Fixing 4d6 drop lowest

How do you determine your character’s ability scores?

According to the Player’s Handbook (page 12), the default is to generate them randomly. You roll four six-sided dice and record the total of the highest three, six times (‘4d6 drop lowest’). Other options are point buy (technically a variant rule) and taking the array: 15, 14, 13, 12, 10, 8.

My group used to be wary of rolling stats. Most rolls in D&D have a chance of failure, but it’s rarely a failure that haunts you for the rest of your adventuring career. A chromatic orb goes wide; you miss a secret door; you don’t pick the lock. Bad ability scores, on the other hand, can feel like a lasting punishment and make your character feel less badass, less fun to play. However: over time, we’ve come to appreciate the hidden benefits of rolling. It makes your character feel more individual, more unpredictable, more ‘spiky’.  

I’ve written before about what to do if you roll bad stats (and, conversely, the character options that open up if you roll exceptionally well). I also make the case for why ability scores don’t matter as much in 5th edition as they did in previous editions. However, in this previous article, I didn’t really examine the mechanics of dice rolling themselves. And here’s my take: 4d6 drop lowest is one way of rolling ability scores, but it has its flaws. I want to explore whether there are other methods that might work better.

Probabilities

Wizards of the Coast

Full disclosure: I am not a statistician. I am not even particularly good at maths. So, if I mess up somewhere, constructive criticism is welcome.

Fortunately, we have a great tool in the form of anydice.com, a probability calculator created by Jasper Flick. Jasper has already written an article comparing 4d6 drop lowest with the default array and the older method of rolling 3d6 six times. On average, 4d6 drop lowest gives you better ability scores than the standard array. I’m fine with this: if the default array were better than rolling, there would be little incentive to determine your ability scores randomly.

However: 4d6 drop lowest can give you some weird or even unplayable stats.

Rolling low

Let’s consider for a moment what a low roll means in the world of D&D. 19.73 percent of players will roll a 6 or lower on at least one of their stats. (Granted, your chance of getting a 6 or lower on two or more stats is pretty low – one in a hundred, roughly – but hey, it’s possible.) In 5e D&D, the most popular dump stat is probably Intelligence. A character with an Intelligence of 6 is no more intelligent than an ape or a dolphin, and a character with an Intelligence of 3 or 4 is about as intelligent as an elephant or an octopus.

Here’s what low stats are equivalent to for the other five ability scores:

  • A low Strength is comparable to the strength of a bird of prey: a medium-sized vulture (Strength 7), a small eagle (Strength 6), or a tiny hawk (Strength 5). A character of Strength 4 has the physical power of a badger or an octopus: a character of Strength 3 is as weak as a house cat.
  • There aren’t any beasts in the Monster Manual with a Dexterity of 6 or lower, but a character with this score is roughly as agile as a zombie, an ooze, or an awakened tree.
  • There is one creature in 5th edition with a Constitution of 6 or lower, and that’s a gas spore. Even tiny creatures like bats and weasels have a Con score of at least 8.
  • Interestingly, low Wisdom seems to correlate with low Dex. A character of Wisdom 6 is about as perceptive as a gelatinous cube. Lower than that, and you’re looking at the Wisdom of an animated object like a rug or a suit of armour.
  • Finally, if you dump Charisma (defined in the Player’s Handbook as ‘force of personality’), you will find numerous beasts to keep you company. Bear, wolves, and ponies have a Charisma of 6 or 7, boars, crocodiles, and camels have a Charisma of 4 or 5, and frogs, lizards, and snakes have a Charisma of 3.

Suddenly, those super-low rolls seem a bit ridiculous.

Wizards of the Coast

Rolling high

What about high stats? Nearly one in ten players will roll at least one 18 for their 1st-level character (9.73 percent, to be precise), and characters have the potential to get their scores as high as 20 without magical help, even at 1st level.

  • A character with Strength 18 can lift 540 lbs and still move 5 feet per turn. A Clydesdale has Strength 18. A character with Strength 20, meanwhile, can lift 600 lbs. They can wrestle grizzlies and polar bears (Strength 19 and 20, respectively).
  • Forget cat’s grace: characters with Dexterities of 18 or higher are almost supernaturally agile, comparable to sprites and vampires. A character with a Dexterity of 20 is as agile as a planetar (angel) or a marilith (demon).
  • What’s a tough as a character with Constitution 18? King Kong, that’s what. And for Constitution 20, you’re talking trolls, golems, and stone giants.
  • Creatures of Intelligence 18 include aboleths and ancient dragons. Mind flayers have an Intelligence of 19, and liches have an Intelligence of 20.
  • The sphinxes have a Wisdom of 18, as do storm giants. In the Monster Manual, only devas and couatls have a Wisdom of 20.
  • Finally, a character with a Charisma of 18 has the same ‘force of personality’ as Count Strahd von Zarovich or Lord Soth (a death knight). A character with Charisma 20 is as charismatic as a succubus, a rakshasa, or a djinni.

