It was specifically the fact that the geometric and the harmonic mean will reduce the total score if there's a variance in your face and height scores. If they don't differ much (like a guy with 4 and 6/10 scores) the mean is very close to the arithmetic mean (little penalty).

But if you score really bad in one of the two, the total score gets significantly lower than your total score predicted by arithmetic mean. This is to model what I called the "20lbs phone" effect

The only reason i prefer the harmonic over the geometric mean is because the penalty is greater

n is the total number of variables. So if you only have face and height it's n=2.

The weights are simply values that give greater relative importance to some characteristics. So if you want to do face 60 and height 40, you can do any variables with such ratios. So .6 and .4, or 6 and 4, or 60 and 40 etc

Let's say you wanna introduce body which is 4 times weaker than height (for instance), and you chose to go with weights of 6 and 4, the weight of body simply becomes a 1

If someone had a 3/10 face, 4/10 height and 5/10 body you'd get

Looks score = (3+4+5)/(3/6+4/4+5/1) = 1.846 ~1.85

Whereas with the same weights, an arithmetic mean in this case would give you a score of 3.55

If you think the penalty is too high use the geometric mean instead