An improvement to OPR

[MikeE]

Thanks for the information Ether. It spurred me to check the details in the Octave documentation

Originally Posted by Ether

I was wondering what was the theoretical basis for assuming a normal distribution.

There is no theoretical or empirical* basis for assuming a normal distribution, it's just a matter of convenience and convention. For the purposes of estimating mean, minimizing the squared-error will give the right result for any non-skewed underlying distribution.

Unfortunately I don't have access to reliable per robot score data otherwise we could establish how well a Gaussian distribution models typical robot performance. (I did check my team's scouting data but it varied too far from the official scores to rely on.) If anyone would like to share scouting data from this season I'd be very interested.

In my professional life I work on big statistical modeling problems and we still usually base the models on Gaussians due to their computational ease, albeit as Gaussian Mixture Models to approximate any probability density function.

* In fact we know for certain that a pure climber can only score discrete values of 0, 10, 20 or 30 points.