The Campaign Builder's Guild

Quote from: SteerpikeI'd suggest that you can't critique a combat maneuver fully until you've explored a diverse array of different contexts in which it might be useful, both in granting straight up numerical combat advantages and in pursuing the plethora of additional goals that may be relevant in a combat encounter.

I agreed, and continue to agree, that maneuvers shouldn't be too broadly useful. The problem, in my opinion, is that many maneuvers are often far too niche, especially ones that grant a bonus. I think the examples of pushing someone off a cliff into lava, or dealing with the the "Wand of Killing You," or whatever, are actually very good examples of maneuvers where it doesn't really matter how useless or how bad the odds are most of the time, because it's very clear where doing the maneuver going to be useful-- if there is somewhere bad you want the enemy to end up, then you can try to shove them in there, and if they have something powerful they shouldn't have, you can try to steal or sunder it. As I've said already, if there are roleplay or situational reasons to choose a maneuver, that's great, go for it.

Something like Pathfinder's feinting or aid another or FATE's abstract "get a +2" just gives a bonus, so it's rather often hard to intuitively tell if that bonus is better than other options, and it's also rather often hard to intuitively tell when it's worthwhile to try to gain that bonus. You guys are right that running the numbers in detail during play usually isn't feasible, but, here's the thing: if our thoughtful analysis of plausible enemy encounters when we do have time to be thorough and do have complete information reveals a broad range of cases when a maneuver is or isn't useful, then, to be honest, we're already doing pretty well. We can't always make the most optimal choice at the game table, due to time constraints and incomplete information, but we can at least have some confidence that we're not going completely awry. Instead, though, what I'm usually finding and have documented-- and what this thread is really about-- is that a lot of combat maneuver bonuses are only ever any good at all in extremely limited circumstances. They seem like they ought to be useful, because, hey, you can get a bonus! ...but in practice they're just almost never worth the opportunity cost. (I'm sure the situation also improves if you've sunk half a dozen feats into specializing into the maneuver, but at that point, it had better be useful!) What this means is that the few times that getting bonuses actually are useful, nobody even thinks to try, because they're so used to the maneuver being not worth it. And that, in my opinion, isn't good.

So, my issue with worthless maneuvers isn't so much about special situational maneuvers where it's at least clear when they're situationally applicable, but much more with general bonus-getting maneuvers. I feel they should either be more clearly explained and specialized so it's clearer from context just when they're useful, or be more broadly effectual so that while not always being a net gain, they're at least mostly worthwhile a decent minority of the time, instead of just in weird corner cases.

Quote from: Steerpikeif one can make a case

So make a case!

When I posted this thread, I honestly half-expected it to get no replies and sink to the bottom like a rock as everyone's eyes glazed over by the amount of math. I'm glad that it hasn't, but I'm honestly a bit confused and frustrated at the amount of vague and unsubstantiated assertions being thrown around. If you are going to claim a maneuver is or isn't useful in a certain situation, I don't think it's too unreasonable to ask you to either crunch some numbers (or at least Google something up) to back up your claims, or stop making them.

Quote from: SteerpikeDirty trick increases the chance of instantly taking an opponent out of combat by 10%, which is not remotely the same as merely dealing 10% of their hit points worth of damage

Quote from: PolycarpHold Person takes out a target immediately; beating an opponent to death generally takes multiple rounds.  You could certainly make the argument that hitting someone for 20% of their HP is better than adding a 10% chance to KO him right then, but that means 4-5 rounds of attacking

This is just statistics. Something that has a 10% chance of causing an enemy to lose instantly is of equivalent worth to knocking off 10% of its hit points because added up over the long term those outcomes lead to the same result in the same amount of time. While you're both correct that hold person could take the opponent out instantly, it's all-or-nothing, so it's important to consider the "nothing" part of it as well as the "all."  The Wizard could very well cast three hold person spells and be no closer to finishing an enemy off, whereas doing actual damage would have been bringing the party closer to winning. When making the comparison, it's also important to remember to consider that the hit point damage is being averaged as well-- our hypothetical "20% damage melee fighter" isn't going to always do 20% damage, because that's an average too. He might roll a critical hit and win the combat in one round, or he might hit for close to average damage every time, or he might miss four rounds in a row. All of these things can and will happen, so the only way to make any sense of it is to compare the averages.

Quote from: sparkletwistI agreed, and continue to agree, that maneuvers shouldn't be too broadly useful. The problem, in my opinion, is that many maneuvers are often far too niche, especially ones that grant a bonus. I think the examples of pushing someone off a cliff into lava, or dealing with the the "Wand of Killing You," or whatever, are actually very good examples of maneuvers where it doesn't really matter how useless or how bad the odds are most of the time, because it's very clear where doing the maneuver going to be useful-- if there is somewhere bad you want the enemy to end up, then you can try to shove them in there, and if they have something powerful they shouldn't have, you can try to steal or sunder it. As I've said already, if there are roleplay or situational reasons to choose a maneuver, that's great, go for it.

OK, cool - what you're saying, then, is that it's not that some manuevers are intrinsically broken because their bonuses aren't powerful enough, it's that the contexts in which their bonuses become useful are too rare.  The "weird corner cases," as you put it.

I agree that lava/death-wand examples are extreme ones, though I think they're far from the only situations where bull rush and disarm are useful, by any means.  Imagine a fight on rooftops where the fall damage isn't too severe but in which a fall would seriously inconvenience enemies, or a a battle above a giant web where a fall deals no damage at all but might entangle enemies - or a situation where you've readied an action to disarm an enemy of a potion or scroll they're about to use.  Perhaps, though, things like disarm aren't the kind of maneuvers you're singling out.

