  Search engine results pages are usually abstracted as binary relevance
vectors and hence are categorical data, meaning that only a limited set of
operations is permitted, most notably tabulation of occurrence frequencies,
with determination of medians and averages not possible. To compare retrieval
systems it is thus usual to make use of a categorical-to-numeric effectiveness
mapping. A previous paper has argued that any desired categorical-to-numeric
mapping may be used, provided only that there is an argued connection between
each category of SERP and the score that is assigned to that category by the
mapping. Further, once that plausible connection has been established, then the
mapped values can be treated as real-valued observations on a ratio scale,
allowing the computation of averages. This article is written in support of
that point of view, and to respond to ongoing claims that SERP scores may only
be averaged if very restrictive conditions are imposed on the effectiveness
mapping.
