What are the maximum bonuses of each type possible?

Question

Different types of bonuses are valued differently by the Pathfinder 1e system. Some, like Enhancement bonuses, are easy to increase to very large amounts. Because duplicate bonuses don't stack, this means that abilities giving small enhancement bonuses aren't terribly useful. Other bonus types, like Trait bonuses, tend to be much smaller and rarer and even a +1 bonus is valuable. The different values also vary depending on what is being buffed: resistance bonuses are very common for saves, but unheard of for attack rolls. The goal of this question is to produce an objective numeric quantification of how valuable different bonus types are in different situations, for the purposes of creating homebrew and optimising characters.

For every combination of a bonus type and one of attack rolls and AC; saving throw bonuses and save DCs; skill bonuses and skill DCs; or ability scores, what is the highest possible bonus of that type which can be achieved in Pathfinder without using exploits? Assume all first party material is available which would be accessible to a typical 20th level party with standard WBL. "Exploits" here refers only to tricks which any reasonable person would say Paizo didn't intend to be possible. If in doubt, include it.

For Armor, Shield and Natural Armor bonuses give the raw values before enhancement bonuses are applied. For enhancement bonuses to attacks and AC, give the largest single enhancement bonus which ultimately applies to your attack/AC, even if it's technically an enhancement bonus to your armor/shield/natural armor bonus.

Answer 1

Below is the highest bonuses I have been able to find for each combination. I do not have comprehensive knowledge of the system, so there may be room for improvement.

Bonus type	Attacks & AC	Saves & Save DCs	Skills & Skill DCs	Ability Scores
Alchemical	+6 Grand Mutagen	+5 Antitoxin	+5 Gravelly Tonic	+8 Grand Mutagen
Armor	+9 Stoneplate	+0	+0	+0
Circumstance	+7 Extend the Bulwark*	+5 Emboldening Strike	+20 Focused Trance	+0
Competence	+10 Burglar Boots (Major)	+10 Burglar Boots (Major)	+10 Burglar Boots (Major)	+0
Deflection	+13 Smite Evil**	+0	+0	+0
Dodge	+13 Canny Defense (Kensai)	+0	+0	+0
Enhancement	+5 Magic weapon, armor, etc	+0	+10 Tears to Wine***	+8 Physical Enhancement
Inherent	+0	+0	+0	+5 Wish
Insight	+10 Sudden Insight	+10 Danger Sight	+20 Third Eye	+0
Luck****	+10.5 (average) Bit of Luck	+4 Lucky Horseshoe	+10.5 (average) Bit of Luck	+0
Morale	+4 Greater Heroism	+4 Greater Heroism	+4 Greater Heroism	+8 Mighty Rage
Natural Armor	+8 Form of the Dragon III	+0	+0	+0
Profane	+10 Vindicator's Shield	+6 Desecrate	+4 Domain Specialisation	+6 Energumen
Racial	+1 Lasting Grudge or +2 Tribalistic (only applies to aid another checks)	+4 Desert Runner	+10 Aquatic Ancestry	+2 any race*****
Resistance	+0	+6 Warding Talisman	+0	+0
Sacred	+10 Vindicator's Shield	+6 Consecrate	+4 Domain Specialisation	+4 Glorious Aura
Shield	+4 Shield	+0	+0	+0
Size	+8 Fine Size	+0	+16 Fine-sized Stealth******	+10 Magical Beast Shape
Trait	+2 Hard to pin down	+2 Hex-Proof	+2 Aerial Observer	+0

*Assumes character is wearing +5 Stoneplate armor

** Assumes an ability score of 36; this can be improved further by optimising ability score bonuses

*** This is the only enhancement bonus to skills I was able to find. I suspect it may have been supposed to be a competence bonus.

**** Luck bonuses can all be increased by 1 via the Fate's Favored trait.

***** There are races which have +4 or more to their stats, but they are only available with GM permission and therefore disqualified for this question.

****** This isn't called out as a size bonus in the Stealth skill itself, but the racial modifiers listed in every small race say it's a size bonus.

Answer 2

The answer by pi4t covers most things accurately.

There are, however, a handful of edge cases because of ‘special’ things in the rules that are not covered by that.

