A few years ago I read something about the value of always rolling for the hit points of creatures and NPCs that the players get to fight and not always taking the average by default. I really like the idea of using different hit points to give individual opponents a bit of a personalized description even though otherwise they have completely identical stats with the same AC, saving throws, hit chance, and damage on a hit. In a fight against some random orcs or bandits, it can be a neat and convenient inspiration to have those with 7 hp look much larger and more menacing and approach the fight different from their otherwise identical buddies with only 2 hp.
But sometimes, you might want to know what actual hit points numbers might be realistically expected for a given number of d8s. So I made this little table. The math magic behind calculating 2 standard deviations for normal distributions isn’t really important here. What this table shows is the range of hit points into which 96% of all random rolls will fall. There is only a 2% chance that a randomly rolled number will be lower than the shown range, and a 2% chance that a number will be greater. It will still happen occasionally, but even then most likely only by 1 or 2 points, and for the purposes of encounters in an RPG, I consider the odds negligible. You can just assume that pretty much all randomly rolled hit points on a d8 will fall into the shown ranges.
|Hit Dice||hit points|