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I'll agree that 3d6 should average out to about a 3 point buy. Statistically, you should have 3 10's and 3 11's. But that's average, and it should vary wildly.
In one group where I created a character not too long ago, we used 4d6, drop the lowest, and reroll any 1's. I compared afterward, and I think my character worked out to a 26 point buy, if I remember correctly. My stats seemed about average for our group, though there was one girl who just had some seriously lucky rolls, and did MUCH better.
Even though I grew up playing with rolling back in the 80's in first edition, I kinda like the consistency that point buy gives. I was thinking that if you want some variety, how about randomizing your point buys? For instance, say you want an average of 20 point buy, but with a little randomization to keep things interesting. Give your players 18+1d4 points to buy their stats. Just a thought.
I think it is an 18 point buy on average assuming all 13 across the board.
It really depends, but generally a 4d6 drop the low makes for characters that usually have anywhere from 15-30+ if it were point buy, at least in my years of playing it has.
You can't really just calculate the average roll, find the point buy for that score and multiply by 6. You have to calculate the chance of each result and multiply that by the point buy for that result.
For 3d6 and 2d6+6, it's pretty easy because those both follow fairly simple patterns. 4d6 is much trickier, since dropping a die really throws off the pattern. The simplest way to calculate the odds for 4d6 is to generate a table of all 1296 results. Tedious by hand, but a simple task for a computer.
Anyway
3d6 - 3 point buy
4d6 drop- approx. 18.72 point buy
2d6+6 - approx. 25.67 point buy
http://rumkin.com/reference/dnd/diestats.php
3d6 average is 10.5: 3 10s and 3 11s. That means 3 point buy.
4d6-drop-lowest average is 12.24: 2 12s, 2 13s, 2 14s, roughly. That comes to, what, 18 point buy?
2d6+6 average is 13 even, so 6 13s. That comes to 18 point buy.
Edit: You could argue 4d6-drop-low would be more like 3 12s, 2 13s, and 1 14, or 17 point buy.
Edit edit: Ninja'd, and probably a bit more accurately on the 2d6+6 portion.
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PRD for NPCs:
Basic NPCs: The ability scores for a basic NPC are: 13, 12, 11, 10, 9, and 8.
Heroic NPCs: The ability scores for a heroic NPC are: 15, 14, 13, 12, 10, and 8.
Basic NPCs would be a 3 point buy and heroic would be a 15 point buy.
Statistically, the basic NPC stats are 3d6 and the heroic NPC stats are 4d6 drop the lowest. You are welcome to look through the 4d6 information here.
I have no clue what the 2d6+6 turns out to be. Do some research on the internet and I am sure you will be able to find it.
There is next to no point to comparing them to each other. One is static and the other one is random. On top of that point buy scales depending on the score.
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I know these things have been cited before, but search isn't finding them.
What are the point buy equivalents of 3d6, 4d6 drop low and 2d6+6. My statistical understanding always implodes. I'd think that 3d6 is equivalent to 0-6 point buy as everything averages out to 10 or 11, but I'm not trusting that conclusion.
I wrote a program to simulate randomly rolling 5 million sets under each method. Adding up the point buy equivalent for every set and dividing by the number of sets (5 million), gave me some averages:
Classic (3d6): 8.390 points (44.18% thrown-out)
Standard (4d6; drop 1): 20.704 points (15.5% thrown-out)
Heroic (2d6+6): 25.665 points (0% thrown-out)
My values will differ from some of the others posting here.
The point-buy table only includes values for scores 7 to 18 (inclusive).
This means any score of 3 to 6 (inclusive) is undefined.
In my simulation, I threw out every set containing a score with an undefined point cost.
The percentage of total sets that I needed to throw out in order to obtain the 5,000,000 "good" sets is indicated above.
Because the undefined numbers are on the low end of the scale, it does push the point-buy values up some.
However, even an incredible set like [18, 18, 18, 18, 18, 6] is thrown out due to the 6 it contains.
