A grad school friend and I do it every year, but in a couple of dollars and put it in my pool (if you are interested in joining my pool, it is cheap - $5, message me). It never wins, however, it can give you some general trends on who to like/avoid. We have data going back the last 15 years for all the teams that are in the tournament a some stats (Sagarin rating, sos, rpi, conference Sagarin, conference rpi, offensive and defensive statistics as well) to create a profile of winners and losers for each round based on the past 13 years of data. In the analysis when two teams fit the "winners" profile, we have two different decision rules for the tie breaker (absolute value of winning score, difference of winner profile score - loser profile score). The absolute value tends to be more liberal, while the difference score tends to be more conservative.

General trends:
Hates Arizona, loves Michigan State and Gonzaga (as you will see below). The conservative bracket has very few upsets, but the ones it has are significant, interestingly they have 3 of the final four teams the same but different winners.

Difference score final four: Kansas, Michigan St, Gonzaga, and Wichita State. Wichita St. over Michigan State
Absolute Value final four: Kansas, Michigan St, Gonzaga, and Michigan. Michigan over Kansas

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Start a bracket pool. Compile a list of the public favorites to win. Bet against the heaviest public favorites when the line is small.

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O judgment! Thou art fled to brutish beasts,
And men have lost their reason.