The common law judge is not concerned with establishing the truth of what did or did not happen on a given occasion in the past but merely with deciding, as between adversaries, whether or not the party upon whom the burden of proof lies has discharged it to the required degree of probability. Adversarial advocacy is not an enquiry into the truth. The adversarial system creates a polite contest: while a judge will seek out the truth as best he can, the advocates use their skill to test the evidence, and to control the way the evidence emerges, and then comment in closing on whether a case has been proved to the necessary standard of proof.
‘After hearing the evidence the judge must decide where the truth lies, decide any points of law, and give judgment… [The] judge is guided by any inherent probabilities, contemporaneous documentation or records, any circumstantial evidence tending to support one account or the other, and impressions made as to the character and motivations of the witnesses. Generally the judge is constrained by the pleadings, and has to make decisions on the pleaded issues. There are limited exceptions. A judge should not be deterred from deciding a case on the correct basis, where through incompetent presentation, the underlying legal cause of action has not been identified by a party’s representatives. The more usual course is to require the correct basis of the claim to be formulated through amended statements of case, which can be done even at the end of closing speeches. The claimant has the burden of proof on the balance of probabilities. It is for the claimant to prove the case, and the judge should be aware of too much speculative reconstruction. The law operates a binary system in which the only values are zero and one. There is no halfway house for the judge who concludes there is a real possibility that a fact in issue took place. If the party with the burden of proof fails to discharge that burden, the fact is treated as not having happened. If the burden of proof is discharged, the court treats the fact as having happened.’ (Blackstone’s Civil Practice 2017).
In Ball & Ors v Ball & Ors  HHJ Paul Matthews, sitting as a judge of the High Court made the following observations about how judges decide civil cases,
‘Lawyers will know this, but it may help the parties (none of whom is a lawyer) to understand this judgment if I explain a few points about the way in which judges decide civil cases. Where there is an issue in dispute between the parties in a civil case, such as this is, the law places the burden of proving the necessary facts upon one party or the other. As a general rule in English law, the person who asserts something has to prove it: Robins v National Trust Co Ltd  AC 515, 520. On the issues whether the testatrix was acting under pressure from her husband amounting to undue influence, or whether the will fails to make reasonable provision for the claimants, these matters are alleged by the claimants. So they bear the burden of proving them. The defendants do not have to prove a negative. As to the question of testamentary capacity of the testatrix, this is more complex. Ultimately the proponents of the will (the defendants) bear the burden of proving that she had capacity, but only once the issue of incapacity is properly raised. Here the claimants say that the testatrix was mistaken at the time she made her will, and thus had no capacity. So, on that basis, it would be for the defendants to show that she had capacity.
The significance of who bears the burden of proof in civil litigation is this. If the persons who bear the burden of proof of a particular matter (here the claimants) satisfy the court, after considering the material that has been placed before the court, that on the balance of probabilities that something happened, then, for the purposes of deciding the case, it did happen. But if those persons do not so satisfy the court, then (for these purposes) it did not happen. Our system of fact-finding is binary. It is either one thing or the other. There is no room for maybe. As I have said, the standard of proof in a civil case is the balance of probabilities, that is, that a thing is more likely to have happened than not. In mathematical terms, more than 50%. It is not scientific certainty at 100%. Nor is it even the criminal standard of “beyond reasonable doubt”, even though sometimes (as in this case) there are some criminal elements in what happened.
There is another point that I should make about the way the English civil courts reach their decisions. This is that it is for the parties to find and put before the court the material which they think will best help the court and prove their case. The English courts do not investigate of their own motion. It may often be that other relevant material exists elsewhere. But the court does not go and look for it. In civil litigation, the court usually makes its decision only on the basis of the material put before it by the parties.
Taken altogether, what all this means is that the decision of the court is not necessarily the objective truth of the matters in issue. Instead, it is what is most likely to have happened, based on the material which the parties have chosen to place before the court. My decision in this case must be seen in that light.’
Whether or not the burden of proof is discharged depends on the weight and value which the judge attaches to the various strands of evidence. This involves weighing up the credibility or reliability of the evidence, and ultimately comes down to deciding which version of the relevant matters is more likely to be correct.