So did you disobey the law on purpose, or were you unaware that your speed had crept up above the speed limit? I can't see any other alternatives.
The former is criminal - do you disobey other laws you don't agree with? The latter is inattentiveness - so much for the machine.
My accident was a single-vehicle accident. There were no casualties and no witnesses. In all measurable terms, it was my fault, since I managed to spin the car - at 20mph. However, the stretch of road (Woodhead Pass, A635, Derbyshire. Look it up, if you can be bothered) was later classified as one of the three worst in the UK less than a month later, due to poor construction methods leading to unexpectedly low temperatures on short stretches leading to sudden patches of "black ice" (which is, of course, invisible) throughout the winter months. I span my car at 8am on 3rd January - slap-bang in the middle of winter. Nevertheless, as I said, the accident was, in all measurable terms, my fault. I didn't see the invisible hazard, whilst driving at 1/3 the speed limit.
With regards to your "odds" game - do you seriously believe that you are a better driver than most (meaning 50.0% or more) other drivers? That's an astonishing claim and one no-one should make themselves - especially not those who are unaware of their speed, or just plain law-breakers. Personally I consider myself to still be learning how to drive - and will be right up until the point I die (hopefully not in a car).
Holding a licence doesn't mean you know it all - or even enough to make you "good". It just means that you've been judged competant to use the highways with everyone else - and remember that the overwhelming majority of those people you consider yourself to be better than, by the "odds game", have had to pass the same (although I'm aware there may be state-to-state variation over there) competancy test. Many have more experience than either of us -in terms of road time/miles, many have less. The odds are that you, and I, are merely "average" drivers. Don't be under any illusions as to your capabilities - that's a very quick way to a metal coffin with a hood badge.