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41.4% Better
With the playtest of Pathfinder 2nd Edition, many people are digging down to mathematical fundamentals in their delight or discomfort with new rules. We have Proficiency modifiers are too low and Level bonus, explain why we need it. The thread The return of linear martials and quadratic casters, and how to address it harks back to the old trope of Linear Fighters and Quadratic Wizards.
The predecessor to Pathfinder, Dungeons & Dragons 3rd Edition, is quadratic. You can see this in its level progression. Second level required 1000 experience points. Third level required 2000 more, for a total of 3000. Fourth level required 3000 more, for a total of 6000. The progression 0, 1000, 3000, 6000, 10000, 15000, 21000, 28000, 36000, 45000, 55000, 66000, etc. is given by the 2nd-degree formula 500×(n^2) - 500×(n). Another sign of D&D 3rd Edition being quadratic is the frequent dead levels that have no new class features at higher levels.
Pathfinder, in contrast, is exponential. This is better than quadratic.
The fast experience progression for leveling in Pathfinder 1st Edition is:
0, 1300, 3300, 6000, 10000, 15000, 23000, 34000, 50000, 71000, 105000, 145000, ....
This grows first near the same rate and later much faster than D&D 3rd Edition's quadratic progression. It strongly resembles the offset exponential sequence:
0, 1300, 3100, 6000, 10000, 15000, 23000, 34000, 49000, 72000, 104000, 150000,...,
which follows the formula 3000×(1.43^(n-1)) - 3000 with some rounding. If we pretend that every character starts first level with 3000 unrecorded experience points, then it is exponential. Childhood in Pathfinder must be quite an experience.
Pathfinder 2nd Edition hides its experience progression under a rescaled 1000 xp per level, but the experience points by creature level in both 1st Edition and 2nd Edition tell the same story of expoential growth. In 1st Edition CR 1 is worth 400 xp, CR 2 is worth 600 xp, CR 3 800 xp, CR 4 1200 xp, CR 5 1600 xp, CR 6 2400 xp, CR 7 3200 xp, CR 8 4800 xp, CR 9 6400 xp, etc. In Table 4: Creature XP and Role in the 2nd Edition playtest Bestiary we find Party’s level – 4 is worth 10 xp, Party’s level – 3 is worth 15 xp, Party’s level – 2 is worth 20 xp, Party’s level – 1 30 xp, Party’s level 40 xp, Party’s level + 1 60 xp, Party’s level + 2 80 xp, Party’s level + 3 120 xp, and Party’s level + 4 160 xp. The 1st-Edition sequence--400, 600, 800, 1200, 1600, etc.--is 40 times the 2nd-Edition sequence--10, 15, 20, 30, 40, etc.--but they grow at the same exponential rate, doubling every two levels.
Since the square root of 2 is 1.414, doubling every two levels gives a ratio of 1.414 between consecutive numbers--10, 14, 20, 28, 40, etc.--but Paizo rounded them to multiples of 5. That is a 41.4% improvement at each level.
41.4% is a good number. If the level-up improvement were only 15%, as it is in many video games, then players would shrug and think that the new perk is nice, but not important. If the level-up improvement were 100%, doubling the power, then the character would be transformed at every level, messing up consistency and trivializing former opponents. We players want enough improvement to eagerly anticipate the level-up but not so much improvement to feel helpless if it is delayed.
A linear progression has improvement ratios that start high but shrink. The linear progression 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, ... , 5 + 5×(n) has ratios 15/10 = 1.5, 20/15 = 1.33, 25/20 = 1.25, 30/25 = 1.2, 35/30 = 1.17, 40/35 = 1.14, ..., so it shrinks well below 41% improvement.
A quadratic progression can mimic the improvement ratios of an exponential progression much longer. The quadratic progression 10, 14, 20, 28, 38, 50, 64, 80, 98, 118, ... , n^2 + n + 8 has ratios 14/20 = 1.4, 20/14 = 1.43, 28/20 = 1.4, 38/28 = 1.36, 50/38 = 1.32, 64/50 = 1.28, ..., and it too drops below 41% improvement.
A fourth kind of curve sometimes appears in Pathfinder. The combat effect of increasing AC is the reciprocal of a linear sequence: 20/6, 20/5, 20/4, 20/3, 20/2, 20/1, 20/1, 20/1, etc. Its ratio increases; in fact, if not for a natural 20 always hitting, it would go asymptotic to infinity. The ratios increase until the nat-20 cap: 1.2, 1.25, 1.33, 1.5, 2, 1, 1, etc. The reciprocal sequence is very swingy and hard to balance in the game. I suspect that this was the main reason D&D 3rd Edition and Pathfinder 2nd Edition severely restricted increases to AC.
Measuring Improvement
Imagine a ranger that tracks wild dire boar for hunts by aristocrats. He has to help fight the boar, too. Let's say the 2nd-level ranger has a +3 STR bonus, +3 DEX bonus, a masterwork sword, a masterwork bow, BAB +2, and his favored enemy is animals, giving a +2 bonus on weapon attack and damage rolls against dire boar. That gives an attack bonus of +8. The boar has AC 15. The ranger must roll 7 or higher, 14 chances out of 20, to hit the boar.
The ranger levels up to 3rd level. His BAB is +3. 3 is 50% better than 2, right? No, I knew that you would not fall for that silly statement. The value of the BAB is based on his chance of hitting. He previously had 14 chances out of 20 of hitting the bandit. Now he has 15 chances out of 20. 15/14 = 1.071, so he became 7.1% better.
In addition, he bought a +1 sword. That improves his damage from 1d8+5 to 1d8+6, 10.5% better. But he still uses his old bow, so his damage is 10.5% better only 50% of the time, so overall his damage is only 5.3% better. Thus his damage per attack is 12.8% better, (1.071)(1.053) = 1.128.
How much improvement should there be? Combat can be split into three parts, each of which contributes to the 41.4%: defense, battlefield control, and offense. Defense keeps the character alive, battlefield control enables winning, and offense wins. Offense is a favorite, so its improvement has to at least match the improvement in defense and battlefield control. We want at least 12.2% improvement to offense at each level-up, calculated as the cube root of 1.414 rather than as one third of 41.4%. The effects of the three areas of combat are multiplicative rather than additive.
His other improvements are 6 more hit points, the Endurance feat, favored terrain, and his 3rd-level feat.
- Let's suppose the ranger has Con 10 and had 16 hit points at 2nd level. Six more is a 37% increase when compared to the point (0 hp) where the ranger would become unconscious and a 23% increase when compared to the point (-10 hp) where he would die. Let's rate that as the average, a 30% improvement.
- Endurance seldom affects combat itself and this is a combat rating.
- Favored terrain gives him +2 to initative in the forest. Winning initiative is a one-turn advantage on a two-turn encounter, and gives him flat-footed opponents with a -1 loss of Dex to AC. The whole formula for that is his chances to hit increase from 13/20 + 13/20 to 14/20 + 13/20 + 13/20, but only 60% of the time instead of 50%, so the improvement ratio is ((0.6)(40/20)+(0.4)(26/20))/((0.5)(40/20)+(0.5)(26/20)) = 34.4/33 = 1.042, a 4.2% improvement.
