Preponderance of the evidence is actually a misnomer since it really means that no evidence at all is needed.
Effectively, the standard is satisfied if there is greater than 50 percent chance that the proposition is true. Lord Denning, in Miller v. Minister of Pensions,[7] described it simply as "more probable than not."
IOW, if general statistical probabilities mean that any accused person is more than 50% likely to be the cheater, then the burden is met. It also means that if it is subjectively felt that the odds that the accuser is lying is as much as 49.99% but still less than 50%, the burden has been met without any evidence being presented to support the guilt of the accused.
It is not used in virtually any criminal cases (outside of the new rape laws in question), because it basically eliminates the presumption of innocence and has the defacto effect of allowing the accusation to count as evidence of itself if it is deemed that that sort of accusation in general is less likely than not to be a lie.
It is used mostly in civil cases, where it can actually make sense. If two parties are fighting over property rights, it is usually known that the property does belong to one of us, and the courts needs to decide which one or there will be no resolution and the property is forever in limbo. So, the court must decide in favor of one party or the other, thus a +/- 50% standard is needed because the odds are high that neither party could reach a higher standard than that and thus the case would have no resolution. IOW, neither you or I can prove beyond reasonable doubt that the property is ours, so the property would just sit there indefinitely without claim unless the courts decides which of us has the better claim to it, which is the same as using a "preponderance of the evidence".
Note that is such a case there really is no guilt or innocence determined, thus the concept of innocent until proven guilty does not really apply. It is a judgment of relative merit for competing claims where there is only a need to determine which claim has more relative merit.
In contrast, guilt or innocence of violating a criminal statute is what a rape case is all about, so the the presumption of innocence needs to apply and it is not relative merit, but proof in a more absolute sense that does and should matter. Thus something much higher than 50% probability of guilt should be required.