College and Research Libraries PAUL METZ AND ELIZABETH A. SCOTI A Proposed Staffing Formula for Virginia's Academic Libraries Formulas and standards play a needed role in the allocation of library resources, but it is difficult to devise formulas that accurately reflect the var- ious factors that shape a library's needs. This report summarizes the means by which a subcommittee of the Virginia Library Advisory Committee de- vised a proposed staffing formula for its academic libraries. The subcommit- tee charged with devising a new formula reviewed past efforts as a means of determining criteria any new formula should meet . Based on this review and on its own research, the committee devised a draft formula , which is discussed. THE USE of formulas and standards to allo- cate or to evaluate resources for academic libraries has received a good deal of atten- tion in recent years. This particular pendu- lum seems to describe a larger arc than most, with formulas. sometimes popular in both theory and practice and at other times mentioned rarely, and then only critically. Since there are trong arguments to be made both for and against the use of objec- tive bases for determining levels of acquisi- tions , staff, or funding , this ambivalence is understandable. On the one hand, formulas are seen as objective and apolitical, and as a means of ensuring continuity and rational planning. On the other hand , formulas are criticized for their procrustean tendency to ignore significant local differences and for the danger that they may actually be used more as ceilings, which set maximum re- source levels , than as floors, with unfortu- nate results, especially when enrollments decline. 1 • 2 These dangers are sometimes avoided by the use of standards explicitly intended to determine minimal resource levels rather than formulas that would de- Paul Metz is user services librarian , Virginia Polytechnic Institute and State University, Blacks- burg; Elizabeth A. Scott is assistant to the presi- dent , Dabney S. Lancaster Community College , Clifton Forge , Virginia . termine allocations with some precision . Although formulas and standards to deter- mine collection levels have received the most attention , there has been no lack of effort to devise objective means to deter- mine staffing levels, as well. While the Association of College and Research Librar- ies has declared that "As such factors (e.g., the number of library units, collection size, and circulation volume) vary widely from one institution to another, no single model or formula can be provided for developing an optimum staff size," it has outlined in a general sense qualitative criteria for what should be expected of a library staff. 3 Other agencies have not been so reluctant about · formulas, and it is interesting that all of the formulas devised to date have been devel- oped to serve states or large city systems of higher education, a level where the need for an apolitical and equitable approach is most keenly felt. New York City and the states of New York, Colorado, Washington, Oregon, Flor- ida, and California have all experimented with staffing formulas, though it is not clear from the literature that all have been appliedYH All of these formulas have used enrollments as a key input to the formulaic equation, but beyond this similarity they have differed in a number of significant ways. Some attempt to determine levels for I 127 128 I College & Research Libraries • March 1981 technical services, public services, and administration while others directly deter- mine the bottom line; some use different constants or different factor weights de- pending on the level of the institution whose staff is being determined, in effect establishing different formulas for commu- nity colleges, four-year colleges, and univer- sities; and some use faculty levels, collec- tion size, or acquisitions rates as input fac- tors while others disregard these parame- ters. Finally, some, but not all, of the for- mulas reflect the diminishing demands of larger enrollments or other parameters on library resource levels, establishing sliding scales for the relationships between input parameters and staff levels. The state of Virginia has used a series of formulas as library staffing guidelines for budget requests from institutions of higher education. It should be emphasized that the current guidelines are indeed guidelines and are not applied rigidly. Adjustments to the guideline staffing levels are made on both the state and the local levels. In mak- ing adjustments to the guideline levels, a general consideration has been given to the recognition that their strict application would yield too few positions for the larger institutions and for community colleges with more than one campJJS . 