Whether you're debating alone or on a team, the way you treat your opponents will affect your credibility.

When asserting the superiority of your arguments, it can be tempting to denigrate the other team:

My opponents are clearly ignorant of  the facts. 
Sadly, my opponent is  ill-informed about the issues concerning this topic.
When we consider B in the light of A, we are forced to conclude that the arguments we've just heard are misguided.
Framing the in this way is simply dishonest.

Though trading barbs is common in political theater, insults—especially in academic —are poor sportsmanship.

You'll curry more favor with the judges if your arguments honor your opponents.

I can see that my opponents put a lot of thought into their position, and I respect that. With respect, here's an alternative viewpoint.
We've heard some very compelling arguments against X today, and I appreciate the challenge. Let's explore a line of reasoning that…
Thank you for stating your case so eloquently and for setting the standards so high for today's

And if you feel like your opponent just handed you an easy-to-refute assertion or an easy-to-disempower point, don't gloat or grin triumphantly. Your ego trip won't make the judges like you.

is not a sport like boxing or wrestling where your goal is to bring your opponent to the mat. Your professional demeanor will impress the judges. And if your opponent fails to follow your lead, their aggressive style will become their biggest disadvantage.