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Does anybody know which (non-learning) bot holds the highest ranking in the 1v1 and melee rumbles?

What is your definition of non-learning? Do you mean perceptual?

IMO as long as you have state, you are in fact “learning”.

Well, we can loosen the limit of perceptual to allow information of k recent turns, e.g. k-perceptual. Under this definition, linear targeting will be 1-perceptual, circular targeting being 2-perceptual, and average velocity targeting with window size k will be k-perceptual.

As long as k is large enough, we can still make effective learning methods. So there’s still not an absolute difference between learning and non-learning. Simple enough methods like averaging velocity is still “learning”.

This is pretty much what I had in mind, particularly "similar states give similar decisions". Another distinction I find helpful is the idea that past results should not influence decisions in the future but past states can. A gun that gathers statistics on hit/miss and adjusts its aim is learning but average velocity targeting is not.

If average velocity (with window size k) is non-learning, how about play it forward using only k recent scans? Both are not changing behavior based on results, only recent scans, plus, play it forward is merely a more precise version of “averageing”.

IMO both are learning using k scans, the only difference is the latter is more precise, and using data more effectively.

I definitely agree that they're both learning, at least in some sense. The main difference is that the accuracy of a linear targeting system would have diminishing returns as k is increased, whereas a PIF system would likely benefit from increased amounts of data.

It's certainly a difficult question to formalise. I suppose that plotting prediction accuracy vs. k would give some idea of how much learning is going on.

I think the best in the 'perceptual' / 'stateless' category is RetroGirl