# How strong is this stat generation method? Roll 20d6, drop 2 lowest, assign groups of 3 dice for stats

Is this imbalanced for character generation? Roll 20d6, drop 2 lowest, assign groups of 3 dice for stats.

Context: We have tried multiple character generation methods in our group and I have come up with a system (emphasis not on me inventing, might have read somewhere).

I am okay at math, but not self confident enough to get into calculating how over- or underpowered it might be.

Question: Compared to roll 4 drop lowest (as the most "overpowered") how strong is this? Roll 20d6, drop 2 lowest (VERY likely two 1s), organize the rest for group of 6*3.

I didn't want to go into details about how we use it in general, but I now feel the need to clarify something as we love high main stats but try to play weaknesses fairly. If anybody whips out a character with a stat:

• 6-7: minor everyday inconvenience
• 4-5: major everyday inconvenience
• 3: make up a good excuse/explanation how are you still alive and adventuring

Nothing really mechanically fleshed out, but sacrifices were made for becoming "superhuman" so there are consequences.

• Is there something about the usual methods that you are trying to fix here? Someone here can certainly tell you the expected value of your method, but I can’t imagine that would be terribly enlightening. What’s your goal with introducing a new method, other than “to be different”? Jan 10, 2022 at 0:19

While working on this, I realized I could can get most distribution I would like to have as a player. Which makes your method pretty close to a point-buy with a random budget. You can read further to see a comparison with 4d6.

Two aspects bring this method closer to a Point Buy. First, I can choose what the shape of the array will look like. Second, I can switch dices around to get better bonus. (For example, turning a 15 to a 14 in order to raise a 7 into a 8. Raising one of the lower bonus at no cost to the higher bonuses)

The system recommended in the official rules is scaled and restricted to stats in the 8-15 range. I have never used it so I can't speak precisely about it. (I am used to non-scaled and restricted to 8-15)

Compared to the official Point Buy, your system allows for higher stats, allow for lower stats (due to lack of limits) and makes it easier to get higher numbers (due to lack of scaling). With the caveat that low stats are actually hard to get because you need low dice for them.

I can compare with the example given in the rules here and try to replicate those arrays in Anydice.

The first example array is a 3-high/3-low that makes [15-15-15-8-8-8]. By adjusting the distribution like this, I get a similar and possibly better array. The low are similar, with a 50% chance of being 8 or better, and probably a 6-7 otherwise. While one of the high are have the same probability of being a 16 or higher.

On the other hand, the average array given is [13-13-13-12-12-12] and my best approximation is closer to a mix of 13,12 and 11 (Here is the AnyDice).

So, compared to standard Point Buy, the method is worse if you try to have an average array. But better as you try to have extreme stats. On top of allowing stats above 15 which are forbidden with point-buy. I would describe it as "not balanced with point-buy, but similar in power" : the important stats are expected to be a few modifier highers and the dumpstats to be significantly lower, but not that out of the norm.

# Comparison with dice-based methods

You do not give any ways that you think your players will use your method, so I'll use the way I would do it.

First I try to get my 3 main stats as high as I can. On most characters, this would be my attack stat, then Dex or Con depending on what kind of character I'm playing. Then the rest is divided as evenly to get as few glaring weakness since I do not expect to actually use those stats, I just don't want a glaring -3 on a skill or a save if I can avoid it. Lastly, my race will probably give me a bonus to my first and either my second or third highest stats.

## The 20d6 method

Here is what I get with this strategy Anydice. The lines are the chances of getting at least X.

Notice how the two main stats are very likely to be at least 17 and 15 before taking into account races. With the third stat around 12-13.

Also notice how the last three stats tend to be close to one another. Similar to the standard array and 4d6 methods.

On a personnal note, I would never take an ASI over a feat with those numbers.

## Comparison with 4d6

For reference, here is the probability curve for 4d6-drop-lowest and 3d6 (Taken from an article on Anydice). I will be basing the following on this curves as well as my personal experience with rolling a complete array with 4d6.

