I am guessing the real question is if you round up or down. I do not remember if this has already been established.
Would Deadly Sneak change the averages given by Measured Response?
It is my understanding that sneak attack dice would still be rolled.
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Would Deadly Sneak change the averages given by Measured Response?
Deadly sneak is a massive flaming trap
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I am guessing the real question is if you round up or down. I do not remember if this has already been established.
Here:
When you hit an opponent with a melee or ranged weapon attack, you may choose to deal average damage (rounded down), as if you had rolled exactly the average amount on the damage die or dice. You add your damage bonuses and penalties as normal.
Seriously, though, how is 3.5 the "average" of d6? I've taken statistics before, there are lots of ways to determine averages. Is this just Paizo's official average method?
So for pathfinder averages, what are these:
d2
d3
d4
d6
d8
d10
d12
d20
Beyond that, I remain unclear with the above feat, if all dices are unrolled for damage, or just the weapon's die. I lean towards all the dice, including sneak attack and weapon special bonus dice (like flaming weapons' d6 fire damage).
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Do the math, dude.
21/6=3.5
It's not the "pathfinder average", it's the actual mathematical average.
d2 = 1.5
d3 = 2
d4 = 2.5
d6 = 3.5
d8 = 4.5
d10 = 5.5
d12 = 6.5
d20 = 10.5
Would Deadly Sneak change the averages given by Measured Response?
Not in the slightest. Deadly sneak is a horrible talent, and increases the sneak attack damage by a measly .16666... per d6 rolled. The average would become 3.666666... instead of 3.5, which still rounds down to 3.
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Do the math, dude.
1+2+3+4+5+6
21/6=3.5
It's not the "pathfinder average", it's the actual mathematical average.
d2 = 1.5
d3 = 2
d4 = 2.5
d6 = 3.5
d8 = 4.5
d10 = 5.5
d12 = 6.5
d20 = 10.5
That would be the "mean" which is one method to determine the average. There are others, which is why I was asking.
I'm not trying to be difficult, I'm just very literal minded.
Thanks for the list.
That would be the "mean" which is one method to determine the average. There are others, which is why I was asking.I'm not trying to be difficult, I'm just very literal minded.
Thanks for the list.
I roll to disbelieve.
I roll to disbelieve.
That would be the "mean" which is one method to determine the average. There are others, which is why I was asking.I'm not trying to be difficult, I'm just very literal minded.
Thanks for the list.
I think the keyword here is 'trying'. He's absolutely correct he's not trying to be difficult, he is being difficult.
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You take the mean value of the dice. Then you sum them together, then you round down.
Based on your quote it is applied to every part of the damage dealt.
If some part of the damage dealt should be applied separately (as an example, a flaming burst weapon doing 1d6 weapon damage and 3d6 fire damage) I think you round down separately for each applicable category.
Yes, Pathfinder uses arithmetic means.
I think you'll find this is the almost universally accepted meaning of "average" outside of mathematical/statistical works.
I am a statistican, and looking at the other common meanings of the word "average," I don't find a difference.
Arithmetic mean makes the most sense for averaging damage. It has the property that the arithematic mean of the sum of several values is the same as the sum of the arithmetic means of those values. Damage dealt is summed, so a method that preserves sum is most fitting for damage.
Median is another common form of average. It means taking the middle value. The middle value of 1d6 is a tie between 3 and 4, and the rounding-down rule means we would pick 3. That is the same result as arithmetic mean. The median gives the same result as arithmetic mean for all dice.
Mode is another common form of average. It means taking the most frequently occurring value. On a single die, the values occur equally often, so there is no mode. However, on the roll of two or more dice, the values concentrate in the middle, at the median. Thus, it gives the same result as median and arithmetic mean.
We have more obscure forms of average, such as geometric mean, harmonic mean, and root mean square, but the writers of the feat would not use an obscure average without explaining it.
I think the keyword here is 'trying'. He's absolutely correct he's not trying to be difficult, he is being difficult.I roll to disbelieve.
That would be the "mean" which is one method to determine the average. There are others, which is why I was asking.I'm not trying to be difficult, I'm just very literal minded.
Thanks for the list.
I think Murdock Mudeater is disbelieving Measured Response as written and hoping that he misinterpreted the word "average." Because as the feat is written, using it is almost always worse than not using it. For a typical damage roll, such as 1d6 or 1d6, Measure Response deals 0.5 less damage on average than an unmodified roll. In a few uncommon cases, such as 1d3 or 2d4, it deals the same damage on average. It is never better.
