Graphing point buy vs. dice comparisons for stat generation


Pathfinder First Edition General Discussion

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Lakesidefantasy wrote:

I think I understand. Does that mean that 5d4-2 is the only other option we have? I tried to think of other rolling methods that generate results from 3 to 18, but it appears that only 3 exist: 1d16+2, 3d6 and 5d4-2.

There are many more if not all dice has to be of the same type; 1d10+2d4, 1d12+2d3, 2d8+1d2 and so on. 1d10+2d4 even sounds quite doable, though there will be very jumpy stats.

And you can get reaaally freaky if you include negative dice to: 3d3+10-d10 is quite special.


Pathfinder Adventure Path, Lost Omens Subscriber
Murph. wrote:

Couple more --

1d10+7 ensures all the stats fall in 7-18 (or 8-17, more precisely), but actually has a wider standard deviation of point buy values than many of the others, because there's less clustering of individual scores around a central value. 0 / 10,000 arrays discarded, mean 22.9 points, std dev 11.4 points...

Actually, in the Way of the Wicked "Focus/Foible" system, you pick one stat as 8, and one at 18, You then roll the remaining four (in order!) with 1d10+7.

I would imagine that a histogram taking that into account would flatten even more.


Lakesidefantasy wrote:


I think I understand. Does that mean that 5d4-2 is the only other option we have? I tried to think of other rolling methods that generate results from 3 to 18, but it appears that only 3 exist: 1d16+2, 3d6 and 5d4-2.

Also, though it isn't with dice, I must mention one additional method that is more similar to what we actually use in our games: A card method.

For a 3-18 score:
Take a standard deck of cards. Pick out 1-6 of hearts, 1-6 of clubs, and 1-6 of spades.

Shuffle these 18 cards and split into 6 piles with 3 cards in each pile (face down). Turn up the cards. These are your stats.

It's a 3-18, that has the same chance of 3 as of 18, but with a very special quirk: Each dice can only be applied once. You only ever get 3 3's and 3 4's etc, so if your first two scores are 4 and 6 (1,1,2 and 1,2,3) you can count on getting quite high stats for your other scores!

It means the party will have a somewhat more even distribution in stats than a standard 3d6, though of course some people will have more optimized stats than others.

We use the same method occacionally, but with 4-9 hearts and 4-9 spades and only two cards per stack, so a random between 8 and 18.


Excellent job Lakesidefantasy - I'm glad you're at least listing the # of "ignored due to <7" - that's a big risk factor when rolling (especially on the high deviation ones with high averages - mostly good rolls but a terrible one might still be played).

I didn't see the requested "reroll 1's on 3d6" (equivalent to 3d5+3).

Also, I was curious about these:

  • 7d4, drop 2, -2
  • 7d6, drop 2, -6
  • 8d6, drop 3, -6

    Lakesidefantasy wrote:
    I think I understand. Does that mean that 5d4-2 is the only other option we have? I tried to think of other rolling methods that generate results from 3 to 18, but it appears that only 3 exist: 1d16+2, 3d6 and 5d4-2.

    Yes, with only xdy+z dice, the only integer results for 3 to 18 are those plus 15d2-12. Lots more if you drop dice or use multiple kinds of dice.


  • Lakesidefantasy wrote:
    Aranna wrote:
    "With point buy your main stats can be as high as you wish, while when you roll you often don't get stats as high as you might like."

    That is what is good about point buy. What I am curious about is the possibility that there may be a rolling method that does "often" give you stats as high as you might like. That's why I'm interested in a method that has a very narrow distribution curve.

    There are 54,264 possible ability score arrays, but with something like a 20 point buy there are only 280. If you don't dump any of your scores you're down to 46 arrays.

    What I would like to know, is how low would a point buy value need to go before something like 5d4-2 looks better?

    In the end I would like to see a hybrid method that gives you the control to get what you want, but also gives you the possibility of getting even better scores. Maybe some sort of risk mitigation method?

    The same avid point buyer answered that question as well "As long as you stick with a SAD build there is NO value of point buy that is worse than rolling, because you can always start with an 18 pre-racial." Of course his logic fails to hold when faced with MAD characters, but his point is valid. Since you only need one stat you can always buy down enough to get the 18.

