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Since there is a current discussion going on about Power Attack being a trap, I would like to offer some considerations on the common practice of DPR calculations and how the miss out on some important aspects. I shall assume that the reader is familiar with the common DPR formula and will discuss it in depth.
tl;dr
Ceteris paribus, high accuracy is better than high damage, because a) lower chance of doing nothing, b) faster kill rate and c) the advantage of smaller slices.
General assumptions
DPR is generally calculated by multiplying to hit chance with average damage per hit, with some extra apparatus for crits etc.
By thus taking the average over an infinite number of hits, one important aspect gets left out: The relationship between frequency of hits and duration of combat. For simplicities sake, I will ignore iterative attacks. Figuring them in is left for the critics.
Let's compared two extreme cases with similar DPR but different dsitribution of raw damage and accuracy.
a) High Accuracy: Hits 90% of the time, does 10 points of damage on one hit.
b) High Damage: Hits 30% of the time, does 30 points of damage per hit.
1) The chance of doing nothing
Now, if we consider the probability of hitting at least once during one combat vs. the probability of always missing, we have a comulative Bernouli sequence with n = number of rounds and p = 0,3 or 0,9. We are interested in the probability of getting no hits, thus not contributing anything during an entire combat.
With some rounding, we can read the data from one of many readily available tables
The HD case: P(n,p=0.3,x=0)
n ::: P
1 ::: .7
2 ::: .49
3 ::: .34
4 ::: .24
5 ::: .17
6 ::: .12
The HA case: P(n,p=0.9,x=0)
1 ::: 0,1
2 ::: 0,01
3 ::: 0,001
...
As we can see, the difference shrinks, the longer the combat lasts, but is rather impressive for short fights. If over all combats are shorter rather than longer the case gets worse for HD. This is a jarring observation if you consider that shorter combats are generally considered desirable.
2: Accuracy kills faster
Next consider an enemy of 30 hit points, a one hit kill for HD, a three hit kill for HA. What are the probabilities for such an enemy to last into round 4 vs HA and HD respectively?
For HD the case is simple. It is identical to the "all misses" case above: 0.34, so roughly a third.
For HA, instead of just wanting to know the probability of not hitting at all, we need the inverse probability of hitting three times out of three. This is simply 1-0.9*0.9*0.9=1-0.73=0.27, roughly a fourth.
3: The Advantage of Smaller Slices
If the enemy has a less fitting amount of hit points, HA is better off still, since for any enemy of 30-40 HP, both HA and HD need one more hit, which is much easier to do for HA. As with combat duration, the difference generally shrinks as hit points grow, yet the Smaller Slices advantage still favours HA over HD every time an enemy has just a bit more hit points that HD can to in x hits and less than HA can do in 3x+2 hits.
I conclude: All else being equal, it is always preferable to have higher accuracy over higher damage. Furthermore, the experience of missing a lot makes playing HD over HA less enjoyable for many players, in particular because combat tends to be short and no one likes never hitting.
Addendum: The advantage of smaller slices also speaks in favozr of many attacks vs. powerful attacks e.g. TWF vs. THW.
Caveat: This does not consider further factors, in particular damage reduction which affects HA much more strongly than HD or miss chance, which affects HD worse than HA.
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I think the main critque I have is the examples you choose to use. They are a bit too extreme and unrealistic.
You don't end up with a 60% swing chance to hit with a difference in static damage of 3 times greater.
It's more like, 30% chance to hit difference (on the high end) with a 12 to 18 point damage difference (considering solely the use of power attack. But don't forget while your example has only a 20 point difference, which is similar to that granted by power attack at high level, it's not a difference of times 3 because of damage from weapon dice, strength, etc.
So, I think you're numbers over emphasize some things and conclusion. I guess my point is, your examples are too arbitrary to be representative of actual game conditions.
I will also add, as a general expereince most combats do not last more than 4 rounds, at least for moderately optimized characters. In general most combats at my table seem to be over in 3 rounds.
Yes you want to be able to hit often, but like claxon said, your example is not practical. If you really wanted a good example find a level and build a TWF compared to a THW or THW with and without power attack and do these calculation.
The example is chosen for clarity. The relationship holds to a correspondingly lesser degree in less extreme cases. A lesser difference is a difference still.
Also it was chosen to be abstract to clarify a particular relationship between abstract concepts.
Thirdly, the issue at hand (DPR calculations) is in general highly abstract and not representative of the diversity of actual play, I hence I do not consider that point all too relevant.
