The balance of probability standard means that a court is satisfied an event occurred if the court considers that, on the evidence, the occurrence of the event was more likely than not.
For instance Bart Ehrmann considers that the existence if a non divine, fully human jesus figure in the first 40 years of the 1st century CE likely on the “balance of probabilities” based on his historiography . Not from direct historical evidence. That verdict would not be available in a criminal trial.
“Beyond reasonable doubt” is the standard in Criminal cases, “Balance of Probabilities” in the Industrial and civil courts.
That does NOT mean “cumulative evidence” which is just not a formal, legal, thing anywhere except in your fevered and overwrought imagination.
There is a third verdict available in Scottish Courts that of “Not Proven”.
As far as I am aware there has never been a court judgement in ANY criminal court that relies solely on formal logic which is a tool of philosophers not legal professionals, nor for that matter professional historians. .