The standard of proof in civil cases requiring only the slightest tip of the balance to decide who wins the case. (Compare the standard of proof in criminal cases requiring the prosecution to prove its case ‘beyond reasonable doubt’.)
In criminal cases any evidential burden placed on the defence need be proved only on the balance of probabilities. For example it is an offence for a person to possess an offensive weapon without lawful authority or reasonable excuse ‘proof whereof shall lie on him’. The defendant need prove this only on the balance of probability.