On the other hand, my abstract conclusion does point, imo, towards an explanation why, in actual play, accuracy is generally valued so highly. That is to say, the presented abstract relation describes an aspect of the structure of actual play, because it describes facts about the rules governing actual play. So "ceteris paribus" is the important factor here. Though other aspects are certainly also efficacious, that does not disprove my results nor show them to be irrelevant.
Yes a 60% difference makes accuracy more important because it's the part you're weak on. But if you compare 80% and 70% (or even better actual to hit differences based on build), with more realistic damage differences or actual damage values, then I feel this would be more worth it.
Your example also doesn't consider the fact on the 30HP enemy of there being another enemy for you to hit. How likely the 1 hit killer is to kill both of them is another important part of this. The 10hp hitter needs 6 hits, the 30 damage hitter only needs 2 hits. I don't know the math off hand, but I feel the 30 damage will kill both of them in the same time or sooner, and the fact that it can be sooner is something that is beneficial.
The pretty clear conclusion, given my math is sound, is that all things being equal, accuracy is always preferable to a corresponding amount of damage.
What happens in actual play is that sometimes you get more in damage than you lose in accuracy and if that is the case you can still come out on top. But given identical DPR, accuracy > raw damage, no matter how extreme the difference.
The real practical question is at what point the HD disadvantages are less relevant than DPR increase. If anyone has a workable analysis on offer, I'd be keen on reading it.
You're conclusions are not altogether incorrect, but the numbers you have chosen greatly exagerate the differences and may lead people to conclude that high accuracy should always be the goal compared to higher damage. But this is certainly wrong.
If you only fail to hit on a 1, higher accuracy is no longer valuable.
Accruacy is important. But so is dealing damage, you want as much of both as you can. A general rule of thumb is that gaining 2 damage is mathematically equivalent to increasing attack by 1, within the limit of autosuccess and autofailure. Which is why, power attack is good. Because it does exactly that, and on average despite your to hit decreasing yields a bonus to damage overall except in cases of high AC relative to your to hit, though the exact values will vary depending on specific builds.
And that's exactly why calculating DPR is a beneficial mechanic because it take into account both your ability to hit and how much damage you can deal based on average probabilities (which essentially represents an infinite amount of dice rolls).
Calculating DPR is a good way to evaluate two similar combat options or understanding how an option will impact your overall damage output capability. It is not an end all summary to evaluate all aspects of character building, but it is a useful tool.
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Actually what you should take away from it is that you want to increase the one that is weakest.
The high damage person should find ways to increase his accuracy. While the high accuracy should look into ways to raise damage.
Find the sweet spot between damage and accuracy is what you should aim for.
The pretty clear conclusion, given my math is sound, is that all things being equal, accuracy is always preferable to a corresponding amount of damage.
What happens in actual play is that sometimes you get more in damage than you lose in accuracy and if that is the case you can still come out on top. But given identical DPR, accuracy > raw damage, no matter how extreme the difference.
The real practical question is at what point the HD disadvantages are less relevant than DPR increase. If anyone has a workable analysis on offer, I'd be keen on reading it.
Well you're still not addressing the "ability to kill two people" factor. What is the likelihood of the high accuracy character killing two 30HP characters in 4 turns? What is the likelihood of the damage character doing that? The damage character had the potential to finish a fight sooner that the accuracy is lacking.
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Your examples don't hold much weight because they are not bringing new information that we do not know, and you are not using real numbers. I have also seen how much damage PA does in real games when used by PC's, and certain NPC's.
Yes accuracy is important, but it can also still not do as much damage overall if another character just has more damage potential. PA trades off accuracy for damage potential, and just like any other ability you have to know when to use it.
Me having to explain this to you already tells me you have no idea what you are talking about.
Sit at one of my games when I am using a giant to power attack you, and the actual game experience might change your mind.
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What is the likelihood of the high accuracy character killing two 30HP characters in 4 turns?
Four attacks, 90% hit chance, 10HP per attack: zero chance of killing two enemies. 66% chance of killing one of them. 99.99% chance of doing at least 10HP damage during this time.
(I am treating 0HP as dead, not disabled as in normal play.)
Four attacks, 30% hit chance, 30HP per attack:
Around 35% chance of getting two kills in this time.
41% chance of getting only one kill.
24% chance of doing no damage whatsoever.
(My sums here were done using a fairly haphazard method and I wouldn't be surprised if I made a mistake.)
Note that this situation is pretty skewed to favor the 30HP damage hitter because it is exactly the right damage with no overkill. Against enemies with 31HP each, the odds are much worse. Against 10HP enemies, the 10HP attacks are way better.
right, but it was one of the example HP he used to say accuracy was better so it was fair game.
