Using randomly generated ability scores is a recurring topic on many 5e forums. Although, standard array and point buy are the most common method by far, rolled ability scores is the default method for 5e. Indeed, random ability scores were the standard for most of the history of Dungeons & Dragons,. Point buy was introduced with 3rd edition, and the Standard Array didn’t come out until Xanathar’s for 5th edition. While I consider standard array better for ensuring parity between players, the appeal of random ability rolls is still there for many.

Like everything in 5e, it all comes down to what you want out of it. So, I thought it would be fun to talk about why random ability scores can be fun and what games can expect from using different methods.

Why Random Generation?

People can find fun in random ability scores for a few reasons. First, the feeling of discovering a character and playing within the constraints of random abilities can be exciting. Second, players can feel this creates a more ‘realistic’ individual that has to deal with the hand nature as dealt them. Third, it can move the baseline of stats to create a more gritty or epic character, depending on the method selected. These can be fun, and I particularly enjoy the discovery and constraints element of rolling abilities. However, be aware that some method can create wild disparities between characters, which can ruin the fun in some groups.

If you’re thinking about using randomly generated ability scores in your game, I have one piece of advice. Know the difference between something you like other people doing, and what those other people actually like to do. That means that the group should not only buy into something like this but be excited about it. There’s a pitfall for DMs who get things into their head that they like to see the players do but ends up being no fun for the players. So, make sure to pick an option the whole party is going to enjoy when considering something like random ability score generation.

Common Methods of Random Generation

There are several methods used to generate random abilities. In most cases it creates a set of 6 scores the player can arrange how they like. Some versions that let players only swap a limited number of scores. A few hardcore rulesets even go so far as to keep them in the order rolled. As with anything, no way is better than another, it all comes down to what you want out if it. The most common methods are:

  • 3d6 rolled for each ability. (3d6)
  • 3d6 rolled 7 times and keep the highest 6. (3d6 7x-k6)
  • 3d6, reroll any 1s. (3d6 r1)
  • 4d6 keep the highest 3. (4d6 h3)
  • 2d6+6 for each ability. (2d6+6)

Break Down of Ranges

The first thing to understand about any random ability score generation method is the range and probability. How high and low a range of rolls can be, versus how likely any individual roll is likely to be. Different methods produce different results and a Distribution Curve graph of the most common methods is presented below.

Common rules DMs use is to reroll abilities below a particular level, let players shift points around, or rerolling if you are below a particular score value. This kind of defeats the purpose of random abilities to me, but these are the base percentages you’ll get from different methods.

line graph featuring the probabilities of different random generation methods
Chart data compiled from Any Dice

The Most Common Results

While distributions curves are great, what people want to know is what the most likely set of abilities from a particular method are. Again, since this is random it will vary but the table below presents the ideal set of stats produced from different generation methods. Note I am presenting the Standard Array as a comparison, and that it essentially corresponds to the method for 3d6 rerolling 1s. If a DM were just interested in shifting ability scores up or down, they could select one of these as a new standard array and avoid the random swings. As should be apparent, these methods can produce very different types of characters.

2d6+6 16 15 14 12 11 10
4d6 Drop lowest 16 14 13 12 10 9
Standard Array 15 14 13 12 10 9
3d6 reroll 1s 15 14 13 12 10 9
3d6 7 times, drop lowest 14 13 12 11 9 8
3d6 14 12 11 10 9 7

The Bounded Accuracy Problem

One thing to note about ability score generation is that 5e was built heavily on the concept of ‘bounded accuracy’. That is to say that the game design intends to tightly control the number of bonuses and their progression throughout the game. So, giving characters higher or lower abilities could slightly impact gameplay difficulty. This is likely not going to be a massive issue, but a group should take this into consideration, particularly the DM when balancing encounters. Additionally, ending up with drastically different primary ability bonuses can be a let down in a group, and the bounded accuracy problem may feel larger than it is.


There is no superior method when generating ability score, it all depends on what you want. This not only includes the ability ranges, but the mystery of what a character will be during character creation. Generally, I prefer standard array or point buy as a DM, but I’ll allow a party to select random scores if they ALL want to and agree. I’ve had some fun with this in various games, notably having played a healer who rolled minimum strength, playing them as having a neuromuscular disability. In all honesty, the striving to be heroic in the face of a setback was a lot of fun for me as it taps into my own emotions and experiences having a disability. I wouldn’t want to do that in every game however, but it is fun now and again. Regardless, it’s good to know what the likely outcomes will be when choosing something like this, so I hope this post helped shed some light onto that.

Now get out there and run some great games.