Insurance and Odds

"But driving slower and within the law reduces your odds of getting into an accident", they say. While this may be true, there's an inconsistency in the model. Let's take me as an example:

1. I've been driving for just about 18 years now.
2. I've been in 1 accident, which was entirely attributed to the guy who rear-ended me.
   2a. In other words, I've caused zero accidents, ever
3. I've been given 3 speeding tickets
   3a. The first was dismissed by my taking a defensive driving course
   3b. The second one stuck on my record for 3 years, costing me about $1000 in added insurance
   3c. The third was dismissed under Washington state's deferral program.

The argument goes that since I have been confirmed speeding, my odds of getting in a wreck are higher. I would argue that since I've had almost 18 years of fault-free driving, my odds of getting in a wreck are no higher than if I'd never been [caught] speeding.

The core issue is that the argument only holds if I phrase it as:
"If I drive within the law, my odds of getting into an accident are lower than if I drive faster". It can only be compared by keeping the driver the same person. In a giant population model, certain factors are correlated because, without keeping the driver constant, they correlate with more accidents. However, after a large enough sample size is collected on a particular driver, the best predictor of future accidents is their past record of being in accidents.

The now-false statistical argument goes that "every time out has an independent odds of getting into an accident, and riskier driving habits increase those odds". However, the past track record establishes a likely upper bound on said risks each time out, which would then be applicable to future trips as well. These independent odds are now the same as anyone else's who has been driving without faulted incident for a similar period of time, regardless of their driving style. And yet, if they are a woman, or older, or drive a Cadillac, their rates are lower than mine. And that's just bad math.