    If you want tighter stat distribution then use more dice. The probability bell curve gets sharper the more dice you use. So 1d16+2 is more unpredictable than 3d6 which is more unpredictable than 5d4-2.


    Ilja wrote:
    Lakesidefantasy wrote:

    I think I understand. Does that mean that 5d4-2 is the only other option we have? I tried to think of other rolling methods that generate results from 3 to 18, but it appears that only 3 exist: 1d16+2, 3d6 and 5d4-2.

    There are many more if not all dice has to be of the same type; 1d10+2d4, 1d12+2d3, 2d8+1d2 and so on. 1d10+2d4 even sounds quite doable, though there will be very jumpy stats.

    And you can get reaaally freaky if you include negative dice to: 3d3+10-d10 is quite special.

    Is there a formula I can use to generate these mixed dice rolling methods?


    If you're only allowed to buy down to 7, then a -4 point buy would prevent you from buying an 18, right?

    It's absurd I know, but I just want to find out where the breaking points are.

    Note: The Classic 3d6 method can readily generate an ability score array equivalent to -4 points. There are 879 of 54,264 ways to do it, although, if we ignore scores below 7 there are only 71 ways.


    Lakesidefantasy wrote:
    Aranna wrote:
    "With point buy your main stats can be as high as you wish, while when you roll you often don't get stats as high as you might like."

    That is what is good about point buy. What I am curious about is the possibility that there may be a rolling method that does "often" give you stats as high as you might like. That's why I'm interested in a method that has a very narrow distribution curve.

    There are 54,264 possible ability score arrays, but with something like a 20 point buy there are only 280. If you don't dump any of your scores you're down to 46 arrays.

    What I would like to know, is how low would a point buy value need to go before something like 5d4-2 looks better?

    In the end I would like to see a hybrid method that gives you the control to get what you want, but also gives you the possibility of getting even better scores. Maybe some sort of risk mitigation method?

    The dice pool allocated system works to produce results like that. Players get a total pool of dice (30 x 6-sided dice as an example) and allocate them to the attributes. Roll all the dice allocated to the attribute and take the highest three. If a character wants to guarantee a high strength then they can allocate 15 dice to strength and usually get an 18 while the other 5 attributes are the result of a straight 3 dice roll.

    Shadow Lodge

    Pathfinder Card Game, Companion, Lost Omens, Maps, Pawns, Rulebook Subscriber
    Lakesidefantasy wrote:
    Ilja wrote:
    Lakesidefantasy wrote:

    I think I understand. Does that mean that 5d4-2 is the only other option we have? I tried to think of other rolling methods that generate results from 3 to 18, but it appears that only 3 exist: 1d16+2, 3d6 and 5d4-2.

    There are many more if not all dice has to be of the same type; 1d10+2d4, 1d12+2d3, 2d8+1d2 and so on. 1d10+2d4 even sounds quite doable, though there will be very jumpy stats.

    And you can get reaaally freaky if you include negative dice to: 3d3+10-d10 is quite special.

    Is there a formula I can use to generate these mixed dice rolling methods?

    Formula?

    Perhaps not, but there are several constraints.

    First of all, how many dice are you rolling? That gives you the minimum score you can get on the dice. You need to add or subtract a constant term in your dice roll to match the minimum score you are trying to obtain.

    Secondly, what is the maximum score you want? The sum of the number of sides on the dice, plus or minus the constant term calculated above, must add up to that number.

    So if you want to roll four dice, and generate scores in the range 3 - 18, the constant adjustment will be -1, and the total number of sides on those four dice must add up to 19.

    That could be 3d5 + 1d4 - 1, 2d6 + 1d4 + 1d3 - 1, or a whole lot of other choices.


    1d8+1d6+1d4 is a method I could actually see used.

    EDIT: What would the difference in distribution of results be between d8+d6+d4 and 3d6? Anyone knows?


    Ilja wrote:

    1d8+1d6+1d4 is a method I could actually see used.

    EDIT: What would the difference in distribution of results be between d8+d6+d4 and 3d6? Anyone knows?

    I tested that one. It acted exactly like the Classic 3d6 method. I suspect that its distribution table matches this one from JohnF. Can anyone confirm that?

