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Math Homework: Secondary DPR Benchmarks


Advice

Grand Lodge RPG Superstar 2012 Top 32

How good must your DPR be in order to make it a better idea to attack the enemy than to use Aid Another to give your ally +2 to hit?

That's the short version of the question. Here's the long version:

Let us assume that your party includes a full-BAB PC with 18 STR and Power Attack who uses a greatsword. For simplicity's sake, let's further assume that Mr. Greatsword only goes for the following basic increases to DPR:
5th level - gains a +2 STR belt
6th level - enchants greatsword to +1
8th level - puts his second stat bump into STR (22 total w/ belt)
10th level - enchants greatsword to +2

I doubt this post's question remains relevant later than that, but if you feel the need to extend the math up to 20th, feel free. :)

Now, let's assume that Bob the Hypothetical Party Member is in Mr. Greatsword's party. Bob is not a primary melee guy. However, he occasionally finds himself in the front lines with a weapon in his hand, enough AC/miss chance for that not to be suicide, and an inclination to make attack rolls (maybe he's out of spells or there's no room to flank for sneak attack or whatever).

In any case, Bob has two realistic options: attack the monster, or use Aid Another to give Mr. Greatsword a +2 to hit on his next attack (not his entire full-attack sequence).

Which should he do? I'm working under the assumption that there's a "line", where if Bob has at least X expected DPR, he should attack, while if he has less than X expected DPR, he should Aid Mr. Greatsword. The question of this exercise, then, is this:
Where is that line? What minimum DPR must Bob have in order for it to be more helpful to attack the enemy than to Aid Mr. Greatsword?

To make answers useful, please give an approximate to-hit/damage breakdown instead of just "13.37 DPR" or whatever. Something like "If he's at least +X to hit for 1dY+Z damage, he should attack instead of Aiding".

But let's not look at every single level. Let's just get some benchmarks for 3rd, 5th, 7th, 9th, and 11th level. (Further if you like.) Also, assume Bob and Mr. Greatsword are always equal in level.

Math nerds, GO!

Cheliax

2 people marked this as a favorite.

Is this going to cost Bob his raid dps spot, if he doesn't meet the benchmark?

Grand Lodge RPG Superstar 2012 Top 32

I don't know what you just said. I'm just curious whether, say, a cleric with a longsword and a high AC and no relevant spells should be attacking or aiding.

RPG Superstar 2014 Top 16, RPG Superstar 2013 Top 16

There's too many variables involved to narrow it down to a single number, but you can derive an expression. If you want to find when the Attack Damage is greater than the Assist Damage, you can express that as the inequality:

(0.1*Dg)*(1-(10-HB)/20) < Da*(1-(AC-HB)/20)

Where:
Dg = Mr. Greatsword average damage on a hit
HB = Bob's Hit Bonus
Da = Bob's average damage on a hit
AC = The AC of the target

That simplifies to:

HB > ((20-AC)*Da-Dg)/(.1*Dg-Da)

(This is assuming that .1*Dg is less than Da, that we are excluding extreme cases where you only hit or miss due to 20s and 1s, and we aren't including critical hits)

Running those numbers for Mr. Greatsword and the level 1 Kyra pregen against a 14 AC mook, we come up with a threshhold of -4.36. So as long as her attack bonus is -4 or higher, she's better off attacking.

Running those at level 10 (assuming an average AC of 23 based on the bestiary, Mr. Greatsword as specified, and Kyra with a +1 Flaming Scimitar and no other damage buffs), we get a threshhold of +7.6. So as long as she has a +8 or higher attack bonus (which she should), you're still better off attacking.


AC = AC of victim
B1 = Attack bonus of melee guy
B2 = Attack bonus of aiding character
D1 = Average damage of an attack from melee guy
D2 = Average damage of an attack from support guy

You can use this formula yourself and plugin whatever BAB and AC and damages you want. Notice that I removed the dependency between BAB of the melee character and the fighter. You can change the numbers indenpendantly.