- For his feat, let's use Dodge, a +1 to AC. A breastplace and Dex 16 give him AC 19, versus the +8 gore attack of a boar, so AC 20 reduces his chance of being hit from 10/20 to 9/20. We look at the ratio upsidedown to see the improvement, because we want a lower number. 10/9 = 1.111, an 11.1% improvement.
We multiply the combat improvement ratios together, (1.128)(1.3)(1.042)(1.111) = 1.698, a 69.8% improvement. That is better than 41.4%, enough better that it is a little unbalanced. The ranger has the advantage that he is specializing in boar hunting in the forest. If he had to make saving throws against spells or deal with a wide variety of terrains, I would be adjusting his improvements downward because sometimes they would not matter.
After another year of boar hunting, the ranger levels up to 4th level. His BAB is +4 and he buys a +1 bow. His attack roll is now 6.7% better (16/15 = 1.067). His damage is now improved from 50% 1d8+5 and 50% 1d8+6 to 100% 1d8+6, 5% better. Overall, his damage per attack is 12.0% better.
Notice that though the ranger's advancement to 4th level has essentially the same new element to offense as his advancement to 3rd level, the amount of improvement is slightly less, 12.0% instead of 12.8%. Adding the same thing is a linear improvement, and linear progressions don't keep up with exponential progressions. Likewise, when he gains another 6 hit points, it is 6 out of 22 rather than 6 out of 16, so the same element to defense is only a 23% improvement instead of a 30% improvement. Fortunately for the ranger, he gains two other big improvements at 4th level, Hunter's Bond and one 1st-level ranger spell. I will skip measuring the total improvement because the measurement of exotic effects like Hunter's Bond is very difficult.
Moving the Goalposts
Providing a 41.4% improvement at each level for a primary spellcaster, such as a wizard, is simple. The spellcaster gains a new spell level every two character level. If the power of the spells at the new level is twice the power of the spells obtained two levels before, then the power of the spellcaster doubles in two levels. However, Pathfinder tends to give more range and versatility to higher level spells in exchange for not doubling the damage, because damage growing exponentially would lead to easy kills.
Martial characters, in contrast, have to assemble their exponential improvement out of linear progressions such as Base Attack Bonus and hit points. Feats also appear regularly. In theory, higher-level feats coul be more powerful, like spells are. In practice, Pathfinder 1st Edition usually uses feat chains rather than level restrictions. Once the chain ends, the character begins a new chain with low-level feats, which reverts the feats to linear growth. Many class features, such as a rogue's sneak attack damage, increase linearly, too.
Despite linear growth mechancis, martial characters use a trick to manipulate the improvement curve to mimic 41.4% growth. Improvement due to increasing attack bonus is measured relative to the AC of the opponent. Changing the AC changes the numerical value of the improvement. I call this trick Moving the Goalposts.
Ava was a 1st-level paladin helping her order stop Lamashtu cultists. Her strength was 13, so her total attack bonus was +2. The cultists had AC 15, so she hit on a 13 or higher, 8 chances out of 20. She advanced to 2nd level while fighting cultists. With her improved BAB, she hit 9 chances out of 20, a 12.5% improvement.
The cultist hired local thugs to defend them. The thugs had AC 16, so Ava hit 8 chances out of 20. She advanced to 3rd level while fighting thugs. With her improved BAB, she hit 9 chances out of 20, a 12.5% improvement.
The paladins defeat the thugs and find the cultist's secret lair. The guards in the lair had AC 17, so Ava hit 8 chances out of 20. She advanced to 4th level while fighting guards. With her improved BAB, she hit 9 chances out of 20, a 12.5% improvement.
The cultist leader sent their death squads after the paladins. The death squads had AC 18, so Ava hit 8 chances out of 20. She advanced to 5th level while fighting death squads. With her improved BAB, she hit 9 chances out of 20, a 12.5% improvement.
Changing her foes let me force Ava's chance of hitting back to 8 chances out of 20. So long as she repeatedly advances from 8 chances out of 20 to 9 chances out of 20, her repeated improvement in offense is an unvarying 12.5%.
Is this an appropriate method for setting up challenges? No, it is a delaying tactic. Moving the goalposts keeps the battles the same, so that each new level and each new enemy seems the same. Repeated too often, leveling up against unreachable goalposts because a treadmill (Vic Ferrari's words) or a Red Queen's Race (Jester David's words).
Moving the goalposts does buy time. After buying time and reaching an appropriate level, the player character will receive a boost in offense besides a routine +1 to BAB. Perhaps the character selects a powerful combat feat. At 6th level full BAB characters receive an extra attack. With a non-BAB improvement to combat effectiveness, the GM does not have to move the goalposts to achieve the designed improvement. The character will probably exceed the goal. Afterward, combat will feel more advanced as the player uses the new feature.
And sometimes we can move the goalposts without changing the opponents. Voluntary methods persuade the player to give chances at hitting in exchange for something better. And that something better makes combat different and new.
Consider Power Attack in Pathfinder 1st Edition. Before 4th level, it gives a -1 penalty to hit in exchange for +2 to damage. Imagine that Ava learns Power Attack at 3rd level. I don't have to increase the AC of her foes by 1, because she has voluntarily accepted a -1 penalty. Power Attack shrinks her 9 chances out of 20 back down to 8 chances out of 20. At 4th level, that -1 penalty has increased to -2, so once again the game does my work of challenging Ava. I need to increase the hit points of her foes, due to the extra damage from Power Attack, but not their AC. Increasing hit points is easier.
Other feats give penalties to attacks: Two-Weapon Fighting, Rapid Shot, and Combat Expertise. Switching to combat maneuver rolls instead of attacks against AC could also shift odds of success downward, putting the goalposts where the GM wants them.
Many players don't use those voluntary options. Fortunately for Pathfinder 1st Edition, at 6th level the full BAB classes have a new penalty, -5 to their second attack.
At 5th level, Ava was still fighting foes with AC 18, this time they're bandits. She was using Power Attack regularly, so with Strength 13, BAB +5, a +1 sword, and the -2 penalty from Power Attack, she needed to roll a 13 or higher to hit, 8 chances out of 20. She advanced to 6th level while fighting bandits. With her improved BAB, she hit hit on a 12 or higher, 9 chances out of 20, a 12.5% improvement. But she also gained a 2nd attack. On that 2nd attack, she need an 17 or higher to hit, 4 chances out of 20. But those extra 4 chances are an additional improvement.
Ava now has a reason to make full attacks. Going from standard attacks at 5th level, with 8 chances out of 20, to full attacks at 6th level, with 9 chances followed by 4 more chances, has an improvement ratio of (9+4)/8 = 1.625, an enormous 62.5% improvement! We cannot assume full attacks every turn, so she sometimes does only 12.5% better a single attack. Combat with half standard attacks and half full attacks would mean that she goes from 8+8 chances on two turns (both standard attacks) at 5th level to 9+9+4 chances on two turns (one standard attack and one full attack), for a ratio of 22/16 = 1.375, a 37.5% improvement.
