Toulson LJ said
34 A case based on circumstantial evidence depends for its cogency on the combination of relevant circumstances and the likelihood or unlikelihood of coincidence. A party advancing it argues that the circumstances can only or most probably be accounted for by the explanation which it suggests. Consideration of such a case necessarily involves looking at the whole picture, including what gaps there are in the evidence, whether the individual factors relied upon are in themselves properly established, what factors may point away from the suggested explanation and what other explanation might fit the circumstances….
So at the end of any such systematic analysis, the court has to stand back and ask itself the ultimate question whether it is satisfied that the suggested explanation is more likely than not to be true. The elimination of other possibilities as more implausible may well lead to that conclusion, but that will be a conclusion of fact: there is no rule of law that it must do so. I do not read any of the statements in any of the other authorities to which we were referred as intending to suggest otherwise.
35 The civil “balance of probability” test means no less and no more than that the court must be satisfied on rational and objective grounds that the case for believing that the suggested means of causation occurred is stronger than the case for not so believing. In the USA the usual formulation of this standard is a “preponderance of the evidence”. In the British Commonwealth the generally favoured term is a “balance of probability”. They mean the same. Sometimes the “balance of probability” standard is expressed mathematically as “50+ % probability”, but this can carry with it a danger of pseudo-mathematics, as the argument in this case demonstrated. When judging whether a case for believing that an event was caused in a particular way is stronger that the case for not so believing, the process is not scientific (although it may obviously include evaluation of scientific evidence) and to express the probability of some event having happened in percentage terms is illusory.
36 Mr Rigney submitted that balance of probability means a probability greater than 50%. If there is a closed list of possibilities, and if one possibility is more likely than the other, by definition that has a greater probability than 50%. If there is a closed list of more than two possibilities, the court should ascribe a probability factor to them individually in order to determine whether one had a probability figure greater than 50%.
37 I would reject that approach. It is not only over-formulaic but it is intrinsically unsound. The chances of something happening in the future may be expressed in terms of percentage. Epidemiological evidence may enable doctors to say that on average smokers increase their risk of lung cancer by X%. But you cannot properly say that there is a 25% chance that something has happened: Hotson v East Berkshire Area Health Authority  AC 750 . Either it has or it has not. In deciding a question of past fact the court will, of course, give the answer which it believes is more likely to be (more probably) the right answer than the wrong answer, but it arrives at its conclusion by considering on an overall assessment of the evidence (ie on a preponderance of the evidence) whether the case for believing that the suggested event happened is more compelling than the case for not reaching that belief (which is not necessarily the same as believing positively that it did not happen).