Here's the data in case it's useful to anyone. The error bars show the upper and lower bound of the Wilson confidence interval at a 95% threshold, i.e. we're 95% sure the true value lies within the error bar (unless I misunderstand). Interestingly, every single error bar includes the 50% level, so this data would not disprove the hypothesis that every single fight is decided at random.
The datapoints with large error bars come from a very small number of fights, so they can be taken with a pinch of salt. I had to manually label each fight so it's possible I got some of the results or robot types wrong. I also know that I missed a couple out because it wasn't clear to me which one had won. In total I recorded 223 fight results.
This shows the win percentage for each weapon type I identified:
And this shows the proportion of fights that ended with different outcomes:
"Pitted by self" includes accidentally driving yourself into the pit and being flung into the pit by energy from your own weapon. "Pitted by spinner" always means you were flung into the pit by your opponent's spinner.
Just from watching videos of fights, I would have said that the spinners are a totally bad idea due to their propensity to throw themselves into the pit, but from the data it looks like the vertical spinners at least might perform better than average.
. Also whether the bot was 4WD or 2WD or a walker. In my opinion, the only weapon distinction that matters is "Spinner" or "Non-Spinner". Beyond that it all comes down to construction quality, drive, and driver; with Weapon being the least important of those 4 categories :p