Here's an adjusted formula for melee damage no aid:
A: ((20+B1-AC)/20)*D1
Melee damage by assisting character:
B: ((20+B2-AC)/20)*D2
Melee damage with aid:
C: ((20+B1-AC+(2*(20+B2-10)/20))/20)*D1

Just sum up A and B and compare with C.

(i haven't double checked this, but it should be ok)


The Fighter is probably going to be hitting on a 2 anyways, so Aid Another literally does absolutely zip. I'd say a good secondary DPR is someone who can either finish off an enemy the fighter charged + full attacked in one round, or at least brought it so the fighter can just standard action attack + move to the next one.

Ranged Builds are much better for this.

Grand Lodge RPG Superstar 2012 Top 32

Thanks for the commentary, Mort.

Let's bring it home a little bit:
Suppose the party is 4th level. Mr. Greatsword is therefore Power Attacking at +7 for 2d6+12. "Bob" has 16 STR and a longsword, attacking at +7 (no Power Attack) for 1d8+3.

Should Bob attack, or aid?

Suppose the party is 8th level. Mr. Greatsword now has a full-attack of +12/+7 for 2d6+19 per hit. Bob can full-attack for +10/+5 for 1d8+3 per hit, or he can aid Mr. Greatsword's first attack (but not his second).

Should Bob attack, or aid?

EDIT: Wow, all kinds of ninja'd. Apparently people like to coordinate and all respond at once. :/


1 person marked this as a favorite.
Pathfinder Card Game Subscriber
Lamontius wrote:


Is this going to cost Bob his raid dps spot, if he doesn't meet the benchmark?

No, because Bob is buddy-buddy with one of the officers so he'll always have a spot reserved for him, even though it pisses some of the more competent DPSers off.

Grand Lodge RPG Superstar 2012 Top 32

RainyDayNinja wrote:

Running those numbers for Mr. Greatsword and the level 1 Kyra pregen against a 14 AC mook, we come up with a threshhold of -4.36. So as long as her attack bonus is -4 or higher, she's better off attacking.

Running those at level 10 (assuming an average AC of 23 based on the bestiary, Mr. Greatsword as specified, and Kyra with a +1 Flaming Scimitar and no other damage buffs), we get a threshhold of +7.6. So as long as she has a +8 or higher attack bonus (which she should), you're still better off attacking.

Let's take these examples and keep working: is there a point where the target's AC gets high enough that it becomes better for Kyra to aid instead of attacking?


Plugging plugging plugging...

In the first case, Bob should aid when he has about 25% chance to hit or less. Assuming Aid Another autosucceeds.

In the second case, he should do it when his chance to hit is 40% or less.

So, it is possible. However, that is pretty dependent on the fact "Bob" has really, really terrible melee ability. Give him some Power Attack, a magic weapon, some other basic bonuses, and things would change drastically.


Damned ninjas jumped on this one ;)

Jiggy, this is an interesting question, but I think more information is needed before a numerical value for the DPR contribution of an Aid Another action can be calculated.

To rephrase the question from your opening post: What is the DPR increase provided by giving your full BAB ally an untyped +2 bonus on their next attack roll? In addition to equipment and ability scores, I think you need to make some assumptions regarding the build of the front line ally: fighter with feat and weapon training progression (with Gloves of Dueling purchased when appropriate), ranger +/- favored enemy +/ flanking from animal companion, barbarian with feat progression and raging. A vanilla fighter with standard weapon feats might give you a good baseline.

Target AC is also needed. My gut feeling is that the DPR value of Aid Another increases when facing above CR opponent armor classes. Calculating DPR change when facing a CR+2 or +3 versus CR or CR -2 average armor class would be useful.

Aid another is also not an automatic success, but requires hitting AC 10 (with a possible -4 for cover if standing behind the fighter with a reach weapon). While this might be achievable on any roll higher than a natural 1 at high levels, at starting levels it's more difficult. Some build info on the assisting class is needed (3/4 BAB, 14 Str, no weapon feats?)

While the standard Aid Another action nets your ally a +2 to hit, many humanoids seem to be adopted by halflings and raised to be helpful. What the halflings get from this is unclear, but the +4 Aid Another from the 'helpful' trait is certainly a boon.