9 ' 10 Those in present use are based on formulas developed by the CUNY system and are supplemented by a prescription that the ratio of nonprofession- als to professionals should be 3:2. Nonstu- dent library positions for each campus are derived as follows: Community colleges: STAFF = 3 + Student FTE/500 + Faculty FTE/50 Four-year colleges : STAFF = 9 + Student FTE/400 · + Faculty FTE/40 Comprehensive universities: STAFF = 9 + Undergraduate FTE/400 + Graduate FTE/100 + Faculty FTE/35 The state's two ARL institutions do not use these formulas but instead determine their funding requests by comparisons with the size of the staffs in the ARL libraries that are their peers in terms of collection size. The result, then, is that there are four yardsticks that affect staff levels. In search of a better means for determin- ing staff needs, the Library Advisory Com- mittee of the State Council of Higher Education in Virginia appointed an ad hoc Subcommittee on Staffing to investigate alternative approaches. This subcommittee proceeded to review the literature, to out- line goals for a revised approach, and to make recommendations for a new formula. As a means of discovering how staff were actually performing the various library func- tions and how needs were being met in the differing colleges, the subcommittee sent a survey to the library directors of the thirty- nine state academic institutions in July 1978. The general conclusion of the survey was that few institutions fulfill the guide- lines and that the number of existing posi- tions is no greater than what 'is needed, and is apparently less in many cases. This con- clusion was based on both subjective data (the assertion by the great majority of direc- tors that their staffing levels were insuffi- cient to provide adequate service) and objective data, most notably the demonstra- tion that many library service points were unattended during long portions of library hours, that some libraries could offer no ref- erence service during certain hours, and that student labor was being enlisted for functions that should probably be assigned to full-time professional or paraprofessional staff.'' GOALS FOR FORMULA CONSTRUCTION Since the number of positions called for by the official guidelines had not been funded, the subcommittee thought that it would be unreasonable to conclude that the present formulas were overly generous until the staff levels they called for had been fully funded and the results of this practice de- termined. Because the problems unearthed by the survey seemed to have been ·more severe in the smaller institutions and be- cause those same institutions were more seriously understaffed with respect to the current guidelines, the subcommittee also determined that its formula should reflect, not the existing distribution of staff across institutional types, but the distribution called for by current guidelines. Together, these observations served as the bases for the first of six precepts that the subcommit- tee adopted for its work: 1. The new formula should call for essentially the same staff levels within each type of institution as is called for by current guidelines , both for the system as a whole and within each type of institution . The first precept grows out of considera- tions that may be peculiar to the Virginia situation. The remaining five of the subcom- mittee's precepts, however, grew out of an examination of what functions a staffing for- mula should serve and out of a review of how previous formulas have succeeded or failed in meeting their goals. Accordingly, a step-by-step discussion of the subcommit- tee's self-imposed guidelines may provide a convenient means of examining the entire question of what makes for a good staffing formula. Each of the remaining precepts is therefore listed and discussed below. 2. A staffing formula should be based on unam- biguous , readily available statistical measures . None of the advantages of a formula- convenience, objectivity, the hope that levels set by formula will be subject to less special pleading than levels set by other means-applies if the input parameters are ambiguous or cannot be readily obtained. Ideally, input parameters should be drawn from data already collected, such as HEGIS (Higher Education General Information Survey) statistics. 