So it doesn't push up quite as much as one might first guess.
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Ironically enough, I rolled a character the other day using 4d6, drop lowest and I ended up with 15, 14, 13, 12, 9, 8.
Who cares if one method is random and the other is static, it doesn't mean it's a bad question or argument. Yes, you can have a random roll that wildly varies, but still have a reasonable assumption that you have a chance of having a roll equate with a certain point buy. The poster with the 5 million roll program shows this, although IMHO, I don't think he should have thrown out any rolls, as doing so invalidates his test (considering the rolls he threw out were valid rolls).
You can't equate them because of the random factor. I've seen on game where the DM offered a 20 point buy vs what he thought was an equivalent rolling scheme.l The roller did well on his dice and got the equivalent of a 35 point buy.
The more the roll deviates from 3d6, the more unpredictable it gets. If you want your PC's at a predictable power level, than use point buy with the budget number that suits.
This guy understands.
Ironically enough, I rolled a character the other day using 4d6, drop lowest and I ended up with 15, 14, 13, 12, 9, 8.
Who care is one method is random and the other is static, it doesn't mean it's a bad question or argument. Yes, you can have a random roll that wildly varies, but still have a reasonable assumption that you have a chance of having a roll equate with a certain point buy. The poster with the 5 million roll program shows this, although IMHO, I don't think he should have thrown out any rolls, as doing so invalidates his test (considering the rolls he threw out were valid rolls).
That's not how statistics works at all. what an average is that after infinite sampling you will come up with that value. That doesn't mean they give a reasonable idea of what you're going to get because a player's roll is one sample. You can't apply something that's random and something that's static to a single character creation. On top of that part of what makes point buy good is because you choose the amount in your stats. A sample of rolled dice could result in something exactly the same as a 15, 20, or even 25 point buy. However it's probably true that the point buy is better in this case. You can't compare them in power.
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That's not how statistics works at all. what an average is that after infinite sampling you will come up with that value. That doesn't mean they give a reasonable idea of what you're going to get because a player's roll is one sample. You can't apply something that's random and something that's static to a single character creation. On top of that part of what makes point buy good is because you choose the amount in your stats. A sample of rolled dice could result in something exactly the same as a 15, 20, or even 25 point buy. However it's probably true that the point buy is better in this case. You can't compare them in power.
True, averages may not be the best test. Though, saying you can't make reasonable comparisons just because one die roll is wildly skewed is kind of silly. Because the die-roll methods give a bell curve, you can have a reasonable assumption that the roll is going to be a certain result. Sure, a roll could be a 3 or an 18, but more times than not, the roll will fall somewhere near the top of the curve. The type of method affects where the curve falls.
You can't roll 4d6 (drop lowest), and then once the results are known say "well, this turned out to be a 25-point buy instead of a 15-point buy". You have to understand that before you roll the dice, you will have a reasonable chance of having stats that fall within a certain range that is roughly equivalent to an associated point-buy, and you then have to decide if the possibility of having some that fall outside of that range is worth the risk.
The fact that there is variation doesn't mean that you can't say that 4d6 (drop low) is roughly equivalent to a 15 point buy.
Or you could be hardcore and roll your stats in order and then use them to decide what class to play. That's made for some interesting games in the past.
Or you could be hardcore and roll your stats in order and then use them to decide what class to play. That's made for some interesting games in the past.
I had a person do that in a 3.5 game he had a con of 5 and was a wizard. He had like 13 health at level 8. Funny thing is that he did pretty well surviving.
Interesting. I wonder what it would look like if the lower numbers were extrapolated out with point buy? Those values can't mirror the upper numbers, because in general a player can compensate for a lower value. Maybe something like 6 [-5], 5 [-8], 4 [-9], 3 [-12]Because the undefined numbers are on the low end of the scale, it does push the point-buy values up some.
However, even an incredible set like [18, 18, 18, 18, 18, 6] is thrown out due to the 6 it contains.
