We study the stability of a time-aware version of the popular Massey method, previously introduced by
Franceschet, M., E. Bozzo, and P. Vidoni. 2017. “The Temporalized Massey’s Method.” Journal of Quantitative
Analysis in Sports 13: 37–48, for rating teams in sport competitions. To this end,we embed the tempora lMassey
method in the theory of time-varying averaging algorithms, which are dynamic systems mainly used in control
theory for multi-agent coordination. We also introduce a parametric family of Massey-type methods
and show that the original and time-aware Massey versions are, in some sense, particular instances of it.
Finally, we discuss the key features of this general family of rating procedures, focusing on inferential and predictive
issues and on sensitivity to upsets and modifications of the schedule.
