The variety of performance measures available for information retrieval sys
tems, search engines, and network filtering agents can be confusing to both
practitioners and scholars. Most discussions about these measures address
their theoretical foundations and the characteristics of a measure that mak
e it desirable for a particular application. In this work, we consider how
measures of performance at a point in a search may be formally compared. Cr
iteria are developed that allow one to determine the percent of time or con
ditions under which two different performance measures suggest that one doc
ument ordering is superior to another ordering, or when the two measures di
sagree about the relative value of document orderings, As an example, graph
s provide illustrations of the relationships between precision and F.