This paper illustrates how statistical decision theory can be used to model aspects of the effectiveness of a course placement system. The illustration is based on data from students who enrolled in a first-year mathematics course at a midwestern university. To model the placement of students, the author first elicited students' and instructors' preferences for the different outcomes of the course. Completed responses were received from 19 instructors and 40 percent of the 270 students questioned. About 3/4 of the student respondents and 4/5 of the instructor respondents were able to supply coherent grade value functions; the median value functions for the instructors were modestly but systematically higher than those for the students. Comparisons were then made of the actual outcomes of students who received remedial instruction before enrolling in the course with their predicted outcomes had they not done so; an analogous comparison was made between expected value functions. Although the number of students with previous remedial instruction was too small to permit drawing firm conclusions, results illustrate how, given sufficient sample sizes, one could use decision theory to develop indicators of the effectiveness of remedial instruction. Appendixes include the questionnaires and discussion of constructing summary value functions for course placement outcomes. (Contains 36 references.) (Author/NAV)