Anyway, I'll try and crunch some numbers in a spreadsheet late today if you haven't received some answers in the interim.

RPG Superstar 2014 Top 16, RPG Superstar 2013 Top 16

Jiggy wrote:
RainyDayNinja wrote:

Running those numbers for Mr. Greatsword and the level 1 Kyra pregen against a 14 AC mook, we come up with a threshhold of -4.36. So as long as her attack bonus is -4 or higher, she's better off attacking.

Running those at level 10 (assuming an average AC of 23 based on the bestiary, Mr. Greatsword as specified, and Kyra with a +1 Flaming Scimitar and no other damage buffs), we get a threshhold of +7.6. So as long as she has a +8 or higher attack bonus (which she should), you're still better off attacking.

Let's take these examples and keep working: is there a point where the target's AC gets high enough that it becomes better for Kyra to aid instead of attacking?

Using my formula and assumptions for Kyra (at level 10), it would be AC 25 when assisting is a better idea. But at that point, you're reaching edge cases where you always have a 95% chance of succeeding at an Aid Another, because the target is so low. That throws the calculations off, because you start having 100+% chances of succeeding, and the actual answer will favor attacking more than assisting.

Grand Lodge RPG Superstar 2012 Top 32

Alright, people are wanting specifics, so let's do it this way:
.
..
...
....
Mr. Greatsword
Level 3: +7 for 2d6+9
Level 5: +9 for 2d6+13
Level 7: +11/+6 for 2d6+13 each
Level 9: +14/+9 for 2d6+19 each
Level 11: +16/+11/+6 for 2d6+19 each

Bob
Level 3: +6 for 1d8+3
Level 5: +7 for 1d8+3
Level 7: +9 for 1d8+4
Level 9: +10/+5 for 1d8+4 each
Level 11: +13/+8 for 1d8+5 each

---------------------------

Now, let's rephrase the question: at each of the levels indicated above, what AC does the target need to have in order for Bob to be better off Aiding than attacking?

RPG Superstar 2014 Top 16, RPG Superstar 2013 Top 16

Geez, I already gave you the formula. Can't you at least plug in the numbers yourself? Didn't you get ANY of the math genes in the family?

Grand Lodge RPG Superstar 2012 Top 32

Less talk! More work! *cracks whip*

RPG Superstar 2014 Top 16, RPG Superstar 2013 Top 16

Alright, I made a spreadsheet using my formula (which took a whopping 5 minutes), and I got values of 23, 23, 25, 24, and 27 respectively. Again, with the iterative attacks and the >9 hit bonus on assisting, the assumptions start to break down, but should give threshhold ACs that are artificially low (i.e., the actual threshhold is higher than what the formula gives).

Grand Lodge RPG Superstar 2012 Top 32

So it looks like if a 3/4 BAB PC with no extra damage bonuses needs a natural roll of ~15+ to hit, it might be worth aiding instead of attacking. Does that sound about right?

Cheliax

Xexyz wrote:
Lamontius wrote:


Is this going to cost Bob his raid dps spot, if he doesn't meet the benchmark?
No, because Bob is buddy-buddy with one of the officers so he'll always have a spot reserved for him, even though it pisses some of the more competent DPSers off.

Oh, of course. But...does Bob have the DKP available to get his +1 longsword, if it drops? Or will the Rogue ninja it?

RPG Superstar 2014 Top 16, RPG Superstar 2013 Top 16

Revising the equation to assume only failing assist rolls on a 1, the threshhold ACs go up to 25 at level 9, 28 at 11, and 29 at 12. Iterative attacks for Bob (or should I say, Thomas the Tiefling Hero?) will make full attacks slightly more attractive, if only for the chance of nat 20s.

EDIT: That equation comes out to:

Attack when AC-HB < 20-(1.9Dg/Da)

And AC-HB is the number you need to hit on the d20 to hit. So is that simple enough for you yet?


