It's that time of year. First, keep this in mind: If Team A has a 70% chance of beating Team B in a single game, who do you bet on to win (assuming an equal payoff either way)? Team A, of course, you have a 70% chance of winning--great odds.
If Team B wins, does that mean you were "wrong," or that Team B is a better team? No. It means that it won one of the 3 games out of 10 it is likely to win. In baseball, a .300 batting average is "good." That player gets out 70% of the time. Does his getting a hit in the at-bat I happen to watch make him better than .300? No. Remarkably, sports commentators are ignorant of this fact. (Ironically, I know a baseball coach who tweets complaints that his local weatherman is "wrong" when the weatherman predicts a 30% chance of rain and it rained. ). That's why brackets "bust" -- a 30% chance is not 0%.
So, do we have any algorithms out there that give us probability? Sort of. We have several systems that rate teams based on their performance. A couple I like are Jeff Sagarin's, which mainly uses a team's points, and Ken Pomeroy's which uses teams' offensive and defensive efficiency (points per possession) to create a Pythagorean winning percentage. Simply use the ratings to determine how teams match up, and you have your pick-- the higher-rated team has a greater than 50% chance of winning that particular game. There are several other ratings systems out there, here you can see them ranked by accuracy.
You can use the ratings to see if there are any obvious "upsets," meaning a lower-seeded team is more probable to win the game. You can also deduce which games are "closer" than their seed makes it appear. Say, a 12 seed that is just barely worse than the 4 seed opponent. Maybe they have a 40% chance to win as opposed to a different bracket where the 12 and 4 are much further apart. (Sorry, you have to do your own homework here.) They are more likely to "upset" the opposing team, and make sense to choose if you want to write down something less than 50% certainty. But, given my example in the first paragraph, it doesn't make logical sense to bet on the less-certain option given an equal payoff. (This is why I like pools where teams are auctioned off. Try to find the "bargain" team with a relatively high probability of advancing that you can buy cheaply.)
The Vegas opening line is also a remarkably accurate predictor. Just following its advice, you have a 73% chance of being correct (just remember that 27% chance of being wrong isn't 0%). You can look up the Vegas oddsmakers' line for the first-round games. The selection committee seeds teams fairly "accurately," meaning it matches the assigned probabilities. One glaring "error" appears to be Florida this year, they should be a 1 seed based on the models.
Another predictor is the engine at Whatifsports.com. You have to trust that its game engine spits output similar to real college games, I've never seen a study done on it. But it's useful for illustrating probability:
My bracket has Louisville beating Florida in the championship. As soon as I tweet that, I'll get responses telling me that I'm "wrong," even though I've gone with the option with the highest probability outcome according to the algorithms I used-- and algorithms beat humans over time (read Kahneman). Perhaps "wrong" simply means there is a greater chance of someone else winning it-- that would be correct. If Florida has an 18% chance, the rest of the field combined has an 82% chance! But it's rational to bet on the team with the highest odds-- go with the 18% team instead of the 14% team-- irrational to do anything else.