You seem to be asking several questions more than just the single word request and with the word-usage tag, I am somewhat inclined to believe they are not implicative rhetoric.
If we have evidence or experience to support our position, then isn't it more than a belief?
It is not. First there isn't anything strictly "more" than a belief because it covers the entire range of acceptance from the probable truth to irrefutable confidence. Before reading the following, keep in mind that Noah Webster was a doubtless Christian from a bygone era:
1: A persuasion of the truth, or an assent of mind to the truth of a declaration, proposition or alleged fact, on the ground of evidence, distinct from personal knowledge; as the belief of the gospel; belief of a witness. Belief may also by founded on internal impressions, or arguments and reasons furnished by our own minds; as the belief of our senses; a train of reasoning may result in belief. Belief is opposed to knowledge and science.
4: In some cases, the word is used for persuasion or opinion, when the evidence is not so clear as to leave no doubt; but the shades of strength in opinion can hardly be defined, or exemplified. Hence the use of qualifying words; as a firm, full or strong belief.
In Webster's Revised Unabridged Dictionary 1913, we also have this example quote, which I slightly disagree with but illustrates that the range can be absolute:
" Belief admits of all degrees, from the slightest suspicion to the fullest assurance." ~ Reid. "
Second, as sense No. 1 mentions, the range of believability includes what is believed due to a foundation in evidence. The best beliefs usually are. "Do you believe me now?" is something somebody might smugly ask after their point has been proven, to which the response is often something to the effect of "Yes, I do. I believe you!" if not awed silence.
However, it should be noted that more specific words might be stronger or weaker on average, depending upon their particular meaning.
But the word "believe" seems like a somewhat flimsy way of persuading someone.
Any one word would have that problem unfortunately. I do not want to go too much into the philosophical aspects but it is always up to the recipient of a message to decide the degree of skepticism applied to it, since the only possibly undeniable thing is perhaps Descartes' creed: Cogito Ergo Sum (I think therefore I am). If believe has any problem, it is that people have used it too much to lend unwarranted credibility to their claims, which would also be a problem that is virtually inevitable for any word concocted to replace it. Try too hard to convince by the power of rhetoric alone and you might damage your credibility by leading your client to suspect your claims are pushy, fraudulent or unrealistic, with nothing to back them up.
This is Not in Conclusion
What about "concluded"?
It would be unfortunate if you used the word "concluded" if you are unwilling to use confident, since this word effectively means the same thing in this context, albeit in a roundabout way. "We have finished making our determination, there is nothing more to be done regarding this matter, except sit and wait to see it unfold."
pp. Shut; ended; finished; determined; inferred; comprehended; stopped, or bound.
If this does not lend itself to the unsavory implications I mentioned above, it minimally edges too close to a guarantee.
Since you have mentioned that you want to indicate that your beliefs are founded on external factors, in the hope that this will add to your credibility, there are at least a few few words words that can fit the bill.
Infer isn't so bad of a word from the definition of concluded but I still think it is stronger than what you are looking for now.
- To deduce; to draw or derive, as a fact or consequence. From the character of God, as creator and governor of the world, we infer the indispensable obligation of all his creatures to obey his commands. We infer one proposition or truth from another, when we perceive that if one is true, the other must be true also.
This basically makes you beholden to the standards of formal logic. If your predictions are wrong, it must because your premises were false/incomplete or your rationale was faulty. This is technically true regardless but I doubt you want to draw attention to the fact:
Convinced is better since it focuses a little more specifically on the evidence. It also sounds somewhat like "concluded" except with a more fitting meaning:
pp. Persuaded in mind; satisfied with evidence;
However, I think persuaded fits best since it can be based upon a number of external factors, like the experiences you have mentioned:
pp. Influenced or drawn to an opinion or determination by argument, advice or reasons suggested; convinced; induced.
Normally I'd explain in further detail but I think the definitions speak for themselves in this case.
All quoted definitions reference The American Dictionary of the English Language by Noah Webster in 1828.