack is nearly impossible without a natural 20.
Now with those data points in mind, you’re that much better equipped to optimize and play your character.