So it doesn't push up quite as much as one might first guess.
With the table extrapolated out as you indicate, the values are:
Classic (3d6): 3.81 points
Standard (4d6; drop 1): 19.04 points
Heroic (2d6+6): 25.67 points
In these tests, no score is undefined, so all 5 million sets are used and none are thrown out.
Of course, the point-buy equivalent for Heroic didn't change, as it only ever generated scores of 8+.
http://rumkin.com/reference/dnd/diestats.php
Edit edit: Ninja'd, and probably a bit more accurately on the 2d6+6 portion.
Negatory on the getting ninja'd, you provided the link to support both posts! good job!
The oddest stat generation was each player rolling 4 keep 3, once. Keep the highest 6 scores as everyone's Stats. I naturally rolled last and got a 17. I started out as a hero.
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Interesting. I wonder what it would look like if the lower numbers were extrapolated out with point buy? ...
Maybe something like 6 [-5], 5 [-8], 4 [-9], 3 [-12]With the table extrapolated out as you indicate, the values are:
Classic (3d6): 3.81 points
Standard (4d6; drop 1): 19.04 points
Heroic (2d6+6): 25.67 pointsIn these tests, no score is undefined, so all 5 million sets are used and none are thrown out.
Of course, the point-buy equivalent for Heroic didn't change, as it only ever generated scores of 8+.
Thanks. I've been running these numbers myself and am grateful for your independent verification. I generated all possible rolls and took averages based on varying point returns for stats less than 7 and no stats less than 7. Makes a bit of a difference.
My first method reduces the number of possible outcomes by disallowing the possibility of scores under 7.For my second method, assigning points for scores under 7 assumes that if you rolled less than 7, you only ever got 4 points back. As a theoretical point buy, this would allow players to buy scores of less than 7 without encouraging them mechanically.
The third point assignment gives some return for low scores, returning 1 point for every stat drop but 2 points for dropping into the next penalty category.
And my fourth point assignment returns points mirroring the incremental growth of costs as scores increase.
My conclusions are:
Classic (216 possibilities, 196 ignoring scores below 7)
Classic varies a lot, but even allowing all scores below 7 to be rerolled isn't quite as good as the 10 point buy (on average).
Classic (3d6): 8.39 points (reject all scores below 7)
Classic (3d6): 5.39 points (6 [-4], 5 [-4], 4 [-4], 3 [-4])
Classic (3d6): 4.11 points (6 [-5], 5 [-7], 4 [-8], 3 [-10])
Classic (3d6): 3 points (6 [-6], 5 [-9], 4 [-12], 3 [-16])
Standard (1296 possibilities, 1260 ignoring scores below 7)
So, Standard is pretty much a 20 point buy and, on average, if players are forced to keep rolls below 7, then 20 point buy is better (on average).
Standard (4d6;drop 1): 20.7 points (reject all scores below 7)
Standard (4d6;drop 1): 19.46 points (6 [-4], 5 [-4], 4 [-4], 3 [-4])
Standard (4d6;drop 1): 19.12 points (6 [-5], 5 [-7], 4 [-8], 3 [-10])
Standard (4d6;drop 1): 18.83 points (6 [-6], 5 [-9], 4 [-12], 3 [-16])
Heroic (36 possibilities, no scores below 7)
Heroic doesn't vary because it gets rid of the problem of what to do with scores below 7.
Heroic (2d6+6): 25.67 points
5d6 (7776 possibilities, 7714 ignoring scores below 7)
Some gamers use the 5d6, drop the lowest 2 method. This is slightly better than a 30 point buy.
5d6; drop 2: 31.21 (reject all scores below 7)
5d6; drop 2: 30.77 points (6 [-4], 5 [-4], 4 [-4], 3 [-4])
5d6; drop 2: 30.68 points (6 [-5], 5 [-7], 4 [-8], 3 [-10])
5d6; drop 2: 30.60 points (6 [-6], 5 [-9], 4 [-12], 3 [-16])
To summarise (on average)-
3d6 < 10 point buy
4d6 < 20 point buy
2d6+6 > 25 point buy
5d6 > 30 point buy
Does anybody know of a random character generation method that's about 15 point buy?