When Ava advanced to 7th level, she was still fighting bandits. Her kingdom had lots of bandits. Her 1st attack improved from 9 chances out of 20 to 10 chances out of 20, an 11.1% improvement. Her 2nd attack improved from 4 chances out of 20 to 5 chances out of 20, a 25% improvement. Her improvement ratio, still assuming half standard attacks and half full attacks, would be (10+10+5)/(9+9+4) = 25/22 = 1.136, an overall 13.6% improvement. And that is without moving the goalposts by increasing the AC of her opponents.
Advancing to 8th level while still fighting AC 18 bandits, Ava had a 10% improvement in her 1st attack and a 20% improvement in her 2nd attack. Her overall improvement ratio was (11+11+6)/(10+10+5) = 28/25 = 1.12, a 12% improvement. The boost from the 2nd attack began wearing off. I would raise the AC of her opponents again before 9th level.
That boost, fortunately, is renewed at 11th level with the 3rd attack. But the 3rd attack is not as influential as the 2nd attack, because it is one attack out of three rather than one attack out of two in a full attack. The linear growth in BAB adding 2nd and 3rd attacks turn the linear progression into a quadratic progresion, which can stay near exponential growth longer but not forever. Hence, in Pathfinder 1st Edition the martial classes fall behind the spellcasting classes past 11th level.
Pathfinder 2nd Edition
Pathfinder 2nd Editon removes the iterated attacks from BAB +6 and every +5 after that, and instead offers three Strike actions per turn. PF2 multiple attacks copy the -5 and -10 penalties of iterated attacks for the 2nd and 3rd attacks of the turn. While many martial characters may find themselves moving or raising a shield with the 3rd action, they will often make two attacks right from 1st level.
Gaining a 2nd attack is no longer a way to convert the BAB linear curve into a quadratic curve at 6th level, because the characters already have a 2nd attack.
The PF2 math does offer an effect like an extra attack. In Pathfinder 1st Edition, critical hits were a fixed percentage of all the hits with a particular weapon. In Pathfinder 2nd Edition, critical hits can also be a reward for hitting with an attack roll 10 more than necessary to hit. And that acts just like an extra attack at a -10 penalty.
I don't fully understand the Pathfinder 2nd Edition options, but I can investigate the options by sampling parts of individual classes and analyzing them.
Since extra attacks had a major effect on the improvement progression of a martial character in Pathfinder 1st Edition, let us sample the Monk class. Monks gain one more attack than most classes due to Flurry of Blows, which allows two unarmed Strike actions at the cost of one action slot, once per turn. (I will distinguish between performing an action and the three actions per turn by calling the latter "action slots".) I don't know for sure whether Flurry of Blows takes an additional multiattack penalty on its 2nd attack, but for the sake of more consistent mathematics, let's assume it does.
Hornet the human monk with nomadic background has scores Str 18, Dex 12, Con 10, Int 10, Wis 16, Cha 12 and has 3 spell points for her ki strike. Against an orc warrior AC 15 while using her ki strike to enhance her attack, her 1st unarmed attack hits on a roll of 9 or higher and deals 1d6+4 damage. Fists are agile, so her 2nd attack has a -4 multiattack penalty and her 3rd and later attacks have a -8 multiattack penalty. In a full four attacks against the orc she would have to roll a 9, 13, 17, and 17 to hit, except she does not have enough spell points for that many ki-strike attacks, so it would be 9, 13, 17, and 18.
At 2nd level, her proficiencies in unarmed attacks and unarmored defense increase with her level and she learns another monk feat. Thus, she would hit the orc warrior on 8, 12, 16, and 17, for a total of 13+9+5+4 = 31 chances out of 20 to hit. That is a 14.8% improvement in offense.
Hornet considers Tiger Stance. It would increase her damage die to 1d8 plus 1d4 persistent damage on a crit, but it costs an action to enter the stance. That increases Hornet's average immediate damage to 1d8+4, a 13.3% increase but losing the hit on a 17 4th attack is a 14.8% reduction in hitting (upsidedown ration 31/27 = 1.148). Oops, Tiger Stance deals 11.5 damage in that turn instead of 11.6. The 1d4 persistent damage, which has an 23.3% chance of being applied, makes up for the loss. If we count the persistent damage as applied once, Tiger Stance would be an overall 3.5% improvement. This would have been a clearer improvement if Hornet had strength 16, which would make the 1d8 damage die better in comparison.
Our first lesson is that the Pathfinder 2nd Edition action economy can be a serious penalty to multiple attacks, even when giving up the worst attack.
Hornet learns Monastic Weaponry instead, because a bo staff deals 1d8+4 damage in her hands and could be used with Flurry of Blows. That gives a 13.3% increase in damage. In addition, she becomes 22% better at throwing shuriken, a ranged attack at which she does not excel, but sometimes she will need a ranged option. Let's dub that a 1% increase (wild guess).
With expert proficiency in unarmored defense, Hornet's AC increased from 13 at 1st level to 14 at 2nd level. Against the orc warrior's +7 to hit, her AC-based defense increased by 7.7%.
Her hit points increasing from 18 to 28 is another 55.6% increase. Unlike Pathfinder 1st Edition, Hornet does not have a reserve of negative hit points to distinguish unconscious from dead, so both conditions have the same starting point, unlike 1st Edition. The severity of dying depends on a Fortitude save against DC 13, but we assume that fellow party members will revive her before that matters.
Thus, her overall increase in combat effectiveness is (1.148)(1.133)(1.01)(1.077)(1.556) = 2.182, a 118% increase. That is double power! First level is pathetic compared to second level.
Sadly, most of Hornet's improvement came from features that all classes receive: level to attack proficiency, level to defense proficiency, and hit points per level.
The monk's class features are set up linearly, possibly with frontloading at 1st level:
[list]
The nonlinear exceptions are unarmored defense proficiency increases at 1st, 13th, and 17th levels; unarmed attack proficiency increases at 1st, 3rd, and 13th levels; path to perfection increases at 7th, 11th, and 14th levels; fierce flurry at 9th level; and perfected form at 19th level. Those are not enough to make the growth exponential.
The only mechanism left to provide exponential progression, beyond the Moving the Goalposts trickery, is for the feats to increase in power by 41.4% per level, like spells do. Let's examine the monk feats. The easiest to compare are the ki feats that use spell points. The Ki Strike 1st-level feat gives a monk a spell point pool the same as a cleric's spell point pool.
Wholeness of Body, Feat 4, Power 2, gives a monk 2 more spell points and the ability to heal himself for 1d8+Wis (2d8+Wis at 6th level) by spending 2 spell points in a Verbal Casting. The cleric healing domain offers Healing Font, Power 2, by which the cleric can cast Heal (1d8+Wis plus 2d8 more for each heightening) for 1 spell point. The monk's feat is weaker and stops improving at 6th level.
