ladwig.indd
Using Cited Half-life to Adjust
Download Statistics
J. Parker Ladwig and Andrew J. Sommese
“Supplying accurate CPU [cost-per-serial use] information to faculty
and appropriate marketing of the alternate modes of delivery ... become
the key to achieving an optimal cost-efficient serials collection in an
academic library.”1
A model is presented for adjusting use statistics using a journal’s ISI
Journal Citation Reports cited half-life.The goal is to improve the method
used to evaluate the raw electronic download figure.The proposed model
will still undercount total use, but the undercounting will be proportional
across disciplines and less severe. By using this model, librarians can
avoid making cancellation decisions that may cost their libraries more
money in the long run.
n the spring of 2004, the
University Libraries of Notre
Dame began another round
of journal cancellations. One
overall goal was to be as cost-
efficient as possible. First, the subscrip-
tion cost of a journal was divided by the
number of full-text downloads for one
year to calculate a cost per download.
Then, this figure was compared to the
average commercial document delivery
(docdel) cost. Those journals that cost
more per download than the estimated
docdel cost became candidates for can-
cellation.
W h e n t h e m e t h o d o l o g y wa s e x -
plained to the Mathematics Depart-
ment’s library committee, questions
were raised not only about the cancel-
lations, but also about the methodology
employed. One obvious question was,
“How could only one year ’s worth of
download statistics be a fair measure
of use?” Upon reflection, the second
author of this article uncovered an even
more serious flaw: the downloads had
not been adjusted for the journals’ half-
lives. Because the electronic runs are
short (e.g., six years for many Springer
Verlag journals as of 2003), raw down-
load numbers would be reasonable for
short half-life journals but would sig-
nificantly undercount the downloads
for long half-life journals.
To demonstrate the significance of the
ISI Journal Citation Reports cited half-life,
this article will discuss the importance of
journal use statistics, explain cited half-
life and its importance, and then present
a model for adjusting download statistics
(including the model’s assumptions and
problems).
J. Parker Ladwig is the Mathematics Librarian in University Libraries at the University of Notre Dame;
e-mail: ladwig.1@nd.edu. Andrew J. Sommese is the Duncan Professor of Mathematics in the Department
of Mathematics at the University of Notre Dame: e-mail: sommese@nd.edu. The authors would like to
express their thanks to the referees of this article for their helpful suggestions.
527
mailto:sommese@nd.edu
mailto:ladwig.1@nd.edu
528 College & Research Libraries November 2005
Importance of Use Statistics
A main reason for the library to collect
use statistics is so that it can maximize
the return on its investment (ROI). For
example, when someone buys a car, he or
she expects to maximize his or her invest-
ment. If the $20,000 car is expected to last
ten years, this is equivalent to expecting
to get at least $2,000 worth of use from it
each year (ignoring the effects of infla-
tion). In the same way, if a library pays
$500 for a subscription to one volume of a
journal (assuming that only one volume is
published for the year), the library expects
that it will get at least $500 worth of use
over the volume’s lifetime.
Journal use statistics are collected in
order to perform this sort of calculation.
Because it is difficult to separate the use
of one volume of a journal over its lifetime
(assuming one volume is published per
year), a library examines the use of the
entire run, calculates the cost per use
(CPU), and asks if the CPU is greater
than the expected ROI. One measure
of expected ROI is the cost of alternate
modes of access, namely, interlibrary
loan (ILL) and docdel. Because docdel
is clearly more expensive than ILL, only
the cost of docdel is compared to the
journal’s CPU. If the CPU (i.e., the cost of
using the entire run of the journal over a
year) is more than the cost of one article
via docdel, there is a strong argument for
canceling the subscription and investing
any net savings in docdel or ILL.
This sort of analysis does not work in
making decisions to subscribe to a journal.
Even if more is spent on docdel per year
for a particular journal than the annual
subscription, there is not sufficient infor-
mation to make a subscription decision
(i.e., the publication years of the requested
articles are generally unknown). Even if
most of the articles are from the last few
years and their docdel cost is significantly
higher than a subscription, the cost for the
first year or two will include both the sub-
scription cost and the cost for docdel (or
ILL) for articles from the years the library
does not own. Thus, the model presented
in this paper is useful for cancellation de-
cisions but would need to be modified for
decisions about new subscriptions.
Definition of Cited Half-life
ISI defines and explains cited half-life as
follows:
The cited half-life is the number of
publication years from the current
year which account for 50% of cur-
rent citations received. This figure
helps you evaluate the age of the
majority of cited articles published
in a journal. Each journal’s cited
half-life is shown in the Journal
Rankings Window. Only those jour-
nals cited 100 or more times have a
cited half-life.
