Yes, "a balance of probability" means more likely true than not true. This is the same as the "preponderance of the evidence" standard used in civil actions in Common Law jurisdictions. However, just because the standard can be explained in quantitative terms does not mean that the evidence in a typical case actually can be quantified with that degree of precision. Also, a common misunderstanding is that because 51-49 can qualify as a preponderance, most or all cases decided under this standard have a very narrow margin. In fact, decisive "wins" are common, although as I noted, this can't really be measured.
The rest of your comment indicates a need to examine a methodological question. What happens when we have two competing explanatory paradigms, one of which has a large volume of supporting evidence, and the other has no supporting evidence at all? The unsupported paradigm may still have partisans, defenders, apologists. How do they advocate for it?
By attacking the first paradigm, that's how. Quibbling. Nit-picking. Looking for any inconsistencies, flaws, or unanswered questions. And a single-minded, aggressive hunt for flaws will almost inevitably find a few, since no human information system is 100 percent comprehensive or self-consistent. Relentless cross-examination of even an honest witness will eventually yield some mistakes or gaps in the testimony.
A classic example of this approach occurs in the context of creationism-evolution "debates." Because evolution is supported by a gigantic amount of evidence from myriad fields, but creationism is bereft of any scientific evidence (only religious pronouncements), creationists spend essentially all their time trying to poke holes in various aspects of evolutionary theory. This question hasn't been fully answered yet! That issue is confusing! This issue draws some disagreement from biologists! That fossil is allegedly missing! And on and on. Sometimes these endless, niggling objections are trotted out in a rapid-fire sequence called a "Gish Gallop," after infamous creationist Duane Gish. The point is to rant and recite enough to distract from the problem that
no evidence supports creationism.
All your comments about how this or that piece of testimony or evidence in Sinner's case seems "odd" or hard to accept overlook the elephant in the room:
there is no evidence at all to support the notion that Sinner was/is a regular, intentional PEDs user, i.e., a "doper." That should be the key takeaway from the ITIA's investigation and hearing process, not whether some bit of a complicated testimonial account seems a little unusual. This is not a 51-49 case because the other side has 0, not 49.
Finally, I think we have to dispense with the apparent premise that sports doping is so far underground and so well-concealed that we can never have any direct evidence of it, and thus are free to believe it's occurring even without evidence (convenient, right?). If we look at the Lance Armstrong case, the many U.S. baseball player cases, and other notorious examples of doping, it's clear that many different kinds of evidence can be available if intensive doping is really going on (remember that all of these are
absent in Sinner's case):
- Evidence of deliberate evasions of drug tests
- Evidence of being tipped off to the time and place of "random" drug tests
- Evidence of the use of substitute urine samples
- Evidence of the use of substitute blood samples
- Evidence of the regular use of masking agents
- Evidence of the regular purchase of PEDs by or on behalf of the player
- Evidence of the regular purchase of masking agents by or on behalf of the player
- Evidence of the regular purchase of ancillary equipment by or on behalf of the player
- Evidence of the regular administration of PEDs by or to the player (this can include "I saw it" eyewitness testimony)
- Evidence of the planning and coordination of a doping scheme by a coach, physician, or athletic trainer connected with the player
- Evidence of rapid, manifest physical changes in the player that do not occur in the absence of regular PEDs use.