Natural science tells a story about what the world is like. But what kind of story is this supposed to be? On a popular (realist) view, this story is meant to provide the best possible explanations of the aspects of the world with which we are all acquainted. A realist also thinks that the story should in some sense provide explanations that are probable in light of our evidence, and that these explanations ought to fit together into a coherent whole. These requirements turn out to be surprisingly hard to satisfy given the received view of how scientific theories are evaluated. However, I argue that if scientific theories are evaluated comparatively rather than absolutely for explanatory purposes -- optimifically rather than satisficingly -- then we can provide a fully realist view of the connections between explanation, probability, and coherence. It is one thing to say what science's story of the world ought ideally be like, it is another to say that the story as it is actually being told lives up to this ideal. Do we have good reasons to believe that the picture as it is currently being presented to us is true, at least for the most part? Yes, answer realists, as long as our theories are empirically successful. Anti-realists respond that success is a poor guide to truth, appealing to the rather depressing history of successful theories that turned out to be false. Although I count myself among realists, I argue that realists have done themselves a disservice by focusing too much on empirical success in arguing for the correctness of the current scientific world-view. Instead I argue that one of the major reasons why currently accepted theories should (typically) be taken as true concerns the fact that they enjoy a certain kind of privileged status within scientific communities.