Or do I have to figure out the stats on the dice pool method? (which is probably easier to crunch with another_mage's 5 million rolls averaged.)
Interesting. I wonder what it would look like if the lower numbers were extrapolated out with point buy? Those values can't mirror the upper numbers, because in general a player can compensate for a lower value. Maybe something like 6 [-5], 5 [-8], 4 [-9], 3 [-12]Because the undefined numbers are on the low end of the scale, it does push the point-buy values up some.
However, even an incredible set like [18, 18, 18, 18, 18, 6] is thrown out due to the 6 it contains.
So it doesn't push up quite as much as one might first guess.
With the table extrapolated out as you indicate, the values are:
Classic (3d6): 3.81 points
Standard (4d6; drop 1): 19.04 points
Heroic (2d6+6): 25.67 pointsIn these tests, no score is undefined, so all 5 million sets are used and none are thrown out.
Of course, the point-buy equivalent for Heroic didn't change, as it only ever generated scores of 8+.
His extrapolation is incorrect. The correct extrapolation is 6 (-6), 5 (-9), 4 (-12), 3 (-16). This follows the pattern where the marginal cost to go from one score to one right above or below is equal to the modifier of the score you are going to (with exception of the 10 to 11 score). For example, going from a 13 to a 14 costs two points because a 13 costs 3, while a 14 costs 5 and the 14 has a modifier of 2, again going from 8 to a 7 "costs" -2 points because 7 has a modifier of -2.
Now if you make the 11 cost 0 instead of 1, one can immediately see that 3d6 would cost 0; any other system with an average of 10.5 would cost 0 as well.
Just as a side note: is your program just a large sampling or does it do the exact computation?
@15 pt. buy: I quickly worked 3d6 reroll all 1's by hand, and it comes out to 15.88 pts. (that's truly 3d5+3)
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3d5+3 works quite nicely.
3d5+3 (125 possibilities, 124 ignoring scores below 7)
This method produces results equal to about 16 point buy (on average).
3d5+3: 16.31 points (reject all scores below 7)
3d5+3: 15.98 points (6 [-4], 5 [-4], 4 [-4], 3 [-4])
3d5+3: 15.94 points (6 [-5], 5 [-7], 4 [-8], 3 [-10])
3d5+3: 15.89 points (6 [-6], 5 [-9], 4 [-12], 3 [-16])
So to update (on average)-
3d6 < 10 point buy
3d5+3 > 15 point buy
4d6 < 20 point buy
2d6+6 > 25 point buy
5d6 > 30 point buy
I'm just using an Excel spreadsheet and creating an array of every possible combination of the dice being thrown.
Then I just assign PF costs to each result, average, multiply by 6 for the 6 ability scores, std dev and graph.
Of course, the distribution for the 'drop the lowest' methods are top heavy, which is different to all the other distributions which are bell curves. And the 3d5+3 and 2d6+6 methods both have higher minimums but lower averages than the 4d6 and 5d6 respectively.
I'd feel comfortable letting players who want to roll randomly use the 4d6 method in a 20 point game.
But I have reservations about letting randomness afficciandos use the 3d6 reroll all 1's method in a 15 point game.
I don't think this qualifies as thread necromancy...
Just popping in to mention this:
I wrote a program to roll stats, evaluate their point costs, and determine an average. I see above that another_mage did so as well, but I used a different method, which I'll get to later. I only used one rolling method: 4d6-drop-lowest, as that was the specific method for which I wanted to find average point cost. I only ran a few thousand iterations, and for my own satisfaction I may run more, but I feel it's enough for an exploratory run.