SoulGambit0 wrote:

The Fighter is probably going to be hitting on a 2 anyways, so Aid Another literally does absolutely zip. I'd say a good secondary DPR is someone who can either finish off an enemy the fighter charged + full attacked in one round, or at least brought it so the fighter can just standard action attack + move to the next one.

Ranged Builds are much better for this.

Bob could also use Aid Another to increase the fighter's AC. Depending on the bad guy, that might turn out to be a better option.


I never saw the point of aid another, in its normal form, that tiny bonus is not going to make a big difference. It would just be more effective to flank the guy, pull out a bow and harass the casters, throw out a buff spell or 2, there are plenty of ways. If build to tweak out a hge bonus then hey more power to you, or well them rather.

Do not bother to just sit around and use aid another, there are more effective ways to be useful.

If you can finish of a severely wounded enemy, go ahead. Unless you would miss it more than 50%.

If the sneak attacker needs a flanker, flank and then either attack the flanked enemy or hamper him more with maneuvers or items.

If for some reason your damage is horrible or you can not hit the broad side of a barn, never underestimate alchemical items or wands.

We used to play with a bard who had an 8str and 8 con. He was captain buff though, wands, alchemical items, bardic performances, bard spells. It was all good, he was a centerpiece of the battles but could not hurt a fly.

Personally I played a Wizard(diviner)/Harrower who was your quintessential fortune teller caster. I never caused a single point of damage to anyone. However I was a beast at battlefield control and enchanting.

If you want actual numbers.

If % to hit enemy x average damage roll < (teammate's % to hit with aid another - teammate's % to hit without aid another) x teammate's average damage roll. Then just go ahead and aid another, but if it is greater just attack.

Ex.

Lets say you have only a 20% chance to hit, and you roll an average of 15 damage, that would be a 3.0 for you.

If your teammate would hit 60% of the time, but with your aid could hit 70% of the time and his average damage is 60, that would be a difference of 10% x 60 = 6.0

This of course would need to be ignored if the % change does not effect a roll such as when your teammate would need a 20 to hit no matter what, or he would hit on a 2 anyway.

Silver Crusade

RainyDayNinja wrote:
Bob (or should I say, Thomas the Tiefling Hero?)

I, uh, don't know what you mean...


You know who aid another is for?
Followers and very low level henchmen (and, on the other side, seriously under CR mooks)
Armies and militias will also often use aid another, because they frequently have a limited number of special purpose ammunition items for use against big nasty things with lots of DR that they need to get the most out of.
But PCs that are full level rarely find it worth the action economy to use aid another PC in combat.


EWHM wrote:


But PCs that are full level rarely find it worth the action economy to use aid another PC in combat.

This so dependent upon so many factors that such a blanket statement can be anything but untrue.

There are many classes, items, and feats that help aid another that someone can often find it much more useful than using a resource such a s a spell to make use of it.


It's always better to attack the enemy, because aid other is a boring ass way to spend your turn. Who knows, you might roll a 20.


P.H. Dungeon wrote:
It's always better to attack the enemy, because aid other is a boring ass way to spend your turn. Who knows, you might roll a 20.

Again not necessarily true. Yes, you may roll a twenty. But you may not do much damage. Your fighter may miss by 1 or 2 and suddenly your group misses out on a ton of damage being done. On the flipside your fighter may be hit by just one or two points and suddenly he takes a ton of damage.

So look at it this way: You have a 5% chance of doing piddly to squat or at least a 50% chance of boosting your big hitter a touch.

Now keep in mind this scenario does not include flanking in which yes it is usually a better idea to go ahead and attack.


There are essentially two factors that contribute here.

The avg damage per attack of the character being aided and the avg damage per attack of the character aiding.

The act of aiding sacrifices one attack so in a case with 50% chance to hit and avg damage of 5.5 (a d10) you're giving up 2.25 points damage for a potential chance to boost hit by +2 on the other character.

You can easily see from this that the only way to compensate for this loss is if the attack that you're aiding actually deals so much potential damage in a hit that it overshadows the loss of the aiding character's attack. You should also take limited resources into account. It MIGHT be worth aiding if the attacker is spending some kind of limited resource to do the attack and you deem that this attack is valuable enough to NEED to hit.