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The real issue with "Acuracy is better than damage" is that when building an optimized combatant you quickly approach the point where you only miss on a 1 vs CR=level+2 enemies. So trading acuracy for damage is hugely beneficial because, "I only miss on a one, and I only miss on a one and do extra damage," is really a simple case.
Also, the swing you use in your example is the same as +12 to hit. There is no single option with that swing. But at lower levels that is literally the difference between a fighter and a wizard with a crossbow. Your examples do not reflect the true nature of making a single choice to sacrifice accuracy for damage. Your example more closely describes intentionally building a non melee combatant and a fighter.
The "high accuracy" character has essentially zero chance to one-shot opponents, or even kill them in two rounds, at least in your example. This means that the opponent is still taking actions in the meantime. The point of KOing them quickly is to stop them from taking actions.
A better metric would be a cumulative probability of life: P1 + P2 + P3 + P4 + ... where P1 is the cumulative probability they are still standing after the first round, P2 is the cumulative probability they are still standing after the second round.
In the HA case against 30 HP, P1 and P2 are going to be 1, where in the HD case they will be 0.7 and 0.49. I don't have time to calculate the whole series right now, but it's an important consideration. Even moreso when you factor in that earlier actions are more valuable, i.e., the wizard will tend to use their best spells in the early rounds of combat.
A more important criticism of DPR calculations, IMO, is the assumption of full-attack.
I personally think that DPR should be calculated as the combination of one standard action attack + one full-attack, which in my experience is much closer to real-game conditions.
If anyone feels like it, there was discussion on this topic last month here.
The interesting thing is then and now is that people often say you'll always hit anyways, which I've found not to *always* be the case. The take away is that sometimes PA is good and sometimes it isn't worthwhile. When it isn't useful it is a wasted feat, literally doing nothing for you.
To expand on not always hitting, eventually you'll pick up an iterative attack or two, and almost always that extra attack will need the accuracy boost to reliably hit. It really depends on where you are on the curve, but the point is that Power Attack shouldn't always be on.
I don't know where that trade off happens, I'd have to go over the math again, but I know that Weapon Focus was better than Power Attack for a lot longer than I expected. One thing I didn't cover then though, is that Weapon Focus is much less likely to be "wasted" than Power Attack. And perhaps more importantly, when Weapon Focus would be wasted it matters less. (What I mean is when your to-hit matters less is when AC is lower, which usually means you're fighting low-CR enemies. low-CR means lower health so extra damage matters even less.)
A more important criticism of DPR calculations, IMO, is the assumption of full-attack.
I personally think that DPR should be calculated as the combination of one standard action attack + one full-attack, which in my experience is much closer to real-game conditions.
The DPR assumes full damage output possible by a single character. It uses a full attack because the point is to compare hypothetical characters NOT to simulate gameplay for a specific character.
This is the same reason that no consumable items are used in the metric, only buff that can be self applied are used. Of those buffs only those which can be applied as a swift or faster action OR last longer than 10 minutes a level are included.
Basically, DPR has nothing to do with in game predictions and only matters for comparing A to B, which it does very well.
A more important criticism of DPR calculations, IMO, is the assumption of full-attack.
I personally think that DPR should be calculated as the combination of one standard action attack + one full-attack, which in my experience is much closer to real-game conditions.
The DPR assumes full damage output possible by a single character. It uses a full attack because the point is to compare hypothetical characters NOT to simulate gameplay for a specific character.
This is the same reason that no consumable items are used in the metric, only buff that can be self applied are used. Of those buffs only those which can be applied as a swift or faster action OR last longer than 10 minutes a level are included.
Basically, DPR has nothing to do with in game predictions and only matters for comparing A to B, which it does very well.
That right there, people use DPR to build characters to play in games. It shouldn't be used for that, since it can't tell you how your character will perform in a game setting.
EDIT: I don't dispute that it can be used to compare options. I'm just saying it shouldn't be used as a guide for building characters to play in games.
A more important criticism of DPR calculations, IMO, is the assumption of full-attack.
I personally think that DPR should be calculated as the combination of one standard action attack + one full-attack, which in my experience is much closer to real-game conditions.
The DPR assumes full damage output possible by a single character. It uses a full attack because the point is to compare hypothetical characters NOT to simulate gameplay for a specific character.
This is the same reason that no consumable items are used in the metric, only buff that can be self applied are used. Of those buffs only those which can be applied as a swift or faster action OR last longer than 10 minutes a level are included.
Basically, DPR has nothing to do with in game predictions and only matters for comparing A to B, which it does very well.
That right there, people use DPR to build characters to play in games. It shouldn't be used for that, since it can't tell you how your character will perform in a game setting.
EDIT: I don't dispute that it can be used to compare options. I'm just saying it shouldn't be used as a guide for building characters to play in games.
