Mimicking Directed Binary Networks for Exploring Systemic Sensitivity: Is NCAA FBS a Fragile Competition System? - Hsieh, Fushing; Fujii, Kevin (Frontiers in Applied Mathematics and Statistics, 2016)
Can a popular real-world competition system indeed be fragile? To address this question, we represent such a system by a directed binary network. Upon observed network data, typically in a form of win-and-loss matrix, our computational developments begin with collectively extracting network's information flows. And then we compute and discover network's macrostate. This computable macrostate is further shown to contain deterministic structures embedded with randomness mechanisms. Such coupled deterministic and stochastic components becomes the basis for generating the microstate ensemble. Specifically a network mimicking algorithm is proposed to generate a microstate ensemble by subject to the statistical mechanics principle: All generated microscopic states have to conform to its macrostate of the target system. We demonstrate that such a microstate ensemble is an effective platform for exploring systemic sensitivity. Throughout our computational developments, we employ the NCAA Football Bowl Subdivision (FBS) as an illustrating example system. Upon this system, its macrostate is discovered by having a nonlinear global ranking hierarchy as its deterministic component, while its constrained randomness component is embraced within the nearly completely recovered conference schedule . Based on the computed microstate ensemble, we are able to conclude that the NCAA FBS is overall a fragile competition system because it retains highly heterogeneous degrees of sensitivity with its ranking hierarchy.