Quote from: sparkletwistSo make a case!

When I posted this thread, I honestly half-expected it to get no replies and sink to the bottom like a rock as everyone's eyes glazed over by the amount of math. I'm glad that it hasn't, but I'm honestly a bit confused and frustrated at the amount of vague and unsubstantiated assertions being thrown around. If you are going to claim a maneuver is or isn't useful in a certain situation, I don't think it's too unreasonable to ask you to either crunch some numbers (or at least Google something up) to back up your claims, or stop making them.

Example (with numbers).  This might not be up to your standards of rigor, so feel free to apply more math to my scenario if you think I'm missing something.

Let's say we have a party of 2 3rd level characters - a Witch (20 hp) and a Fighter (30 hp).  They're wandering the hills in a wilderness exploration scenario, searching for signs of a Barghest that's been terrorizing the local village, and they've heard there's a small handful of giants up in the hills, but it's unlikely they'll encounter one.  However, the DM rolls on a random encounter chart and produces a Hill Giant with 85 hp, AC 21, CMD of 24, and a +3 Will save.  It has +14/+9 to hit and deals 2d8+10 damage per hit (12-26 damage, average is 19).  It has -1 Initiative.

Let's say I am the Fighter and I have 18 Strength, attacking with a masterwork longsword with which I have Weapon Focus, for a total attack bonus of +9 (+3 BAB, +4 Strength, +1 Weapon Focus, +1 Masterwork).  I deal 1d8+4 damage per hit - a maximum of 12 damage excluding the possibility of a critical, average is 8.5 (10% of the Giant's hp).  Chipping away at the thing, it's going to take me 10 rounds to kill it, assuming I hit every time (which is far from guaranteed - in fact I have only a 45% chance to hit each time so if it's just me bashing away at this thing it's going to taker more like 20 rounds, assuming the giant has no potions).  In the meantime this giant can likely incapacitate either of us in a given round, maybe two.  Even if I'm wearing Full Plate and have a Heavy Steel Shield - giving me an AC of 22 - the Giant has a 65% chance of hitting me with its first attack and taking out (on average) nearly two thirds of my hp.

We cannot go toe-to-toe with this thing in an extended fight: it's suicide.  If I am smart I should realize that chipping away at the thing's hp 10% at a time is not a viable strategy.  If you want to actually crunch the numbers on the possibility of defeating the giant in hand-to-hand combat before one or both of the PCs get squashed, go ahead, but I take them to be so low as to be near-pointless to consider.  In other words practically speaking, dealing 8.5 points of damage to the Giant does not bring the party appreciably closer to victory in anything but the most technical sense because, realistically, we're going to die well before the damage can add up.

Essentially, then, it is exceedingly unlikely that we will both survive an encounter with the giant if I try and just fight the thing.  What's more, the giant has a war-horn.  It can summon its inbred hill giant family members if it blows that thing, in case it gets in trouble.  Then we'd be really screwed.  So the longer the fight goes on, the worse off we're going to be.  In fact, our chances of survival are probably better if we just run than if we wound the giant badly and give it a chance to alert its kin.

Now we could turn and run, but the Giant can throw rocks that deal 1d8+10 damage and can keep pace with us (30 ft. speed - and if I am in Full Plate I'm going to be slow), so just running away is no guarantee of survival.

Fortunately the Witch has prepped Hold Person (DC 16) and also has the Slumber Hex (DC 15) - both spells which could incapacitate the Giant.  Because of the Giant's poor Initiative (-1) and our decent Initiative (+1 for both of us) we are likely to go first.  It has a Will save of +3.  It thus has a 40% chance of saving vs. Hold Person and a 45% chance of saving vs. Slumber.

I also have Improved Dirty Trick.  My CMB is +7, +9 for Dirty Tricks.  I am less likely to land a Dirty Trick (30% chance) than hit the Giant (45% chance).  But if I do manage to land a Dirty Trick and give the Giant the Shaken condition its chances of saving drop to 30% and 35% against Hold Person and Slumber respectively.  And if the Witch manages to get the Giant with Hold Person or Slumber we can both coup-de-grace it (with a Fortitude save of +11, it only has a 25% chance of surviving my average coup-de-grace of 17 damage) - or we could use the few rounds the thing is sleeping/held to run the hell away (preferably after putting out its eyes, if the DM allows us to, which I think any sane DM would) and/or hide somewhere.

If we fail to get the Shaken result, well, we only wasted one round.  The odds are that after a round or two one of the Witch's two spells/Hexes will stick.  This timing is important.  It takes much longer (10 rounds+) to kill the giant by chipping away at its hp than it does to incapacitate it with Slumber or Hold Person.  We only get 2 chances, because the Witch can only target the Giant once with Slumber and only has one use of Hold Person, so if the dice are against us and we fail on both we've only wasted a maximum of 2 rounds - at which point we might as well run, because again, our chances of killing the giant with my sword and the Witch's other powers & dagger is too small to be significant.