3. A staffing formula should be based on factors that measure demands on the library, and not on internal processes within the library's con- trol. In order to promote efficiency and to re- tain its credibility, a formula must not be based on any procedural elements within the control of the library administration . It would be possible, for example, to base a formula in part on the length of time de- voted to authority searching and cataloging per new title, or on the number of catalogs maintained , or on the number of service desks regularly staffed. But such a formula could establish a feedback loop from ques- tionable library procedures to staffing levels, perpetuating existing staff levels and rewarding inefficient practices. On the other hand, if a library's staff level is deter- mined by external demands, more efficient libraries will be rewarded for their econo- mies. Instead of having their "idle" staff taken away by an intrusive bureaucracy, Proposed Staffing Formula I 129 they will be free to assign any staff time gained through efficiencies to new service uses. 12 Some potential factors fall on the border line between "demand" and "process" fac- tors, but must be rejected in any event be- cause they do not satisfy the second pre- cept. Circulation counts, for example, are not calculated in the same way in every li- brary; some libraries count renewals as equivalent to first-time circulations, while others do not. Moreover, circulation volume is partly an outcome of library policies, such as the length of circulation periods or the extent of the library's reliance on reserve reading. 4. If possible, there should be a single formula, rather than a series of formulas, applied to different institutional types . This precept is based on the goals of con- ceptual clarity and ease of application for a formula and reflects a belief that the impor- tant sources of variation among types of in- stitutions are not necessarily more signif- icant than the sources of variation among institutions of the same type. The precept is also based on the observation that institu- tions can change categories. If a four-year college is upgraded to a comprehensive uni- versity and finds that its formula-driven staff level has dramatically changed, this is an in- dication that the formula imposes arbitrary and inappropriate staffing levels. This unfor- tunate tendency is exacerbated if multiple formulas are heavily based on the use of different additive constants (rather than different factor weights, or multipliers). The use of constants tends to homogenize staffing levels within institutional types, car- rying the risk that smaller institutions with- in a type will be overstaffed while larger in- stitutions are relatively deprived. 5. The formula should achieve a close statistical fit with existing staffing levels. This precept does not speak to the total number of positions that the formula should call for (precept 1), but rather to the de- sired statistical relationships between actual and formula-predicted staff levels. The pre- cept proceeds from the assumption that fac- tors that influence the effective use of li- brary staff-initiative, careful management, or even mismanagement-are probably ran- 130 I College & Research Libra.ries • March 1981 domly distributed across types of institu- tions and across individual institutions. If this is true, then a formula that closely cor- relates with existing staff levels will succeed in introducing rationality and in rewarding efficiency, and will do so without imposing a systematic redistribution of staff based on any arbitrary theory about which institu- tions require more staff. 6. The formula should be based on a balanced variety of parameters , and should not be too heavily dependent on enrollment levels or on other measures highly correlated with enroll- ments. Both a desire for an accurate formula and political pragmatism provide rationales for this precept. It is unrealistic to believe that any one input parameter can be relied on to yield valid staff levels for academic libraries whose environments vary in so many other important respects. Certainly the greatest demands within an academic library system do not always come from the departments with the highest enrollments. Politically, it is unwise to endorse a staff formula that is heavily based on a parameter whose future levels are unknown, with either a steady state or absolute decreases a realistic possibility. 13 PROPOSED VIRGINIA FORMULA Given the constraints outlined above, the subcommittee identified a set of parameters that reflect demands on the library and for which unambiguous statistics are readily available. The following factors were iden- tified: undergraduate FTE , graduate stu- dent FTE , faculty FTE, volumes held , volumes added (gross), and the number of distinct library sites that serve' either a physically discrete campus or a professional program . Undergraduates, graduates, and faculty are common input parameters for staffing formulas. They clearly represent external demands on the library. For most state sys- tems , including that of Virginia, funding for colleges and universities is based in large measure on enrollments, so that a staffing formula with this basis is apt to be generally in line with overall institutional funding. Each of the three factors measures a some- what different facet of external demand, not only because graduate students and faculty make heavier demands on the library but also because the proportion of graduate stu- dents and faculty on campus is a useful in- dex of the overall nature