  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.
