Standard array and point buy generally gives a total of +5 in ability score bonuses. If given the option to roll what are the odds of rolling +5 or better? Even better if anyone knows of a chart that shows the chances of getting various total bonuses, like +3 total, +6, +9, etc.
When I created my first character in 5e, he was a bard half-elf. Being a half-elf, he received +1 in two stats and +2 in Charisma. Using point buy I settled on 10, 12, 12, 14, 14, 16 after applying racial bonuses. So he ended up with +1, +1, +2, +2, +3 = +9. Without racial bonuses he would have started with 10, 12, 12, 13, 13, 14, and this would have been +1, +1, +1, +1, +2 = +6. I would expect +6 or more would be the expected result.
I have started an Excel spreadsheet to brute force compute the probabilities using 4d6 drop the lowest. It is far from being done, but I can give you the probability for many combinations at the "top end of the spectrum. I have computed and checked all the combinations from 18 - 18 - 18 - 18 - 18 - 18 down to 11 - 11 - 11 - 11 - 10 - 9. That covers over 800 thousand of the possible outcomes. I am getting close to knowing the answers to your question, because assuming you would be satisfied with everything down to straight 10s, I only have a little ways to go. But I haven't had the motivation to pursue it over the last three months or so.
Now my results will initially only account for straight results from the dice, not applying racial modifiers.
I'm sure there are websites that can do something like this for you, but you may have to input several queries to get the answer you seek.
This web thread shows a graph of the 4d6 drop lowest method. I can't vouch for its accuracy. The results in the graph don't include effects from racial modifiers.
This web page gives a number of graphs that illustrate probabilities for rolling certain series of stats, but again there would be some work required to get the specific answer you want.
Standard array and point buy generally gives a total of +5 in ability score bonuses.
This is true if you're trying to max out one score and dumping another, but if distribute your points more evenly you can get a total of +7 across all modifiers.
If given the option to roll what are the odds of rolling +5 or better? Even better if anyone knows of a chart that shows the chances of getting various total bonuses, like +3 total, +6, +9, etc.
This is pretty easy to answer with Anydice. Check out this program. In short it's a bell curve with an average of +5. There's about an 11% chance you'll get exactly +5 and the remaining 89% is split almost evenly between higher and lower values. So while there's a 47% chance you'll get a +6 or higher total, there's also a 41% chance you'll get a +4 or lower.
This lines up with the Anydice article that MusicScout linked, which shows the average array from rolling is [15.66, 14.17, 12.96, 11.76, 10.41, 8.50], very close to the standard array. It also shows that the average of 4d6 drop lowest is 12.24, which means you'd expect your scores to average 73.44 vs the 72 from standard array.
The takeaway is that the standard array is about as good as the average result from rolling, but it's consistent. With rolling you're basically flipping a coin to see if you'll do slightly better or slightly worse than point buy, and you'd better be prepared to live with either outcome.
4d6h3 has an average of 12.24, which should produce +6~7 average of stat mod totals.
One of the articles musicscout linked summarized the average rolls into an array of: 16, 14, 13, 12, 10, 9. Which totals +6 and is an easy +8 after racial ASIs, and easily has a +4 in your main stat starting out.
Compared to 5e standard array of 15, 14, 13, 12, 10, 8. Which totals +5, +7 after race ASI, and only a +3 in your highest stat.
So generally speaking, rolling your stats will put you at about 1 whole ASI ahead of standard array and point buy, but not much more.
Thanks, I like the variability of rolling but really don't like the idea of playing a substandard character.
I like point buy (but not 5e's cap at 15).
I wonder if there is a point buy rule based on the likelihood of rolling a number with 4d6h3.
I came up with one years ago, but I don't remember the details. I believe I changed the stat range from 8-15 to 6-16 or 6-18. It's very possible, but there's no way to perfectly nail it without making the math so messy almost no players will willingly engage with it (e.g. people won't enjoy making the points costs and starting points pool radically bigger to add granularity - bigger numbers are more time-consuming to do arithmetic on manually). I'm quite sure I had stats costing more than 9, even so, and the starting pool was more than 27 (since you started at all 6s, and had to buy your way up to even 8s).
It seems there are so many posts making the case the starting stats need to be higher. Is this an issue to allow a feat to be taken at level 4 instead of an ASI?
I'm enjoying the game as it is already.
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It seems there are so many posts making the case the starting stats need to be higher. Is this an issue to allow a feat to be taken at level 4 instead of an ASI?
I'm enjoying the game as it is already.