The chronological distribution of the
cumulative percent of citations re-
ceived per publication year is shown
in the Cited Half-Life Calculation
dialog box.
A higher or lower cited half-life does
not imply any particular value for
a journal. For instance, a primary
research journal might have a longer
cited half-life than a journal that
provides rapid communication of
current information. Cited Half-
Life figures may be useful to assist
in collection management and ar-
chiving decisions. Dramatic changes
in Cited Half-Lifes [sic] over time
may indicate a change in a journal’s
format. Studying the half-life data of
the journals in a comparative study
may indicate differences in format
and publication history.2
To illustrate cited half-life, consider the
ISI citation figures for Nature Cell Biology,
Communications in Partial Differential Equa-
tions, and Mathematische Annalen listed
in table 1. Data from 2003 are the most
recent available.
In 2003, Nature Cell Biology had an ISI
cited half-life of 2.7 years. Specifically, of
Using Cited Half-life to Adjust Download Statistics 529
TABLE 1
Percent of Citations to Each Journal
“Breakdown of the citations to the journal by the cumulative percent of 2003
cites to articles published in the following years” (JCR)
2003 2002 2001 2000 1999 1998 1997 1996 1995 1994
1993-
all
Nat. Cell. Biol. 5.1 28.8 57.6 84.4 99.9 99.9 99.9 99.9 99.9 99.9 100.0
Comm. PDE 0.5 3.6 10.7 18.0 24.3 29.5 35.9 42.2 47.5 53.1 100.0
Math. Ann. 0.5 2.5 6.4 9.3 11.8 15.1 17.5 19.6 21.7 24.2 100.0
the total number of citations referring to
Nat. Cell. Biol. from all the journals tracked
by ISI, 5.08 percent were to articles pub-
lished in 2003; 28.84 percent to articles
published in 2002 or 2003; 57.62 percent
to articles published in 2001, 2002, or 2003;
and 84.39 percent to articles published in
2000, 2001, 2002, or 2003. Thus, with just
the four most recent years of Nat. Cell. Biol.
readily available, a researcher would be
able retrieve more than 80 percent of the
current citations to it.
Communications in Partial Differential
Equations had a cited half-life of 9.5 years.
Of the total number of citations referring
to Comm. PDE, 0.52 percent were to ar-
ticles published in 2003; 3.60 percent to
articles published in 2002 or 2003; 10.72
percent to articles published in 2001, 2002,
or 2003; and 17.99 percent to articles pub-
lished in 2000, 2001, 2002, or 2003. Thus,
with just the four most recent years of
Comm. PDE available, a researcher would
be able to retrieve less than 20 percent of
the citations to it.
For Mathematische Annalen, a leading
pure mathematics journal, the situation
is even more dramatic. The cited half-life
is listed as > 10 (if the ISI cited half-life is
calculated as described below, it would
be approximately 23 years). Of the total
number of citations referring to Math.
Ann., 0.51 percent were to articles pub-
lished in 2003; 2.53 percent to articles
published in 2002 or 2003; 6.39 percent to
articles published in 2001, 2002, or 2003;
and 9.31 percent to articles published in
2000, 2001, 2002, or 2003. Thus, with just
FIGURE 1
ISI Half-lives for Three Journals
0%
25%
50%
75%
100%
0 1 2 3 4 5 6 7 8 9
Number of years before 2003 that cited
Nat. Cell. Bi
Comm. PDE
Math. Ann.
ISI half-
life 2.7 yrs ISI half-
life 9.2 yrs
ISI half-
life >10 yrs
C
u
m
u
la
ti
ve
p
er
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n
ta
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20
03
ci
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s
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530 College & Research Libraries November 2005
FIGURE 2
Least-squares Estimate for Nature Cell Biology
0%
25%
50%
75%
100%
0 1 2 3 4 5 6 7 8 9
Number of years before 2003 that cited articles were published
ISI data
Least-squares
est.
C
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m
u
la
ti
ve
p
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ce
n
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f
20
03
ci
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s
fr
om
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er
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s
the four most recent years of Math. Ann.
available, a researcher would be able to
retrieve less than 10 percent of the cita-
tions to it.
Please note, however, one oddity in
ISI’s method of determining half-life.
ISI considers the publication year (e.g.,
2003) as “year one” of half-life rather than
“year zero.” Thus, when the half-life is 3.0
years, ISI does not mean that half of the
articles were cited a er 2000 (= 2003 - 3)
but, rather, a er 2001 (2003 was the first
year, 2002 the second, 2001 the third). For
our calculations, the beginning of the publica-
tion year must start at zero; therefore, the ISI
half-life is simply adjusted by subtracting one
year. (See figure 1.)
