Prove Team A > Team B (transitively)

College football is rife with heated debates about which team is truly the best. Fans often rely on subjective opinions, biased statistics, or plain supposition to back up their claims. QED (Quasi-Empirical Decisions) Sports was created to provide a clear, objective method for determining team superiority using the transitive property of victories.

The transitive property states that if Team A beats Team B, and Team B beats Team C, then Team A must be better than Team C. This process can be repeated ad infinitum with no issue. QEDSports finds the shortest chain of victories connecting any two teams, providing mathematical backing to claims of superiority.

Arguing against undefeated teams is no problem for QEDSports. We rely on a special technique called persistence to explain why your team will be able to break the streak.

Persistence is a tried-and-true method of weather forecasting. If it was sunny today, then it will certainly be sunny tomorrow. This logic can be seamlessly applied to college football.

As we all know, players and coaching staff tend to remain on the team that recruited them. Frequent transfers betweem institutions hamper academic progress, a high priority for every student-athlete. With all of their core pieces intact, the quality of a team remains the same year-over-year. This aligns with our understanding of perennial powerhouses and underperformers. A team that only won three games, for instance, is destined to be a bottom-dweller in their division for years to come. Suggesting that said team could turn it around and compete for a national championship in only two years is utter nonsense.

The logical conclusion of this is that if Team A defeated Team B last year, persistence says that the result will be the same this year. QEDSports makes full use of persistence when creating the path to victory. Should your team have no path within the confines of the current season, QEDSports will step back in time to give you the evidence you need.

In exceedingly rare cases, no transitive path of victories can be found between two teams, even after applying persistence. When this occurs, QEDSports leverages the power of generative AI to provide a convincing argument for why Team A is better than Team B. You may ask: "What criteria is used when picking between teams?" The answer is simple- which mascot would win in a fight. This metric is underutilized by the sports analytics community, and we are proud to champion its use here at QEDSports.

Example:

Game results and team information are sourced from the College Football Data API. The graph is precomputed from seasons 2020 through 2025, capturing tens of thousands of games across all divisions of college football.

QEDSports draws inspiration from My Team Is Better Than Your Team, which uses similar ranking principles. For those wishing to dive deeper or contribute to QEDSports, the source code is available on GitHub.