of the academic enterprise. That is , large graduate enroll- ments and high faculty-to-student ratios may be useful indexes of a strong research orientation that will place heavy demands on the library. The remaining factors are not so com- monly used in staffing formulas. Perhaps the custodial role, rather than that of direct service, is easily overlooked in library plan- ning because it has little appeal. In any event, the human resources required to maintain large collections and the buildings that house them, to shelf-read, periodically to move, and to provide reference access to large numbers of books are not to be dis- counted. Baumol and Marcus, in their well- known study, have shown that collection size bears the single strongest statistical re- lationship to staff levels , a finding that Metz and Halstead have independently repli- cated . 14-16 The relationship between additions to the collection and staff is obvious. The number of new titles added to the collection is a chief determinant of needs for technical ser- vices staff. Gross volumes added (rather than net, which would reflect discards) was chosen as the most appropriate, readily available statistic to measure this factor. The selection of sites as the final factor stemmed from the fact that one of the most common criticisms of the previous Virginia formulas had been their insensitivity to this parameter. 17 Apart from the fact that disper- sion of library sites increases overall user demand, keeping each site open and operat- ing calls for a certain minimum fixed ex- penditure of human resources. The use of physical sites as an input param- eter does raise problems of definition that require careful negotiation . Sites are only ambiguously a "demand" factor, as the establishment of a new site often represents a policy decision made by the library ad- ministration. Certainly any staffing formula should not encourage the undue prolifera- tion of branch libraries. The subcommittee sought to solve this dilemma by defining a site, for the purpose of the formula, as "any physically separate campus of the same in- stitution, or a physically separated location Proposed Staffing Formula I 131 TABLE 1 RATIO OF INPUT PARAMETERS TO STAFF LEVELS Undergrad. Grad. Faculty Volumes FTE FTE FTE Holdings Added Sites Universities 77:1 19.1:1 7.9:1 7863:1 447:1 0.021:1 Four-year colletes 160:1 8.8:1 11.3:1 8043:1 415:1 0.052:1 Community col eges 210:1 14.8:1 4400:1 274:1 0.152:1 Entire system 120:1 13.2:1 9.9:1 7203:1 406:1 0.053:1 Note: There are five universities, ten four-year colleges, and twenty-four community colleges in the Virginia system. of a professional school responsible for its discipline offering within the institution and for earning separate accreditation. " 18 In deriving weights to relate the input parameters to staff levels, the subcommittee made no effort to establish empirically the precise contribution that each makes to the use of staff time. Two approaches to this type of solution are possible, but each has serious flaws. Time study analyses can be and have been used to determine the rela- tionship of various factors to time expendi- ture, but this requires very careful and ex- pensive studies whose outcomes inevitably depend on key issues of interpretation. 19 Statistical analysis poses· an alternative methodology that, while useful, is ultimate- ly limited by the extreme multicollinearity among library measures, where correlations among collection size, enrollments, faculty size, and other parameters are often as high as 0. 90. 20 The subcommittee did in fact ex- periment with the use of ridge regression, a form of multiple regression that takes ex- plicit account of multicollinearity, and was able to derive a formula with highly satisfac- tory "goodness of fit" to existing staff levels. Several draft formulas developed in this manner satisfied all of the subcommittee's precepts, but this approach was ultimately rejected because the weights it yielded were wildly counterintuitive and would therefore be generally unpalatable and po- litically unacceptable. No formula could be found through this means that did not in- clude at least one negative coefficient, seemingly punishing a library for the size of its constituency or of its collection.