March Madness Wins Cluster
A Monte Carlo + knapsack optimization pipeline that picks the optimal NCAA Tournament roster for "Expected Wins" bracket contests — separately optimizing men's and women's 100-point budgets to maximize simulated tournament wins.
This project builds an end-to-end pipeline for optimizing entries in NCAA Tournament "Expected Wins" contests, where each team costs a fixed number of points (scaled by seed) and the goal is to maximize total tournament wins under a shared budget. For every team, a composite score blends T-Rank (Torvik) efficiency ratings, NCAA NET rankings, and a seed-based "chalk" factor, with the blend weights backtested across six historical tournaments (2019, 2021–2025) to find the combination that would have scored best in real contests, landing on an 80/10/10 T-Rank/NET/chalk split for the men's field and a chalk-heavier 30/20/50 split for the women's, whose NET data is less reliable pre-tournament.
Win probabilities between any two teams come from a logistic model on composite-score differences, calibrated so a 1-seed beats a 16-seed about 98.7% of the time, then run through 50,000 Monte Carlo simulations of the full bracket to get each team's expected wins and win distribution. From there, the men's and women's rosters are each solved as independent 0/1 knapsack problems to find the team cluster that maximizes total expected wins for a 100-point budget: for 2026, a 14-team men's cluster (anchored by Gonzaga, Vanderbilt, and a run of 5- and 8-seeds) projecting 17.54 expected wins, and a 10-team women's cluster (led by three 3-seeds and three 5-seeds) projecting 17.25.
The analysis goes further with sensitivity testing across budget levels, alternative near-optimal clusters within 0.2 expected wins of the top pick, and a full risk profile featuring simulated win distributions, standard deviations, and the probability of rostering an eventual champion, all so that the optimizer isn't just chasing a single point estimate but showing the range of realistic outcomes.