Abundant Step, Feat 6, Power 3, gives a monk 2 more spell points and the ability to teleport himself a 10 feet within his line of sight by spending 1 spell point in a Somatic Casting. The distance auntomatically increases at 12th and 16th level. Given that somatic casting triggers an attack of opportunity, I don't see the advantage over walking or leaping. The wizard gains an identical feat at 8th level, so the monk is ahead of the wizard there.
Ki Blast, Feat 6, Power 3, gives a monk 2 more spell points and the ability to blast 4d4 force damage in a 30-foot cone by spending 2 spell points in a Somatic Casting and Verbal Casting. The damage heightens by 2d4. This is similar to the 5d6 elemental damage, heightens by 1d6, in a 30-foot cone from the sorcerer's Draconic bloodline Dragon Breath Power 3, which costs only 1 spell point. The monk's Ki Blast damage equals the sorcerer's Dragaon Breath damage at 16th level, but still costs twice the spell points.
Wild Winds Stance, Feat 8, Power 4, gives a monk 1 more spell point and a stance that increases AC by 1 and allows an unarmed 1d4 propulsive ranged Strike up to 30 feet away for 1 spell point. The wording seems to say that the spell point is spent to enter the stance rather than make the attack. This does not resemble any spellcaster power.
Wind Jump, Feat 10, Power 5, gives a monk 2 more spell points and the ability to fly for 1 minute by spending 2 spell points in a Verbal Casting. Before 12th level, the monk must land every turn. A potion of flying is 8th-level treasure costing 60 gp.
Wild Winds Gust, Feat 14, Power 7, gives a monk 2 more spell points and the ability to make an unarmed 1d4 propulsive ranged Strike against every creature in a 30-foot cone by spending 2 spell points in a Somatic Casting and Verbal Casting. The damage would be pathetic at that level, except that the monk could be using +3 handwraps of mighty fists for 4d4+2×Str damage, which still leave the damage less than the Ki Blast.
Quivering Palm, Feat 16, Power 8, gives a monk 2 more spell points and the ability to make a melee unarmed Strike that can kill the target on a critically failed Fortitude save by spending 2 spell points in a Somatic Casting and Verbal Casting. On a non-critical failure, the target is stunned for one round and the monk can try again.
Empty Body, Feat 18, Power 9, gives a monk 2 more spell points and the ability to turn ethereal for 1 minute by spending 2 spell points in a Somatic Casting and Verbal Casting. It is identical to Ethereal Jaunt, Spell 7, except it does not require concentration, so ending the spell is more difficult.
Thus, the monk's ki powers do resemble similar spellcaster powers but at double the spell point cost and with a few useless powers. Double the cost means half the uses, but half an exponential curve is still an exponential curve with the same improvement rate. I suspect the double cost is not from balance issues; instead because the Pathfinder 1st Edition monk's ki pool was a small pool, equal to 1/2 his monk level + his Wisdom modifier. The monk's use of ki was supposed to be infrequent.
In contrast to class feats, the ancestry feats do not go above feat 5, so past 5th level ancestry feats are purely linear. The non-skill general feats are limited to feat 1 and feat 2, except for Expeditious Search feat 7, so they likewise are linear. Skill feats come in levels 1, 2, 7, and 15. Do the 7th and 15th-level feats live up to their level? A 7th-level feat, on a 41%-improvement exponential progression, should be 8 times as powerful as a 1st-level feat, and a 15th-level feat should be 16 times as powerful as a 7th-level feat.
The Intimidation skill feats have Intimidating Glare and Quick Intimidation at 1st level; Group Coercion, Intimidating Prowess, and Lasting Coercion at 2nd level; Battle Cry at 7th level; and Scare to Death at 15th level. Battle Cry is an action-economy feat, allowing Demoralize as a free action when rolling initiative. It compares readily to Quick Intimidation, another action-economy feat that allows Coercion in one turns rather than ten turns. Battle Cry saves about one action out of six or nine; Quick Intimidation saves nine turns out of ten. The 1st-level feat seems more powerful. Scare to Death can kill a foe on a critical Intimidation success and a failed Fortitude save. It is not an attack, so a critical success is as easy as regular success on a third attack with its -10 multiattack penalty. It would be great, except for a bolster-against limitation that prevents repeating it until the Fortitude save fails. That makes it effective only as an opening action or against several enemies. It fails to meet the goal of 16 times as powerful as Battle Cry.
In the Athletics skill line, Quick Climber (7th) permits climbing at half land speed on a regular success and Legendary Climber gives a climb speed equal to land speed. The climb speed is not only twice as fast, it also removes flat-footedness, permits sneaking, and gives automatic success on ordinary climbs, so it is about 4 times as powerful as Quick Climber. But at 15th level, the exponential progression wants 16 times as powerful. Legendary Climber should be an 11th-level feat at the latest, especially since flying becomes more frequent around that level. For another comparison, Spider Climb, Spell 2, grants a 25-foot climb speed for 10 minutes. Spider Climb can be cast at 3rd level. Unlimited duration would make Legendary Climber appropriate for 11th level.
Sampling two skill lines shows that the skill feats do not keep up to the exponential curve.
Finally, I claimed that spells could keep a spellcaster on the exponential improvement curve if their power doubled every spell level. Do they?
Spell DC is the caster's level plus the modifier for his or her spellcasting ability score. Since it is level-based, all spells with saving throws are subject to the Moving the Goalposts effect. Outside of Moving the Goalposts, it is linear.
For the effects of spells, the arcane Wall spells make a convenient sample. Wall of Wind, Spell 3, stops arrows and creates difficult terrain. Wall of Fire, Spell 4, deters enemies from crossing with 3d6 fire damage, which is at least twice as powerful. Wall of Ice and Wall of Stone, both Spell 5, create actual walls, at least twice as powerful as Wall of Fire. Wall of Force, Spell 6, creates an wall that can block incorporeal creatures and is much stronger, twice as powerful as Wall of Ice. Blade Barrier, a different Spell 6, is more like Wall of Fire and deals 6d8 force damage on a failed Reflex roll. That is 2.5 times the damage, so it is not 4 times as strong as the comparable Spell 4 Wall of Fire. Chromatic Wall, Spell 5, has a random color and each color has different effects. Prismatic Wall, Spell 8, has all seven colors and their effects, which is a little short of 8 times as powerful but close enough.
The wall spell sample has the spells doubling in power with each spell level. The spellcasters can achieve the 41.4% improvement exponential curve.
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I confess I had too much time on my hands when the Paizo forums were down, so I just kept writing.
The TL;DR summary is that spellcasters can keep up with the exponential growth by level due to their spells improving. The martial characters cobble togther their exponential growth out of linear growth, an unstable balance that can be made more stable by forcing them to regain lost ground every level. Pathfinder 2nd Editon leans toward that boring lost-ground stability.
I am having a hard time following why 41.4% is relevant here. 41% is just the way experience scales. At best, it is a measure of time needed to advance if you are not challenging higher level foes. So the ranger hunting the same boars would need to spend 41% of his previous career to advance to the next level. It does not matter to characters fighting greater challenges at all; they experiance linear growth (every 13 encounters in 3.5).
