Again, your overall strategy should be to look for situations where the national bracket values a team much higher than the objective statistics. (I should stipulate that all of this advice assumes standard NCAA pool rules, where the points for a correct guess double each round, from one point in the first to 32 for the final game.) For example, a mere 6.8 percent of those who have entered ESPN's pool as of this writing predict Duke will win the whole tournament—the right-most column on this table—while Pomeroy's ratings give the Blue Devils a whopping 24.3 percent chance of winning it all and Sagarin rates them the second-best team. This makes Duke a fantastic bargain. While the dispassionate analysis gives them a 1-in-4 shot at the title, only one in about 15 people has chosen them to win—probably because they're so reviled. (Duke was also the best bargain in the field last year, but by a smaller margin—Jeff Sagarin gave them a 7.7 percent chance of winning, but only 3.8 percent of people chose them to go all the way. The crowd was wiser than Sagarin: Duke got blown out by Villanova in the Sweet 16.)
Kansas, by contrast, is not a good bargain. In ESPN's Tournament Challenge, 38.8 percent of the crowd has Kansas taking the title, while the team's Pomeroy odds stand at 23.3 percent, lower than Duke. While anyone who's watched basketball this year would agree that Kansas is a much better team than Duke—even Pomeroy says that "Duke is clearly somewhat overrated by my system"—the Blue Devils are still a tremendous deal. Which would you take, the team that more than one-third of your pool will also pick (Kansas) or one that nearly no one else will favor (Duke)? I would take the second—at least, if I wanted a chance to win the prize money instead of just placing respectably. (This assumes your pool resembles the country at large, of course; a pool among Duke undergraduates probably would not offer the same generous odds.)
Biostatistician Bradley Carlin, who co-authored a 2005 paper (PDF) on contrarian strategies in NCAA brackets, suggests a "champion-only" technique. While most people spend a lot of time puzzling over potential first-round upsets, the mathematical reality is that it's difficult to win a pool without securing those boffo championship game points. The payoff for risk-taking also increases in later rounds. Consider the first round game between 14-seed Montana and three-seed New Mexico. Less than 5 percent of ESPN users predict Montana will win this game, while Pomeroy gives them a 23.4 percent chance of making the second round. On paper, that fivefold differential looks like a great bargain. But consider that this upset will reward the lucky Montana fan with a mere one extra point. If New Mexico does win—still the most likely outcome—you're suddenly missing an important player in the bracket.
Whom should you pick as your champion? You want to look for teams with a respectable chance of winning that don't come in with high expectations. As the size of the pool balloons, so must your audacity. You may skate to victory with traditional choices in a group of 12 people, but in a pool of 100, you'll have to get fancy and prepare to lose miserably if the cards don't fall your way. Even a team like Wisconsin—a four seed with a 6.1 percent chance to win it all, according to the Pomeroy tables—starts to look attractive, given that less than 1 percent of the participants in ESPN's pool have them winning.
Of course, the trouble with a strategy like this is that its benefits materialize only in the long term. Another author of that 2005 paper on bracket strategies, Jarad Niemi, told me that he has won back three to four times his investment in entry fees over the years, but a great deal of that came from a good year in 2008. (Considering how good they are at calculating risk, it's no surprise that guys like Niemi and Carlin excel in pools that award bonus points for upsets. Carlin said he won one such pool three out of five years.) A strategy that wins you a lot of money a small amount of the time may work well in sports with long seasons, but it can be tough to keep the faith when you finish in the cellar for six straight Marches. But look at it this way: Did you ever win with your old strategy?