Filling in Your Brackets:
Where to Begin?

Many people default to a natural order of filling out a bracket: pick the games in the Round of 64, then pick the games in the Round of 32, and so on, ending with the National Championship game. Others start by selecting the National Champion (perhaps their favorite team) and then filling in the remaining games from the beginning. But which approach is better? And what happens if we start by picking which teams reach a different round?

For the strategy of starting by picking the winners in one of the six main rounds, this trade-off between initial risk and decision reduction can be captured using a simple formula: subtract the number of decisions (picked teams) from the number of additional game outcomes fixed. This difference quantifies the net benefit, in terms of reduced decisions, of the corresponding strategy.

The following table depicts these calculations for each possible starting round, giving the number of games picked, and the total number of games that become fixed as a result of these picks.

Round Number of Teams Picked Total Number of Games that Become Fixed Difference
Round of 32 32 0 -32
Sweet Sixteen 16 16 0
Elite Eight 8 16 8
Final Four 4 12 8
National Finals 2 8 6
National Champion 1 5 4


In the Round of 64, there are 32 game winners to pick (the Round of 32 teams), with no other games fixed as a result of these picks.

In the Round of 32, there are 16 game winners to pick (the Sweet Sixteen teams), with each of these games fixing one Round of 64 game, resulting in 16 fixed games in total.

In the Sweet Sixteen, there are 8 game winners to pick (the Elite Eight teams), with each of these games fixing two games (one each in the Round of 32 and the Round of 64), resulting in 16 fixed games in total.

In the Elite Eight, there are 4 game winners to pick (the Final Four teams), with each of these games fixing three games (one each in the Sweet Sixteen, the Round of 32, the Round of 64), resulting in 12 fixed games in total.

In the Final Four, there are 2 game winners to pick (the National Final teams), with each of these games fixing four games (one each in the Elite Eight, the Sweet Sixteen, the Round of 32, the Round of 64), resulting in 8 fixed games in total.

In the National Championship Game, there is one game to pick (the National Champion team), with this game fixing five games (one each in the Final Four, the Elite Eight, the Sweet Sixteen, the Round of 32, the Round of 64), resulting in 5 fixed games in total.


The net decision reduction is greatest when starting by picking the teams that reach the Elite Eight or Final Four (that is, the winners in the Sweet Sixteen and the Elite Eight respectively), suggesting these strategies are best for balancing initial pick risk against the number of decisions. Computational experiments further support these strategies: As detailed in our forthcoming paper “Models for Generating NCAA Men's Basketball Tournament Bracket Pools,” to appear in the Journal of Quantitative Analysis in Sports in 2020 (Click here for pdf), bracket generators that start by picking the seeds that reach the Elite Eight or Final Four tend to outperform generators that start with the Round of 64 or the National Champion. Keep this in mind as you build your brackets.


 

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