One instance that I am familiar with is "innocent unless proven guilty beyond a reasonable doubt." So if you think that someone is "probably" guilty, but have a "reasonable doubt" covering, say 5%-10% of possible outcomes, my understanding is that you're supposed be give the defendant the "benefit of the doubt" and vote to acquit.
In a civil case, where the burden of proof is "preponderance of evidence," the standard of proof is more like 50-50. In this case, you might give someone the benefit of the doubt if you felt that that party was 50% or more in the right.
So is "benefit of the doubt" tied to a quantitative measure or probability? That the party receives the benefit of a very small doubt in the criminal case, and "50%" in the civil case?