Given a set of $n$ vectors $\def\vv{\vec{v}} \vv_i$ with the additional property that they all have the same absolute value $||\vv_i||=c$, define the average of the vectors as $\vv = \frac{1}{n}\sum_{i=1}^n \vv_i$.
If all $\vv_i$ are identical we have $||\vv|| = c$, but if they all have different directions, a not to complicated derivation yields
$$ c^2 - ||\vv||^2 = \frac{1}{n^2}\sum_{i<j}^n ||\vv_i-\vv_j||^2 .$$
The sum on the right side is the average mutual delta squared of the individual vectors.
It vaguely reminds me of variance, which it is obviously not. Does the formula have a name? Does it appear prominently in another context?