4d6h3= 4d6 keep highest 3 rolls (aka drop the lowest). It is the official option of how to roll for ability scores.
The only issue with the standard array/point buy is that it is statistically worse than rolling dice by about 2 whole points. In addition to never starting with more than a +3 modifier (where rolling dice is almost guaranteed at least 1 +4).
There isn't anything wrong with playing the game as is, it is just some power balance nit picks by those of us into math.
I think it is deliberate that point buy scores on average lower rolling. With point buy you have the flexibility to distribute the stats as you see fit. Building a Monk where three stats are important you can go 15/15/15/8/8/8 building a rogue that only really needs dex and a bit of con but you want to be reasonably good at all your skill checks you can go 15/12/12/12/12/11. If you roll you have to take what you get so the higher average balances out the flexibility.
In reality though the difference in power between point buy and rolling is higher. If you roll 12/11/10/8/7/5 pretty much any DM will allow a re-roll (or maybe use standard array instead) even if they don't you are likely to die very quickly (possibly via suicide) so a low roll is replaced by a higher one. It would take a brave DM to tell a player who rolls 18/17/16/14/14/12 that their character is too powerful compared ot the rest of the party and they have to re-roll.
The only issue with the standard array/point buy is that it is statistically worse than rolling dice by about 2 whole points. In addition to never starting with more than a +3 modifier (where rolling dice is almost guaranteed at least 1 +4).
I don't think this is a very practical way of looking at it. Rolling is slightly better in the long run; if you were to roll a bunch of characters and average them out you'd find that the average of their scores was slightly better than point buy. But in practice you only get one shot to roll stats for each character and then you're stuck with that outcome for quite a while. And there's going to be quite a bit of variability in those characters: most will be either above average or below average.
Saying rolling is better is kinda like saying that when you're on your death bed, the average of all your D&D character will have been slightly stronger. True, but you'll never actually play as the average of all your D&D characters. The benefit is so small, abstract and takes so long to manifest that you're better off asking yourself if you're ok with getting burned by the dice and playing with below average scores for months at a time. How much fun you had along the way is probably going to matter more to you than some statistical function of your characters.
OK. I always heard it called 4d6 drop1 or 4d6 drop lowest. Never saw it written as 4d6h3.
I have done enough of the calculations to know rolling will produce a better character, ON AVERAGE, but I think it is even better than you describe DxJxC because no DM in the world is going to make you keep a character that gets too many low numbers. While I can't quantify where that line is, when you eliminate the bottom scores, the average moves up even more. I suspect most DMs would let you choose standard array is your rolls were that pathetic.
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The thing I don't like about standard array or point buy is your melee characters are almost always dumb and your casters are almost always weak.
I think if I were running a game I'd have people roll but only allow rolls that total maybe between +4 or +5 and +8 or +9 stat bonuses. Prior to racial mods.
Saying rolling is better is kinda like saying that when you're on your death bed, the average of all your D&D character will have been slightly stronger. True, but you'll never actually play as the average of all your D&D characters.
True, you will mostly play the characters with way above average rolls. Most DMs wouldn't make 1 player be the only one stuck with a character WORSE than standard array, or they will just die/retire early. So the fact that 60% of the time you will roll better than the default stats is skewed further by the fact that low stats will get used less.
OK. I always heard it called 4d6 drop1 or 4d6 drop lowest. Never saw it written as 4d6h3.
It is easier to write it that way for dice rollers (I think I've also seen k3 for keep, but I prefer h3 to specify highest, where rolling with disadvantage for example is 2d20l1 for keep lowest 1).
True, you will mostly play the characters with way above average rolls. Most DMs wouldn't make 1 player be the only one stuck with a character WORSE than standard array, or they will just die/retire early.
I don't know why any DM would want to force players to roll and deliberately create a situation where some players will be below average through and others punch well above their weight through no fault of their own. And if a player chose to gamble on their stats they should know their odds and accept the result.
The thing I don't like about standard array or point buy is your melee characters are almost always dumb and your casters are almost always weak.
I think if I were running a game I'd have people roll but only allow rolls that total maybe between +4 or +5 and +8 or +9 stat bonuses.
You'd still see this happen even if everyone rolled stats. Odds are they'll have some score close to 8 and another close to 15 and many others in between, so they're still going to optimize their important scores and minimize their least relevant scores. More importantly I don't think ability scores are all that important to creating an interesting characters or a substitute for giving them personality.