The rest of the post seems to be a linear martials/exponential wizards comparison, which is correct but not new.
Am I missing something?
Very interesting. Would you say that there seems to be a problem with improvement for martial classes not keeping up with the exponential curve?
Sadly, most of Hornet's improvement came from features that all classes receive: level to attack proficiency, level to defense proficiency, and hit points per level.
The more the improvement comes from options that the player chooses (ie. feats) the better, so this is a little worrisome.
I guess an alternative solution could be to decrease the improvement for all classes to doubling in power every fourth level, making it easier for martial options to keep up. However, then the improvement per level is only 19% and thus close to the 15% that you argue is bad.
I am having a hard time following why 41.4% is relevant here. 41% is just the way experience scales. At best, it is a measure of time needed to advance if you are not challenging higher level foes. So the ranger hunting the same boars would need to spend 41% of his previous career to advance to the next level. It does not matter to characters fighting greater challenges at all; they experiance linear growth (every 13 encounters in 3.5).
The rest of the post seems to be a linear martials/exponential wizards comparison, which is correct but not new.
Am I missing something?
The 41.4% is both the time to advance and the amount of advance. Earning experience points is the time to advance, and it grows at 41.4% to reach the next level, though tougher challenges speed up the advance proportional to the challenge. The challenge rating system to design tougher challenges for each level tells the amount of advance, and it grows at 41.4% per level. The two rates do not have to be the same, but keeping them the same seems fair and that is what Paizo did.
The rest of the post is about what a 41.4% amount of advance means and the mechanisms by which 1st Edition and 2nd Edition achieve it.
Hmmmmm. This is thought provoking. I have been hoping to see crazier effects from high level feats. This could be a good way of estimating what such high level feats could be capable of.
Of course, if spellcasters do indeed become exponentially more powerful, comparing the capabilities granted by a feat vs a spell that casters would receive could achieve the same effect, adjusting for the expendable nature of the spell of course).
And would 2e's magic weapons help with the power of martial classes? adding damage dice instead of a +1 seems to be a large improvement. Or is this boost in damage just meant to counteract the comparative lack of flat bonuses that 1e had?
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It's almost like you are saying that the answer to life, the universe, and everything is "42".
41.4% *
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Very interesting. Would you say that there seems to be a problem with improvement for martial classes not keeping up with the exponential curve?
Sadly, most of Hornet's improvement came from features that all classes receive: level to attack proficiency, level to defense proficiency, and hit points per level.The more the improvement comes from options that the player chooses (ie. feats) the better, so this is a little worrisome.
I guess an alternative solution could be to decrease the improvement for all classes to doubling in power every fourth level, making it easier for martial options to keep up. However, then the improvement per level is only 19% and thus close to the 15% that you argue is bad.
It appears that the martials will keep up with the exponential curve, but it will mostly be a matter of having gigantic bonuses to attacks and armor class and less about performing interesting tactics.
Slowing down the improvement progression while keeping the same bonus progression of adding level to proficiency would mean that feats would be entirely crowded out. Speeding up the progression would create a gap that could be filled by better feats. However, I am accustomed to the 20-level progression using from original Dungeons & Dragons, through Advanced D&D, D&D 2nd Edition, D&D 3rd Edition, and Pathfinder 1st Edition. I don't want to change it.
Reducing the level bonus to proficiency would be a more conservative method, but we have only two workable rates: +1 per level or +0 per level. +1/2 per level would mean a massive increase in numbers at even levels and no increase at numbers at odd levels, which would make the levels behave very differently. In Pathfinder 1st Edition, we have +1/2 level to good saving throws, but those are only a small part of a character's numbers, so their even-level-only progression is smoothed out by other improvements in the character's numbers.
If the to-hit rates were higher, the effect of bonuses would be a small percentage. That is about the only smooth control we could manage with level to proficiency.
In contrast, hit point progression is easier to throttle down. Imagine an elf cleric, Con 12. At 1st level in Pathfinder 2nd Edition, the elf has 15 hit points due to 6 from ancestry, 8 from class, and 1 from Constitution. His hit points from 1st to 10th level would be 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, which means ratio increases of 60%, 37.5%, 27.3%, 21.4%, 17.6%, 15%, 13%, 11.5%, 10.3%.
Suppose we went to an exponential improvement in hit points rather than a linear improvement. A straight 23% increase would be 15, 18, 23, 28, 34, 42, 52, 64, 79, 97. But 23% is over half of the improvement per level, leaving little room for improvements that are more fun. A straight 13% increase would be 15, 17, 19, 22, 25, 28, 31, 35, 40, 45, and would leave more room for interesting feats.
And would 2e's magic weapons help with the power of martial classes? adding damage dice instead of a +1 seems to be a large improvement. Or is this boost in damage just meant to counteract the comparative lack of flat bonuses that 1e had?
I haven't analyzed the effect of magic weapons yet. The analysis will take a few days.
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And would 2e's magic weapons help with the power of martial classes? adding damage dice instead of a +1 seems to be a large improvement. Or is this boost in damage just meant to counteract the comparative lack of flat bonuses that 1e had?I haven't analyzed the effect of magic weapons yet. The analysis will take a few days.
I'm curious to see the real math of this but I just don't see how it keeps up. If you get 1 die of damage every 4 levels via magic improvements and enemies effectively get 1 full die of HP every level then I can only see you falling behind.
Like his cleric's HP. It goes from 15 to 51, that's more than a 3x increase and your damage a hit has not even doubled. Even if his HP only doubled (which is basically lv3) You've still not kept up your damage to HP assuming the same chances to hit.
So yeah, super curious how close or off my off the cuff math is to Mathmuse's real math.
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My takeaway from this is that mid- and high-level feats are rubbish. We knew that just by looking at them, but it's nice to see an analysis.
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There's also an elephant in the room: spells auto-scale, but martials need to spend their class feats to scale, which gives more room to casters for conceptual development, rather than running to keep up with the tide.
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There's also an elephant in the room: spells auto-scale, but martials need to spend their class feats to scale, which gives more room to casters for conceptual development, rather than running to keep up with the tide.
I've been pushing for scaling feats since 3.0 for exactly this reason. Why does anyone need to take Cleave, then Great Ckeave, then Greater Cleave, then Greatest Cleave? Taking Cleave should eventually scale up to better Cleaves as your character advances.
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And would 2e's magic weapons help with the power of martial classes? adding damage dice instead of a +1 seems to be a large improvement. Or is this boost in damage just meant to counteract the comparative lack of flat bonuses that 1e had?I haven't analyzed the effect of magic weapons yet. The analysis will take a few days.
Analyzing magic weapons was faster than I predicted, because Paizo shifted the cost of weapons to the same exponential scale, too! Well, not exactly the same, improvement in both cost and wealth per level is 46.8% rather than 41.4%. In Pathfinder 1st Edition, wealth by level followed the offset exponential formula (5000×1.3^n - 8000) gold pieces, but in Pathfinder 2nd Edition, it follows the formula (500×1.4678^n) silver pieces for level 4 and higher, and gives less wealth at levels 1, 2, and 3. 1.4678 is the 6th root of 10.
