For those folks without legal training or knowledge, "more probable than not" means nothing beyond "at least 50.00000000000000001%" likelihood.
It's a very low bar of proof. To spend weeks and weeks and thousands of dollars in an investigation and come forward with "more probable than not," and nothing more specific than that, is pretty weak.
Well, it's also the same burden of proof as in almost every civil case in the entire country, and has been for hundreds of years. It's not quite as flimsy as you're suggesting. "More likely than not" means that the facts weigh in the direction of culpability.
In our legal system, damages aren't determined by how confident the finder of fact is that a plaintiff has proved his case. Once the case is proved -- whether it be 50.01% or 100.0% -- it's proved, period. Damages are what they are, and if the NFL follows that model, penalties should be the same whether there was a smoking gun or simply a likelihood of guilt.
You're right. When it comes to civil cases, 50.000001% is sufficient to meet the burden.
My point is that however much some people may want to make of this report, the conclusions are a far cry from definitive proof that the Patriots are cheaters and that Tom Brady was in on it.
Proving your case in a civil trial is a long way away from clearly proving that the other person did something wrong.
Also, damages can depend on what was actually proven at trial and to what degree. Meeting the burden often just means that you are entitled to damages. It's then up to the jury, in many cases, to determine how far above the minimum penalty they will choose to go in penalizing the defendant.