The image above is an attempt at a recommended bracket using a utility function that minimizes your regret of being wrong. Fan distributions count almost as much as win probabilities with this utility function (which is not peer reviewed). So how much you regret an incorrect pick depends both on the probability of you being wrong (based in win probability) and on the number of other entries likely to get it correct (based on fan distributions). The resulting bracket is mostly robust to the size of your pool (beyond a dozen other entries) and to most common scoring methods.
One of the problems with the utility function used to generate the “which team to pick” widget, is it assumes all you care about is getting the champ right and not having too many other entries also get the champ right. It ignores the possibility of hedging popular picks (eg, Kentucky and Duke), and can recommend some quite improbable champions.
The approach depicted above reflects the mindset of a quantitative portfolio manager. The portfolio manager might choose to minimize his regret of not picking popular picks that turn out to win. He won’t always pick the team most likely to win, because he would really regret being wrong if so many other entrants pick the underdog and the underdog wins. If nobody in your pool picks Northern Iowa, then not picking Northern Iowa either really can’t hurt you.