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Our objective is to find the five best college sports coaches of past centuryfor three different sports. We decided to look at men's basketball, football,and baseball. We wanted to use an approach that could definitively determineteam skill from the games played, and then use a machine-learning algorithm tocalculate the correct coach skills for each team in a given year. We created anetworks-based model to calculate team skill from historical game data. Adigraph was created for each year in each sport. Nodes represented teams, andedges represented a game played between two teams. The arrowhead pointedtowards the losing team. We calculated the team skill of each graph using aright-hand eigenvector centrality measure. This way, teams that beat good teamswill be ranked higher than teams that beat mediocre teams. The eigenvectorcentrality rankings for most years were well correlated with tournamentperformance and poll-based rankings. We assumed that the relationship betweencoach skill $C_s$, player skill $P_s$, and team skill $T_s$ was $C_s \cdot P_s= T_s$. We then created a function to describe the probability that a givenscore difference would occur based on player skill and coach skill. Wemultiplied the probabilities of all edges in the network together to find theprobability that the correct network would occur with any given player skilland coach skill matrix. We was able to determine player skill as a function ofteam skill and coach skill, eliminating the need to optimize two unknownmatrices. The top five coaches in each year were noted, and the top coach ofall time was calculated by dividing the number of times that coach ranked inthe yearly top five by the years said coach had been active.

A Networks and Machine Learning Approach to Determine the Best College Coaches of the 20th-21st Centuries