I'm not saying that it isn't a useful tool for building characters to play in a game. It's very good for that too. It is good for telling you if IN A REAL GAME option A or B is better. It will tell you if build A or B will do more damage. It won't tell you that you will average 137.42 damage a round. The damage number itself is largely worthless but the greater than/ less than is supremely useful.
If it's useful then it would describe accurately which option is better than which.
Example using (edit: EXTREME) simplifications to illustrate a point:
Attack Option 1: Hits 100% for a static 10 damage.
Attack Option 2: Hits 5% of the time for a static 10000 damage.
That makes:
Attack Option 1 DPR: 10
Attack Option 2 DPR: 500
Now say you're fighting someone with 10 hp, which option is better?
DPR would tell me option 2, but it is wrong.
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If it's useful then it would describe accurately which option is better than which.
Example using (edit: EXTREME) simplifications to illustrate a point:
Attack Option 1: Hits 100% for a static 10 damage.
Attack Option 2: Hits 5% of the time for a static 10000 damage.That makes:
Attack Option 1 DPR: 10
Attack Option 2 DPR: 500Now say you're fighting someone with 10 hp, which option is better?
DPR would tell me option 2, but it is wrong.
What's really interesting is how folks looking to point out flaws with DPR calculations use extreme-beyond-possibility numbers instead of the actual, buildable, playable numbers that actual DPR calculations deal with.
Rather ironically, the other common way people try to debunk DPR calcs is by labeling them as too theoretical and therefore not applicable to "actual play".
I should go check and see if there's anyone who does both critiques, because that would be hilarious.
If it's useful then it would describe accurately which option is better than which.
Example using (edit: EXTREME) simplifications to illustrate a point:
Attack Option 1: Hits 100% for a static 10 damage.
Attack Option 2: Hits 5% of the time for a static 10000 damage.That makes:
Attack Option 1 DPR: 10
Attack Option 2 DPR: 500Now say you're fighting someone with 10 hp, which option is better?
DPR would tell me option 2, but it is wrong.
DPR will predict performance of a character over the course of a campaign, not a single combat. And certainly you can muck the numbers too get bad results. But if you use real numbers instead of "point making exaggerations" then you will see that those problems don't occur. GIGO, after all.
If it's useful then it would describe accurately which option is better than which.
Example using (edit: EXTREME) simplifications to illustrate a point:
Attack Option 1: Hits 100% for a static 10 damage.
Attack Option 2: Hits 5% of the time for a static 10000 damage.That makes:
Attack Option 1 DPR: 10
Attack Option 2 DPR: 500Now say you're fighting someone with 10 hp, which option is better?
DPR would tell me option 2, but it is wrong.
What's really interesting is how folks looking to point out flaws with DPR calculations use extreme-beyond-possibility numbers instead of the actual, buildable, playable numbers that actual DPR calculations deal with.
Rather ironically, the other common way people try to debunk DPR calcs is by labeling them as too theoretical and therefore not applicable to "actual play".
I should go check and see if there's anyone who does both critiques, because that would be hilarious.
If you go to the thread I linked to you'll see I did the work with actual reasonable numbers.
But that's beside the point, to show a theory is wrong you only have to show one case where it is wrong which I've done. While I don't relish the idea of linking to a wikipedia article on scientific theory I feel like I need to. link
Also, the point is presumably to achieve a better understanding of the game. The best way to do that is to constantly challenge what you "know". You shouldn't accept DPR as fact, but strive to understand where it falls short, and also why it falls short.
to show a theory is wrong you only have to show one case where it is wrong which I've done.I think you need to look reeeaaal close at what it really is you've proven wrong, and then see if you can find where anyone ever said that was right.
You need to read what I was saying that in reference to.
Does it do?
It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations.
Check.
Does it do?
Every "good" scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.
Nope, it doesn't forbid non-"REAL GAME OPTIONS"
And lastly, what seems to be happening here:
Some genuinely testable theories, when found to be false, are still upheld by their admirers—for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status.
If it's useful then it would describe accurately which option is better than which.
Example using (edit: EXTREME) simplifications to illustrate a point:
Attack Option 1: Hits 100% for a static 10 damage.
Attack Option 2: Hits 5% of the time for a static 10000 damage.That makes:
Attack Option 1 DPR: 10
Attack Option 2 DPR: 500Now say you're fighting someone with 10 hp, which option is better?
DPR would tell me option 2, but it is wrong.
The problem here is that DPR doesn't tell you anything of the sort.
It tells you numbers, you have to understand numbers in the context.
Also, I would like to point out you don't have a 100% chance to hit, the upper limit is 95%.