Cited half-life as an Exponential Decay
Curve
As the term half-life suggests, the fraction
of it to decay away.... A plot of the re-
maining nuclei as a function of time
shows a steady decrease as the curve
tends to, but never actually reaches,
zero. The kind of behavior is called
exponential decay.... The fraction of
the original material remaining a er
n generations is (1/2)n, instead of 2n
for exponential growth.3
The fractional amount decaying each
year does not change as the source disap-
pears. Say, for example, that the half-life
of a chunk of radium is 1,620 years. A er
1,620 years, one half of the chunk is le .
A er 3,240 years, the original chunk does
not have 0 percent radium le but, rather,
100% • 1/2 • 1/2 = 100% • 1/4 = 25%. A er
T years the fraction of the total atoms of
radium le is
T
1
of citations from a given year satisfies to a
first approximation a curve for exponen-
tial decay. One can illustrate this by plot-
1620
2
.
ting the ISI data against a least-squares
fi ed exponential decay curve (discussed
below). (See figure 2 for an example.)
Many physical models serve as analo-
gies. For example, in the field of physics,
the half-life of a radioactive sub-
stance is the time required for half
The empirical data provided by ISI
may be used to find the exponential
decay curve with the best least-squares
fit to the data. As illustrated in figures 2,
3, and 4 (with the half-life corrected as
indicated above), the least-squares fi ed
decay curves fit the data surprisingly well,
especially for long half-life journals.
Using Cited Half-life to Adjust Download Statistics 531
FIGURE 3
Least-squares Estimate for Communications in Partial Differential Equations
0%
25%
50%
75%
100%
0 1 2 3 4 5 6 7 8 9
Number of years before 2003 that cited articles were published
ISI data
Least-squares
est.
C
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la
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p
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n
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f
20
03
ci
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Importance of Cited Half-life
Among its many advantages, the half-life
is particularly important for providing
more accurate use data for all types of
journals. For example, assume that only
the print version of a journal is available,
that the library has a complete run, and
that the library is gathering reasonably
accurate annual use statistics. If two of the
example journals were used in print one
hundred times over the course of a year,
it would be expected that fi y of those
uses for Nat. Cell. Biol. were to articles
published in the past 1.7 years (= 2.7 - 1),
and fi y of those uses for Comm. PDE
were to articles published in the past 8.5
(= 9.5 - 1) years.
Imagine now a second scenario where
the electronic version is available for the
past seven years, and prior to that, only
the print was available (back to volume
one, issue one). Further, assume that the
year ’s use data include only electronic
downloads. For Nat. Cell. Biol., because
its corrected half-life is 1.7 years and the
electronic version is available for seven
FIGURE 4
Least-squares Estimate for Mathematische Annalen
0%
25%
50%
75%
100%
0 1 2 3 4 5 6 7 8 9
Number of years before 2003 that cited articles were published
ISI data
Least-squares
est.
C
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u
la
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p
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20
03
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532 College & Research Libraries November 2005
years, virtually 100 percent of the total
use (print and electronic) is reflected in
the download statistics (assuming that
one electronic download is equal to one
print use). For Comm. PDE, because its
corrected half-life is 8.5 years, only 36
percent of the total use is reflected in the
downloads; and for Math. Ann., because
of its very long half-life, only 18 percent
is reflected in the downloads.
Not only is the total use undercounted
in the second scenario (only electronic
downloads were captured), but the
undercounting is not comparable. For
one journal, the electronic use captures
nearly 100 percent of the total use and for
another, less than 20 percent.
The striking difference in these figures
also points to a difference across fields that,
if not adjusted for, could lead to cancella-
full-count at some date in the future. To
understand this, recall how this adjusted
figure will be used. It will be divided into
the yearly subscription cost to obtain the
CPU. Because costs are involved in cancel-
ing a subscription and then resubscribing
at a later date, the model is calculating the
electronic downloads per year that one
would expect in the future assuming the
ER increases one more year each year.
To derive AF, the overall adjustment
factor to be applied to DL, convert DL to
FC as follows:
FC = DL • AF
Le ing HL denote the adjusted ISI cited
half-life of the journal (i.e., = ISI HL - 1);
1
AF
=
ER
tions ultimately costing the library more
than was initially saved. For example, of
the 327 mathematics and applied math-
ematics journals listed in ISI, 39 percent
have an ISI cited half-life of at least ten
years, 70 percent have an ISI cited half-life
of at least six years, and 11 percent have no
half-life given (e.g., new journals). Com-
pare this with biochemistry and molecular
biology. Of the 261 journals listed in ISI,
1
−
The Mathematics
The mathematics is straightforward. As
noted in the radium example above, the
fraction of the total atoms of radium re-
maining a er T years is:
HL
2
. (equation 1)
1
7 percent have an ISI cited half-life of at
T
least ten years, only 38 percent have an ISI
cited half-life of at least six years, and only 1
1620
1 percent have no half-life given. 2
.
