Height Distributions

If you so desire, your character's height can be randomly generated based on their sentient's typical distributions.
Sentients tend to follow the same kind of height distributions:

• There is a mean height for the sentient and sex combination.
• The standard deviation of the distribution of heights is approximately equal to 0.0438 times the mean height for both sexes. Standard deviation × 0.0438 is the height factor.

In order to generate a height, follow these steps:

1. Find the mean height for your race and sex.
2. Generate a random height factor, or choose one based on how relatively tall you want your character.
3. Multiply your height factor by the mean, then add it to the mean. Alternatively, use the formula (mean × [1 + height factor]).

Let's use a female human as an example for this process.

1. I looked at the Human article and saw that female humans are typically 5.40 fl (about 5'4.8" or 165 cm).
2. I randomly generated a height factor and rolled a 93 on my d100 roll. That corresponds to a height factor value of 0.0646, which is in the 93rd percentile for the species and sex -- that's pretty tall!
3. I multiply my height factor by my mean value and get (5.40 fl × 0.0646 = 0.3488 fl). I add this to my mean of 5.40 fl and have a final height of 5.75 fl, or about 5'9" or 175 cm.

This isn't stopping you from choosing a higher or lower percentile, or picking one you like. You can look up different percentiles and their standard deviations from the mean (aka z-scores) by using a cumulative standard normal table. Some more extreme examples are:

• 99.9th percentile is a height factor of 0.1354 (3.09 standard deviations)
• 99.99th percentile is a height factor of 0.1629 (3.72 standard deviations)
• 99.999th percentile is a height factor of 0.1868 (4.26 standard deviations)
• 0.1st percentile is a height factor of -0.1353 (-3.09 standard deviations)
• 0.01st percentile is a height factor of -0.1629 (-3.72 standard deviations)
• 0.001st percentile is a height factor of -0.1868 (-4.26 standard deviations)

Remember! 1 frul (fl) is 1 ft! See Standardized Units of Measure for more information.

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^{Data source: https://ourworldindata.org/human-height}