Generally, if an idea is common knowledge, there's no need to support it with evidence, because everyone already accepts it as truth. But if an idea is not universally accepted (or even at all), it needs evidence or credible sources to give it substance, or your audience has no reason to believe you over the other guy.
What is really hampering new ideas is the tendency of people to accept ideas that lack evidence or credible support, preventing new or different ideas from gaining ground.
Proofs are their for science and math, For a reason.
Proofs are integral to debate and almost all subjects. Proof makes your arguement legitimate, no proof means your arguement can be easily refuted by one with proof.
Proofs come in many shapes and sizes ( Im giving own right now )
Practically based proofs,, such as historical data state: ok this happened during this time etc.
Logic based proofs, proof that is given through a logical approach such as giving them example, proving my point is right.
Mathematical proofs, don't even think im going to explain this.
So in almost all your debates, you are actually giving proofs, sometimes without you noticing it, even for common knowledge,
When I state a common fact, I tend to say "as everyone knows" or "as we all are aware of" so that my audience knows that this is common, irefutable facts. But I would then say, "as discovered by Einstein" or "pioneered by Gates" etc. To make sure that people know who did it, who proved it or who discovered it.
When you go to politcal or historical debates, you have to have proof for everything you say, as the judges are quite meticulous about facts.
Unlike what Schicksal said, common knowledge without evidence is not enough. For thousands of years, it was common knowledge around Europe that the earth was flat and the sun revolved around it. This "common knowledge" kept the truth from coming out to the masses. Even when evidence was found, to teach the theory was considered blasphemy. At the time, blasphemy was against the law so if convicted of it you could face punishments including death.
As far as needing proof, no, the people that develop science almost never have proof till they follow where the evidence leads.
Yes, using sources is helpful in debate judging here. But not all debaters use sources, and even fewer always, and you don't have to use sources if your opponent isn't. For example, I myself don't use sources by default, but I'm usually more than happy to provide some if my opponent offers any. But OP, what do you mean by "entirely new idea"?
I am me, and i must cite the source in debates or else some undiscerning voters will penalise me for not giving my source. I refute some very simple points using common logic and i must give my source. I propose an entirely new idea and i must also provide evidence. Very Rational.......