DPR tells you the average amount of damage to expect over the course of enough rounds. That's all. When you start trying to say that DPR says theoretical option 2 is better than theoretical option 1 you're incorrect because it doesn't make any sort of judgement about which is better. You as a human being are making the judgement, based on flawed premises to illustrate a false point that doesn't exist.
When you start trying to say that DPR says theoretical option 2 is better than theoretical option 1 you're incorrect because it doesn't make any sort of judgement about which is better. You as a human being are making the judgement, based on flawed premises to illustrate a false point that doesn't exist.
Calculating DPR is a good way to evaluate two similar combat options or understanding how an option will impact your overall damage output capability. It is not an end all summary to evaluate all aspects of character building, but it is a useful tool.
That right there, people use DPR to build characters to play in games. It shouldn't be used for that, since it can't tell you how your character will perform in a game setting.
EDIT: I don't dispute that it can be used to compare options. I'm just saying it shouldn't be used as a guide for building characters to play in games.
Given that this is what has been said, what is your "false point that doesn't exist?"
And from the thread I linked to which includes a calculation on "actual, buildable, playable numbers that actual DPR calculations deal with."
Extending that thought a bit further, you can see that Power Attack isn't always a "great thing".
Mind you I'm only inspecting points on this curve, I'm sure there are places where its much better to Power Attack, but given the following:
Say you're building a
Level 1 Fighter:
Str: 16, Shortsword +4 1d6+3 (Keeping things simple, ignoring two-handed and other feats).
Say you're only every going to attack a target with the following stats:
AC: 15, HP: 5
Now lets say you're attempting to decide between taking these two feats, Power Attack and Weapon Focus:
Let's first figure out our baseline:
Expected Rounds to Kill with 75% confidence:
Rounds to Hit: ln(.25)/ln(.5) == 2Then we know:
Chance a hit is a killing hit: 5/6
Chance a hit is a wounding hit: 1/6
Chance a hit after wounding is a killing hit: 6/6So we should expect something like (2 * (5/6)) + (4 * (1/6)) == 2.333 rounds.
Now using power attack we have:
A 45% chance to hit, but when we do we'll defeat them which makes that:
Rounds to defeat with 75% confidence: ln(.25)/ln(.55) == 2.318 rounds.
So Power Attack is only 1.006 times better than not using it.
Now with Weapon Focus:
Roughly the same, but the rounds to hit is:
ln(.25)/ln(.45) == 1.736
Which becomes:
(1.736 * (5/6)) + ((1.736*2) * (1/6)) == 2.025 rounds. Which is 1.152 times better.
So in this case you should always take Weapon Focus.
EDIT: As I said around that time, I could be wrong somewhere on that math, so if you see something wrong let me know.
To me it looks like your test case is an issue here, and checking the rounds to kill for DPR. Rounds to kill isn't the same thing as DPR.
To me it looks like your test case is an issue here, and checking the rounds to kill for DPR. Rounds to kill isn't the same thing as DPR.
If I understand what you're saying right, I'm not using the rounds to kill to generate DPR. I'm using the rounds to kill to show that a higher DPR doesn't result in a faster kill.
EDIT: Which is to say Weapon Focus is a better option for that character than Power Attack in this circumstance. The reason is, they'll kill faster and thus the enemy will have less opportunities to cause harm to the group.
I'm going to take issue with the following statements:
DPR tells you the average amount of damage to expect over the course of enough rounds. That's all.
DPR will predict performance of a character over the course of a campaign, not a single combat.
Basically, DPR has nothing to do with in game predictions and only matters for comparing A to B, which it does very well.
To the first two statements: DPR calculated using full attacks does not accurately predict damage over a number of rounds, or over a campaign, because you won't get a full attack every round throughout a campaign. In my experience, it's more reasonable that you'll be able to full attack about 50% of the time, so using 1 standard attack + 1 full attack would be a measure with more "ecological validity".
To the third statement: DPR calculated using the "standard + full" metric is 100% as capable of comparing A vs. B, with the added bonus that it more closely mimics real-game conditions. Of course, it's impossible to come up with a test which perfectly captures real-game conditions, as games differ, but it's clearly true that 100% full attacking is a flawed premise. I argue that a better premise is equal numbers of full-attacks and standard action attacks, with the exception of archers, who can reasonably assume 100% full-attacks.
How many rounds it takes to kill is based on what you're fighting.
if you do X damage then them having X or X+1 health is a big difference. Also if I kill them in 2.01 or 2.99 rounds it will still take me 3 rounds (yes I know that it's the average so sometimes it will only be 2 rounds). if you're going to be doing a round compare you probably should say % chance they are dead in 2 rounds and % chance dead in 3 rounds.