* The methodology actually used was an in- *Kendon Stubbs, associate director of the Uni- versity of Virginia Library and a member of the subcommittee, was responsible for the analysis of the capabilities and limitations of ridge regres- sion. teractive trial-and-error process of finding the factor weights that would yield a for- mula most in line with the subcommittee's goals. First consideration went to satisfying precepts one and five, calling for a formula that would give each category of institution about the same total level of staff as the old formula while achieving a high statistical fit with existing staff levels for individual insti- tutions. The information in table 1 provides the basis for manipulating the weights to meet the various constraints. The table reflects the ratio of each input parameter to the number of library staff, within each category of institution and for the thirty-nine colleges and universities as a whole. Using these data as a basis for adjusting the weights (which in this formula take the form of denominators), the subcommittee arrived at the formula given below: Library staff = Undergraduate FTE/ 1,000 + Graduate FTE/100 + Faculty FTE/33 + Volumes Added/5, 000 + Hold- ings/22, 000 + (2) Sites For any given parameter, a heavy factor weighting (small denominator) will yield more positions for those institutions for which the ratio of the parameter to staffing is high, while making a smaller contribution to staff levels for those institutions for which the same ratio is low. To the extent that a formula assigns staff on the basis of under- graduate enrollments or faculty, then, the smaller institutions will benefit. The rela- tionship is reversed for the weighting of holdings and acquisitions, which benefits universities and four-year colleges at the relative expense of community colleges. The use of graduate enrollments as an input fac- tor benefits universities more than four-year colleges, and, of course, adds nothing to li- 132 I College & Research Libraries • March 1981 brary staff for community colleges . The use of sites counterbalances the differential effects of graduate enrollments on universi- ties and four-year colleges , as heavier weighting for sites will contribute relatively more staff to the four-year colleges than to the universities. Note that the very methodology used for deriving the weights makes it impossible to defend them on grounds other than that they supply a satisfactory mathematical solu- tion. That is , while it may be possible to argue that graduate students affect library needs ten times more than do undergradu- ates, such an argument would be strictly post hoc. The particular weights chosen will have to stand or fall on the extent to which the formula they yield is acceptable . . The formula does seem to meet the spe- cified criteria quite well. It is a single for- mula (precept 4) and it is based on demand factors (precept 3) for which statistical mea- sures are readily available (precept 2) . The formula is not wholly based on enrollments, but on a balanced set of inputs, which sat- isfies precept 6. In fact, if one divides the total count on any parameter by the formula denominator to see how many staff positions that parameter determines, one discovers an interesting symmetry between the three parameters describing the academic constit- uency of the library and the three that per- tain to its internal work load. Fifty-one per- cent of predicted staff is determined by the academic constituency: 11 percent by un- dergraduates , 12 percent by graduate stu- dents, and 28 percent by faculty . Forty-nine percent is determined by library measures : 8 percent by acquisitions, 31 percent by holdings , and 10 percent by sites. (The rela- tive weights of each factor appear to have a different degree of importance if compari- sons are confined to any one type of institu- tion; from the point of view of a community college making comparisons to its peers, the formula is heavily "driven" by student and faculty counts , while for the larger institu- tions volume counts and acquisitions appear to be more salient.) The formula calls for very nearly the same staff levels as were dictated by the former guidelines (precept 1), as table 2 shows. The statistical relationships between the formula and existing staff levels are also TABLE 2 STAFF LEVELS CALLED FOR BY OLD AND NEW GUIDELINES New Form er Formula Guidelines Percentage Universities 673 677 99 .4 Four-year colletes 263 267 98 .5 Community col eges 270 275 98 .2 Totals 1,206 1,219 98 .9 high (precept 5). Table 3 shows the correla- tions between the formula-driven staff levels and two measures of current staff, one taken as part of the subcommittee's 1978 survey and one based on a preliminary analysis of the latest HEGIS data. TABLE 3 CORRELATIO NS BETWEE N FOR MU LA AND C URRE NT LEVELS Universities Four-year colleges Community colleges Overall 1978 Survey 0.9996 0.9465 0.9801 0.9939 DISCUSSION Preliminarv HEGJS . 0.9986 0.9657 0.9858 0.9965 One reason that formulas have come in and out of fashion may be an excessive de- sire on the part of those who apply them to see a formula as an authoritative dictum that will make decisions in a nearly auto- matic way , combined with a reluctance to understand the problems a formula seeks to address and the logical problems a formula must solve . 