    JohnF's 3d6 distribution table:

    3: 1
    4: 3
    5: 6
    6: 10
    7: 15
    8: 21
    9: 25
    10: 27
    11: 27
    12: 25
    13: 21
    14: 15
    15: 10
    16: 6
    17: 3
    18: 1

    I like it because it is cute, but I'll have a hell of a time convincing my GM to let me do it.

    Shadow Lodge

    Pathfinder Card Game, Companion, Lost Omens, Maps, Pawns, Rulebook Subscriber
    Lakesidefantasy wrote:
    Ilja wrote:

    1d8+1d6+1d4 is a method I could actually see used.

    EDIT: What would the difference in distribution of results be between d8+d6+d4 and 3d6? Anyone knows?

    I tested that one. It acted exactly like the Classic 3d6 method. I suspect that its distribution table matches this one from JohnF. Can anyone confirm that?

    Well, it's easy enough to check.

    In fact all we need to test is whether 1d8 + 1d4 has the same distribution as 2d6.

    So - how many ways are there of rolling 1d8 and 1d4?
    There are 8 possible results for the first die, and 4 for the second die, for a total of 32 possible rolls.

    Of those, exactly one will yield a total of 2.

    So, for 1d8+1d4, the probability of rolling a score of 2 is 1/32.
    For 2d6, though, the probability of rolling a score of 2 is 1/36.

    So no, the distribution tables are not the same.

    The exact distribution table for 1d8 + 1d6 + 1d4:

    3: 1
    4: 3
    5: 6
    6: 10
    7: 14
    8: 18
    9: 21
    10: 23
    11: 23
    12: 21
    13: 18
    14: 14
    15: 10
    16: 6
    17: 3
    18: 1


    Okay, I tried pushing the average of the 15d2-12 method up by rolling more dice and adding up the best 15. The results are as follows:

    Method, Average, Standard Deviation (Point-buy equivalents):

    Best 15 of 15d2-12, 3, 6
    Best 15 of 16d2-12, 7, 6
    Best 15 of 17d2-12, 11, 7
    Best 15 of 18d2-12, 15, 8
    Best 15 of 19d2-12, 20, 9
    Best 15 of 20d2-12, 25, 10

    I may be mistaking correlation and causation again, but it appears that adding more 'uncounted' dice will not help me reach my arbitrary goal of a method that produces an average of 20 points and a standard deviation of 5 points.

    I don't have much faith in mixed dice methods either. Correct me if I'm wrong, but it appears that I had to push the limit and roll 15 d2s in order to get a standard deviation of 6 points. That presents a problem because I can't think of any mixed dice methods that roll that many dice, and I feel that rolling less will lead to higher standard deviations.


    Majuba wrote:

    Excellent job Lakesidefantasy - I'm glad you're at least listing the # of "ignored due to <7" - that's a big risk factor when rolling (especially on the high deviation ones with high averages - mostly good rolls but a terrible one might still be played).

    I didn't see the requested "reroll 1's on 3d6" (equivalent to 3d5+3).

    Also, I was curious about these:

  • 7d4, drop 2, -2
  • 7d6, drop 2, -6
  • 8d6, drop 3, -6

    Lakesidefantasy wrote:
    I think I understand. Does that mean that 5d4-2 is the only other option we have? I tried to think of other rolling methods that generate results from 3 to 18, but it appears that only 3 exist: 1d16+2, 3d6 and 5d4-2.
    Yes, with only xdy+z dice, the only integer results for 3 to 18 are those plus 15d2-12. Lots more if you drop dice or use multiple kinds of dice.
  • Best 5 of 7d4-2, average 23, standard deviation 10


    1d8+1d6+1d4, average 3 points, standard deviation 12 points.


    Majuba wrote:

    I didn't see the requested "reroll 1's on 3d6" (equivalent to 3d5+3).

    3d5+3, average 16, standard deviation 9.


    None of these really deal with the fundamental problem of rolled stats.

    Alice wants to play a fighter and gets stuck with a one high stat array that's useless for anything but a full caster.

    Bob wants to play an offensive full caster and doesn't get the single high stat he needs to make saving throws stick.