Its use would be in a few rare cases. For example, if your weapon deals 1d8+2 damage and your opponent is at 5 hp, and you know this, then a roll of 1 or 2 would leave your opponent standing but a measured response of 4 would drop it. But that requires a GM who tells his players exactly how many hit points the opponent has remaining. Otherwise, the opponent could be at 7 hp and a die roll of 6, 7, or 8 would drop it but a measured response of 4 would leave it standing.
Measured Response is a worse feat than Deadly Sneak!
Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.
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Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.
Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Study
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It's good to speed up play, especially when rolling large numbers of dice, such as critical hits, using enlarged weapons, or polymorph effects, or when using large die like a d12 that can be especially swingy.
While it is almost always mathematically inferior to rolling dice for the reasons stated by others, in most cases the difference is small enough to be negligible and the increase in turn speed is massive.
Especially if you are playing with someone who is poor at quickly adding numbers.
If I understand your hypotheses correctly, if you were to take a group of people and have them roll dice and record every number rolled along with what dice types, over a long enough period of time the lists would contain the exact same number of each number for each die type. The questions then become, how big of a group, how many dice rolls, and how much deviation would be significant? I am not sure where I lie on the spectrum of curious vs trying to stir up trouble.
Especially if you are playing with someone who is poor at quickly adding numbers.
This. I'm seriously considering talking my snappiness-challenged buddy, whose character is conveniently Abadaran, into this feat. The time savings would be incredible.
What is the interaction with abilities that refer to the minimum/maximum damage of an an ability when measured response is used?
Example: the splash damage of an alchemist bomb.
Would Deadly Sneak change the averages given by Measured Response?Not in the slightest. Deadly sneak is a horrible talent, and increases the sneak attack damage by a measly .16666... per d6 rolled. The average would become 3.666666... instead of 3.5, which still rounds down to 3.
Are you sure? The Deadly sneak feat changes the minimum damage of each dice of sneak attack to 3 (the practical effect of all 1's and 2's being changed to 3's), and the average of the 3-6 range is 4.5.
So, combined with measured response, it would make each die of sneak attack be 4.5.
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Deadly sneak won't interact with Measured Response at all. Measured Response treat your damage as if you had rolled the average damage. Deadly Sneak does nothing if you don't roll a 1 or a 2. You never roll a one or a two with Measured Response, so Deadly Sneak never activates. You are giving yourself a -2 to hit for nothing in return.
Would Deadly Sneak change the averages given by Measured Response?Not in the slightest. Deadly sneak is a horrible talent, and increases the sneak attack damage by a measly .16666... per d6 rolled. The average would become 3.666666... instead of 3.5, which still rounds down to 3.Are you sure? The Deadly sneak feat changes the minimum damage of each dice of sneak attack to 3 (the practical effect of all 1's and 2's being changed to 3's), and the average of the 3-6 range is 4.5.
So, combined with measured response, it would make each die of sneak attack be 4.5.
Changing 1s & 2s to 3s makes the average 4, not 4.5.
3(1) + 3(2) + 3 + 4 + 5 + 6 = 24
24/6 = 4
The standard high value plus low value over two method doesn't work because there isn't an even distribution anymore (3 will appear 3 times as often as the others).
Powerful Sneak raises 1s to 2s. So 22/6 instead of 21/6. That's likely what Paladin was referring to with the 1/6 increase in average.
Devastating Sneak (3pp) raises 1s, 2s, & 3s to 4s. 27/6 = 4.5 average
Hardly worth it for three Rogue Talents. None of them are worth the Rogue Talents, to be honest. Thought there maybe was a new ART that had Deadly Sneak as a prereq that might almost make it worth it, but could be thinking of something else. Really any way you slice it, these are objectively bad options.
If I understand your hypotheses correctly, if you were to take a group of people and have them roll dice and record every number rolled along with what dice types, over a long enough period of time the lists would contain the exact same number of each number for each die type. The questions then become, how big of a group, how many dice rolls, and how much deviation would be significant? I am not sure where I lie on the spectrum of curious vs trying to stir up trouble.
If the results after such an experiment were the exact same number, then I would suspect fakery. Statistics predict some variation.
A die, such as a d8, has an probability distribution, {1,2,3,4,5,6,7,8 | each with 1/8 chance}. That distribution has a mean, 4.5, and a variance 5.25. The square root of the variance, 2.29, called standard deviation, tells how much the die roll varies from the mean, on average. The reason to start with variance instead of standard deviation is that the variance of the sum of several dice is the sum of the variances of the dice. Thus, 10d8 would have mean 45, variance 52.5, and standard deviation 7.25.