Can we really claim that helping the Witch take out the Giant with Slumber/Hold Person using a Dirty Trick is less valuable than the effectively pointless action of just pricking the thing for 8.5 points of damage?  I don't think so, personally.  I think the 1 in 3 chance of helping the Witch by 10% is worth more than 8.5 points of damage, because dealing 8.5 points of damage to a giant that can crush you in a couple of rounds is pretty much worthless in this scenario.  Even if the penalty we're giving the giant is a modest one, it's still improving our chances of winning the encounter, but dealing a small amount of damage to the giant does not appreciably improve our chances of winning the encounter.  The two are not equivalent, especially once you factor in qualitative factors likle the war-horn.

I think this illustrates my former statement that "Dirty trick increases the chance of instantly taking an opponent out of combat by 10%, which is not remotely the same as merely dealing 10% of their hit points worth of damage."  The two are not the same thing.  Dealing damage in 10% blocks to a monster that can kill you in a few rounds is not an effective strategy for winning an encounter.  Trying to knock that monster out in 1 or 2 rounds with Hold Person of Slumber is a viable strategy, so it makes more tactical sense to use the Dirty Trick rather than attack.

EDIT: It should be noted that Shaken also decreases the enemy's attack rolls and ability checks.  If the Giant got lucky and goes before the Witch can use a Hex/spell, it could use a Move action to get rid of the condition, but then it loses out on one of its attacks, thus improving our chances of surviving the round.

Other Combat Maneuvers that could be more useful than a standard attack in the above scenario:

Disarm, Sunder, or Steal (war-horn)
Reposition (next to a cliff, away from the Witch)
Bull-Rush (off a cliff)

Thank you for the detailed example and analysis! This is something we can actually crunch on. :grin:

Quote from: SteerpikeI think this illustrates my former statement that "Dirty trick increases the chance of instantly taking an opponent out of combat by 10%, which is not remotely the same as merely dealing 10% of their hit points worth of damage."  The two are not the same thing.

Yes, generally speaking, they are. They have an equal expected value and are thus equivalent by law of large numbers. However, an important caveat that I should have been more clear about is that they are only equivalent if the two situations being analyzed are independent-- that is, one character beating on an orc for an average of 25% of its hit points and another character repeatedly attempting to cast a save-or-lose spell with a 25% chance of success on a different orc will both, on the average, win their respective battle in four rounds, and, as such, the two tactics are statistically equivalent. With two characters each trying to act on the same target, their influence on each other has to be worked into the math, though.

Let's go on a brief tangent and say our intrepid duo decided to just run, and they thought they escaped, but then they encountered a second Hill Giant! Oh no! Their one lucky break is that this second one is looking quite bruised and beleaguered, with a large poorly-bandaged cut on its arm. It turns out that this one only has 10 hit points left. Now, they're boxed in, so they have to fight-- it's going to be very tough for them, but they want to use smart tactics to maximize their chances of survival. Obviously, the Fighter is going to attack the weak one, because its 10 HP is within his realm of possibility to defeat. The Witch, on the other hand, can do "all the damage" with her save-or-lose spells, so it's going to be the better choice to try to essentially (for the sake of evaluating things in a mathematically equivalent way) take 85 HP off the 85 HP giant than to try to take 10 HP off the 10 HP giant. Doing it the other way would be a poor move and a waste of both of their capabilities.

The point of that example is that the key thing about instant-win spells is that, when analyzing them in terms of damage, they do "all the damage," but they do that regardless of what the damage actually is. Put another way, a fighter attacking a target and causing hit point damage is actually reducing the expected value of the Witch's save-or-lose. It's a better call to do a maneuver if the Fighter's damage reduces the Witch's expected damage value to the point that his bonus to her expected value is higher. Imagine if the Witch's spell was a blast that hit the target for whatever HP it currently had-- that means, if the fighter hits the 85 HP giant for 9 damage, then the Witch's spell is no longer worth 85 HP of damage, but rather only 76 HP of damage.

The Witch's normal chance of succeeding at her hold person is 60%. A fighter with a 30% chance of adding 10% raises that to 63%. So the total expected value for the pair is 85*0.63 = 53.55.
What if the Fighter attacks instead? He has a 45% chance of dealing 8.5 damage, so, an average of 3.825. The Witch then has a 60% chance, so her expected value is 81.125*0.60 = 48.705, plus the fighter's damage, makes the total 52.53.
Dirty trick is the right choice in this case.

Here's the equation, simplified, to determine if a dirty trick is worthwhile:
(pf and df are the fighter's hit probability and damage, pw is the witch's chance of success, pfm is the fighter's chance of pulling off his maneuver, b is the bonus the maneuver gives, and H is the monster's hp total)



The end result ends up being that a dirty trick is worthwhile if the Fighter's expected damage times the Witch's chances of failure is less than or equal to the monster's hp times the bonus times the fighter's chances of succeeding at his maneuver. Which makes sense, really!

In other words, you're absolutely right that dirty trick is the right call in this case, but nothing about that conclusion actually refutes anything I've been saying, nor does it really raise the general effectiveness of dirty trick, as the formula I posted above demonstrates. The extra factors complicate things a little, but if you assume pfm and 1-pw are equal, such as with a 40% chance to do a maneuver and a 60% to hit a save-or-lose, you can cancel those by division-- and that means "10% of HP" is still a decent ballpark estimate.

A note on my use of the term "value": I may not be using the term the same way you are using the term, and I may not be using the term in a strictly "mathematical" sense.  When I'm talking about the more valuable move I'm talking about the move that makes more sense in a given context - that's all.  In my above example the bonus granted from Dirty Trick is thus "more valuable" than the damage one might be dealing because, in that example, the small amount of damage you can deal is functionally worthless - valueless.  I get that its mathematical value is still 8.5 - but its strategic value, holistically, is basically nil as I see it (because you stand such a negligible chance of killing the giant with just your longsword before it kills you).