    Even using mirror methods or cards to keep total deviation limited no system suggested so far can reliably give Alice the 12-14s she needs for con, dex, and wisdom Bob the single 18 he wants so he can actually use the fun spells with saving throws with a reasonable expectation of success.


    Atarlost: Agreed, but for some people that's a wanted feature, rather than a problem. Having a larger sense of randomness and risking encountering problems you have to work around is something you may want in certain games.


    Ilja wrote:
    And you can get reaaally freaky if you include negative dice to: 3d3+10-d10 is quite special.

    Love this. (And you sweetheart.) How you know Troll math is base negative ten?

    one = 1
    nine = 9
    ten = 190 (one hundred minus ninety)
    twelve = 192
    thirty four = 174
    one thousand eleven = 19191 (ten thousand minus nine thousand plus one hundred minus ninety plus one)

    Human arithmetic algorithms still work.


    Atarlost wrote:
    Even using mirror methods or cards to keep total deviation limited no system suggested so far can reliably give Alice the 12-14s she needs for con, dex, and wisdom Bob the single 18 he wants so he can actually use the fun spells with saving throws with a reasonable expectation of success.

    I hate to say it, but my patented Dice Point system can do this! :)

    It's not perfect, but it was created to combine the control of point buy with the thrill of random rolling.


    Hello everybody. If you're still interested in this subject I ran 10,000 random ability score generation simulations for each of the methods people proposed. You can find yours in the list below.

    I found that most methods have a standard deviation of around 10 points in regards to equivalent point-buy. So, most methods have about a 20 point spread within which over 2/3 of the random ability score arrays fall. (For comparison 10, 10, 10, 10, 10, 11 = 1 point and 13, 13, 13, 13, 13, 14 = 20 points).

    Earlier in this conversation I arbitrarily proposed that a method which generates scores with an average of 20 points and a standard deviation of 5 points would be ideal. That would be a 10 point spread; the difference between a 15 point-buy and a 25 point-buy.

    I found a handful of methods among those proposed that get close to this admittedly arbitrary and "ideal" method. They are: Jubal's 1d10+7 method from Way of the Wicked wherein you roll for only four scores and the other two are an automatic 8 and 18. This method had an average of 23 points and a standard deviation of 8 points. Another method is Manimal's 1d8+8 with an average of 20 points and a deviation of 9 points. Another is Azran's 6d3 method with an average of 15 points and deviation of 7 points.

    The method that came the closest was Kaisoku's method which isn't actually a random rolling method, instead you roll 3d6+10 to generate a number of points with which to buy your scores. The average point-buy for this method was 21 with a standard deviation of 3 points.

    THE FULL SET
    Many of these methods produce scores that do not have a defined point-buy, so I extrapolated the point-buys out to cover all of the possible results. This resulted in some mighty ludicrous point-buys. For instance, one method, Glutton's 5 lowest of 8d6, can possibly generate a score of 30 which would cost 101 points. Another method had the possibility of generating a score of -1 which would cost -36 points.

    THE SEVEN SET
    So, I also calculated the equivalent point-buy averages and deviations after dropping all of the arrays with scores below 7 and above 18. I found this generally has the effect of raising the average and lowering the standard deviation for many methods, but not all of them and the three random rolling methods mentioned above were unaffected. However, the percentage of scores that are dropped is rather large in some cases, making it hard to compare them to the point-buy method.

    THE REROLL SET
    I also calculated the results after applying the rerolling rule from 3.5 Dungeons and Dragons, wherein I dropped arrays with a total modifier of less than 1, or if the highest score was lower than 14. This generally had the effect of raising the average and lowering the standard deviation. This did affect the three random rolling methods mentioned above, with the closest of the three, Azran's 6d3 method resulting in an average of 17 and a standard deviation of 6 after some 22% of the arrays were dropped. That's not too bad.

