Large Scale Diverse Combinatorial Optimization: ESPN Fantasy Football Player Trades

TL;DR

This paper presents a novel combinatorial optimization system for fantasy football trades that uses diverse quantum and classical algorithms to improve trade quality and diversity, validated by expert evaluations over NFL seasons.

Contribution

The paper introduces a new multi-model ensemble system for personalized fantasy football trades, combining quantum, classical, and expert rules to enhance trade quality and diversity.

Findings

Trade quality improved from 76.9% to 97.3% with system deployment.

Achieved 100% trade uniqueness across models.

Validated system effectiveness through NFL season expert evaluations.

Abstract

Even skilled fantasy football managers can be disappointed by their mid-season rosters as some players inevitably fall short of draft day expectations. Team managers can quickly discover that their team has a low score ceiling even if they start their best active players. A novel and diverse combinatorial optimization system proposes high volume and unique player trades between complementary teams to balance trade fairness. Several algorithms create the valuation of each fantasy football player with an ensemble of computing models: Quantum Support Vector Classifier with Permutation Importance (QSVC-PI), Quantum Support Vector Classifier with Accumulated Local Effects (QSVC-ALE), Variational Quantum Circuit with Permutation Importance (VQC-PI), Hybrid Quantum Neural Network with Permutation Importance (HQNN-PI), eXtreme Gradient Boosting Classifier (XGB), and Subject Matter Expert (SME) rules. The valuation of each player is personalized based on league rules, roster, and selections. The cost of trading away a player is related to a team's roster, such as the depth at a position, slot count, and position importance. Teams are paired together for trading based on a cosine dissimilarity score so that teams can offset their strengths and weaknesses. A knapsack 0-1 algorithm computes outgoing players for each team. Postprocessors apply analytics and deep learning models to measure 6 different objective measures about each trade. Over the 2020 and 2021 National Football League (NFL) seasons, a group of 24 experts from IBM and ESPN evaluated trade quality through 10 Football Error Analysis Tool (FEAT) sessions. Our system started with 76.9% of high-quality trades and was deployed for the 2021 season with 97.3% of high-quality trades. To increase trade quantity, our quantum, classical, and rules-based computing have 100% trade uniqueness. We use Qiskit's quantum simulators throughout our work.