Quote from: sparkletwistWith two characters each trying to act on the same target, their influence on each other has to be worked into the math, though.

Right, yeah!  Math is still useful - I don't want to dismiss it, here.  I think this is actually the chief purpose of penalty-granting combat maneuvers in Pathfinder, though - setting up moves for allies.  Feinting to set up the Rogue.  Using a Dirty Trick to shake up an enemy for the Wizard.  It's about gauging/estimating which contexts the math is going to work out - without knowing most of the numbers on the spot.

QuoteLet's go on a brief tangent and say our intrepid duo decided to just run, and they thought they escaped, but then they encountered a second Hill Giant! Oh no! Their one lucky break is that this second one is looking quite bruised and beleaguered, with a large poorly-bandaged cut on its arm. It turns out that this one only has 10 hit points left. Now, they're boxed in, so they have to fight-- it's going to be very tough for them, but they want to use smart tactics to maximize their chances of survival. Obviously, the Fighter is going to attack the weak one, because its 10 HP is within his realm of possibility to defeat. The Witch, on the other hand, can do "all the damage" with her save-or-lose spells, so it's going to be the better choice to try to essentially (for the sake of evaluating things in a mathematically equivalent way) take 85 HP off the 85 HP giant than to try to take 10 HP off the 10 HP giant. Doing it the other way would be a poor move and a waste of both of their capabilities.

Agreed!  In that situation, a combat maneuver would be sub-optimal (until you'd dropped the weak Giant, at which point it might become viable again).  Dealing damage is more valuable in this case than helping the Witch, just as helping the Witch was more valuable in the previous example than dealing damage.  The strategic value of Dirty Trick varies from context to context, but there are lots of contexts where it makes more sense to use a Dirty Trick than just attack.

Quote from: sparklewtwistThe end result ends up being that a dirty trick is worthwhile if the Fighter's expected damage times the Witch's chances of failure is less than or equal to the monster's hp times the bonus times the fighter's chances of succeeding at his maneuver. Which makes sense, really!

Cool!

Really, the only point I was making is that sometimes using Dirty Trick makes more sense than attacking - that Dirty Trick can be more "valuable" than the damage dealt in a standard attack because, in the right situation, it can supplement a viable strategy (in cases where just dealing damage normally isn't a viable strategy).  Which, in my mind, is exactly what a combat maneuver should be for.  In lots of other situations it's not necessarily the best move to make (nor, I'd suggest, should it be).

Quote from: SteerpikeThe strategic value of Dirty Trick varies from context to context, but there are lots of contexts where it makes more sense to use a Dirty Trick than just attack.

I don't know what your idea of "lots of contexts" is. All that math up there is to prove the idea generally true that using up your standard action to give someone a minor buff (or an enemy a minor debuff) is only useful when the damage you would have done (or its equivalent) is less than some trivial percentage-- usually around 10% or so-- of the target's HP. I don't think you even really dispute it; if you do, your example certainly didn't do anything but support the idea, because the Fighter in the example was doing far less than 10% damage on the average. So I don't see where you're even getting this "lots of contexts." I know that I sure don't find such a limited situation "lots of contexts," anyway. It's only useful when you have pretty much no options anyway, so you do something that maybe helps a little rather than waste your turn doing nothing. I don't find this particularly worthwhile.

Personally, I want maneuvers that matter-- I want them to be helpful more often than just in fringe cases, have a pretty sizable actual impact when they are used, and not be presented like they're actually worthwhile when they're not. As I've already mentioned, I am in no way advocating maneuvers that are effective all of the time or even most of the time. I just want maneuvers that aren't awful. If you think something that's only useful when all your other options are equivalent to doing less than 10% damage is not awful, then... we have very different opinions about how the game should probably work, and I'm not sure what else I can even say beyond that. I feel like we're just going around in circles now.

Quote from: sparkletwist
Here's the equation, simplified, to determine if a dirty trick is worthwhile:
(pf and df are the fighter's hit probability and damage, pw is the witch's chance of success, pfm is the fighter's chance of pulling off his maneuver, b is the bonus the maneuver gives, and H is the monster's hp total)



The end result ends up being that a dirty trick is worthwhile if the Fighter's expected damage times the Witch's chances of failure is less than or equal to the monster's hp times the bonus times the fighter's chances of succeeding at his maneuver. Which makes sense, really!

This equation only addresses one side of the combat, that being the effective offensive power of the PCs vs the staying power of the monster. The other side - the monster's effective offensive power vs the PCs' staying power - is ignored. Don't you think that both sides should be relevant when it comes to estimating the worth of a combat maneuver?

Some monsters pose much more of a threat to the life of PCs than others, particularly since PCs often have access to healing, which may potentially enable them to last for a very long time against a monster with low damage output. Against one that could single-hit KO a PC though, prolonged combat may be a tactically bad idea even if by strictly average damage-dealing you'd expect to win in the long run. There are also monsters and NPCs with really nasty special attacks that you can't afford to let them use against you. Level drain for example could send you on a death spiral as each negative level reduces your combat stats further.

Thank you, Ghostman!  That's exactly what I was trying to convey.  The value of an instant KO spell is that they hold the potential to prevent the enemy from hurting you very badly, whereas just attacking, even with critical hits, does not hold that potential.  This holds true even if we acknolwedge that sometimes instant KO spells simply fail.