    So, here are the results presented in the following format for the Full set, the Seven set, and the Reroll set:

    :NAME method……….Full average , deviation ; ……….Seven (percent dropped) average , deviation ; ……….Reroll (percent dropped) average , deviation

    List of Methods:

    :ARENGREY 4d6 27/26/25 (mirror)……….Full 34 , 8 ; ……….Seven (45%) 28 , 5 ; ……….Reroll (0%) 34 , 8

    :ARRSANGUINUS 5d4-2………………………..Full 3 , 8 ; …………Seven (29%) 6 , 7 ; ………….Reroll (65%) 11 , 5

    :AZRAN 6d3 ………………………………………….Full 15 , 7 ; ……….Seven (1%) 15 , 7 ; ………….Reroll (22%) 17 , 6

    :CLASSIC 3d6…………………………………………Full 3 , 11 ; ……….Seven (44%) 8 , 9 ; ………….Reroll (60%) 13 , 7

    :GLUTTON 5 lowest of 8d6……………………Full 27 , 19 ; ……..Seven (37%) 21 , 12 ;…….. Reroll (11%) 30 , 17

    :GLUTTON 4 lowest of 7d6……………………Full -4 , 11 ; ………Seven (62%) 3 , 9 ; ………….Reroll (83%) 13 , 8

    :HEROIC 2d6+6……………………………………..Full 26 , 10 ; ……..Seven (0%) 26 , 10 ; ……….Reroll (4%) 26 , 10

    :ILJA 2d8+1d2……………………………………….Full 3 , 13 ; ……….Seven (55%) 11 , 10 ;…….. Reroll (57%) 14 , 8

    :ILJA 1d10+2d4……………………………………..Full 3 , 13 ; ……….Seven (55%) 11 , 10 ;…….. Reroll (56%) 14 , 8

    :ILJA 1d8+1d6+1d4……………………………….Full 3 , 12 ; ……….Seven (47%) 9 , 9 ;…………. Reroll (59%) 14 , 8

    :ILJA 3d3-1d10+10………………………………..Full 3 , 12 ; ……….Seven (54%) 10 , 10 ; ………Reroll (58%) 14 , 7

    :ILJA 1d12+2d3……………………………………..Full 3 , 15 ; ……….Seven (66%) 14 , 11 ;……… Reroll (56%) 16 , 9

    :JOHNF 2d6+1d4+1d3-1……………………….Full 3 , 10 ; ……….Seven (38%) 7 , 8 ;…………. Reroll (61%) 12 , 6

    :JOHNF 3d5+1d4-1……………………………….Full 3 , 9 ; …………Seven (34%) 7 , 8 ; …………..Reroll (62%) 12 , 6

    :JUBAL 1d10+7 (Way of the Wicked)……Full 23 , 8 ;………. Seven (0%) 23 , 8 ;…………. Reroll (7%) 25 , 7

    :KAISOKU 3d6+10 (points)……………………Full 20 , 3

    :LAKESIDEFANTASY 4 of 5d3+6…………….Full 45 , 10 ; …….Seven (0%) 45 , 10 ; ………..Reroll (<1%) 45 , 10

    :LAKESIDEFANTASY 3 of 4d4+6…………….Full 43 , 10 ; …….Seven (0%) 43 , 10 ;……….. Reroll (<1%) 43 , 10

    :LAKESIDEFANTASY 2 of 3d6+6…………….Full 42 , 12 ; …….Seven (0%) 42 , 12 ; ………..Reroll (<1%) 42 , 12

    :LAKESIDEFANTASY 15d2-12………………..Full 3 , 6 ; …………Seven (10%) 4 , 5 ;…………. Reroll (78%) 10 , 4

    :LURK3R 2d4+10…………………………………..Full 47 , 10 ; …….Seven (0%) 47 , 10 ; ………..Reroll (0%) 47 , 10

    :LURK3R 3d5+3 (reroll 1s)…………………….Full 16 , 9 ;………. Seven (5%) 16 , 9 ; ………….Reroll (18%) 19 , 8

    :MAJUBA 5 of 7d6-6…………………………….Full 83 , 27 ; …….Seven (88%) 51 , 14 ; ………Reroll (<1%) 83 , 27

    :MAJUBA 5 of 8d6-6…………………………….Full 62 , 25 ; …….Seven (74%) 41 , 14 ; ………Reroll (<1%) 63 , 24

    :MAJUBA 5 of 7d4-2…………………………….Full 24 , 10 ; …….Seven (4%) 24 , 10 ; ………..Reroll (5%) 25 , 9