Thus, to compare fairly the total use
of one journal with another across dis- Thus, the total percentage spent a er
ciplines, electronic download statistics T years is:
should be adjusted by incorporating cited
T
half-lives.
Model for Adjusting the Download
Statistics
Let DL denote the number of electronic
downloads in a given year. This is the “use
statistics” that publishers provide.
Let ER denote the electronic run (i.e.,
the number of years of the journal from
1
−
By modeling citations to a given vol-
ume of a journal as atoms decaying from
a chunk of radium for a single volume of
a journal, the fraction of total of expected
citations unaccounted for j years a er
publication is found to be:
1620
• 100%
2
1
.
T years in the past to the present with j
1
electronic, but not paper available).
HL
Let FC denote the full-count of use in
a given year. The goal is the steady-state 2
.
Using Cited Half-life to Adjust Download Statistics 533
Thus, for a single volume of a journal, and T equal to ER. Thus, by the above,
the total citations accounted for in the jth FC = k • C. Notice that this FC is the future
year a er publication is: steady-state count.
From this, we conclude that 1
HL
−j j
1
1
−
where C is the total number of citations
HL
C
TC DL
=2
2
FC = k •C = k • ER
ER
1
1 −
HL HL ,
1
−
1
2 2
from a given volume of a journal. For sim- .
plicity, one volume is assumed to equal a Thus,
1
year’s worth of a journal’s articles. 1
AF
= .
Thus, assuming the same number of to- ER
1
tal citations for each volume of the journal HL
1
volumes up to T years ago is the sum of the Note that if ER was equal to the full
above quantities for j from 1 to T, that is: run of the journal, this would still give a
is the same number C, the total number of 2
−
citations TC in the current year from all
small increase to DL.T
1
HL
1 −
TC
=
C
Model Assumptions2
. The model is based on a number of as-
Note that as T increases TC approaches sumptions summarized in table 2. For
C. Thus the citations in a given year from each assumption, difficulties are first
the most recent T volumes of the journal presented, then a justification.
account for a fraction equal to:
1. Citations Decay Exponentially T
1
HL Assumption: The fraction of this year’s
citations of the journal from volume one
until T years ago will be:
1 −
2
of the number of total citations of the
Tjournal per year that will be approached
1
HL
1 −
in the future.
Assume that DL is proportional to
TC (i.e., DL = k • TC for some constant k
2
.
TABLE 2
The Model’s Assumptions
Assumption Difficulty
1. Citations decay exponentially. 1. May be linear, but doesn’t fit data
2. Half-life is continuous. 2. ISI assumes discrete, but doesn’t fit
publishing practices
3. Half-life is relevant for journals. 3. Not true for all articles, but more true for
journals
4. Half-life is similar across all volumes. 4. Probably does change over time, but
difficult to correct
5. Local half-life and ISI half-life are
proportional.
5. Proportionality fits data, but need more
research
6. Citation and use are proportional. 6. Proportionality fits data, but need more
research
534 College & Research Libraries November 2005
Difficulties: First, half-life itself may
not be the best way to describe journal
obsolescence. This is discussed by Endre
Száva-Kováts, whose article, “Unfounded
A ribution of the ‘Half-Life’ Index-Num-
ber of Literature Obsolescence to Burton
and Kebler,” is required reading for
anyone fond of half-life data. “[I]n their
1960 article Burton and Kebler first made
critical and later ambiguous statements,
and finally a ribute only ‘some validity’
to the idea of literature half-life.”4
Second, in 1961, R. E. Burton and B. A.
Green Jr. suggested that statistical “me-
dian-age” be used instead of half-life, im-
plying a linear rather than an exponential
relationship.5 Despite the term median-age,
Burton and Green employ an exponential
decay curve to graph the citation pa ern.
Further, the use of a linear median-age
rather than an exponential half-life does
not fit the data presented by ISI. (See
figures 2, 3, and 4.) Even if median-age
were used instead of half-life, however,
it would still adjust the download figures
in such a way as to give a be er estimate
of use than a simple cost per download
calculation.
Third, the model is not needed for
short half-life journals because nearly all
the use is likely to occur in the run of elec-
tronic access available. Thus, the model is
intentionally designed to be most helpful
for medium to long half-life journals.
Justification: Despite these difficulties,
the model’s assumption of exponential
decay is a good first approximation as
illustrated by the remarkably good fit of
the model data to the ISI data in figures
2, 3, and 4.