While DPR says, against this AC (usually the suggested AC for monsters of a certain CR) I will deal approximately this much(A) damage a full attack using this type of fighting, if I do a different type of fighting I get this much(B) damage per full attack. If A > B then A is probably the stronger choice all around.
And I say your example is bad because it skewed to favor weapon focus. If you use the "suggested values" for CR 1/2 or CR 1 you have 11 or 12 AC and 10 or 15 hp. Heck in your example if the fighter used two hands on the sword he'd kill it in 1 hit every time. Thus yes, weapon focus is clearly better because you only need the 1 hit and it's a bit difficult to hit. If you're wanting to use a good example you either need many different test cases, or use the average but realize that it's the average over all types of encounters.
I'm going to take issue with the following statements:
DPR tells you the average amount of damage to expect over the course of enough rounds. That's all.DPR will predict performance of a character over the course of a campaign, not a single combat.Basically, DPR has nothing to do with in game predictions and only matters for comparing A to B, which it does very well.To the first two statements: DPR calculated using full attacks does not accurately predict damage over a number of rounds, or over a campaign, because you won't get a full attack every round throughout a campaign. In my experience, it's more reasonable that you'll be able to full attack about 50% of the time, so using 1 standard attack + 1 full attack would be a measure with more "ecological validity".
To the third statement: DPR calculated using the "standard + full" metric is 100% as capable of comparing A vs. B, with the added bonus that it more closely mimics real-game conditions. Of course, it's impossible to come up with a test which perfectly captures real-game conditions, as games differ, but it's clearly true that 100% full attacking is a flawed premise. I argue that a better premise is equal numbers of full-attacks and standard action attacks, with the exception of archers, who can reasonably assume 100% full-attacks.
I think you're on to something here, but this really seems like an ad-hoc addition to the DPR theory. I do think Standard+Full will better describe your options (thus giving feats like Vital Strike and Cleave their due), but I still think the underlying issue is still present.
We should probably be looking for something that says, we can expect something to happen at x confidence.
How many rounds it takes to kill is based on what you're fighting.
if you do X damage then them having X or X+1 health is a big difference. Also if I kill them in 2.01 or 2.99 rounds it will still take me 3 rounds (yes I know that it's the average so sometimes it will only be 2 rounds). if you're going to be doing a round compare you probably should say % chance they are dead in 2 rounds and % chance dead in 3 rounds.While DPR says, against this AC (usually the suggested AC for monsters of a certain CR) I will deal approximately this much(A) damage a full attack using this type of fighting, if I do a different type of fighting I get this much(B) damage per full attack. If A > B then A is probably the stronger choice all around.
And I say your example is bad because it skewed to favor weapon focus. If you use the "suggested values" for CR 1/2 or CR 1 you have 11 or 12 AC and 10 or 15 hp. Heck in your example if the fighter used two hands on the sword he'd kill it in 1 hit every time. Thus yes, weapon focus is clearly better because you only need the 1 hit and it's a bit difficult to hit. If you're wanting to use a good example you either need many different test cases, or use the average but realize that it's the average over all types of encounters.
Those are all less than CR 1, so I dispute your claim "If you use the "suggested values" for CR 1/2 or CR 1 you have 11 or 12 AC and 10 or 15 hp."
This is the case of a first level fighter, fighting things most first level fighters fight.
Frankly, a lot of things that are true or untrue for the vast majority of levels are the opposite at levels 1-2 (or near 20th, for that matter).
This is just moving the goal posts.
Frankly, a lot of things that are true or untrue for the vast majority of levels are the opposite at levels 1-2 (or near 20th, for that matter).This is just moving the goal posts.
For power attack perhaps, but certainly not for DPR.
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Frankly, a lot of things that are true or untrue for the vast majority of levels are the opposite at levels 1-2 (or near 20th, for that matter).This is just moving the goal posts.
Not when I never set any to begin with. I've just been watching, coming along for the ride, and occasionally commenting on what I see people doing. I never set any goals for anyone, so I can't be moving the goalposts.
Which tells us something interesting about your decision to throw up a (false) catchphrase defense instead of actually responding.
I've shown, beyond doubt, using a real game example, that DPR cannot predict which option is better. If this problems exists in the most simple case (i.e. 1st level fighter, fighting things first level fighters fight), what makes you think that problem magically goes away when you hit level 3?
Frankly, a lot of things that are true or untrue for the vast majority of levels are the opposite at levels 1-2 (or near 20th, for that matter).This is just moving the goal posts.Not when I never set any to begin with. I've just been watching, coming along for the ride, and occasionally commenting on what I see people doing. I never set any goals for anyone, so I can't be moving the goalposts.