    :MANIMAL 1d8+8………………………………..Full 20 , 9 ; ……….Seven (0%) 20 , 9 ; ………….Reroll (7%) 21 , 8

    :MURPH 9d2………………………………………..Full 3 , 6 ; ………..Seven (10%) 4 , 5 ; …………..Reroll (78%) 10 , 4

    :SCYTHIA 3d4+6? (reroll 1s and 2s)……..Full 29 , 9 ; ………Seven (0%) 29 , 9 ; …………..Reroll (2%) 29 , 9

    :STANDARD 3 of 4d6…………………………….Full 19 , 11 ;…… Seven (15%) 21 , 11 ; ……….Reroll (13%) 21 , 10

    I think I may redo these simulations but use the total modifier for each array generated as a measure for comparing the methods, thus avoiding the need to drop scores from the analysis.


    Pathfinder Maps, Starfinder Maps Subscriber
    Adamantine Dragon wrote:

    I prefer the James Tiberius Kirk approach to stat generation:

    "Never tell me the odds!"

    I am pretty sure that was Han Solo.

    Liberty's Edge

    Try graphing the grid system, 3 of 4...

    I'm good with math...but that one is tough. :p

    The Exchange

    I have a stat rolling option I would like to see tested out:
    1 stat- 2d4+10
    1 stat- 2d6+6
    1 stat- 2d8+2
    the three remaining at 3d6.

    I would want the top three assigned to stats prior to rolling then roll everything in order and allowing the swapping of any 2 stats.


    Fake Healer wrote:

    I have a stat rolling option I would like to see tested out:

    1 stat- 2d4+10
    1 stat- 2d6+6
    1 stat- 2d8+2
    the three remaining at 3d6.

    I would want the top three assigned to stats prior to rolling then roll everything in order and allowing the swapping of any 2 stats.

    I'll see what I can do, but I expect that one fall in the midst of the pack.

    My question is what spread in the results would people be comfortable with? Where would you like 2/3 of the results to fall?


    One of the things I'm also looking for in an ability score generation method is one that can produce scores in the full spectrum from 3 to 18.

    Most of the methods proposed aren't full spectrum. And, of those that are, none have particularly good characteristics approaching the "ideal".

    Fake Healer's method is a full spectrum method, so we'll see how it does.

    Liberty's Edge

    Lakesidefantasy wrote:

    One of the things I'm also looking for in an ability score generation method is one that can produce scores in the full spectrum from 3 to 18.

    Most of the methods proposed aren't full spectrum. And, of those that are, none have particularly good characteristics approaching the "ideal".

    Fake Healer's method is a full spectrum method, so we'll see how it does.

    Seriously, look up the grid system...but best of luck charting it!

    Shadow Lodge

    Pathfinder Card Game, Companion, Lost Omens, Maps, Pawns, Rulebook Subscriber

    You can craft just about anything you want using only d6.

    Basically, you want to keep 3d6, to give you the spread of 3-18.

    You can reduce the standard deviation by rolling more dice.

    And, finally, you can adjust the mean value by deciding which dice to drop.
    To raise the average, drop dice from the low end; to lower the average, drop high rolls.

    For example: you could roll 6d6, and drop the two lowest and one highest.


    This is fun. Ok my 3.5 DM has us roll 4D6 drop one (normal) roll three sets, pick the best set. Any idea of average here?

    The Exchange

    DrDeth wrote:
    This is fun. Ok my 3.5 DM has us roll 4D6 drop one (normal) roll three sets, pick the best set. Any idea of average here?

    I think someone did that one a few years back and got something like 25pt buy...28? Not exactly sure but it was high enough that I ruled it out as an option for me.


    When it comes to rolled stats, I prefer the dice pool method. Roll 3d6 for 6 stats and track individual dice numbers (ie. if you roll 2, 6, and 4, track those numbers and not just the total), then you have a pool of dice (4-10 depending on fantasy level), with which to assign to certain totals. For example, if for one of your stats, you roll a five and two sixes, you don't need to add an extra dice to that one so you take one of the dice from what would have been a 4d6/best 3 roll and "move" it to another total. Alternatively, roll 20-28d6 and take the best 18 and put those dice on whatever stats you want.