2. Half-life Is Continuous
Assumption: The exponential decay
model is a continuous time model; treat-
ing time as discrete leads to error.
Difficulty: One particularly worrisome
area is implicit in the ISI measurement of
half-life. The ISI half-life figure assumes
that a year ’s issues of a given journal
may be treated as if they appeared at the
beginning of the year, when, in fact, they
are spread out over the year. ISI’s assump-
tion does not cause harm for long half-life
journals, but it does for those with a short
half-life.
Justification: Because there is li le ef-
fect on long half-life journals and, in fact,
more accuracy for short half-life journals,
the model employs a more straightfor-
ward calculation based on continuity.
3. Half-life Applies to Journals
Assumption: The exponential decay
model applies for journals, but not for
articles.
Difficulties: Helmut M. Artus argued
forcefully that “the generally accepted
assumption of the steady obsolescence
of scientific literature is refuted,” and one
would agree that half-life is undoubtedly
not true in a useful way for all articles.6
As an example of this, consider Leonard
Roth’s article, “On the Projective Clas-
sification of Surfaces.”7
Algebraic geometry was at the center of
mathematics at the end of the nineteenth
century. For a variety of reasons, objects
of such complication were being studied
that controversies arose over what had
been proved and not proved. The subject
slumbered until the middle of the twenti-
eth century, when general tools (e.g., sheaf
cohomology and algebra) had advanced to
the point that many of the difficult com-
plications could be handled by the new
machinery. Many of the invariants of the
classical period that had not been rigorous-
ly defined had natural interpretations as
invariants of the new machinery. This led
to a renaissance of the subject in the middle
of the twentieth century. Sommese (one of
the authors of this paper) discovered the
important article by Roth and quoted it
prominently in his article, “Hyperplane
Sections of Projective Surfaces I—The Ad-
junction Mapping.”8 Performing a citation
search on Roth’s article shows that the first
citation in ISI is by Sommese. Therea er,
a sequence of twenty citations (excluding
Sommese’s) continues through 2004.
Justification: Some articles continue to
be cited despite their age; others are cited
Using Cited Half-life to Adjust Download Statistics 535
once or twice and then forgo en. This dis-
tinction is an important one to remember,
but for the present model, what is being
used is the citation pa ern for a collection
of articles (i.e., a journal), not the citations
of any individual article.
4. Half-life Is Similar across All Volumes
Assumption: Different volumes of the
same journal have the same half-life.
Difficulties: As the explanation of the
cited half-life from the JCR points out,
“Dramatic changes in Cited Half-Lifes
[sic] over time may indicate a change in
a journal’s format.”
This could be caused by a change in the
number of articles published in a given
year (e.g., more pages with same density
of print or the same number of pages, but
denser format); a change in editorial poli-
cies; or a change in a field of study.
Justification: An investigation into half-
lives changing over time was not pursued.
It would be worthwhile to explore the
effect of such a change further.
5. Local Half-life and ISI Half-life Are
Proportional
Assumption: Local half-life is proportion-
al to the corrected ISI half-life figures.
Difficulty: Even if ISI’s half-life figures
are a good proxy for the citation pa erns
of the general scholarly community, they
might differ markedly from the citation
pa ern of a particular university or re-
search institute. In “Library Journal Use
and Citation Half-Life in Medical Sci-
ence,” Ming-Yueh Tsay studied cited half-
life and local use half-life. “[I]n general,
journals with shorter citation half-lives
also have shorter use half-lives.” But,
“[t]here is ... a [statistically] significant
difference between the mean citation half-
life and the mean use-half life for journals
of each category [studied].”9
Justification: Further research is need-
ed on this assumption.
6. Citation and Use Are Proportional
Assumption: The journal being cited and
the journal being downloaded should
be in about the same proportions (with
some time lag).
Difficulty: The other, more significant
problem is that in-house use half-lives
may differ significantly from citation
half-lives. Tsay demonstrates that for the
journals held by the medical library she
studied, use half-life was less than cited
half-life (e.g., for 266 clinical medicine
titles, the use half-life was 3.02 years, but
the citation half-life was 6.06 years).10 The
implication is that in this case, citation
half-lives may overestimate local use.
In “Biology Journal Use at an Academic
Library: A Comparison of Use Studies,”
Diane Schmidt and Elizabeth B. Davis
argued that “this technique [of studying
citations] does not address the influence
of background reading or information
gathered for personal, as opposed to
professional, use. Another problem ... is
that, in general, they measure only the
use of journals by faculty or occasionally
graduate students.”11 The implication
here is that citation half-lives underestimate
local use.