Which tells us something interesting about your decision to throw up a (false) catchphrase defense instead of actually responding.
You set a goal when you said:
What's really interesting is how folks looking to point out flaws with DPR calculations use extreme-beyond-possibility numbers instead of the actual, buildable, playable numbers that actual DPR calculations deal with.
Rather ironically, the other common way people try to debunk DPR calcs is by labeling them as too theoretical and therefore not applicable to "actual play".
I should go check and see if there's anyone who does both critiques, because that would be hilarious.
That is a "actual, buildable, playable numbers that actual DPR calculations deal with" so saying that levels 1-2 don't count after the fact is moving the goal posts.
As for an "actual" response, that did come in after your post, but I'll repeat that here:
"If this problems exists in the most simple case (i.e. 1st level fighter, fighting things first level fighters fight), what makes you think that problem magically goes away when you hit level 3?"
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I've shown, beyond doubt, using a real game example, that DPR cannot predict which option is better. If this problems exists in the most simple case (i.e. 1st level fighter, fighting things first level fighters fight), what makes you think that problem magically goes away when you hit level 3?
At level 1, lots of things die in one hit if you're even remotely built to do damage (i.e., have a decent STR and attack with a martial weapon). Your math absolutely reflects that.
However, the rate at which your damage output increases fails to keep up with the rate at which enemy HP increases.
For instance, a fighter dealing a realistic 1d8+3 damage at 1st level is still dealing the same 1d8+3 damage at 3rd level. Meanwhile, enemy HP has gone from the 5-ish range to the 30-ish range. So the fighter who was happily one-shotting things without Power Attack at 1st level now needs something like 4-5 hits at 3rd level.
That's a huge change.
What I would recommend, if you're interested in figuring all this out, would be to follow your fighter through his career and doing the math at several intervals through the range of levels where most gameplay happens. I know I'm always curious about this kind of thing, as I have an interest in game design.
I'd love to see a summary of the data you come up with. :)
I was going to say something about getting too technical about things like this takes all the fun out of RPGs, but then I remembered that this IS fun to some people. (even me to a smaller extent)
However, shouldn't you include in your conclusions about which is preferable the character and the player?
A half-orc with a battleaxe doesn't (usually) care if he hits everytime, so long as when he does hit, he destroys his target in an awesomely gory fashion.
Likewise, the (usually) frail elf knows she doesn't have the strength of a half-orc and so she trains to ensure that every rapier strike hits and whittles her targets health away.
True, both would likely find ways to improve what they're lacking in, but they both have different ideas on how to take down their opponents. Same with the player. One may find it more fun to be helpful every round, while another enjoys the moment when that one attack lands and ends the fight.
What's preferable from a statistics point of view and what's preferable from a character's/player's point of view may be completely different things, but they're both equally important.
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You set a goal when you said:
That is a "actual, buildable, playable numbers that actual DPR calculations deal with" so saying that levels 1-2 don't count after the fact is moving the goal posts.What's really interesting is how folks looking to point out flaws with DPR calculations use extreme-beyond-possibility numbers instead of the actual, buildable, playable numbers that actual DPR calculations deal with.
Rather ironically, the other common way people try to debunk DPR calcs is by labeling them as too theoretical and therefore not applicable to "actual play".
I should go check and see if there's anyone who does both critiques, because that would be hilarious.
Pointing out that some people have done X instead of Y is not the same as setting a challenge or goal for others to do Y. It was just an observation of something I'd seen some people do. Turning it into a challenge or goal is something you did on your end.
Frankly, a lot of things that are true or untrue for the vast majority of levels are the opposite at levels 1-2 (or near 20th, for that matter).This is just moving the goal posts.Not when I never set any to begin with. I've just been watching, coming along for the ride, and occasionally commenting on what I see people doing. I never set any goals for anyone, so I can't be moving the goalposts.
Which tells us something interesting about your decision to throw up a (false) catchphrase defense instead of actually responding.
You set a goal when you said:
That is a "actual, buildable, playable numbers that actual DPR calculations deal with" so saying that levels 1-2 don't count after the fact is moving the goal posts.What's really interesting is how folks looking to point out flaws with DPR calculations use extreme-beyond-possibility numbers instead of the actual, buildable, playable numbers that actual DPR calculations deal with.
Rather ironically, the other common way people try to debunk DPR calcs is by labeling them as too theoretical and therefore not applicable to "actual play".I should go check and see if there's anyone who does both critiques, because that would be hilarious.
But you didn't subject DPR to the scrutiny of your test. You divised a new test standard which measured rounds to kill and then tried PA in one scenario and WF in the same scenario. WF came out on top in that scenario. OK, thats fine.
