Using the Kirkpatrick–Seidel Algorithm in NCAA Football Betting Predictions: A Computational Geometry Approach

Introduction

In the ever-evolving world of sports betting, data-driven strategies have become the cornerstone of profitability and edge-seeking. Especially in NCAA football—a domain marked by high team variance, frequent upsets, and complex inter-conference dynamics—leveraging advanced algorithms and artificial intelligence (AI) has proven increasingly vital. One of the less traditional yet incredibly potent tools that can be applied to this domain is the Kirkpatrick–Seidel algorithm, a computational geometry method originally designed for efficient convex hull construction.

This article explores the Kirkpatrick–Seidel algorithm, its mechanics, and how it can be applied in combination with machine learning models to refine betting predictions in NCAA Football. We’ll demonstrate how this geometric algorithm, typically used in spatial data analysis, can optimize feature selection, outlier detection, and multi-dimensional performance comparison within a betting model framework.

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Section 1: Overview of the Kirkpatrick–Seidel Algorithm

1.1 What Is the Kirkpatrick–Seidel Algorithm?

The Kirkpatrick–Seidel algorithm is a classic algorithm in computational geometry used to compute the convex hull of a set of 2D points in O(n log h) time, where n is the number of input points and h is the number of points on the hull. It’s known as the “Ultimate Convex Hull Algorithm” due to its elegant use of a "marriage-before-conquest" strategy—an inversion of the typical divide-and-conquer model.

In short, the algorithm efficiently identifies the boundary of the smallest convex polygon (hull) that contains all the points in a plane.

1.2 Why Is This Relevant to Sports Betting?

While seemingly distant from sports analytics, the geometric concept of a convex hull can be repurposed to identify optimal boundaries in multi-dimensional datasets—such as those containing features like team performance metrics, player statistics, weather data, betting lines, and more. Specifically:

• Outlier Detection: Teams or games that fall outside the convex hull may represent upsets or hidden opportunities.

• Performance Envelopes: Define the upper limits of performance combinations, useful in power ranking systems.

• Feature Filtering: Identify key variables that contribute to “frontier” performance for elite or poor-performing teams.

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Section 2: NCAA Football Data Landscape

2.1 Characteristics of NCAA Football Data

NCAA Football presents unique modeling challenges and opportunities:

• Over 130 FBS teams, with wide disparities in team strength.

• Uneven scheduling across conferences.

• High player turnover, especially at skill positions.

• Limited season length, increasing the weight of each data point.

• Sharp line movements due to limited public data on lesser-known teams.

2.2 Data Sources Commonly Used

• Historical box scores (offense, defense, special teams)

• Play-by-play data

• Weather and altitude information

• Recruiting and player ratings

• Betting lines (spread, moneyline, totals)

• Injury reports and coaching changes

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Section 3: Applying Kirkpatrick–Seidel in NCAA Football Prediction Models

3.1 Dimensional Reduction and Feature Filtering

One of the first applications of the Kirkpatrick–Seidel algorithm is in feature optimization.

• Each game or team is represented as a point in an n-dimensional space (e.g., [offensive yards, defensive stops, penalties, etc.]).

• The convex hull identifies the frontier performers—teams that dominate some combination of metrics.

• By analyzing which variables appear in the dimensions of the convex hull, we can select the most discriminative features.

This enables more efficient input to machine learning models, reducing noise and improving generalization.

3.2 Betting Edge Detection via Outlier Games

Games or teams that lie outside or near the extreme edges of the convex hull—either above or below—may signify mispriced games by the betting markets:

• Overlooked underdogs may have statistical profiles similar to favored teams but are excluded from the “dominant cluster” due to one or two underweighted variables.

• Overvalued favorites may sit inside the cluster with no clear edge metrics.

Using this analysis, a predictive betting model can flag these games as candidates for value betting.

3.3 Opponent Normalization Using Geometric Projections

In NCAA football, teams don’t play balanced schedules. Using convex hulls of opponent performance, we can normalize team metrics relative to the convex boundary of their opponents:

• Project each team’s stats into the performance space of their past opponents.

• This removes inflation effects from weak schedules.

• Helps train neural nets or XGBoost models with better-calibrated input data.

3.4 Dynamic Adjustment Over the Season

The Kirkpatrick–Seidel algorithm can also be run week-by-week, updating the convex hull as more data becomes available.

• Allows for temporal performance tracking, seeing how a team moves within or outside the hull across time.

• Highlights teams peaking late or declining due to injuries or fatigue.

These time-based shifts can trigger model alerts or change weightings in ensemble forecasts.

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Section 4: Integrating With AI & Machine Learning Models

4.1 Model Architecture

A typical AI-enhanced betting model that integrates Kirkpatrick–Seidel would have the following architecture:

1. Data Ingestion Layer:

   • Scrapes and cleans NCAA football data.

2. Geometric Preprocessor:

   • Applies Kirkpatrick–Seidel algorithm.

   • Tags data points with hull membership, edge proximity, or outlier status.

3. Feature Engineering Pipeline:

   • Integrates convex hull insights.

   • Projects team stats into opponent hulls.

4. Modeling Layer:

   • Ensemble of models (e.g., XGBoost, LSTM, Random Forests).

   • Includes convex-derived tags as categorical features.

5. Bet Recommendation Engine:

   • Runs probabilistic simulations.

   • Compares predicted edge vs implied probability (from odds).

   • Outputs unit recommendations.

4.2 Machine Learning Techniques

• Anomaly Detection Models (e.g., One-Class SVM) augmented with convex hull outputs.

• Graph Neural Networks (GNNs) with team-season nodes and convex boundary edges.

• Reinforcement Learning models that adjust betting strategy as new boundary shifts occur.

• SHAP (SHapley Additive exPlanations) analysis to see if hull membership or distance is a significant predictor.

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Section 5: Real-World Betting Strategy Example

Let’s walk through a simplified use case:

• Week 6 of NCAA Football

• Model identifies an underdog with an offensive/defensive efficiency combo that lies just outside the convex hull of top-20 teams.

• Public perception underrates them due to early-season blowout loss.

• Betting model flags this team as a strong ATS (against the spread) candidate.

• Bet is placed at +7, and the underdog wins outright.

Over a season, systematically applying this framework to identify hidden value bets using geometric and AI synergy can outperform standard models by identifying the non-linear, multi-variable clusters that define true team strength.

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Conclusion

While the Kirkpatrick–Seidel algorithm wasn’t created for sports analytics, its geometric precision makes it an underappreciated tool in modern AI-driven betting models, especially in complex environments like NCAA football. By capturing the true outer limits of performance in multi-dimensional stat space, this algorithm enables machine learning models to be smarter, cleaner, and more edge-focused.

As the sports betting industry becomes more data-savvy, incorporating such elegant computational geometry methods may become a hallmark of the most successful syndicates and algorithmic bettors.

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If you're building a proprietary model or considering syndicate-level strategies, don't just look for new data—look for new mathematics. The Kirkpatrick–Seidel algorithm is one such key that can unlock a hidden layer of predictive power.

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