Type +1 magic weapon; Level 4; Price 100 gp
This expert weapon has a +1 weapon potency rune.
Type +2 magic weapon; Level 8; Price 500 gp
This expert weapon has a +2 weapon potency rune.
Type +3 magic weapon; Level 12; Price 2,000 gp
This expert weapon has a +3 weapon potency rune.
Type +4 magic weapon; Level 16; Price 10,000 gp
This master weapon has a +4 weapon potency rune.
Type +5 magic weapon; Level 20; Price 70,000 gp
This legendary weapon has a +5 weapon potency rune.
Further details on the pricing of weapons can be found on pages 370-372 under Runes. Yes, the complicated details came 25 pages before the simple price list: the rulebook layout is strange.
The rulebook lacked a PF1-style Wealth by Level table. Instead, Table 11-2, Character Wealth, on page 348 of the rulebook gives magic items and loose change by level. Extrapolating the value of the magic items from the value of magic weapons, I turned it all into cash values:
1st level 150 sp
2nd level 500 sp
3rd level 1,400 sp
4th level 2,350 sp
5th level 3,400 sp
6th level 5,000 sp
7th level 7,500 sp
8th level 11,200 sp
9th level 16,750 sp
10th level 24,000 sp
For higher levels, look back six levels and multiply by 10. In theory a 3rd level character could afford a +1 magic weapon for 1,000 sp, but in practice he would have to sell his other items for half price so his wealth would drop below 1,000 sp.
What is more likely is that the PC will find a magic weapon while adventuring. Party Treasure Gains rules and Table 11-1, Party Treasure by Level, suggest that between 3rd and 4th level, the party should find two 4th-level magic items in their loot. Given four party members, half of them will get to claim a 4th-level magic item by the time they level up to 4th level. The other half will have to wait.
What happens when a martial character acquires a +1 magic weapon at 3rd or 4th level? First, he probably trades in an expert-quality weapon for the magic weapon, so he does not gain any additional item bonus to attack rolls. The only effect is overcoming resistance bypassed by magic, hitting incorporeal creatures, and an extra weapon die. That extra weapon die is a lot. For a 1d8 weapon wielded with Str 18, that is an increase from an average of 8.5 damage per hit to 13 damage per hit, 52.9% better.
52.9% is better than 41.4%. Gaining the first +1 weapon improves combat better than gaining a level.
For the first +2 weapon, the chance of hitting increases, too. Assuming the martial character has a 60% chance to hit a level appropriate opponent, which means a 10% crit chance, an additional +1 to the attack roll means a 14.3% improvement in hits, because I count a crit as a double hit. 3d8+4 damage insteaad of 2d8+4 damage is a 34.6% improvement. Combined they give (1.423)(1.346) = 1.538, a 53.8% improvement.
The first +3 weapon begins to lost its luster (maybe not, I haven't considered magic properties yet, just the numbers). Once again a 14.3% improvement in hits, but the improvement in damage from 3d8+4 damage to 4d8+4 damage is only 25.7%. That is (1.423)(1.257) = 1.437, a 43.7% improvement overall. That is as good as leveling up.
This is bad, very bad. Magic weapons are more important than levels.
Do spellcasters also benefit from magic items that much? Well, the other 4th-level item the party could have found could have been a 4th-level wand with a wand of a 2nd-level spell. Giving that to a 4th-level sorceress who carefully conserves its charges and her resononace by using it only once per day gives her five 2nd-level spells a day rather than four, a 25% improvement. Or suppose the 4th-level magic item was Bracers of Armor 2nd, which give +2 to AC. That would reduce an enemy's hits against the spellcaster by 21%, or save the spellcaster the 2nd-level slot to cast Mage Armor.
Okay, a +1 magic weapons appears twice as beneficial as other 4th-level magic items.
I'm curious to see the real math of this but I just don't see how it keeps up. If you get 1 die of damage every 4 levels via magic improvements and enemies effectively get 1 full die of HP every level then I can only see you falling behind.
Like his cleric's HP. It goes from 15 to 51, that's more than a 3x increase and your damage a hit has not even doubled. Even if his HP only doubled (which is basically lv3) You've still not kept up your damage to HP assuming the same chances to hit.
So yeah, super curious how close or off my off the cuff math is to Mathmuse's real math.
Valeros did not have time to wipe the sweat off his brow as he took another swing at the evil elf cleric of Lamashtu. This fight was taking too long. The female cleric was his equal, "fourth level" as the fighter's guild ranked them, and she was tough. Valeros was tough, too, so he was going to win this battle, but he fondly remembered quickly hacking through the novice clerics of Lamashtu back when he was a novice himself. Experienced fighters--and clerics too--made for long battles. And for each round of battle, the mysterious masked leader of the Lamashtu cult was running farther away as he made his cowardly escape.
Due to symmetry, with each side gaining hit points at the a similar linear rate, the extra hit points don't affect who wins. Instead, they merely increase the length of the battle. That might be a problem for a blaster wizard who consumes valuable prepared spells each turn, and for the party healer will have to heal up the long-battered fighter afterwards, but the length of battle does not hinder the fighter himself.
How much does the battle lengthen? It is just as Chess Pwn calculated. The elf cleric at 1st level had 15 hp. Against 1d8+4 damage, that would take 1.8 hits to knock her out. At 5th level with 51 hit points, against a 2d8+4 magic weapon, it would take 3.9 hits. At 9th level with 87 hp against a 3d8+4 weapon, it would take 5.0 hits. At 13th level with 123 hp against a 4d8+4 weapon, it would take 5.6 hits. At 17th level with 159 hp against a 5d6+4 weapon, it would take 6.0 hits. This sequence converges to 8 hits long after 20th level. At 17th level with 159 hp a 5d10+4 weapon would take 5.0 hits and a 5d12+4 weapon would take 4.4 hits. Since Pathfinder 2nd Edition offers few ways to gain many more hits per turn than 1st level gives, combat will run longer.
At least rocket tag will no longer be a problem. But I think if I play a martial character at 17th level, I will favor a monk with Quivering Palm. A possible one-strike kill looks better than I thought.
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^^^ Should calculate how often Quivering Palm is gonna actually kill a level-equivalent enemy then. I'm sure you won't be that optimistic on it then.
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^^^ Should calculate how often Quivering Palm is gonna actually kill a level-equivalent enemy then. I'm sure you won't be that optimistic on it then.
Oops, I forgot that Quivering Palm needed a critical Fortitude failure to kill in less than one day. For a level appropriate opponent, that would require a natural 1 on the save after the hit, 1 time out of 20. That is worse than requiring 6 hits.
A regular failure could be managed on a roll of 3 or less versus a Water Yai Oni, comparable to 6 hits. Against many 17th-level human opponents, an 8 or less might fail. Alas, regular failure means the opponent could die later that month, which is no fun for either the monk or the target.
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Well Mathmuse, your analysis is very very interesting.