    But the more meaty thing to consider is, if you do use rolled stats, how to handle disparity between a character with high point buy equivalent value and one with a low equivalency. I've favored Hero Points on this; if you're rocking the equivalent of a 30-35 point buy, you have to do something pretty significant for it to qualify as a heroic challenge of your abilities. By contrast, the character who netted an equivalent point buy of -1 will find that successfully surviving breakfast without choking to death is a heroic challenge worthy of a point or two. Another way is through templates. If you rolled far below the mean, you may be given a template to "make up the difference".


    That is a creative solution to the problem of disparity between players. The rerolling rules from the Player's Handbook are another way, unfortunately that rule was not a part of the Standard Reference Document and it did not make its way into Pathfinder.

    What are some other ways for handling the disparity problem? Because, if a particular random method is generates the full spectrum of scores from 3 to 18, no matter how small the deviation it can still produce disparity.

    One method to curtail disparity mentioned in this thread is the Mirror method wherein you roll one score then subtract it from a constant and the difference becomes your next score.

    Another common method is to limit the range of possible scores generated. So the 2d4+10 method would have very little disparity because it only generates 7 different scores--less than half of what the Classic 3d6 method produces.

    Damn! now I have to come up with a way for measuring the disparity of a particular method.


    Pathfinder Maps, Starfinder Maps Subscriber

    In my experience I have found that when people roll their characters that they roll several sets of stats and take the best one. As a result we use point-buy. That said, I have wondered about other methods. I have rolled some pretty cool characters over the years, and I have rolled some lame characters as well. A fun character was a Minotaur wizard with a 14 Intelligence.

    For example, Shadowrun, I think 4th edition (I cannot recall which) had you prioritize between your different character creation blocks. I think in that game it was Attributes, Skills, Magic, Wealth, and Race. I thought that concept was actually pretty cool, even though I was not really a fan of the game system itself.

    So, thinking along those lines, I wonder what sort of tiers to offer. Maybe for attributes have some arrays. For races, you could have different power-levels (as some races are tougher than others). You could also have Traits (so you can have more than two Traits), you could get skill points (not quuite as useful at level 1, though), bonus feats, and class availability (so full-casters are full magic, and non-casters are no magic). This could also help to balance out the party a bit, where a fighter, who has no magic, might have better stats, even more feats, or whatever.


    Pathfinder Maps, Starfinder Maps Subscriber

    The creation method that we used the most in 2nd edition was 4d6, reroll 1 and 2, and drop one die. I tried it once in Pathfinder and it had a substantially greater effect.


    Murph. wrote:

    Couple more --

    1d10+7 ensures all the stats fall in 7-18 (or 8-17, more precisely), but actually has a wider standard deviation of point buy values than many of the others, because there's less clustering of individual scores around a central value. 0 / 10,000 arrays discarded, mean 22.9 points, std dev 11.4 points.

    ** spoiler omitted **...

    ... How do you get an average of 8.5 out of 5d4-2? The average stat would be exactly 10.5

    The average on a d4 is 2.5. 5*2.5 = 12.5. 12.5-2 =10.5.


    He is probably using a rolled sample rather than the actual statistical breakdown.


    That's average point-buy equivalent, not average score.


    Wouldn't it be 3 pb then on average? (0.5 x 6 = 3)


    Pathfinder Adventure Path Subscriber

    It really all comes down to what you play as far as rolling goes. If you're going to do a 1st/2nd edition run put that point buy stuff out of your head now. Stats never increased back then without serious magic, books/wishes/etc. You didn't get a freebie handout to your scores every few levels. Worse for some classes, if you didn't have an 18 your casting abilities were limited to say the least.

    All that aside I still use 4d6 drop the lowest reroll 1s. What can I say, old habits die hard. Since I'm the DM I really don't care what your stats are like, I'm pretty sure I can come up with something you'll find challenging.

    I guess a better question would be how similar are stats from a 15 point buy by level 20 Vs. 4d6 drop the lowest but never getting any stat increases via leveling?