Circumstance bonuses

Circumstance bonuses can theoretically be arbitrarily high if you do not require that the answer is a single source. Per the rules: ‘Circumstance bonuses stack with all other bonuses, including other circumstance bonuses, unless they arise from essentially the same source.’. What this means is that you can have multiple things contributing circumstance bonuses to the same value. However, it’s impossible to say a ‘max’ here if we accept this, because just about anything that could logically improve the chances of something succeeding can provide a circumstance bonus (that’s the whole point of circumstance bonuses, they’re supposed to be the ‘catch all’ for things the rules don’t explicitly cover).

Dodge bonuses

The max possible dodge bonus is also complicated, because unlike most other bonus types, dodge bonuses do stack with themselves. There are a lot of feats and class features that give dodge bonuses though, but many of them are conditional in some way, so it’s difficult to get an exact max. A quick cursory attempt suggests a total of +25 against attacks by an enemy who is only threatened by you and who is wielding a weapon from a specific fighter weapon group by:

• Having an INT of 36 and DEX of 13 as a prerequisite
• Having 13 levels in Kensai and wielding your chosen weapon to get +13 from Canny Dodge
• Having 4 levels in Gunslinger, taking the Frantically Nimble dare in place of the level 4 Gunslinger bonus feat, and having no grit points to get +2 from Frantically Nimble
• Having the Dodge feat for +1
• Having the Artful Dodge feat for +1 while you are the only ally threatening a given opponent
• Having the Defensive Weapon Training feat for a +2 against the fighter weapon group your foe’s weapon belongs to
• Taking the Total Defense action for a +4
• Being a Halfling and having the Cautious Fighter feat for a further +2 while taking the total defense action

It’s theoretically possible to go even higher than that by coming up with a more contrived scenario (for example, if both you and your opponent are using reach weapons, you can also add the feat Just Out of Reach for a further +2), but this gets increasingly difficult to compute because most things that give a Dodge bonus have more specific criteria than those listed above.

Racial bonuses

In theory, racial bonuses also stack with themselves. However, this is essentially never relevant in practice, since racial bonuses are functionally always tied to your race and are lost when your race changes in some way.

Natural armor bonuses

Natural armor bonuses are special, and arguably not in a good way, because there are some very specific things that directly increase an existing natural armor bonus without being an ‘enhancement to natural armor’, which gets around the stacking requirement and avoids violating the limitation on enhancement bonuses to natural armor.

The most interesting one is a feat called Improved Natural Armor, which increases an existing natural armor bonus by 1 and can be taken any number of times. This is technically a ‘monster’ feat, but RAW there is not technically anything preventing a PC from picking up ‘monster’ feats that they meet the prerequisites for (the exact wording of the rules essentially amounts to ‘ask your GM, they may think this is too OP for a PC’). And Improved Natural Armor is one of the few that is actually easy to meet the requirements for since it just needs a CON of 13 and an existing natural armor bonus inherent to the creature. By picking a race with existing natural armor, starting with a CON of at least 13, and having a permissive GM and some single minded determination, you can use this to get a PC to a natural armor bonus of at least +13 at level 19 by starting with a Sahaugin for a +3 base natural armor bonus, and then taking Improved Natural Armor for every feat you get from odd-numbered levels. There may be a way to get it even higher, but I am not aware of any first-party race that gets better than a +3 baseline natural armor bonus, nor any first-party class that would allow taking Improved Natural Armor as a bonus feat.

However, it gets more interesting because of animal companions. They are not explicitly ruled out by the wording of the question, and they actually can get much higher natural armor bonuses than players (or most monsters) can because they get usually get a baseline natural armor bonus, usually get an increase to this baseline when their master hits a specific level, get further increases to this baseline for every 3 levels their master gains, and can also take feats (up to 8 total). If we ignore feats initially, we have a max of +23 for an ankylosaurus animal companion with a level 18 master (+9 base for an ankylosaurus, +2 more for the upgrade they get when their master hits level 7, and +12 total additional from their master being level 18). If we also factor in feats and assume they take Improved Natural Armor for all 8 possible feats, the total instead comes to +31.