I have been thinking since the start that high-level feats should be GREAT, and style feats (bow shooting, TWF, etc...) should just scale and give more things when you level up instead of requiring the martial PC to take the next one.
This would keep their progression exponential, and also allow them to get multiple styles if they like (less power, but more versatility).
This is even more evident with ancestry feats. Give me the option to build a truly magic-resistant dwarf, or an elf with a vision that is beyond keen, when they reach the legendary levels!
There's also an elephant in the room: spells auto-scale, but martials need to spend their class feats to scale, which gives more room to casters for conceptual development, rather than running to keep up with the tide.
I have an entire herd of elephants in the room that I have avoided mentioning. Fortunately, it is a big room. The power that spellcasters gain from their feats in addition the the power they gain from their spells is part of a family of elephants that deal with characters that have multiple methods of success in adventuring.
I kept my analysis to pure martial characters and primary spellcasters because they are farthest from the multiple-methods elephants. But let's greet those elephants by considering the delightful jack of all trades, the bard.
A bard has many ways to contribute to the party: by attacking enemies with a weapon, by casting spells, by playing compositions, and by skills. The bard cannot be great at all of these, and the choice of muse at 1st level encourages the bard to specialize.
A bard character could have Dexterity 18 and fight in the front line of the party with a finesse weapon such as a rapier. Such a bard would try to cast buff spells, such as Magic Weapon, before combat and learn Lingering Composition to make more actions available during encounter mode. In contrast, another bard character could have Charisma 18 and rely on casting spells during combat from safely in the rear. A third bard character rely on magic without Charisma 18 by learning additional compositions, such as Dirge of Doom, and use them at optimal times.
My analysis of improvement would have to treat those three builds differently, as if they were three different character classes. I generally assume that combat is best defined by the character's best attacks. If the attack uses a limited resource, such as highest-level spell slots or spell points, then I average that attack by how much it can be used with the alternative attacks that don't require that resource. Defenses are always averaged, because a savvy enemy tries to attack weak points, but some defenses are tactical, such as a squishy wizard staying in the back.
In general, suppose a character uses one technique 80% of the time and another technique 20% of the time. A 10% improvement to the 80% technique would be a 8% improvement to the character. A 10% improvement to the 20% technique would be a 2% improvement to the character. Specialization pays off.
The previous paragraph is an oversimplification. Perhaps the 80% technique is 5% better than the 20% technique but has a resource limit restricting it to 80% of combat. The 20% technique is the backup for when the resource runs out. A 10% improvement to the 20% technique could cause the character to use the 20% technique almost always because it would become better than the 80% technique, for an overall 5% improvement. Multiple-method characters are complicated.
Back to Makarion's original point: while a martial is relying on class feats to improve, a spellcaster--even a bard, a full spellcaster in PF2--can rely on new spell levels and more spell slots to improve. This leaves the class feats for even more improvement. However, the spellcaster has a choice. The spellcaster can specialize and use the class feats to make the spells more powerful and improve more than 41.4% in that area. Or the spellcaster can generalize and use the class feats for something else, perhaps eliminating weaknesses.
Let's look at a wizard's class feats up to 4th level. Reach spell, Widen spell, Conceal Spell, and Steady Spellcasting make spellcasting more powerful. Counterspell, Eschew Materials, Familiar, Cantrip Expansion, Empowering Focus, Enhanced Familiar, Magical Striker, and Quick Preparation add another dimension to the wizard, though they still have a spellcasting aspect, such as a familiar delivering touch spells.
Those extra dimensions add new possible tactics, but often the tactics switch the wizard to another method of success in adventuring. For example, a wizard with an enhanced familiar could chose a talking bat that scouts ahead in dark caves. That does not make the wizard's spellcasting more effective and spellcasting is still the core of the character, so it won't improve the power much. But good scouting lets the party use planning and teamwork, and those are extremely powerful advanced tactics. My calculations can't cover such advanced tactics, except by guesswork.
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I've been pushing for scaling feats since 3.0 for exactly this reason. Why does anyone need to take Cleave, then Great Ckeave, then Greater Cleave, then Greatest Cleave? Taking Cleave should eventually scale up to better Cleaves as your character advances.
Scaling feats feel more fun than feats that don't scale. Scaling feats have little to do with exponential progression, however. But a good rate of progression, such as exponential, does give room for growth and scaling feats need room for growth.
How much growth? Let's suppose a class gains class feats at 2nd level and every 4 levels after that. If the power of the feats grew at 41.4% improvement per level, then the 4-level gap between feats would make each feat 4 times as powerful as the previous level's feats: power 1 at 2nd level, power 4 at 6th level, power 16 at 10th level, power 64 at 14th level, and power 256 at 18th level. Except that if the power of the feats is cumulative (spells are not good at cumulative power because casting high-level spells leave less time to cast low-level spells), then we need to subtract away the power of the previous feats, so the progression goes from 1, 4, 16, 64, 256 to 1, 3, 12, 48, 192.
With scaling feats, cumulative power matters even more, because the low-level feats gain power with level. Scaling feats run a power progression 1, 2, 5, 16, 51. One scaling feat at 2nd level is 1, two scaling feats at 6th level are 2+2 = 4, three scaling feats at 10th level are 5+5+5 = 15, four scaling feats at 14th level are 16+16+16+16 = 64, and five scaling feats at 18th level are 51+51+51+51+51 = 255.
Moro used Cleave, Great Cleave, Greater Cleave, and Greatest Cleave as an imaginary example of a feat chain that could be replaced by a scaling feat. Pathfinder 2nd Editon offers Cleave and Great Cleave as actual feats, in the barbarian class feats.
[[R]] Cleave Feat 6
Barbarian, Rage
Trigger Your melee Strike kills or knocks a creature unconscious, and another foe is adjacent to them.
Make a melee Strike against the second foe. If you somehow Cleave without taking a multiple attack penalty, take a –2 penalty to your attack roll instead.
Great Cleave Feat 10
Barbarian, Rage
Prerequisites Cleave
When you Cleave, if your Strike also kills the target or knocks the target unconscious, you can continue
to make melee Strikes until you make a Strike that doesn’t kill or knock unconscious a creature or until there are no creatures adjacent to the most recent creature you attacked while Cleaving, whichever comes first.
If we assume that Cleave has power 4 as a 6th-level feat, then our Scaling Cleave ought to have half the power for power 2 at 6th level. And scaling feats need simplicity, so let's replace the -2 penalty with the full multiattack penalty, -4 or -5, to reduce the power. That weakens Great Cleave, too, which really doubles the power of Cleave rather than adding 12 power of its own, so we can leave that close to the same.
[[R]]Scaling Cleave Feat 6
Barbarian, Rage
Trigger Your melee Strike kills or knocks a creature unconscious, and another foe is adjacent to them.
Make a melee Strike against the second foe after the first foe is downed. Multiattack penalties apply to this Strike.
At 10th level, when your Strike from a Scaling Cleave kills the target or knocks the target unconscious, and another foe is adjacent to them, this triggers Scaling Cleave as a free action [[F]] rather than a reaction [[R]]. This can continue repeatedly.