Justification: Because the estimate is
applied across the board, one journal’s
cost per use will be more comparable to
another’s than an unadjusted calculation.
However, further investigation is needed
on this assumption.
Practical Problems
Practical problems stemming from the
model’s assumptions and methods for
handling them are summarized in table
3. Because Notre Dame’s cancellation
project was postponed, the effects of these
practical decisions are demonstrated with
a sample set of journals listed in table 4.
1. Do the download statistics need to be
adjusted at all?
The first thing a user of download statistics
will have to decide is whether to adjust
them. The authors are convinced that
download statistics should be adjusted,
except in the case of a small set of journals
with generally short half-lives. Even if the
corrected download statistics do not figure
http:years).10
536 College & Research Libraries November 2005
TABLE 3
Practical Difficulties
Choice Our Decision
1. Do the download statistics really need to
be adjusted?
1. We had many long half-life journals,
so the adjusted download figures were
calculated.
2. How should you generate one year’s
download statistics?
2. We had data problems, so only one
complete year’s worth of data was used.
3. How should you calculate the electronic
run?
3. We had runs available for each journal, so
they were used.
4. What do you do if the print and electronic
runs overlap?
4. We didn’t have good print statistics, so
the print was ignored.
5. What do you do if part of the run is
available for little or not cost?
5. We didn’t consider this at the time, so the
current issues were focused on.
6. What do you do with a half-life > 10
years?
6. We used a corrected half-life of 9.0 and
were ready to perform least-squares analysis
for the borderline cases.
7. What if the half-life is unavailable from
ISI?
7. We were prepared to use a corrected
half-life of 9.0 or to calculate the half-life
needed to make a given cost-per-use cutoff.
8. How do you convert print use to
downloads?
8. We needed to make some estimate, so five
downloads: one print use was the ratio used.
largely in a library’s cancellation decisions,
the adjusted figures can inform decisions
about borderline cases. Corrected half-lives
for the sample set of journals is listed in table
5. Of the seventeen journals listed, seven
have half-lives greater than eight years.
2. What time period should be used to
compute DL, the download statistic for a
year? Should the DL be from the most re-
cent year or should an average of several
years be used?
If there are K years of download data, and
the total count of all downloads is TDL
for those K years, TDL/K could be use for
DL to smooth out fluctuations. Caution
should be exercised, however, because:
• Usage might increase from year to
year as the comfort level and dependence
on electronic journals continues to increase.
TDL/K could be replaced with TDL/K times
the overall ratio of increase over the K years
(i.e., if the total downloads for a given univer-
sity increased overall by 3%, the TDL/K for
each journal could be adjusted by 3%).
• If K is not an integer, seasonal varia-
tions in downloads will skew the figures (i.e.,
if K only covered 18 months, K would be
1.5). Because the variation could be caused
by whether classes are in session or not, for
example, one could attempt to make an ad-
justment for seasonal variation. However, it
is probably best for K to be an integer.
• The electronic run will not be constant
over the K years (i.e., this year there might be
five years of electronic access, but last year
only four).
• Lastly, publishers generally acknowl-
edge that there are problems with the statistics
when they first began to collect them.
A library should begin with one year’s
worth of statistics and build from there
over time. In table 4, download statistics
are listed for 2003 and 2004; in table 5, only
download statistics from 2004 are used.
3. What method should be used to calcu-
late the electronic run?
Another minor difficulty is calculating the
number of years of electronic availability,
Using Cited Half-life to Adjust Download Statistics 537
ER. Even for the same publisher, the ER
for individual journals can vary from a
few years to more than ten (especially
for new journals). Also, the calculations
assume no overlap between electronic
and print versions. (See the discussion
below.) The library should use the num-
ber of years for the entire electronic run,
realizing, of course, that even the adjusted
download figures from the model will un-
dercount, especially for disciplines more
comfortable with paper journals than
electronic journals. These subjects also
appear to be ones with the preponderance
of long half-life journals (e.g., journals
in the humanities). However, because
the model has been applied across the
board, the adjusted download figures are
more comparable than the raw download
figures by themselves. (See table 5 for
ER figures for each journal. Notice that
Nature Cell Biology only began in 1999 and
is adjusted accordingly.)
4. What should be done if the print and
electronic runs overlap?
At Notre Dame, many print subscriptions
have been cancelled in favor of the elec-
tronic version only. With few exceptions,
however, there was a period of time when
the library received both the print and
electronic versions of a journal.
If a library is gathering reasonably
accurate print and electronic use statis-
tics, the statistics could simply be added
together for the overlapping time period.
Of course, there is the problem of the
definition of “use.” Download statistics
count the use of one article as one use;
print statistics generally count one current
issue or one bound issue as one use. Obvi-
ously, these are not comparable.