Here is a the key difference: rather than throw out illegal point buy costs, I extrapolated the point costs for the illegal, but still possible by rolling, values, since the rules do not say to discard insufficient arrays. I'll detail that extrapolation method later.
To get to my point at long last: with the possibility to roll 3-6, the average point buy ended up being 18 (if you floor) or 19 (if you round to the nearest integer). I don't want to cite an exact number (and besides, it's from a pseudorandom number generator, anyway).
Ultimately, I was trying to determine whether 20 point buy was too generous of an ability score generation method, as members of my group have conjectured. So the answer is a technical "yes", but not really that much, and definitely not if ability arrays with scores between 3-6 get discarded (and I will trust another_mage's results to save me the effort of calculating that method myself).
Extrapolation of point costs:
10 through 18**: add up the modifier values of the attributes starting at 12, and counting up to the value, and add 1 to the result. For example, 16 costs 1 + 1 + 2 + 2 + 3 + 1 = 10. **This was mainly an academic exercise to see if the same method worked for attributes less than 10. And it almost does; just don't add the final 1.
9 down to 3: add up the modifier values of the attributes starting at 9, and count down to the value. For example, 5 costs -1 + -1 + -2 + -2 + -3 = -9.
EDIT: My extrapolation of 3-6 is consistent with erik542's listing.
Interesting. I wonder what it would look like if the lower numbers were extrapolated out with point buy? ...
Maybe something like 6 [-5], 5 [-8], 4 [-9], 3 [-12]With the table extrapolated out as you indicate, the values are:
Classic (3d6): 3.81 points
Standard (4d6; drop 1): 19.04 points
Heroic (2d6+6): 25.67 pointsIn these tests, no score is undefined, so all 5 million sets are used and none are thrown out.
Of course, the point-buy equivalent for Heroic didn't change, as it only ever generated scores of 8+.Thanks. I've been running these numbers myself and am grateful for your independent verification. I generated all possible rolls and took averages based on varying point returns for stats less than 7 and no stats less than 7. Makes a bit of a difference.
My first method reduces the number of possible outcomes by disallowing the possibility of scores under 7.
For my second method, assigning points for scores under 7 assumes that if you rolled less than 7, you only ever got 4 points back. As a theoretical point buy, this would allow players to buy scores of less than 7 without encouraging them mechanically.
The third point assignment gives some return for low scores, returning 1 point for every stat drop but 2 points for dropping into the next penalty category.
And my fourth point assignment returns points mirroring the incremental growth of costs as scores increase.My conclusions are: ...
I too can corroborate these conclusions. Although my methods were different I came up with about the same numbers.
One thing I did though was collect a set of real 20-point buys from real players because I felt some of the possible 20-point buy arrays were such that no real player would ever choose them. I found that real 20-point buys were averaged considerably better than the standard 4d6 method and fell somewhere in between that and the heroic 2d6+6 method.
P.S. Generating all possible arrays of ability scores is one heck of a math problem when, like me, you can't just generate a computer program to do it, but it was fun none the less. ;)
I created a simple method of generating ability scores that combines some of the control of point buy with the randomness of standard rolling methods.
I call it the Dice Point system.
You start with 4 dice points. Each dice point equals a 6 on a die. You decide at the beginning how many dice points you are going to spend on each ability score but you can only spend up to 3 dice points for any one ability score. Afterward you roll 3d6 for each ability score in order. If you spent a dice point in an ability score you set one die as a 6 and roll the other two. If you spent two dice points on an ability score you set two dice as 6s and roll one dice to add to the total. Three dice points equals an 18 in that ability score.
This method is roughly equivalent to the standard 4d6 method, allows for scores ranging from 3-18 and is much simpler than other methods I've seen that combine point buy with rolling.
For more or less heroic characters you can use more or less dice points. The heroic 2d6+6 method is similar to 6 dice points. 20-point buy is roughly equivalent to 4 or 5 dice points, and 15-point buy is roughly equivalent to 2 or 3 dice points.
Something to make all of your lives easier: http://anydice.com/