Jiggy wrote:
So it looks like if a 3/4 BAB PC with no extra damage bonuses needs a natural roll of ~15+ to hit, it might be worth aiding instead of attacking. Does that sound about right?

Close.

Using the specifics you provided for Mr. Greatsword and Bob/Thomas, I ran some dpr numbers looking for the break even point for the +2 Aid Another action versus normal attack. From levels 5-11, Aid Another was the superior choice if Bob/Thomas needed an attack roll of 16+ to hit on his initial attack. This represented an opponent AC of approximately CR+4.

Using the same specifics, I looked for the break even point if Bob/Thomas had the helpful trait which grants a +4 on Aid Another actions. Between levels 5-11, Aid Another was the superior choice when Bob/Thomas needed an attack roll of 12-13+ to hit on his initial iterative attack. This represents an opponent AC of about CR+0 to +1.

(The break even point was +1 higher at 3rd lvl for both the +2 and +4 Aid Another specs as the success chance of Aid Another is lower and the difference in combat output between Mr Greatsword and Bob was less.)

TLDR: For some support characters, using the Aid Another action in combat can be a superior choice over using their normal attack sequence versus high AC opponents.


Easy, if you aid another you give them 10% more DPR (10% more hits), assuming they aren't already hitting on a 2 or less.

Just look at the average damage the BSF is doing and figure what 10% of that is, then look at your chance to hit * your average damage and go with whichever is higher. Remember to calculate your multiple attacks.


More correctly, if you aid another, the party's total DPR increases by 10% of the aided person's damage per hit (and decreases by your DPR, obviously).

Basically, the question is simply "is 10% of your friend's damage per hit greater than or less than your DPR?" If yes, aid another. If not, don't bother. For 10% of their damage per hit to exceed your entire DPR, you clearly need to have either a really low chance of hitting the opponent or a really low damage per hit (or your friend needs to have truly ridiculous DPR, at which point the entire discussion becomes moot anyway).

At level 7, using your example, your DPR needs to be less than 2. Since your damage per hit it is about 8.5, aid another is only the right choice when your probability of hitting is less than ~ 23% - i.e. when you need to roll a 17 or more.

Also worth remembering: you need to factor in your chance of succeeding on aid another, too, which is why I carefully picked level 7 where it stopped mattering!

Shadow Lodge

Looked at lvl 1:

Assumed +4 to hit for average damage of 13 (1 BAB + 4 STR - 1 PA || 2d6base +6 str +3 PA)

and a Str 14 0 BAB cleric with a Scimitar.

Using the DPR formula hd+tchd

I get the following for both attacking.
AC DPR
10 14.16
11 13.11
12 12.06
13 11.01
14 9.96
15 8.91
16 7.86
17 6.81
18 5.76
19 4.71
20 3.66

If instead of adding the cleric's damage I add .65*2 to the fighter's to hit (8+ to aid)
I get the following
AC DPR
10 11.9184
11 11.1384
12 10.3584
13 9.5784
14 8.7984
15 8.0184
16 7.2384
17 6.4584
18 5.6784
19 4.8984
20 4.1184

Meaning that assisting is better than attacking only at AC 19+

Thinking about it more generalized:

If DPR is < %THAC10*2 added to the fighter's hit% in their DPR formula then you should aid, otherwise attack.

So if your hd+tchd < Their (h+YOUR%THAC10*2)d+tc(h%YOURTHAC10*2)d
You should aid another rather than making your own attack.

If you have something cool that makes your aid better than +2 replace the multiplier in the %THAC10*2 bit of the formula with whatever your bonus is.

Grand Lodge RPG Superstar 2012 Top 32

This thread has given me exactly what I was after. Thanks, all!


Just found this thread and have been playing around with an aid an another bard build. I have been using Tejon's spreadsheet for this build (@ lvl 12) and a proven destroyer of worlds Barbarian (my lvl 12 PFS Barb) to receive the aid. What I found was that my aiding was absolutely useless as the Bards inspire courage brought the Hit high enough that more hit from an aid was worth 0 damage (first attack had 95% chance of hitting before aid another). So this has me thinking:

Maybe the aid is better to hand out to a 3/4 bab player with high damage potential (i.e. a rogue).