Apologies for the double post.

sparkletwist, I think I was misinterpreting your formulae slightly - though I'd stand by my assessment even if the Giant were at slightly less than half health and thus the Fighter was dealing roughly 10% per round on average.  It still is more worthwhile to try and take him out quickly and thus to supplement the Witch's spell.

I fully agree that maneuvers shouldn't be awful.  I can't speak to FATE's maneuvers, but with regards to Pathfinder's, I don't think they are awful (especially because most of them aren't actually about simple debuffs).

Some other contexts where the debuff use of Dirty Trick (or even the much-maligened Aid Another) is useful - some of them using your formulae rather than arguing against it:

- Enemy has DR and you don't have the right weapon, but an ally does.
- Enemy has Regeneration and you don't have Fire or Acid, but an ally's spell/weapon does.
- Enemy can use Dominate to mind-control allies and you're setting up an ally's Hold Person/Dominate/Sleep/Polymorph spell because otherwise you strongly suspect you're going to be Dominated next round.  Even if you could take out plenty of the enemy's HP, you're just going to be Dominated anyway, so it makes more sense to aid your ally in trying to take out the enemy quickly rather than risk Domination.
- Same as the above but insert Petrification/Disintegrate/Finger of Death/whatever.
- Forcing an enemy into using an attack of opportunity in order to allow a spellcaster impunity to cast a spell in melee range (here the debuff penalty is a side-effect).
- Ally has a poisoned weapon that will severely deplete the enemy's ability to counterattack and you know that if they don't hit, the monster is going to dish out some serious pain.
- As above but with a debuff spell instead of poison.

Remember, also, that the debuff from Dirty Trick can potentially last multiple rounds if your roll is high enough, and also that it applies to a very broad array of the opponent's stats, including their attack rolls.  Part of its utility is defensive, and that needs to be accounted for.

Or, as you state in your opening post  "This also means that if the chances of a hit after a maneuver aren't 100%, or you don't want to double the damage, then there has to be some sort of bonus for doing a maneuver instead of just attacking."  Well, quite!  But I'd suggest that it's those other bonuses that are the most important ones in combat manuevers.

EDIT: More uses of Dirty Trick when considering conditions beyond Shaken and Sickened:

- Creatures entangled by Dirty Trick can't reach vulnerable allies and spellcasters and also can't cast spells as easily.
- Blinded characters can be sneak attacked (with an additional -2 to AC in addition to losing a Dex bonus, using Dirty Trick to blind a foe is potentially more effective than Feint if you have a good CMB) while also suffering a 50% miss chance and losing the ability to use scrolls.

Quote from: GhostmanThis equation only addresses one side of the combat, that being the effective offensive power of the PCs vs the staying power of the monster. The other side - the monster's effective offensive power vs the PCs' staying power - is ignored. Don't you think that both sides should be relevant when it comes to estimating the worth of a combat maneuver?

When determining the expected value of a maneuver, I'm basing it on wanting to win as quickly as possible. You want to do the most "damage," whether that's winning through actual HP damage or a 100%-damage-equivalent combat-ender. I'm assuming that no matter what else the PCs are doing, the monsters will be attacking-- often, this means that "monsters attacking" is a constant on both sides of the equation, and, as such, can be cancelled by subtraction. I'm not saying that it's not important in play, but, from the perspective of mathematical optimization, choosing the attack with the statistically best results is always the best idea, independent of what the monsters do. However, if an important draw of the maneuver is a debuff on the enemy, then, yes, it is definitely worthwhile to consider, and multiplying every expected value times your "probability of not being dead" or whatever other way to incorporate the enemy's offense wouldn't be a bad amendment to the formula.

Quote from: SteerpikeI'd stand by my assessment even if the Giant were at slightly less than half health and thus the Fighter was dealing roughly 10% per round on average.  It still is more worthwhile to try and take him out quickly and thus to supplement the Witch's spell.

Look, I completely understand that RPGs are a lot like poker in the sense that you can run the numbers and you can determine what is the statistical winner, and that information is absolutely useful and helpful to know, but what you actually have are not dry statistics but rather a game with a lot of human social factors and random numbers. So maybe you're feeling lucky, or you have a read on someone, or whatever, and what the cold numbers say is the best move isn't actually the best move at your table at that very moment. Or maybe you're warming the cold numbers slightly using some kind of adjustment based on risk, see below.

All I'm saying is that certain moves are statistically not the best choice, and doing (or at least trying to do) the math to back that up. If that doesn't actually end up meaning anything at your game table, then fine, but it doesn't invalidate the analysis.

But anyway, here's how I'd look at your list.

Quote from: Steerpike- Enemy has DR and you don't have the right weapon, but an ally does.
- Enemy has Regeneration and you don't have Fire or Acid, but an ally's spell/weapon does.

These are situations where you basically can't do anything so you do something that might help a little instead of wasting your turn. You're not going to be the MVP either way. If you're a spellcaster and you have no offensive ability at the moment, you cast a buff or protection or battlefield control spell spell, but if you're a mundane you... can't do nearly so much. A big part of my point is that I wish general purpose maneuvers allowed for more flexible options like this, so maybe this thread is actually just a "mundane characters don't get nice things" discussion by another name.

