Rolling hit points for monsters

As I was delving into the ancient ruins to seek the wisdom of the sages of past ages, I came upon this nice little gem on Planet Algol: Non-randomized Monster Hit Points is the F’ing Devil. The unknown author (seriously, there’s no name anywhere on the site) makes a point that you really should roll the hit dice for monsters and NPCs the players might fight an not just assume the average, as it has a real impact on customizing individual opponents. Would players ever notice the difference between a 2d8 creature with 8 hp and an otherwise identical one with 11 hp? Probably not. But they very much would notice the difference between a 3 hp and a 15 hp one.

A note  is being made about perhaps rolling only one die and multiplying the result by the number of die, to make more extreme results more common than under the normal distribution you get from rolling and adding up multiple dice. But I was also curious about the results you would be getting from rolling hit points normally for every opponent and so I pulled up AnyDice to check.

The added up results of multiple die rolls are a classical of a normal distribution. The classic bell curve. A typical way to compare and interpret the distributions of these curves is by using the Standard Deviations as reference points. I once learned how to calculate standard deviations and also understood the reason why they are typically used instead of any other arbitrary reference lines. I’ve forgotten all of that years ago, but I am going to use them anway. (And it turns out AnyDice can just tell you that number, spring me the need to manually crunch numbers for other reference values.) The only thing that’s really important to know is that 68% of all results will lie within 1 SD of the median value (the line between the lower 50% and the upper 50% of all cases), and 96% of all results within 2 SD.

Since almost all creatures use d8 for hit points, I’m going to do the whole thing only for d8s. Obviously the spread will be somewhat smaller for smaller Hit Dice, and larger for larger ones, but the pattern remains the same.

Now how to read this table for the not statistically trained? What this means is that 68% of all results you get will be between the -1 SD and the +1 SD columns. 96% of all results you get will be between the -2 SD and the +2 SD columns. Or in other words, only 2% of results will be smaller than the left column and only 2% larger than the right column.

Here’s the same data a bit more condensed, showing the range of hit points for 68% of the creatures if you roll their hp.

Here the left column is the range you will see for 68% of your creatures, and the right column what you’ll see for 96% of your creatures. Results outside the range of the right column will occasionally happen, but will really be quite rare. As the number of dice goes up, the spread of the result will be come relatively narrower. The difference between 34 and 47 really is not that big and players might not notice. But the vast majority of enemies that will be fought in groups will have much lower number of Hit Dice, especially those in larger groups. Going from 6 to 12 means double the amount of hit points for 2d8 HD opponents, and when you deal 3 or 4 damage, that makes a real difference. And that’s only for the 68% group. A 2d8 creature with 2-3 or 15-16 hp will be rare, but still account for about 5% of individuals each. In a group of 10, you’d expect to see one of these outliers.

So yeah, I agree with the anonymous author. Rolling the hit points for every opponent individually seems very much worthwhile when you have a game with few fixed bonuses to the dice roll and PCs commonly dealing single digit damage.