The main stat can be safely expected to be a 15-16 (+3 or better with races). With the bulk of the stats falling between 12 and 14 (+2 for important stats, +1 for most of them). And the lowest being -1 or +0.

Compared to this, your method gives:

• a guaranteed +1 or +2 for the main stat when compared with 4d6;
• a guaranteed +1 for the two secondary stats
• the lowest stats are -2 compared with expected results form 4d6.

## Conclusions

I don't think this will be that gamebreaking. But I would feel like my character is a full power from Lvl1. As mentionned, I wouldn't take more than 1 ASI until my build is complete from a feat point of view.

While the 4d6 bell-curve ensures most character have a bonus around +1 in all stats and a main stat around +3 for their specialty, you method gives higher highs and lower lows. More precisely, the highs appear to be slightly better than 4d6 (by +1 usually) while the lows are significantly worse ( by probably -2).

All in all, this method appears less gamebreaking than it does at first sight. It actually looks fun for a high-power game. You will absolutely need feats to make those Lvl4-8-12 interesting. Especially for a fighter.

## This method promotes lopsided characters

If you believe that for a given character the six scores are each worth a constant amount per point, then the optimal strategy is to allocate your top three dice to the most important score, the next three highest to the second-most important, and so forth.

Here's what happens if you do this:

AnyDice.

The six curves represent the chance of rolling at least X on your highest score, second highest score, etc. Note that the joint distribution of the six scores is not independent.

The "median" array is 18, 15, 12, 10, 7, 5. In particular, you have about a 2/3 chance of getting at least one 18. Compared to standard array or 4d6-drop-lowest, the ability to allocate higher primary scores comes at the cost of a lower mean score.

It's possible to compute the exact probability distribution of the total point-buy cost of this strategy in polynomial time. The key elements are:

• Iterating through faces rather than through dice.
• Using binomial coefficients to quickly go through the possibilities of how many dice rolled each face, rather than which dice rolled each face---the former is polynomial, while the latter is exponential.
• Dynamic programming/memoization to cut out redundant intermediate calculations: there are only a polynomial number of possible running totals and remaining dice.

Here's a Starboard notebook that computes the exact distribution for this strategy. You can compare this to my calculator for a variety of other ability score generation methods.

• "Finding the probability distribution of the total point-buy equivalent value is computationally feasible using the right algorithm" I'm not so sure it is, because this system routinely produces characters with ability scores both much higher and much lower than 5e's point buy system allows. Jan 10, 2022 at 3:59
• Certainly you would have to extend the cost table upwards and downwards, e.g. chicken-dinner.com/5e/5e-point-buy.html though there is no official table beyond 8-15. What I meant by "computationally feasible" is just that, once you've decided on a cost table, the result can be computed in polynomial time. Jan 10, 2022 at 4:10
• Brute forcing a million iterations: 3=-5, 4=-4, 5=-3, 6=-2, 7=-1, 8=0, 9=1, 10=2, 11=3, 12=4, 13=5, 14=7, 15=9, 16=11, 17=13, 18=15. Average stat is 11.25, average buy cost is 25.15. Not the distribution, but might help. Jan 10, 2022 at 8:13
• imgur.com/a/eHSMJxD has a chart with the distribution curves. Minimum is -9, max is +69, average is 25.15. Obviously, different stat costs will change the curve. Jan 10, 2022 at 9:18
• To compare to a point buy, try comparing to a non-scaling point buy that starts from 0. Then you might be able to convert that to a scaling point buy. You roll an average of, perhaps 67, which converts in that point buy to a range from all 11s and a 12, to 18 18 18 8 3 3. By converting any roll total to its points and distributing them across the stats to maximize high numbers, you can approximate a 'best case' to compare random roll distributions to, and then perhaps get a 'point buy' value. Jan 10, 2022 at 17:08

It is fairly hard to statistically analyze your system because there's a lot of human decision making involved. Depending on how your players choose to assign the 18 dice they have for their stats, you may find you have different balance issues. But there are a few things that are clear:

First, a characters' total stats will be a bit worse on average. As this AnyDice program shows, the total of all the character's attribute scores will average about 6 points less than with the standard rolling method. That's not huge, but it's not trivial either.

