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The sample size was fairly small since I did it by hand. But the key point is, "when one exists."
But know of the problem you mentioned and it does happen. But when one exists means generally means one of two things. Either you are in a corner, or you are on an edge. In a perfect world, the first means you have a 75% chance of pointing away from all opponents, where as the other you have about a 50% chance (the actual percentages are much different since you are not perfectly on the edge, etc). The other cases were where such an arc did not exist.
I know the radar isn't perfect, which is why I am not claiming it as a solution. I did have a tick counter of sorts, but it was to help it find a better distribution. Which had about the same failure rate, which is why I omitted it. As for the last part, that is possible, and it could very likely happen. I will see if I can improve it any based on a revision of the tick idea.
