Formal metrics have a number of appealing properties. Foremost of these is that they include the possibility of developing an analytic framework for understanding different aspects of Internet behavior.
Formal metrics are also easier to define than empirical metrics.
A key problem with formal metrics, however, relates to exactly this easier form of definition. At first blush it might seem straight forward to define a formal metric, but often the underlying notions prove slippery. Then the transmission time for B bits depends on the bits being sent. It is easy to overlook that an analytic notion does not match a real-world notion, such as transmission time in the face of possible compression. If a formal metric fails in either of these ways, then not only is the metric not useful, but it may well mislead us because its failure is subtle.