Maybe all the ways of bumping aid another (halfling trait, Benevolent enchantment, etc.) are not as great as they seem because they are wasted on the primary first iterative and so your likelihood of maxing out on hit chance is high.

Maybe Bards are just a bad example for aiding another as they already hand out big to-hit bonuses.

I actually find this a very interesting topic that is harder to peg down that the typical should I take power attack or weapon focus question that DPR spreadsheets usually help us answer.


Jiggy wrote:
This thread has given me exactly what I was after. Thanks, all!

You probably want to consider that average DPR is not what matters at the table.

A fighter that hits 50% of the time for 30points never deals 15damage, but rather it comes in chunks.. even more so when figuring criticals.

Why is this important?

Average damage might say that the cleric should swing, when in reality he should assist.

Of course the assisting cleric should look to flank as well, and if they want to do this as their contribution in combat might consider increasing the bonus you give when doing it.

Here's a fun trick as well when the main attack hits on a 2.. ready to assist the iterative attack...

In general this becomes viable when your expected damage is very low- you can see this from average damage calculations.

It is also viable when one hit from the fighter will drop the enemy, but one hit from you will not. This you won't see from average damage calculations.

If you hit but the monster lives because the fighter misses by 1 or 2 when the fighter's hit would have taken it out.. then what's the point of your hit, or even trying to? This doesn't model well, so on the internets people go to average damages.

The table doesn't run that way.. count number of hits to the center of the tootsie roll pop...

-James


Like I said. Their is a lot more going on in this type of question than a typical DPR question. I wish someone would take into account something better for combat than DPR. I would like to see something that calculates the average number of rounds that an enemy is combat active. This might be a better indicator of combat effectiveness and show your point better.

Thanks for the tip on readying an aid. That can help out a lot in making sure your aid helps the chances of the receiver hitting.


The best one to Aid Another is a summoned creature with a good hit bonus but negligible damage (eg a bat), especially if it's flanking. A Giant Frog (SM2) is awesome for this as it has a reach of 15' and can jump like crazy to get to places. With the +2 for flanking it needs only a 5 to Aid.


Lab_Rat wrote:

Like I said. Their is a lot more going on in this type of question than a typical DPR question. I wish someone would take into account something better for combat than DPR. I would like to see something that calculates the average number of rounds that an enemy is combat active. This might be a better indicator of combat effectiveness and show your point better.

Thanks for the tip on readying an aid. That can help out a lot in making sure your aid helps the chances of the receiver hitting.

I wonder if something like that has been done yet, dpr vs dpr.

Monster X has Y hp and Z dpr
vs
Player U has V hp and W 2 dpr

Monster X will be defeated in Y / W turns
Player U will be defeated in V / Z turns

(these assume that the players are monsters attack without taking other actions)

Then we look at which dies quickest. We multiply their dpr by that amount and compare to total HP of the survivor. That's how many HP they have left when winning...

I dunno what you'd actually USE this for, though.


The answer is easy:

- First calculate the weaker character's DPR as a function of AC (secondary DPR = sDPR).
- Then calculate the same for the fighter as a function of AC and AC-2, subtract the first from the second (this is the marginal DPR contribution of Aid Another = mDPRoAA).
- When mDPRoAA > sDPR the secondary character should use Aid Another.


Mudfoot wrote:

The best one to Aid Another is a summoned creature with a good hit bonus but negligible damage (eg a bat), especially if it's flanking. A Giant Frog (SM2) is awesome for this as it has a reach of 15' and can jump like crazy to get to places. With the +2 for flanking it needs only a 5 to Aid.

How are you getting animals to aid other?

-James


Handle Animal.

Though I find it easier to do with creatures that have a language such as Lemures or Elementals.


Speak with animals. Given that druids can summon pretty much at will, it's not so hard. But it is of course easier with intelligent creatures.

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