Another example of vector values

Team A may regularly beat team B. Team B may regularly beat team C, And team C may regularly beat team A. This will make no sense if one tries to rank teams with a scalar value from “best” to “worst.” It does happen, however, due to the ways in which teams happen to “match up.” Suppose (american football) teams are described by four component quantities: passing ability, running ability, pass defense, and run defense. Perhaps team A has a very good passing defense and can run. Team B has a very good passing game and can defend the pass. Team C can run and can defend the run.