# Inheriting stats in generational D&D play

Suppose the particular stats (say, wisdom), of character’s parents are 12 (rolls 5, 2, 5) and 14 (rolls 5, 5, 4). How to determine the stat for the character?

### Motivation

This might be useful for generational play, or when starting a new game or campaign in a same setting but later in time. Playing as the children of previous, possibly retired, characters might add depth to the game.

### Basic method

Stats are usually rolled with 3d6. We take first of those rolls from one parent, second from the other parent, and roll a new result for the third die. Using the example scores above: 5 from the first parent (rolled 1 with d3 to determine which die roll of the parent is used), 4 from the second parent (rolled 3 with d3), and new die score of 2; total is 11.

### Special cases

If the stats of only one parent are known, then only one die is inherited, the other two rolled. If character is a result of asexual reproduction (with some variety, so not a perfect clone), then two separate dice are inherited from the single parent and one new die is added; this might be the dwarves of Dwimmermount or some insectile or vat-grown species.

If only the total score (such as 8) is known but the rolls are not, then any combination of die rolls with the correct sum is acceptable (for example 1, 3, 4). If one wants a little practice in calculating discrete probabilities, then one can figure out the probabilities of different combinations of scores by Bayes’ theorem and select one of them randomly.

### Changes in stats due to adventuring

If a change alters the genotype of a character, including gametes, then the die rolls that constitute the stat should be changed accordingly. For example, if character is turned into supersoldier with strength of 20 and charisma of 2, then the corresponding rolls might be 6, 7, 7 and 0, 1, 1. It does not matter if they are not within the range of 3d6. Stat changes due to experience, age or practice should not influence the constituting rolls.

### Exotic races

If the game uses stat requirements for non-humans, then any offspring not meeting the requirements dies before birth or shortly after it. A miscarriage or a stillborn child. If stat bonuses are used, then they don’t affect the constituting rolls of a stat and are applied after determining the base stat.

### Justification

The new score of a child is affected by the scores of parents, but not determined by them. The expected value of a new score is the average of the following: first parent’s score, second parent’s score, and $21/2$ ($= 10 + 1/2 = 10.5$). This gives regression towards the mean: no matter how bad or good the scores of the parents are, those of the child will tend to be somewhat average.

If the stats of parents were rolled with 3d6, and the stats of a child were rolled according to this method, then the scores of the child would be distributed as if they were also rolled with 3d6. This means that in the long run a population governed by this law (and no selection pressures) will have the stats of any given character being rolled with 3d6. This is true regardless of the stats of the first generation.