Mathematical Modeling
MCM Strategic Football Analytics
Outstanding Winner model linking squad decisions to relegation risk and revenue for Crystal Palace FC.
Result
Outstanding Winner
Distinction
1 of 6 COMAP Scholars
Field
93,977 participants
01
Overview
In the 2026 Mathematical Contest in Modeling, our team built a quantitative decision framework for Crystal Palace Football Club: how should a club balance player investment, injury risk, ticket pricing, and revenue when the downside is relegation from the Premier League?
The paper earned Outstanding Winner status — one of 30 teams from 93,977 participants across 28 countries — along with the MAA Award and Leonhard Euler Award. I was subsequently named one of 6 COMAP Scholars worldwide, and the paper is under consideration for publication in the UMAP Journal.
02
Technical approach
- 01
Match outcomes as Poisson processes
Goal scoring is modeled with Poisson processes parameterized by squad strength, converting roster decisions into win, draw, and loss probability distributions over a full season.
- 02
Relegation risk via logistic regression
Logistic regression maps simulated season point totals to relegation probability, calibrated on historical Premier League outcomes.
- 03
Constrained revenue maximization
Ticket pricing and player investment enter a constrained optimization that maximizes expected revenue subject to budget limits and an acceptable relegation risk ceiling.
- 04
Nonlinear financial risk
Relegation is not a marginal loss — broadcast revenue collapses. The objective explicitly prices this asymmetric, nonlinear downside rather than optimizing expected value alone.
03
Architecture
01
Historical Data
EPL results + finances
02
Poisson Match Model
Season simulation
03
Logistic Relegation Model
Points to risk mapping
04
Revenue Optimizer
Constrained maximization
05
Strategy Recommendations
Decisions under uncertainty
04
Challenges
96-hour constraint
The entire framework — data work, modeling, optimization, and a publication-quality paper — had to be built in four days, forcing ruthless prioritization of model complexity.
Coupled subsystems
Squad strength, match outcomes, league position, and revenue all feed back into each other. The models had to be composed carefully so uncertainty propagated honestly through the chain.
Asymmetric risk
A naive expected-revenue objective recommends dangerously aggressive strategies. Capturing the catastrophic cost of relegation required explicit nonlinear risk modeling.
05
Results
Outstanding Winner — one of 30 teams from 93,977 participants in 28 countries.
MAA Award and Leonhard Euler Award; selected as one of 6 COMAP Scholars worldwide.
Karl Menger Award from Duke Mathematics for competition performance.
Paper under consideration for publication in the UMAP Journal.
06
Media & links
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