For the sample set of journals, the as-
sumption was that there was no overlap
between electronic and print and that the
print use statistics could be ignored (they
are not generally collected well or with
TABLE 4
Sample Set of Journals
Rank Title
2004
Cost
2003
DL
2004
DL
2004
CPU
1 Nature Cell Biology $899 n/a 348 $2.58
2 SIAM Journal on Numerical Analysis $508 61 69 $7.36
3 Evolution and Human Behavior $808 89 109 $7.41
4 Library & Information Science Research $315 17 13 $24.23
5 Accounting, Organizations & Society $1,633 65 50 $32.66
6 Acta Psychologica $936 43 28 $33.43
7 Probabilistic Eng Mechanics $832 771 24 $34.67
8 International Journal of Industrial Organization $1,169 40 32 $36.53
9 Physics Reports $5,599 198 153 $36.59
10 Immunology Letters $2,734 89 69 $39.62
11 Journal of Molecular Structure: Theochem $7,633 216 192 $39.76
12 Earth Science Reviews $1,334 13 33 $40.42
13 Mathematische Annalen $2,760 58 60 $46.00
14 Communications in Partial Differential Equations $1,995 n/a 38 $52.50
15 Poetics $433 19 3 $144.33
16 Technological Forecasting & Social Change $839 5 4 $209.75
17 Journal of Logic and Algebraic Programming $923 1 1 $923.00
538 College & Research Libraries November 2005
regularity). The adjustments were made
using only the complete electronic run.
5. What should be done if part of the run
is available for little or no cost?
Because the ultimate goal is to maximize use
while minimizing cost (i.e., maximizing the
ROI), there are implications for journals
available for li le or no cost a er some
number of years (e.g., through JSTOR or
via various open-access arrangements).
As a first example, consider Math-
ematische Annalen. The years 1996 to the
present of this journal are available elec-
TABLE 5
First Adjustment to the Sample Set of Journals
Rank Adj.
Rank
Title 2004
Cost
2004
DL
2004
ER
2003
HL
AF FC Adj.
CPU
1 1 Nature Cell Biology $899 348 6 1.7 1.1 381.0 $2.36
2 2 SIAM Journal on
Numerical Analysis
$508 69 8 9* 2.2 150.0 $3.39
3 3 Evolution and Human
Behavior
$808 109 8 3.0 1.2 129.4 $6.25
14 4 Communications in
Partial Differential
Equations
$1,995 38 4 8.5 3.6 136.5 $14.61
9 5 Physics Reports $5,599 153 7 7.7 2.1 327.3 $17.11
5 6 Accounting,
Organizations & Socty
$1,633 50 10 9* 1.9 93.1 $17.54
4 7 Library & Information
Science Research
$315 13 10 5.3 1.4 17.8 $17.68
6 8 Acta Psychologica $936 28 10 9* 1.9 52.1 $17.95
12 9 Earth Science Reviews $1,334 33 10 9* 1.9 61.4 $21.71
13 10 Mathematische
Annalen
$2,760 60 9 9* 2.0 120.0 $23.00
7 11 Probabilistic Eng
Mechanics
$832 24 10 6.1 1.5 35.3 $23.54
8 12 International
Journal of Industrial
Organization
$1,169 32 10 6.6 1.5 49.2 $23.75
10 13 Immunology Letters $2,734 69 10 4.4 1.3 87.0 $31.42
11 14 Journal of Molecular
Structure: Theochem
$7,633 192 10 4.3 1.2 239.8 $31.82
16 15 Technological
Forecasting & Social
Change
$839 4 10 8.6 1.8 7.2 $116.07
15 16 Poetics $433 3 10 n/a $144.33
17 17 Journal of Logic And
Algebraic Program-
ming
$923 1 10 n/a $923.00
* ISI Half-life > 10
Using Cited Half-life to Adjust Download Statistics 539
tronically by subscription from Springer (for us, 2003) plus the i years before that.
Verlag. However, EMANI (Electronic Find the value of HL such that
Mathematical Archiving Network Initia- 2
tive) makes all the issues from 1996 and
i
HL
1−
1
9
∑
earlier available for free. This is laudable, Ci −
i=0 2
but because the older issues are free to
anyone (even nonsubscribers), the down-
load statistics from Springer for the sub-
scribed issues should not be adjusted. As
a result, the cost per download is higher
and it is more likely that the subscription
should be replaced by some other means
of access (like commercial document
delivery).
As a second example, consider journals
that are available before a certain moving
wall at a cost less than a subscription.