The problem

Wizards of the Coast

To be clear, there isn’t necessarily a huge issue with 1st-level characters having stats as low as 3 or as high as 20. Adventurers don’t all look the same and can come from any background. On average, rolling 4d6 drop lowest will produced a balanced array, with some high scores, some average scores, and one or two low scores.

My issue with rolling is that the super high scores and the super low scores turn up more often than I feel they should. Statistically, if you have five characters in a party, it is highly likely that at least one of them will have a score of 6 or lower somewhere. This means that in most D&D parties there is at least one character with chimp-level Intelligence, or zombie-level agility, or the Wisdom of a gelatinous cube. Aren’t these people supposed to be semi-competent adventurers? Similarly, there’s about a fifty-fifty chance that one of your characters will be as wise as a sphinx, as tough as King Kong, or as smart as an ancient dragon . . . but at 1st level, when your heroes are just starting out?

For you and your table, this might not be an issue: it’s all part of the fun. But for me, it just feels a bit odd. So, how can we get around it?

Solutions

Wizards of the Coast

Of course, the simplest and least controversial solution is to not roll stats at all. Point buy and the default array limit players to scores between 8 and 15, what we might call ‘the heroic average’. You lose the ‘spikiness’ and unpredictability of rolling, but you also don’t run the risk of playing a character with the Charisma of a frog.

The second option is to introduce some kind of ‘floor’. In 3rd edition, for example, you could reroll your scores if your highest score was 13 or lower or if your total modifier was +0 or lower. While this protects against crashing out with multiple bad scores, the 18s appear just as frequently, and you can end up with some truly weird arrays like 18, 18, 12, 10, 4, 3. Unlikely, but still possible.

The final option is use a different method of rolling. There is arguably a precedent for this already: 4d6 drop lowest was probably a revision of the original ‘3d6 down the line’. The 3rd-edition Dungeon Master’s Guide also offered a variant for ‘high-powered characters’ which was essentially 5d6 drop two. While this protects better against super-low scores, it also leads to super-high scores more frequently, with nearly twice as many 18s as the default method.

Here’s my method:

  • Roll 3d6 seven times.
  • Reroll any 1s.
  • Take the best six of the seven scores.

That’s it!

With this system, you can’t roll lower than a 6. In fact, your chance of rolling lower than an 8 is very low: just 2.15 percent. Your chance of rolling an 18 is also lower, however: 5.6 percent. The average array is 15, 14, 13, 12, 11, 10: statistically, these stats are better than taking the default, so there’s still an incentive to roll, but there’s more of a cushion at the bottom. The super-high scores are still possible, but they are more exceptional, and, therefore, more special.

This method is easy to explain and continues to rely on d6s, the dice most likely to be in abundance. You will probably end up rolling about the same number of dice as you would do if you went with the 4d6 drop lowest method, and you’re also less likely to generate unplayable scores that need to be completely rerolled.

Here are five arrays I rolled, to give you a sense of what to expect:

  • 15, 14 13, 10, 9, 9
  • 16, 13, 13, 12, 12, 12
  • 16, 16, 15, 12, 10, 10
  • 13, 13, 12, 12, 12, 11
  • 17, 16, 13, 12, 11, 11

The biggest downside to this method is that, on average (56.53 percent of the time, to be exact), you won’t have any scores lower than 10. If that bothers you, a possible fix is to only reroll 1s once. This keeps open the possibility of rolling a 3, 4, or 5, but shouldn’t affect your chances of rolling playable stats in the main. (Think of it this way: if you roll 3d6 seven times, you will probably only roll three or four 1s, and if you reroll these ones once then you are unlikely to have more than one 1 left in the entire spread. Given that you drop lowest score anyway, it doesn’t make a big difference.)

What do you think? Would you use this method? Will you stick with 4d6 drop lowest? Or are you more of a point buy person, anyway? Add your thoughts in the comments below.

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3 thoughts on “Fixing 4d6 drop lowest

  1. I have been experimenting with a Tic-Tac-Toe style grid with my group. So roll your same 4d6 and drop, but you roll 9 times instead of six.

    Arrange your numbers left to right, top to bottom so you should have a grid that looks something like

    12 16 14
    18 09 12
    10 13 13

    From there you can choose to select one row and one column as your stats, but you cannot overlap the highest number twice. So in the case above, you couldn’t chose Column A and Row 2 since they both would have the 18.

    Allows players a little more choice and not have to be stuck with 1 or 2 very bad rolls.

    1. Interesting! I like that method. I wonder if it leans a little towards being high powered, though, as you’re increasing the chances of super-high scores by 50 percent (nine rolls over six).

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