Oh, are you sure? A court CAN judge and will judge based on statistics... if it is appropiate to do so.
Why? Simple...
Lets say the defense presents, for whatever reason, the theory that a witness is fat in comparism to an anorexic model. The theory is plausible due to statistics - and that is all the proof the defense, so far, needs to present that theory. After all, the high probability of a normal person being "fatter" than an anorexic person is enough proof.
However: Now the ball lies with the prosecution. They have the burden of proof, as their scenario is that said "normal person" is not fatter than said "anorexic person". Due to the low probability of that claim, they need to bring evidence to proof their case.
In our case, I am the anorexic person. Okay, I am not anorexic but I weigh around 60kilo on 2 meters... As I said, I cannot gain weight for some reason.
With this, I am skinnier than the vast majority of humans on this planet, especially if they live in a "normal" situation.
This leads to the burden of proof falling on to you, naturally. I have proven to the judge, aka me, that I weigh 60 kilo on 2 meters and thus am extraordinarily skinny. You have done no such thing. However, as this is no trial or anything, I take your testimony as proof enough - you have not given me any testimony so far. Thus, if you refuse to give said testimony, the verdict would be clear.
And if you are ticked off by me being the judge.. I can at least trust myself to be impartial and a good judge. I can not trust another person to be a good judge in any sort of argument. May sound arrogant, but a friend of mine once told me "It is not arrogant if it is the truth" and i try to adhere to those words.