2 1 Such a rigid attitude toward any formula will limit its transportability from one situation to another or its ability to be adapted over time to accommodate changing realities. There are at least three ways in which, if put into practice , the formula discussed here may require adjustment for particular circumstances. Recent practices in Virginia have led to staffing levels for the senior in- stitutions that more or less met the formula- driven levels, while the community colleges have been staffed below formula. The Vir- ginia subcommittee sought to reaffirm its support of the overall levels called for by the former approach by constraining its for- mula to predict the same number of posi- tions in each category as the previous guidelines had called for . A later decision ·that the trend in staff allocation had been a healthy one and the subcommittee's deci- sion incorrect would necessitate a revision of the formula (specifically, a greater weighting for collection parameters and less weight for enrollments). It may also be necessary to adjust the for- mula if it is applied to an institution larger than those found in Virginia. If applied to the library system of one of the nation' s largest universities, the formula might pre- dict an inappropriate number of positions, necessitating some sort of adjustment of weights, such as the introduction of sliding scales . Finally, it is critical to bear in mind that any formula cannot reflect all of the many Proposed Staffing Formula I 133 kinds of unique needs that individual in- stitutions may have. The Virginia subcom- mittee sought to address this issue when it noted that "there are certain library activi- ties the Subcommittee feels are appropriate to acknowledge as non-quantitative factors not reflected in the formula which play a significant role in establishing good staff levels. A particular example is the responsi- bility to maihtain a notable rare books and archives collection which carries with it a heavy demand for library staff. Accordingly , the formula should apply only to functional staffing areas. Requests for additional staff in support of auxiliary functions may well be legitimate and should be recognized on a case-by-case basis. "22 REFERENC ES 1. F . William Summers , "The Use of Formulae in ResoJJrce Allocation, " Library Trends 23 :631-42 (1975). 2. David R. Watkins , " Standards for Universitv Libraries, " Library Trends 21 :190-203 (1972). 3 . Association of College and Research Li - braries , " Standards for University Libraries ," College & Research Libraries News 40:101- 10 (1979). 4. Gilbert W. Fairholm , " Essentials of Library Manpower Budgeting," College & Research Libraries 31:332-40 (1970). · 5. An excellent review of several librarv staff- ing formulas , including those of Caiifornia, Florida, and Washington , is give n in Peter Spyers-Duran ' s " Prediction of Resource Needs : A Model Budget Formula for Upper Division Universities " (Ph . D . dissertation , Nova Univ. , 1975), ED 112 883. 6. H. William Axford , " An Approach to Per- formance Budgeting at the Florida Atlantic University Library ," College & Research Li- braries 32:87-104 (1971). 7. Subcommittee on Librar y Development, " Recommendations for the Support of Cali- fornia State College Libraries" (Second Re- port to the Chancellor, 1966). 8. Freeman Holmer, "A Revised Budgeting Sys- tem for the Oregon Department of Higher Education," NACUBO Professional File 8 , no .3 (Washington , D.C. : National Association of College and University Business Officers , 1976), ED 129 140. 9 . Edward Huber and others , Report of Staff- ing-Recommendations for Virginia Institu- tions of Higher Education (Richmond , Va.: Virginia State Council of Higher Education, 1976). 10. Elizabeth A. Scott and others, Report of the Subcommittee on Staffing of the Library Advisory Committee of the Virginia State Council of Higher Education (Richmond, Va. : Virginia State Council of Higher Education , 1980). 11. Ibid. 12. Joe K. Taylor, internal memorandum to the Virginia Subcommittee on Staffing, 1978. 13. Summers , "The Use of Formulae," p.639. 14 . William J . Baumol and Matityahu Marcus , Economics of Academic Libraries (Washing- ton, D .C .: American Council of Education, 1973). 15. Paul Douglas Metz, "The Academic Library and Its Director in Their Institutional En- vironments" (Ph. D. dissertation , Univ. of Michigan , 1977). 16. D. Kent Halstead, Statewide Planning in Higher Education (Washington, D .C .: Govt . Print. Off. , 1974) p.709. 17. Huber, Report of Staffing . 18. Scott , Report of the Subcommittee on Staff- ing , p.26 . 19 . See, for example , Fairholm , " Essentials of Library Manpower Budgeting." 20. Baumol and Marcus , Economics of Academic Libraries , p.85--86. 21. Watkins, "Standards for University Librar- ies, " notes that " according to Clapp, [the Clapp-Jordan formula] was published only as a basis for discussion," though its critics may have viewed it as a much more definitive statement (p . 198). 22. Scott, Report of the Subcommittee on Staff- ing, p .29 .