Preponderance in general terms means to be superior in number or weight. Preponderance as used in evidence law means having the greater weight of the evidence required in a civil lawsuit needed to convince the jury or judge without a jury to decide one's favor. Preponderance of the evidence is the level of proof required in a civil case, as opposed to the stricter "beyond a reasonable doubt," standard of proof required to convict in a criminal trial.
Preponderance of the evidence could be interpreted to mean a 51% chance that the evidence presented is to be believed. However, the actual application of the standard of proof is more subjective and not capable of numerical quantification.