At 14th level, you may take a Step before the melee Strike against the second foe, but the total movement you take in Steps from Scaling Cleave during one turn cannot exceed your speed. Also at 14th level, dealing more damage to a swarm creature than 1/10 of its maximum hit points triggers Scaling Cleave, and a swarm creature can be the second foe even if it was the first.
At 18th level, the second foe no longer has to adjacent to the first foe, and the Steps can be 10 feet.
Hm, if the power-2 level of Scaling Cleave allows 1 extra attack, then the power-51 level ought to allow 25 extra attacks. I don't think I managed this, due to miss chances and lack of enemies. But I like the image of a barbarian cutting a swath through a mob of minions.
Let's try another, Acute Scent, the first 2nd-level barbarian feat.
Acute Scent feat 2
Barbarian
Prerequisites darkvision, low-light vision
When you Rage, your olfactory senses improve. You gain scent (see page 302) with a range of 10 feet.
Scaling Senses feat 2
Barbarian
Prerequisites darkvision, low-light vision (such as offered by Acute Vision)
Your primordial vitality improves your senses. When you Rage, you gain scent (see page 302) with a range of 10 feet.
At 6th level, the range of scent increases to 20 feet.
At 10th level, when you Rage, you gain blindsense through both echolocation and precise scent with a range of 20 feet. The range of imprecise scent increases to 40 feet.
At 14th level, your low-light vision, darkvision, scent, and blindsense also function while not Raging.
At 18th level, Seek, Identify Alchemy, Identify Magic, and Recall Knowledge for arcane, nature, occultism, and religion become Rage actions for you. When you Seek while Raging, you can sense the presence of magic and gain a +2 conditional bonus to find creatures or objects with active magic, magic traps, and magic items. You may identify in one minute instead of one hour if Raging during that minute. If a creature or magic item uses magic on you while you Rage, you may use a Recall Knowledge action before the end of your next turn to learn the full details of that magic ability.
Hm, scaling abilities can be lengthy.
Rather, as their weapon proficiency advances.
A barbarian's weapon proficiency improves only once, at 13th level, from trained to expert. A single instance of scaling would be rather disappointing.
Interesting take on scaling feats. I think it could be tweaked enough to be both usable and a reasonable start towards closing the caster/martial gap.
Seems like they need to get higher than expert proficiency then *nudge nudge* :D
I find it a bit bizarre that they have the same accuracy as a Rogue. Especially now that Criticals trigger off of accuracy.
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Seems like they need to get higher than expert proficiency then *nudge nudge* :DI find it a bit bizarre that they have the same accuracy as a Rogue. Especially now that Criticals trigger off of accuracy.
The ranking for highest weapon proficiency is
Fighter > Monk and Ranger > Paladin > Barbarian and Rogue > Alchemist and Spellcasters.An equal place in the ranking does not mean the same weapon proficiency. For example, rangers achieve mastery in one weapon group of their choice and are expert in other weapons, while monks achieve mastery in unarmed strikes alone and are untrained in other weapons.
Proficiency seems to represent formal training. Fighters, monks, and paladins in fiction and history train with their weapons every day. Barbarians don't have training, they have rage. Rogues don't have training, they have street skill. Rangers don't have training, but they use their weapons every day to put food on the table. I guess that has the same effect as training. Except, don't barbarians hunt their food, too? The reasons fall apart if examined too closely.
In game terms, fighters are supposed to be the best at combat, so they have the best proficiency. Monks are supposed to be the best at unarmed combat, and some people have already expressed dismay that monks are one notch below an unarmed-specialist fighter. The ranger is supposed to be really good with bows; hence, outstanding proficiency in one weapon group. Paladins are a religious fighter, so they piggyback on the fighter's proficiency. Barbarian are the other martials, so they have to have proficiency in martial weapons. Rogues could have been left in the dust like alchemists and spellcasters, but they fight with weapons rather than potions or spells, so Paizo had mercy on them and gave them expertise in simple and rogue weapons at 13th level. It is a careful ranking of class niches while ignoring the backstory of how a class gains proficiency.
I think critical hits represent something different in Pathfinder 2nd Edition than what they represented in Pathfinder 1st Edition. Since skills and saves have critical successes too in PF2, the meaning shifted. In PF1, critical hits were luck aided by a keen edge. The character cut the opponent in the right place for extra damage. In PF2, they represent extra damage from extra martial proficiency. The character knows how to exploit an opening to give a mighty blow.
There's also an elephant in the room: spells auto-scale, but martials need to spend their class feats to scale, which gives more room to casters for conceptual development, rather than running to keep up with the tide.I've been pushing for scaling feats since 3.0 for exactly this reason. Why does anyone need to take Cleave, then Great Ckeave, then Greater Cleave, then Greatest Cleave? Taking Cleave should eventually scale up to better Cleaves as your character advances.
I'm kinda toying with this in PF1. Take the base feat, and you auto get the next level when you meet the prerequisites.
However testing it in PF1 and right now with Style feats. PF2 doesn't have feat chains to really make auto progress ideas a thing. Maybe, don't have the PDF. Maybe let Martails have "Growing feats"
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Casters in pf2e aren't quadratic. Heck they aren't even linear. The game as is stands will have parties of martials and clerics.
The number of Magic Missile spells a wizard can cast grows with level: 2, 3, 5, 6, 7, 9, 11, 12, 14, 15, ..., roughly 1.5 times level. That is linear. Magic Missile also has the clause, "Heightened (+2) You shoot one additional missile with each action you spend." That means the power of a single Magic Missile spells grows linearly too: 1, 1, 2, 2, 3, 3, .... Combining the two linear progressions gives a quadratic progression. At 1st level, a wizard can throw 6 individual missiles with his two spells in a day, at 2nd level 9 missiles with 3 spells, at 3rd level 21 missiles with 5 spells, at 4th level 27 missiles with 6 spells, at 5th level 45 missiles with 7 spells, at 6th level 54 missiles with 9 spells, and so on. That is at least (1.125)x(level)x(level+2).
The wizard is at least quadratic.
Exponential levels mean that quadratic is not good enough.
Well, the old "linear Fighter, quadratic Wizard" claim was always a bit mathematically dubious, since a PF1 level 20 Fighter was worth hundreds of level 1 Fighters. Maybe it should have been something like "exponential Fighter, factorial Wizard".
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Well, the old "linear Fighter, quadratic Wizard" claim was always a bit mathematically dubious, since a PF1 level 20 Fighter was worth hundreds of level 1 Fighters. Maybe it should have been something like "exponential Fighter, factorial Wizard".
Dungeons & Dragons 3rd Edition was a game with quadratic levels. Both the fighter and the wizard improved quadratically, but the fighter's curve was flatter, barely above a linear curve, so "linear fighter, quadratic wizard" made sense as a comparison in D&D 3.0 and 3.5.
Paizo changed the level-up system in Pathfinder to exponential, one of their acts of genius. It made higher levels more interesting and enabled high fantasy.