That said if you do want variability in the scores but not in the total (e.g. you want everyone to have a +5) you can try rolling for 5 scores and choosing the 6th accordingly. E.g. If you roll 16, 15, 15, 12, 10, your last score has to be a 4 so that the -3 offsets the +8 from the rest. If by some freak chance you roll stats so low or so high that you can't hit the total with a +/-5 on your 6th score, reroll the highest or lowest score. You could do something similar with a d10 instead of 4d6 to generate random point buy arrays.
Standard array and point buy generally gives a total of +5 in ability score bonuses. If given the option to roll what are the odds of rolling +5 or better? Even better if anyone knows of a chart that shows the chances of getting various total bonuses, like +3 total, +6, +9, etc.
When I created my first character in 5e, he was a bard half-elf. Being a half-elf, he received +1 in two stats and +2 in Charisma. Using point buy I settled on 10, 12, 12, 14, 14, 16 after applying racial bonuses. So he ended up with +1, +1, +2, +2, +3 = +9. Without racial bonuses he would have started with 10, 12, 12, 13, 13, 14, and this would have been +1, +1, +1, +1, +2 = +6. I would expect +6 or more would be the expected result.
I have started an Excel spreadsheet to brute force compute the probabilities using 4d6 drop the lowest. It is far from being done, but I can give you the probability for many combinations at the "top end of the spectrum. I have computed and checked all the combinations from 18 - 18 - 18 - 18 - 18 - 18 down to 11 - 11 - 11 - 11 - 10 - 9. That covers over 800 thousand of the possible outcomes. I am getting close to knowing the answers to your question, because assuming you would be satisfied with everything down to straight 10s, I only have a little ways to go. But I haven't had the motivation to pursue it over the last three months or so.
Now my results will initially only account for straight results from the dice, not applying racial modifiers.
I'm sure there are websites that can do something like this for you, but you may have to input several queries to get the answer you seek.
This web thread shows a graph of the 4d6 drop lowest method. I can't vouch for its accuracy. The results in the graph don't include effects from racial modifiers.
https://rpg.stackexchange.com/questions/1528/what-is-the-statistically-superior-character-creation-method-twelve-3d6-or-six
This website allows you to roll a character using 4d6 very quickly, but won't give you the probabilities you seek.
https://rgbstudios.org/dnd-dice/char?r=
This web page gives a number of graphs that illustrate probabilities for rolling certain series of stats, but again there would be some work required to get the specific answer you want.
https://anydice.com/articles/4d6-drop-lowest/
I recommend that you learn a little about probability because it is fun.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
This is true if you're trying to max out one score and dumping another, but if distribute your points more evenly you can get a total of +7 across all modifiers.
This is pretty easy to answer with Anydice. Check out this program. In short it's a bell curve with an average of +5. There's about an 11% chance you'll get exactly +5 and the remaining 89% is split almost evenly between higher and lower values. So while there's a 47% chance you'll get a +6 or higher total, there's also a 41% chance you'll get a +4 or lower.
This lines up with the Anydice article that MusicScout linked, which shows the average array from rolling is [15.66, 14.17, 12.96, 11.76, 10.41, 8.50], very close to the standard array. It also shows that the average of 4d6 drop lowest is 12.24, which means you'd expect your scores to average 73.44 vs the 72 from standard array.
The takeaway is that the standard array is about as good as the average result from rolling, but it's consistent. With rolling you're basically flipping a coin to see if you'll do slightly better or slightly worse than point buy, and you'd better be prepared to live with either outcome.
The Forum Infestation (TM)
4d6h3 has an average of 12.24, which should produce +6~7 average of stat mod totals.
One of the articles musicscout linked summarized the average rolls into an array of: 16, 14, 13, 12, 10, 9. Which totals +6 and is an easy +8 after racial ASIs, and easily has a +4 in your main stat starting out.
Compared to 5e standard array of 15, 14, 13, 12, 10, 8. Which totals +5, +7 after race ASI, and only a +3 in your highest stat.
So generally speaking, rolling your stats will put you at about 1 whole ASI ahead of standard array and point buy, but not much more.
Thanks, I like the variability of rolling but really don't like the idea of playing a substandard character.
I like point buy (but not 5e's cap at 15).
I wonder if there is a point buy rule based on the likelihood of rolling a number with 4d6h3.
Just making this up on the fly. But how about a 30 point buy where a 16 costs 12 points, 3 more than 15?
I came up with one years ago, but I don't remember the details. I believe I changed the stat range from 8-15 to 6-16 or 6-18. It's very possible, but there's no way to perfectly nail it without making the math so messy almost no players will willingly engage with it (e.g. people won't enjoy making the points costs and starting points pool radically bigger to add granularity - bigger numbers are more time-consuming to do arithmetic on manually). I'm quite sure I had stats costing more than 9, even so, and the starting pool was more than 27 (since you started at all 6s, and had to buy your way up to even 8s).