    Aranna wrote:

    Wouldn't it be 3 pb then on average? (0.5 x 6 = 3)

    Yes, the 5d4-2 method (Arrsanguinus) has an average point-buy of 3 and a standard deviation of 8. If you drop the sevens then the average is 6 and the deviation is 7. These are all approximate values of course.


    Vexous wrote:

    All that aside I still use 4d6 drop the lowest reroll 1s. What can I say, old habits die hard. Since I'm the DM I really don't care what your stats are like, I'm pretty sure I can come up with something you'll find challenging.

    I guess a better question would be how similar are stats from a 15 point buy by level 20 Vs. 4d6 drop the lowest but never getting any stat increases via leveling?

    There, that's another way to limit disparity--rerolling 1s!

    And, you're question is a good one.


    JohnF wrote:


    You can reduce the standard deviation by rolling more dice.

    And, finally, you can adjust the mean value by deciding which dice to drop.
    To raise the average, drop dice from the low end; to lower the average, drop high rolls.

    I will try this.


    I played with a group that liked high power.

    They used 4d6, drop lowest, replace the lowest score with 18 arrange as desired.

    Everybody was equal on their primary stat, and the rest of the stats added color. Everyone was quite happy even if somebody rolled far better than other because the important stats were still equal. Even MAD builds generally worked out nicely.


    As I see it, the advantages of rolling stats are: you might get lucky; and the element of randomness means you might have to play with some stats a bit higher or lower than is 'ideal'.
    The disadvantages are that you might not be able to play the 'perfect' character you had in mind; and more importantly the differences between players' rolls can be unfair.

    My current GM rolled one set of stats (probably using 4d6 drop lowest) which all players are using. Problems mostly solved.


    Hark wrote:
    They used 4d6, drop lowest, replace the lowest score with 18 arrange as desired.

    Cool, yet another way to counter disparity among player characters.

    And I think you bring up an important point. It's not so important that each player character be equal, but that each one has what they need to be successful.

    Which brings me to another point: How much is enough to be successful? In the above method it is enough for each of the gaming group's player characters to to have one ability score maxed out.

    I tend to think a 15 might be good enough for a standard game. Of course, high powered games would need more.

    The Exchange

    Fake Healer wrote:

    I have a stat rolling option I would like to see tested out:

    1 stat- 2d4+10
    1 stat- 2d6+6
    1 stat- 2d8+2
    the three remaining at 3d6.

    I would want the top three assigned to stats prior to rolling then roll everything in order and allowing the swapping of any 2 stats.

    I test rolled this 5 times, broke the numbers down into point buy and averaged and got an 18 Point buy average....I need to do a larger set to really determine if I just rolled high or low but I am thinking I may have a new rolling method for future endeavors.


    One thing I was going to try was 4d6keep3 in order but if you wish you can replace your primary stat with a 16 after stats and class are assigned.


    Fake Healer wrote:


    1 stat- 2d4+10
    1 stat- 2d6+6
    1 stat- 2d8+2
    the three remaining at 3d6.

    FAKE HEALER.........Full Set 15 , 11

    So an average of 15 points and a standard deviation of 11 points puts this method at the back edge of the pack and not particularly close to the ideal of 20 and 5.

    The real advantage of this method, in my opinion, is that it is a way of mixing qualities from both point-buy and random rolling.

    My Dice Point method combines the two as well, but does not fare any better with an average of 25 points and a deviation of 11 points. The Dice Point method is just on the other edge of the pack.


    Aranna wrote:

    One thing I was going to try was 4d6keep3 in order but if you wish you can replace your primary stat with a 16 after stats and class are assigned.

    Your method is similar to Thenobledrake's method. I will need to retool my spreadsheets to simulate them because of that replacing the lowest score with a 16 part.

    Keep in mind that "straight" rolling has no impact on average point-buy equivalency and standard deviation, even though it has a big impact on the character you end up with. I like the idea of straight rolling--with caveats. The method I proposed is a straight method as well.


    I played in an AD&D game once that used 5d6, reroll 1's and 2's, keep 3 highest. Good times, good times.

    I will always favor rolling (4d6 drop 1, or 3d6 x 12, take 6 highest), but then, I use the stat-generation process to help me decide what sort of character to play, rather than the other way around.

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