The author has very poor statistical understanding here. You don't generally use expected value as a measure of statistical randomness.

You can use expected value to ensure that your dice are giving a fair amount of damage every turn, but it's not useful for much else, and good grief look at these plots: The very first plot on the page has a bar plot for standard deviation, and a CONNECTED LINE PLOT for expected value, even though adjacent data points have no correlation with each other!

If you're going to connect points together, the slope of that line has to be meaningful in some way.

Hasn't the author ever heard of a box plot?

The author also needs better measures of statistical randomness. Average/expected value is NOT a measure of randomness; a simple such measure would use the frequency between appearances of a certain value. For instance, find the distance between all the "1" rolls, and diff that distribution against the distribution of a truly random distribution. Do this for all the numbers through 20, then find the standard variation of standard variations.

So for instance with a d4, if I always get:

1 2 3 4 1 2 3 4 1 2 3 4...

The expected value (2.5) and standard deviation (2.23...) measures are exactly correct, but it has no randomness! The distance between 1s will always be 4. The distance between appearances SHOULD have a geometric distribution (iirc).

In 4000 rolls, I would expect 1s to appear back-to-back 250 times, a distance of 2 about 190 times, a distance of 3 about 140 times, and so on.

Since the actual series always has a distance of 4 with 1000 times, this means our standard deviation is... 959. 95.9%.

Now do this for all the numbers. I think you can average those together and get a final "randomness" result.

And this is just one test of statistical randomness! Cryptographically secure random number generators, by definition, pass ALL tests of randomness, i.e. they're indistinguishable from a true random number generator if you don't have the secret key/internal state (or enough computing power).