That doesn't prove DPR is a bad indicator. You need to run the EXACT SAME TEST again using DPR instead of your RUD test. If the DPR test shows that the WF option is superior then you have proven nothing about DPR.
Also, you should use actual real builds that you can define the important variables such as attributes, weapon choice, all feat choices, class, AC, and saves.
And you should pit it against expected AC and HP by level. For CR 1, that's AC 12, HP 15.
edit: moved some things. Somehow I put half of my post in to Jiggy's quote... weird.
I've shown, beyond doubt, using a real game example, that DPR cannot predict which option is better. If this problems exists in the most simple case (i.e. 1st level fighter, fighting things first level fighters fight), what makes you think that problem magically goes away when you hit level 3?At level 1, lots of things die in one hit if you're even remotely built to do damage (i.e., have a decent STR and attack with a martial weapon). Your math absolutely reflects that.
However, the rate at which your damage output increases fails to keep up with the rate at which enemy HP increases.
For instance, a fighter dealing a realistic 1d8+3 damage at 1st level is still dealing the same 1d8+3 damage at 3rd level. Meanwhile, enemy HP has gone from the 5-ish range to the 30-ish range. So the fighter who was happily one-shotting things without Power Attack at 1st level now needs something like 4-5 hits at 3rd level.
That's a huge change.
What I would recommend, if you're interested in figuring all this out, would be to follow your fighter through his career and doing the math at several intervals through the range of levels where most gameplay happens. I know I'm always curious about this kind of thing, as I have an interest in game design.
I'd love to see a summary of the data you come up with. :)
While I'd love to do this, I just don't have the time. That's a lot of work, unless someone knows where a bunch of free data exists? I certainly wouldn't mind analyzing it in that case.
For now, I'm comfortable ignoring DPR. I know it doesn't accurately express which is the better of given options.
That said, if anyone wants to collaborate on finding a better method, I'd be extremely open to the opportunity. In fact, I'm also open to investigating other aspects of the game (I find optimizing damage to be a bit dull). Just shoot me a PM.
Frankly, a lot of things that are true or untrue for the vast majority of levels are the opposite at levels 1-2 (or near 20th, for that matter).This is just moving the goal posts.Not when I never set any to begin with. I've just been watching, coming along for the ride, and occasionally commenting on what I see people doing. I never set any goals for anyone, so I can't be moving the goalposts.
Which tells us something interesting about your decision to throw up a (false) catchphrase defense instead of actually responding.
You set a goal when you said:
That is a "actual, buildable, playable numbers that actual DPR calculations deal with" so saying that levels 1-2 don't count after the fact is moving the goal posts.What's really interesting is how folks looking to point out flaws with DPR calculations use extreme-beyond-possibility numbers instead of the actual, buildable, playable numbers that actual DPR calculations deal with.
Rather ironically, the other common way people try to debunk DPR calcs is by labeling them as too theoretical and therefore not applicable to "actual play".
Also, you should use actual real builds that you can define the important variables such as attributes, weapon choice, all feat choices, class, AC, and saves.
And you should pit it against expected AC and HP by level. For CR 1, that's AC 12, HP 15.
I should go check and see if there's anyone who does both critiques, because that would be hilarious.
But you didn't subject DPR to the scrutiny of your test. You divised a new test standard which measured rounds to kill and then tried PA in one scenario and WF in the same scenario. WF came out on top in that scenario. OK, thats fine.
That doesn't prove DPR is a bad indicator. You need to run the EXACT SAME TEST again using DPR instead of your RUD test. If the DPR test shows that the WF option is...
You are correct, give me a moment and I'll get back with DPR's answer. That's my mistake.
Here is my test:
Level 1 Fighter:
Str: 16, Shortsword +4 1d6+3 (Keeping things simple, ignoring two-handed and other feats).
Say you're only every going to attack a target with the following stats:
AC: 15, HP: 5
This is your DPR Formula from this thread.
The damage formula is h(d+s)+tchd.h = Chance to hit, expressed as a percentage
d = Damage per hit. Average damage is assumed.
s = Precision damage per hit (or other damage that isn't multiplied on a crit). Average damage is again assumed.
t = Chance to roll a critical threat, expressed as a percentage.
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3.
DPR before selecting a feat:
.45(6.5)+.05(13) = 2.925 + .65 = 3.575 DPRDPR with Power Attack:
.405(8.5)+.045(17) = 3.4425 + .765 = 4.2075 DPR
DPR with Weapon Focus:
.495(6.5)+.055(13) = 3.2175 + .715 = 3.9325 DPR
So DPR predicts Power Attack > Weapon Focus.