Quote from: Steerpike- Enemy can use Dominate to mind-control allies and you're setting up an ally's Hold Person/Dominate/Sleep/Polymorph spell because otherwise you strongly suspect you're going to be Dominated next round.  Even if you could take out plenty of the enemy's HP, you're just going to be Dominated anyway, so it makes more sense to aid your ally in trying to take out the enemy quickly rather than risk Domination.
- Same as the above but insert Petrification/Disintegrate/Finger of Death/whatever.

The thing about save-or-lose spells is that they are good because they take enemies out of combat instantly. However, taking off all of an enemy's hit points in one hit takes enemies out of combat instantly. If you have a hex that takes out an enemy 60% of the time, that is of equivalent worth to an attack that, on average, takes off 60% of an enemy's hit points. You're basically power attacking a level 1 commoner. Either way is a smart move because either way has a strong chance of taking out this enemy that is a big threat to you.

That said, I think what you're getting at here is the greater variance of save-or-lose, and I think this is something important that my formulas, thusfar based solely on the mean (i.e., average value), could sometimes benefit from including. For example, if you were facing an enemy with 12 HP that you had to take out as quickly as possible, you'd probably prefer take the risk to roll 2d6 rather than do a guaranteed 7 damage, because, although they both have the same mean, one option has enough variance you might one-shot the enemy, while the other does not. What's more interesting to consider is that you might even prefer to roll d12, because of its higher chance of rolling a 12 and thus getting a one-shot win, even though its mean is actually lower.

We can incorporate this factor by adopting the financial concept of risk-adjusted returns, but instead give a bonus to "riskier" behavior rather than penalizing it like the financial formulas usually do. According to anydice.com, the standard deviation (i.e., the square root of the variance) of 7 is of course 0, the standard deviation of 2d6 is 2.42, and the standard deviation of d12 is 3.45. In finance, they use a "risk tolerance" that is using complex heuristics based on the behavior of individual investors; at this point, the interesting thing is that subjective preferences come into play, which brings the "human element" I describe earlier into play even when doing a cold mathematical analysis. By using the formula m + v/a (mean plus variance over "risk aversion," our version of risk tolerance) we can determine an optimal course of action incorporating one's tolerance for risk.

You'll notice that if one's aversion to risk is effectively infinite, then this expression is simply the mean, meaning that analyzing numbers using solely the mean is still valid, but assumes an extremely conservative approach, which may not always be what players in a real game want to do. You'll also notice that if one's aversion to risk is very low, then the result with the higher variance-- i.e., the riskier one-- will always be superior.

If your risk aversion is 15, then rolling a 2d6 generates a result of 7.39, while a d12 generates a result of 7.29. However, if your risk aversion is 10 (lower values means you'll tolerate more risks) then 2d6 gives a result of 7.59 while a d12 gives a result of 7.69. If you're more willing to take risks, then the d12 becomes a better option for you.

Quote from: Steerpike- Forcing an enemy into using an attack of opportunity in order to allow a spellcaster impunity to cast a spell in melee range (here the debuff penalty is a side-effect).

That's a clever tactic, though I'd analyze the actual use of this one in terms of the opportunity cost of not making a ranged attack or unarmed attack or some other damage-dealing attack that also provoked.

Quote from: Steerpike- Ally has a poisoned weapon that will severely deplete the enemy's ability to counterattack and you know that if they don't hit, the monster is going to dish out some serious pain.
- As above but with a debuff spell instead of poison.
- Creatures entangled by Dirty Trick can't reach vulnerable allies and spellcasters and also can't cast spells as easily.
- Blinded characters can be sneak attacked (with an additional -2 to AC in addition to losing a Dex bonus, using Dirty Trick to blind a foe is potentially more effective than Feint if you have a good CMB) while also suffering a 50% miss chance and losing the ability to use scrolls.

These are cases where the aforementioned "probability of not being dead" multiplier would be useful, probably.

Quote from: sparkletwistFor example, if you were facing an enemy with 12 HP that you had to take out as quickly as possible, you'd probably prefer take the risk to roll 2d6 rather than do a guaranteed 7 damage, because, although they both have the same mean, one option has enough variance you might one-shot the enemy, while the other does not.

I think that is the gist of it, yeah.  With your other example - the "taking out the enemy 60% of the time" or "taking out 60% of the enemy's hp," I'd tend to go for the former, because with the latter even if you deal the full 60% damage, you're still going to receive a smack in return (or at least the chance of one), whereas if the former works, you get off clean.  They're equivalent in a statistical sense because, over time, they take out monsters at the same rate over the same amount of time, but the former has the chance of getting you off with no damage whatsoever.  Ergo, in situations where chipping away at an opponent's hp is a bad strategy - where you're going to get squashed before you kill the monster - I think it's better to throw your weight behind the save-or-die strategy, even when the statistics seem to suggest that's disadvantageous.

This all feels very prisoner dillema or something.

So, sparkletwist, if we were to apply your insights to Pathfinder's selections of combat manuevers to come up with some house-rules, which of the following would you change and how?  I'm genuinely curious, here: I love houserules.

Bull Rush
Dirty Trick
Disarm
Drag
Grapple
Overrun
Reposition
Steal
Sunder
Trip
Feint

I'm actually also very curious what you make of Feint in general, because it seems like such a slippery, weird move - so dependent on how much an enemy's Dex is boosting their AC and on how high their Sense Motive is.  Does it fit the bill as an acceptable combat maneuver given that there are some contexts where it's very useful and others where it's totally useless?

