It seems that Jar-Jar has some very lucky breaks during the battle of Naboo. Is it possible that he has some innate hidden Force ability?
Out-of-universe answer: Jar-Jar's war antics were clearly done for comic effect to entertain the kiddies. I think the Accidental Aiming Skills trope applies.
In-universe: I don't see how we could come to any other conclusion; Jar-Jar must have innate Force-related abilities. Anakin's amazing luck in the fighter in Phantom Menace when he didn't know what he was doing seemed exactly like Jar-Jar's luck earlier in the film. In fact a Reddit user wrote a brilliant defense of the Jar-Jar Binks character as an obvious Force-adept and perhaps the true Phantom Menace of the first movie.
There's actually a whole discussion of Jar Jar possibly being a Sith lord, and some hints that Lucas had a much more important role for him in mind until the negative reactions got him to back off the character. I believe the good people at Cracked summed the issue up wonderfully in the following video:
Jar Jar's clumsiness made his movements unpredictable, confusing the simplistic targeting software used by the battle droids.