For enough die rolls to make the distribution resemble a bell-shaped curve (technically known as a normal distribution), we can use standard deviation to estimate which fraction of the sums fall into various ranges. About 68% of the results ought to be within one standard deviation away from the mean; about 95% of the results ought to be within two standard deviations; and about 99.7% of the results ought to be within three standard deviations. So for 10d8, we can expect 68% of the attempts to be in the range from 38 to 52. Only about 9% of the results would be exactly 45.
One standard deviation is a large range, and for more dice it gets larger. However, compared to the the size of the mean, the standard deviation looks relatively small. For 1d8, the chance that a die would roll 4 or 5 is 25%. The equivalent for 10d8 would be rolling between 36 and 54, and those odds are around 80%. (I performed a quick estimate rather than a precise calculation.)
Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.
4. The player got tired of this argument and tracked thousands of die rolls over a period of several years using many different die.
As a statement of fact: my die rolls are significantly below average. Playing 40K, my average d6 roll came out to about 2.7
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Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.4. The player got tired of this argument and tracked thousands of die rolls over a period of several years using many different die.
As a statement of fact: my die rolls are significantly below average. Playing 40K, my average d6 roll came out to about 2.7
I did leave case 3 for people like you. I am married to a woman who warps probability, not for good luck nor for bad luck but for weird luck. It runs in her family, too. But she trained most of her Pathfinder dice to behave, except for one bag of dice that she named "the plot dice" for when she wants events to get weird.
Changing 1s & 2s to 3s makes the average 4, not 4.5.
3(1) + 3(2) + 3 + 4 + 5 + 6 = 24
24/6 = 4
The standard high value plus low value over two method doesn't work because there isn't an even distribution anymore (3 will appear 3 times as often as the others).
Powerful Sneak raises 1s to 2s. So 22/6 instead of 21/6. That's likely what Paladin was referring to with the 1/6 increase in average.
Devastating Sneak (3pp) raises 1s, 2s, & 3s to 4s. 27/6 = 4.5 average
Hardly worth it for three Rogue Talents. None of them are worth the Rogue Talents, to be honest. Thought there maybe was a new ART that had Deadly Sneak as a prereq that might almost make it worth it, but could be thinking of something else. Really any way you slice it, these are objectively bad options.
Ok, an average of 4 I can deal with.
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Again, Deadly Sneak does not affect the average of Measured Response.
Benefit: When you hit an opponent with a melee or ranged weapon attack, you may choose to deal average damage (rounded down), as if you had rolled exactly the average amount on the damage die or dice. You add your damage bonuses and penalties as normal.
You are treated as if you had rolled the average damage on all weapon dice. Since Powerful/Deadly Sneak only triggers if you roll less than the average result on the die, it will not effect the average granted by Measured Response, because the weapon die is still 1d6. Because you rolled 3.5 per die with Measured Response, Powerful/Deadly Sneak will have no effect, except giving you a -2 to hit.
I did leave case 3 for people like you. I am married to a woman who warps probability, not for good luck nor for bad luck but for weird luck. It runs in her family, too. But she trained most of her Pathfinder dice to behave, except for one bag of dice that she named "the plot dice" for when she wants events to get weird.Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.4. The player got tired of this argument and tracked thousands of die rolls over a period of several years using many different die.
As a statement of fact: my die rolls are significantly below average. Playing 40K, my average d6 roll came out to about 2.7
Exactly. But it's still math.
I've witnessed a player roll four natural 20s in a row. I've witnessed another player roll four natural 1s in a row. The odds of those particular sequences is one in 160,000. Neither player has rolled 160,000 times in their playing career.
Meanwhile, I'm certain there are a lot of players who have never rolled either of those improbable sequences. (Yes, yes, I recognize any specific sequence of four rolls has the same likelihood. That's why I'm calling out these specific ones, which are notable, but not special.)
That's what random means. Some very,exceptional people will fall outside of the middle of the bell curve and while their results are real, they are a} statistically meaningless for predicting the experiences of anyone else and b} statistically likely to not be sustained.
If Snowlilly discarded their old records and started fresh, odds are their d6 average would be found to be 3.5 as expected, shortly. Once you have anomalous data, it's difficult to recognize things have improved. If we take a statistical freak player and give them a thousand 1s to start with, they're going to only asymptotically approach 3.5 on average, and that over a very large number of additional rolls.
So, long story short... yes, I agree. <Grin>
I think the math actually says that you would expect to observe about 80,000 rolls before you saw somebody make one of those sets of rolls, since the individual wasn't specified beforehand. And from our perspective, since anybody could have chimed in with that story, that 80,000 observed rolls can be spread across everybody reading the thread.
