Of course judges are not always good as well. In the US they are often elected by a blood thirsty population. If they are not elected that has other issues in that the will of the people is not held by the judges.
In the US, juries typically decide questions of _fact_ that are not already agreed upon by both parties (i.e. are in dispute). Judges handle questions of law.
If a fact is not known, how can some random person produce it? Out of what.
E.g. in the situation of a crime: only activities like crime scene investigation, and interviewing of witnesses can produce anything that can be called a fact.
Now so from all that have some collection of real facts from the investigation which do not add up to an absolute proof that some particular defendant "dun it".
The next best thing you could do is use some sort of probabilistic reasoning.
Well, what training in probabilistic reasoning do the these random people off the street have?
Probabilities should be quantified in concrete numbers. Instead of some flaky "shadow of a doubt" nonsense, there should be some 99.99% (or whatever standard level) confidence which is somehow calculated.
Yes, it might be better if jurors were all acquainted with Bayesian reasoning and it would definitely be better if things like expert testimony and so forth came with confidence estimates.
And yes, "beyond a reasonable doubt" is pretty qualitative.
My point was that if you are expecting your jurors to have a deep understanding of the law, you are definitely doing it wrong.