Tournament Spectator Scoring

In late March in the United States, there is a college sporting event known as March Madness in which the top 64 (sort of) mens college basketball teams compete in a lose-once tournament to determine the annual champion.

I'm not a huge basketball fan---mostly because I have no sense of verifying whether a foul happened---but as with any sport, it can be tons of fun to watch. With March Madness, there is a different level of spectating that occurs. Instead of watching all the games, fans instead predict who will win each game by filling out a bracket (such as this one) before the tournament.

Fans then compete with others using their brackets. You gain or lose points by correctly or incorrectly predicting winners at each round, respectively. How does this scoring usually work?

The first time I did this with some friends in grad school, we scored by simply counting the number of incorrect guesses. The "contestant" with the least won.

Alternatively, you can assign a different number of points per incorrect guess at each round. For example, each correct guess in the first round could be worth 1 point, each in the second worth 2, then 4, then 8, 16, and the final game is worth 32 points if predicted correctly. This is apparently the preferred method (using the scientific method of web browsing).

The problem with this is that after the first few rounds, many of your teams have been eliminated. Sports are much more fun to follow if you always have a team to follow, independent of the game. If I didn't predict either of the teams to take part in a game, then I don't care who wins! Instead, whenever a team you picked loses, you cross them off everywhere in your bracket they appear (losing points at each step) and replace them with the team that beat them. This year, I picked Villanova to "go all the way" but they lost in the second round to St. Mary's College. Now, I am rooting for St. Mary's to win their next game.

This year, my competition is colleague Bill Higgins, who knows something about basketball. We agreed to score this way, with each "correction" costing 1 point. Villanova losing has already cost me 5 points, but it could cost me more if St. Mary's loses (especially if they lose soon).

One problem here is that the final game is likely not super exciting. It is only worth 1 point! Instead, each correction could cost different amounts depending on the round the correction was made. Then, using the 1, 2, 4, ... 32 sequence, I would have lost 10 points due to Villanova's loss instead of 5. In this case, everyone has a stake in the final game and it's worth 32 points. Here, however, because more than 32 points can be lost in any other round, it does not eclipse the weight of other rounds.

Perhaps that would be better to use...

Anyone familiar with other good scoring methods?