The other significant difference is how easy your system will make it for the player to get exceptionally high or low scores for certain attributes. It is very rare for a PC to start with an 18 or a 3 in a stat, but in your system is will be very easy for a player to choose a combination of dice that give them stats like that. Almost every roll will give at least 3 sixes for the player to use for their best stat, if they want to. And while ones are a bit rarer (since the lowest two dice are dropped), there are still going to be a lot of low dice that will often go into "dump" stats that the player hopes never to roll.

Here's another graph showing the highest and lowest possible rolls from each system (generated by this AnyDice program).

• Thank you for the detailed explanation I was generally worried about hidden imbalances in the system, but lower total of average for an almost guaranteed 18 to be able to flavour with feats instead of ASI -s fits our play style just fine, so thank you for the confirmation. Jan 10, 2022 at 19:29
• @Sypherien: FYI, 21d6 drop lowest brings the median total up to 70.5, from 67.8. (vs. 73.47 for the best 3 of 4d6 method). Adding yet another extra die, 22d6 keep 18, brings the median up to 72.1. Presumably those gains are spread through the lower 5 stats if you do prioritize linearly, making it a lot more likely to avoid a 3 even if you put your lowest 3 dice into one stat. (Which would probably be a mistake for most parties / games... Also because you want to aim for even numbers if you want to min/max your total ability modifiers; distributing this way makes it easier to aim for even) Jan 12, 2022 at 2:26

Okay, so as one of your players i've just rolled my stat generation dice.

I'm going to play a Fighter. I've selected my race as Half-Orc. I place 3 6's into Str, giving me 20 Str (18 + 2 racial). I place 6 5 5 into Con, giving me 17 Con (16 + 1 racial). I take 5 5 4 into Dexterity, giving me 14 Dex. I decide I want a good Wisdom, for Perception checks and saving throws. So I put 3 4's into Wis, giving me 12 Wis. That leaves me with 2 3 3 to put into Charisma, giving me 8 Cha, and 2 2 1 to put into Int, giving me 5 Int.

20 Str 17 Con 14 Dex 5 Int 12 Wis 8 Cha

This method allows me to minmax whichever scores I desire most above others, resulting in very focused characters with lower-than-usual 'dump' scores. If you like 3 cha fighters and 5 str wizards, this may be ideal for you.

Overall I would rate it lower than most other methods, including the simpler 'roll 4d6 drop 1'.

• I agree. This method will encourage dump-stats. Point Buy tends to make more well rounded characters since buying from 8 to 12 is cheap and 13 to 15 is expensive. This is the opposite, and the player is rewarded for prioritizing their main stats and dumping hard on the ones they don't need. Jan 11, 2022 at 22:40

It is rather tough to directly compare your method with "4d6 drop lowest". Looking at the total score it might look like your method is overall weaker with an average of ~67 compared to ~73 for "4d6 drop lowest".

However, you allow the 18 remaining dice to be grouped however the player wants which can be rather powerful. This is hard to visualize in a single graph so to illustrate let's look at the probabilities when grouping the highest 3 dice together, which will be the highest one of the player's stats can be and in practice what most players will likely do for their class' primary stat.

There is a ~67% chance a player will have the option to have a score of 18 in their primary stat (before class bonuses), compared to the mere ~2% when using "4d6 drop lowest".

Overall it kind of depends on preference and perhaps even the chosen class. Players who prefer a min-max approach would probably greatly favor your method, but players who prefer a more balanced stat distribution might not. Equally, classes that can really benefit from one high stat (like Rogues) will likely prefer your method more than classes that generally try to increase three stats (like Paladins).