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I think Murdock Mudeater is disbelieving Measured Response as written and hoping that he misinterpreted the word "average."
No, as mentioned, I'm just hopelessly literally minded, and wanted to be sure that "average" refereed to the mean and not some other method.
You lot seem very bent on the idea that people post questions for the sole purpose of exploiting rules. I post for clarification.
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Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.
As I read the feat when you roll multiple dices you use the median, rounding down only the last fraction, so you get constant damage at the expense of losing 0.5 or 0 (depending if you roll a odd or even number of dices). My experience with the d6 (and d6 only) is that I roll consistently under the average with single instances of rolling very high setting the average near the normal value. Rolling 20-30 hp of damage with 10d6 fireball or similar spells and then getting a single one with 50+ hp of damage is common for me. At the expense of 0 or 0.5 points of damage being guaranteed of a decent result is a good thing for me. (Registered several gaming sessions and for some reason my average with the d6 is between 2.9 and 3.1. I used a lot of different dices so it isn't a problem with a single die)
It can be interesting for healers too. With a swing dices often enough you waste some point or get a bad roll and cure too little. With this ability you cure a precise amount at the expense of 0/0.5 points. Not bad if it mean not using a extra spell to get a character at near maximum health.
It's also a useful feat if you happen to know that the average is enough.
For instance, let's say that you're toting a greataxe with 18 Strength, for 1d12+6. You're in a fight with some mooks that you know have 11 hp from the last time you dropped a mook. With Measured Response, you drop the foe unconscious automatically, whereas without it, your chances of doing so are only 7/12 (1/12 to disable at 0 hp).
I believe there was a (fairly controversial) study involving thousands of die rolls that showed the rounded-edge, hollowed-pop style six sided dice (like the ones sold by Chessex) show a statistically greater likelihood of rolling 1 than would be expected for a perfectly shaped cube.Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.4. The player got tired of this argument and tracked thousands of die rolls over a period of several years using many different die.
As a statement of fact: my die rolls are significantly below average. Playing 40K, my average d6 roll came out to about 2.7
If so, then it's lucky we use mean rather than mode for "average", or else you'd be dealing minimum damage when you take the average!
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I did leave case 3 for people like you. I am married to a woman who warps probability, not for good luck nor for bad luck but for weird luck. It runs in her family, too. But she trained most of her Pathfinder dice to behave, except for one bag of dice that she named "the plot dice" for when she wants events to get weird.Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.4. The player got tired of this argument and tracked thousands of die rolls over a period of several years using many different die.
As a statement of fact: my die rolls are significantly below average. Playing 40K, my average d6 roll came out to about 2.7
Exactly. But it's still math.
I've witnessed a player roll four natural 20s in a row. I've witnessed another player roll four natural 1s in a row. The odds of those particular sequences is one in 160,000. Neither player has rolled 160,000 times in their playing career.
Meanwhile, I'm certain there are a lot of players who have never rolled either of those improbable sequences. (Yes, yes, I recognize any specific sequence of four rolls has the same likelihood. That's why I'm calling out these specific ones, which are notable, but not special.)
That's what random means. Some very,exceptional people will fall outside of the middle of the bell curve and while their results are real, they are a} statistically meaningless for predicting the...
Last Sunday I rolled 6 natural 20 in a row: first to see if my animal companion would fight or flee when reduced to 3 hit points. Then 1 for its to hit, one for the critical confirmation, one for the trip (it is a wolf), one for the haste attack and one for the critical confirmation. As the bard called it "Anubi's bite". Remove 1 frost giant.
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I did leave case 3 for people like you. I am married to a woman who warps probability, not for good luck nor for bad luck but for weird luck. It runs in her family, too. But she trained most of her Pathfinder dice to behave, except for one bag of dice that she named "the plot dice" for when she wants events to get weird.Measured Response can be a very good Feat. Mathematically it does not make sense, but there are those do constantly roll poorly for damage. I would say that this feat is really designed for these people.Consistently rolling poorly means
1. The player rolls a biased die. Buy a fair die and replace the bad one.
2. The player remembers his or her bad rolls and forgets the good ones. Keep better records.
3. The player magically warps the laws of probability. Studymathematicsmagic and learn how to warp them in his or her favor instead.4. The player got tired of this argument and tracked thousands of die rolls over a period of several years using many different die.
As a statement of fact: my die rolls are significantly below average. Playing 40K, my average d6 roll came out to about 2.7
For the weirdness part one of the members of our gamin club rolled a large d6 with rounded corner and it stopped on the corner. Several of us witnessed that involuntary feat (it was during a normal gaming session, not an attempt to do that purposefully).