Quote from: Steerpike
Ergo, in situations where chipping away at an opponent's hp is a bad strategy - where you're going to get squashed before you kill the monster - I think it's better to throw your weight behind the save-or-die strategy, even when the statistics seem to suggest that's disadvantageous.

In some cases it might even be your only reasonable course of action.

For example, let's assume that you can reliably do 1d10 hp of damage per round, and need to kill, as quickly as possible, a monster that has 55 hp. On average you'll cause 5.5 damage per round, which translates to 10 rounds to defeat the monster. And you are guaranteed to cause at least 1 hp per round, so in the worst (extremely unlikely) case it'll take 55 rounds. The best case rate of 10 hp per round requires 5.5 (so effectively 6) rounds of combat. That is how long you would (at LEAST) have to be able to last to be able to win.

Let's assume that instead of causing damage, you could opt to use a special attack that might instantly end the fight, at a 10% chance. This is equal to the 5.5 hp damage average you'd get by attacking. However, the best & worst case scenarios look very different now. In the best case you defeat the monster in the first round of combat, in the worst case... never. The instant battle-ender has the potential to be much quicker than damage from your attacks could ever be: 1 round as opposed to 6 rounds. But it also gives no guarantees of getting the job done in any number of rounds.

Now, if the monster is expected to kill you in 6 rounds, attacking it for damage is worse than a bad idea - it's actually futile. You would expect to lose even if rolling nothing but 10s. But if you instead opt for the 10% chance/round battle-ender strategy, you actually have a significant chance to win:

1 - (9/10)^5 = ~0.409

That's roughly 41% chance of victory in 5 rounds.

Once again Ghostman has made the point I was trying to make more eloquently and expansively!

Quote from: Steerpikeif we were to apply your insights to Pathfinder's selections of combat manuevers to come up with some house-rules, which of the following would you change and how?

I'm not totally sure how much I can help, here. While I can break apart the math of Pathfinder in a general sense, it is definitely not my system of choice, so I'll probably miss some small but important details, and I'm not sure if I have the time or the mathematical prowess to post a worthwhile analysis of each and every maneuver. On the other hand, proclaiming that I've found a problem and offering no solution whatsoever is kind of no fun, so I'll at least try to offer something useful-- but I'll have to digress a bit into the favorite pastime of the CBG, talking about my own stuff.

As you may know, my homebrew system Asura uses FATE-like rolling, in this case, an opposed attacker+2d6 vs defender+2d6, meaning the dice results are a bell curve. Also like FATE, the degree of success contributes to the damage done. Using a weapon with 1d6 inherent damage, rolling a result of +2 (i.e., the attacker's roll exceeds the defender's by 2) means you do d6+2 damage while rolling a +5 means you do d6+5 damage. Asura also scales weapon damage down by half at results of +0 and +1 and adds bonus damage for a hit of +6 or better, leading to a more sharply scaling curve. What this leads to is that near the low end and into the center of the bell curve, each +2 bonus you gain corresponds to an approximate doubling of damage output. There are diminishing returns at the high end, but when you've got the numerical advantage, you aren't as likely to try fancy maneuvers to get an edge anyway. Since Asura uses the FATE-like concept of a basic maneuver being something that grants a +2 bonus, this means, on a very superficial level, each maneuver is balanced with its opportunity cost-- you can attack twice, or you can do a maneuver that will grant a bonus that roughly doubles your damage. Of course, the +2 bonus granted by a maneuver can be used for other things than just helping the next attack (making them better) but maneuvers are far from 100% successful (making them worse) but resounding success on a maneuver roll can create not one but two conditions (making them better again) so the math gets a bit funky-- but the basic result is that a maneuver done at a decent level of competence followed by an attack is statistically "worth" somewhere between 1.7 and 1.9 attacks. (That's assuming one turn for each, so two turns of attacks are "worth" 2.0 attacks) That means it's not at all worthwhile to try to maneuver before every attack every single time, but sometimes the greater flexibility for having the "floating" +2 bonus will make it more attractive to try than just attacking twice, and even if you do end up just attacking and getting less than "optimal" damage, the bonus is still never going to be so pathetic it makes you feel dumb for using it or feel like maneuvering is a trap option.

So, going back to Pathfinder, something vaguely like that is how I'd like to see stuff like aid another and dirty trick work in practice. Rather than have to justify them using contrived scenarios or invest in massive feat chains to get anywhere close to something worthwhile, you instead have a basic bonus you can grab that you know is always going to be at least feel worth it, even if it's not always the perfectly optimal choice. And when maneuvers click and the whole team is on board to make the situation work out in your favor, they should really work out in your favor. Like, if you can dirty trick blind someone who loses a +3 Dex AC bonus (in addition to the blindness AC penalty) and then have two 3d6+12 heavy hitters dogpile onto that victim and both take advantage of the big bonus to hit before the victim can spend a move action to clear the condition, I think that ought to be a crowning moment of awesome. You should win battles that way. But in reality, while dirty trick sometimes does work out to be the mathematically optimal choice in that situation, it also ends up working out that after all that there is still only around a 4 HP total gain to the group's net damage, and that gain only exists if you're normally swinging for 1d6 damage with no bonus at all... once again putting us in the "don't even bother unless your damage is less than 10%" ballpark. And if that's the case, you're probably a spellcaster who likely has far better ways to use a standard action to buff those heavy hitters. That kind of thing just makes me sad, and that's really what I'd like to do something about.