What is 4d6h3? I've never heard of that.
It seems there are so many posts making the case the starting stats need to be higher. Is this an issue to allow a feat to be taken at level 4 instead of an ASI?
I'm enjoying the game as it is already.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
4d6h3= 4d6 keep highest 3 rolls (aka drop the lowest). It is the official option of how to roll for ability scores.
The only issue with the standard array/point buy is that it is statistically worse than rolling dice by about 2 whole points. In addition to never starting with more than a +3 modifier (where rolling dice is almost guaranteed at least 1 +4).
There isn't anything wrong with playing the game as is, it is just some power balance nit picks by those of us into math.
I think it is deliberate that point buy scores on average lower rolling. With point buy you have the flexibility to distribute the stats as you see fit. Building a Monk where three stats are important you can go 15/15/15/8/8/8 building a rogue that only really needs dex and a bit of con but you want to be reasonably good at all your skill checks you can go 15/12/12/12/12/11. If you roll you have to take what you get so the higher average balances out the flexibility.
In reality though the difference in power between point buy and rolling is higher. If you roll 12/11/10/8/7/5 pretty much any DM will allow a re-roll (or maybe use standard array instead) even if they don't you are likely to die very quickly (possibly via suicide) so a low roll is replaced by a higher one. It would take a brave DM to tell a player who rolls 18/17/16/14/14/12 that their character is too powerful compared ot the rest of the party and they have to re-roll.
I don't think this is a very practical way of looking at it. Rolling is slightly better in the long run; if you were to roll a bunch of characters and average them out you'd find that the average of their scores was slightly better than point buy. But in practice you only get one shot to roll stats for each character and then you're stuck with that outcome for quite a while. And there's going to be quite a bit of variability in those characters: most will be either above average or below average.
Saying rolling is better is kinda like saying that when you're on your death bed, the average of all your D&D character will have been slightly stronger. True, but you'll never actually play as the average of all your D&D characters. The benefit is so small, abstract and takes so long to manifest that you're better off asking yourself if you're ok with getting burned by the dice and playing with below average scores for months at a time. How much fun you had along the way is probably going to matter more to you than some statistical function of your characters.
The Forum Infestation (TM)
OK. I always heard it called 4d6 drop1 or 4d6 drop lowest. Never saw it written as 4d6h3.
I have done enough of the calculations to know rolling will produce a better character, ON AVERAGE, but I think it is even better than you describe DxJxC because no DM in the world is going to make you keep a character that gets too many low numbers. While I can't quantify where that line is, when you eliminate the bottom scores, the average moves up even more. I suspect most DMs would let you choose standard array is your rolls were that pathetic.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
The thing I don't like about standard array or point buy is your melee characters are almost always dumb and your casters are almost always weak.
I think if I were running a game I'd have people roll but only allow rolls that total maybe between +4 or +5 and +8 or +9 stat bonuses. Prior to racial mods.
True, you will mostly play the characters with way above average rolls. Most DMs wouldn't make 1 player be the only one stuck with a character WORSE than standard array, or they will just die/retire early. So the fact that 60% of the time you will roll better than the default stats is skewed further by the fact that low stats will get used less.
It is easier to write it that way for dice rollers (I think I've also seen k3 for keep, but I prefer h3 to specify highest, where rolling with disadvantage for example is 2d20l1 for keep lowest 1).
I don't know why any DM would want to force players to roll and deliberately create a situation where some players will be below average through and others punch well above their weight through no fault of their own. And if a player chose to gamble on their stats they should know their odds and accept the result.
You'd still see this happen even if everyone rolled stats. Odds are they'll have some score close to 8 and another close to 15 and many others in between, so they're still going to optimize their important scores and minimize their least relevant scores. More importantly I don't think ability scores are all that important to creating an interesting characters or a substitute for giving them personality.
That said if you do want variability in the scores but not in the total (e.g. you want everyone to have a +5) you can try rolling for 5 scores and choosing the 6th accordingly. E.g. If you roll 16, 15, 15, 12, 10, your last score has to be a 4 so that the -3 offsets the +8 from the rest. If by some freak chance you roll stats so low or so high that you can't hit the total with a +/-5 on your 6th score, reroll the highest or lowest score. You could do something similar with a d10 instead of 4d6 to generate random point buy arrays.
The Forum Infestation (TM)