Determinism and responsibility

If determinism is true, then given the past, you could not have done otherwise from what you did. If you committed a murder, it is because, given the actual past, you could have done nothing other than commit that murder, and the past stretches back before you were born. If you bravely save people from a burning building, then given the past, which you did not control, you could have done nothing else. Ultimately, if determinism is true, whether we are virtuous or not is a matter of happening to be on the end of a good or bad causal chain. If that's true, how can anything really be anyone's fault, or to anyone's credit, any more than winning or not winning the lottery is to anyone's credit or discredit?