If the maneuver was at least reliable, things wouldn't be quite so bad. In my above example, everyone was hitting everything 50% of the time. If you could instead pull off your dirty trick 100% of the time, the group's net damage gain in that scenario rises to 12 HP. While you're still not going to be scoring any crushing victories that way, it at least starts to make the option seem attractive. Unfortunately, however, Pathfinder goes the other way-- with CMB equaling d20 + BAB + Str and CMD equaling 10 + BAB + Str + Dex, in all likelihood, the gap between CMB and CMD is going to increase as characters improve. The only way to reverse this trend, of course, is again by taking lots of feats or otherwise expending lots of resources. In my opinion, any revision of Pathfinder's maneuver system would have to do something about this shortfall, too.

Quote from: SteerpikeI'm actually also very curious what you make of Feint in general, because it seems like such a slippery, weird move - so dependent on how much an enemy's Dex is boosting their AC and on how high their Sense Motive is.  Does it fit the bill as an acceptable combat maneuver given that there are some contexts where it's very useful and others where it's totally useless?

Personally, I don't mind maneuvers that are very useful in some contexts and totally useless in others, as long as it's clear what those contexts are. Steal is probably useful when an orc is holding a "Wand of Murdering You With Magic" and not so useful when he's holding a slightly overripe mango. This is evident from just looking at the situation. Feint is... not like that. It costs a feat to let anyone but you benefit from your feints, which kind of hurts its usability; on the other hand, I acknowledge its bonuses can be significant in some cases, but the times I've tried to analyze it have not come out in its favor. So I'm pretty unsure.

Perhaps I'm a bit biased by what has worked pretty well in Asura, but, personally, I would remove some of feint's "slippery weirdness" and revise it to be a general "do this move, get a flexible bonus" maneuver and make sure that bonus works out to be some worthwhile fraction of "two turns worth of doing stuff" without being the overwhelming best choice every time.

Quote from: GhostmanIn some cases it might even be your only reasonable course of action.

Well, I think that the example you gave is rather contrived: the attack for damage has a variance of 8.2369, while the save-or-lose has a variance of 272.25, which is pretty exaggerated. In normal play, melee has a higher variance because you're not hitting 100% of the time but you're also doing more damage when you do hit, while most save-or-loses are more dependable than 10% which in turn lowers their variance. In actual play, you generally won't be choosing between two otherwise statistically equal outcomes with that much difference in variance. That said, I definitely understand and agree with the point that, when considering two otherwise equal attacks, an attack with a greater variance is sometimes preferable due to the ability to win now, with drawback of you might not ever win being less significant in those cases.

Interesting.  It sounds like your biggest beef with Pathfinder combat maneuvers is their reliability, which is a product of the disparity between CMD and CMB.  I wonder whether a simple house-rule could mitigate this: instead of adding both Strength and Dexterity to CMD, you can add one or the other.

I do think that carefully chosen Feats can help improve the reliability of combat maneuvers immensely, and the one big advantage that Fighters have over other classes is a buttload of feats, so there is that, I suppose.  For some, that opens a can of worms about the "feat economy" and character optimization, though.

I will say that what you're calling "contrived scenarios" I'd probably call "tactically optimal contexts," but I think this is a result of the slightly different roles we ascribe to combat maneuvers.  I get the feeling you want debuff combat maneuvers to be generally viable, reliable, and effective in a diverse array of situations as part of a repertoire of moves any character can do regardless of class of training - even if they're not always the optimal choice they will be broadly efficacious in most combats, or at least enough so that save in a few niche situations choosing a combat maneuver over an attack is never a totally bad idea.  Statistically, over a large enough selection of contexts, you want debuff combat maneuvers to be approximately equal in value to attacking.  Is that an accurate assessment or am I distorting your view?

Quote from: SteerpikeIt sounds like your biggest beef with Pathfinder combat maneuvers is their reliability

Well, partially, but their general effectiveness, too. You got it right below.

As I said before, I'd prefer that scenario where both of the heavy hitters can dogpile onto the guy you've successfully dirty tricked to be something that is going to significantly raise damage-- because you're definitely not always going to be able to get things to click that well.

Quote from: SteerpikeI do think that carefully chosen Feats can help improve the reliability of combat maneuvers immensely

Generally speaking, carefully chosen feats can improve the reliability of a combat maneuver. Singular. Each maneuver has its own feat chain, and forcing such focus while meanwhile spellcasters have lots of different spells can help to feed the phenomenon of "Fighters can't have nice things." Enough about this has been written by other people (or even by me at other times) that I won't bother to rehash it and just leave things at that.

Quote from: SteerpikeI will say that what you're calling "contrived scenarios" I'd probably call "tactically optimal contexts,"

The specific case I considered contrived was choosing between a melee attack that hits 100% of the time for one die and no bonus vs. a save-or-lose that hits 10% of the time. Most actual melee attacks found in Pathfinder games have a higher variance than the example melee attack, and most actual save-or-loses found in Pathfinder games have a lower variance than the example save-or-lose, so the difference in variance in an actual game is probably going to be a lot less. I don't disagree that considering the variance as well as the mean can be useful in deciding the "best" option between two choices that are otherwise statistically equal or very close.

Quote from: SteerpikeStatistically, over a large enough selection of contexts, you want debuff combat maneuvers to be approximately equal in value to attacking.

Yes, I'd agree with that summary. If the maneuvers aren't approximately equal, I don't think they have enough general utility to be worthwhile, and players-- used to lackluster results-- will not be inclined to try maneuvers even when they are worthwhile.