The SIAM Journal on Numerical Analy-
sis (SINUM) was available before 1996
through JSTOR (JSTOR:SINUM). Because
the decisions for both these subscriptions
are separate and because “all the years
for each period” are available electroni-
cally, the raw download statistics should
be used with no half-life corrections. A
2004 subscription to SINUM is $508, and
the cost of JSTOR:SINUM is about $25.
During 2004, the raw downloads were
sixty-nine and sixty-six, respectively. Here
are the results of the analysis:
• The cost per download was $7.36 for
SINUM and $0.38 for JSTOR:SINUM.
• If JSTOR:SINUM was not available,
the figures for SINUM would be adjusted,
resulting in a cost of $3.39 per download as
indicated in table 5.
6. What should be done with an ISI half-
life of “> 10” years?
For a journal with an uncorrected ISI
half-life of at least ten years, ISI simply
gives > 10 as the half-life. When ISI’s data
are corrected, the journal has a half-life
> 9 years. Can this be calculated more
accurately?
For these cases, a least-squares fi ed
exponential curve can be employed to
compute a more accurate estimate of half-
life. The procedure would be as follows:
Let Ci denote the cumulative fraction of
cites from the journals in the current year
is minimized (e.g., using the solver
function in Excel™).
The citation data were adjusted so that
0 percent was the prediction for cites from
year zero (i.e., cites in 2003 journals to the
2003 volume of the journal in question).
For long half-life journals this is close to
true because the fraction C0 is typically
less than 0.5 percent.
More accurate computations of the >
10 half-lives using least-squares minimi-
zation could give valuable guidance in
contested cases. However, for journals
with half-lives greater than four or five
years but less than ten, least-squares
minimization tends to give a half-life
slightly less than the half-life given by ISI.
For journals with half-lives less than four
years, least-squares minimization should
not be used. (For the sample set’s results
employing least-squares minimization,
see table 6.)
7. What if the half-life is unavailable from
ISI?
JCR does not provide cited half-lives
for journals cited less than one hundred
times nor does it provide half-lives for
every journal published (for example,
new journals). As noted above, of the
327 mathematics and applied mathemat-
ics journals listed in ISI, 11 percent (36
journals) have no half-life given. Of the
261 biochemistry and molecular biology
journals listed in ISI, 1 percent (3 journals)
have no half-life given. The analysis un-
covered the fact that nearly 50 percent
of the journals across all subjects did not
have half-life data available.
If ISI has data on a particular journal
(even if it has been cited less than one hun-
dred times), it might be able to estimate
the half-life as was done for those with >
10 years (above). Another approach is to
540 College & Research Libraries November 2005
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Using Cited Half-life to Adjust Download Statistics 541
simply use a figure of 9.0 years across all
subjects without a half-life (ISI half-life of
= 10.0 - 1). If journals having a half-life of
> 10 were le with a corrected half-life of
9.0, this estimate gives journals without
half-lives the maximum benefit.
For borderline cases, the model could
be employed in reverse using the goal-
seek function in Excel™. If there were a
particular CPU cutoff, say, $40 per down-
load, one could calculate what the half-life
would need to be for a particular journal
to make that cutoff. In table 5, Poetics
would need a half-life of approximately
twenty-one years to make the $40 CPU
cutoff. This might be reasonable. The
Journal of Logic and Algebraic Programming,
however, would need a half-life of 156
years. This is clearly unreasonable and
the journal should be a candidate for
cancellation.
8. How is use from electronic downloads
converted to expected document delivery
requests?
One of the major problems with analyzing
use statistics is estimating the conversion
factors between downloads, print uses,
and commercial document delivery re-
quests. Would a journal used five times
electronically be used only once in paper?
Would a print volume used once result
in one commercial document delivery
request? Does it ma er if the docdel is
mediated or unmediated? Estimating
this conversion factor is critical when
determining whether a subscription (print
or electronic) is more cost-effective than
docdel. Unfortunately, there appears to
have been no previous published research
in this area.
During the project, the plan was to use
a conversion factor of five downloads to
one mediated docdel request. Conversion
factors for print use were not estimated.
The download to docdel figure was based
on docdel requests before the library had
access to journals electronically and on a
sense that patrons would request fewer
articles if they had to ask for them (rather
than clicking on a hyperlink).
Final Remarks
For the sample set, the average cost of
docdel for the University of Notre Dame,
roughly $35 per article, was used. An
estimated internal processing cost of $5
was added, and the cutoff was set at $40
per article. Journals that cost more than
$40 per adjusted, converted use would be
candidates for cancellation. In tables 4, 5,
and 6, journals are ranked from lowest to
highest CPU. In tables 5 and 6, previous
rankings for the journals are included.
Even the results in table 5 are be er than
those in table 4.
No model is perfect, but the half-life
model fits the citation data surpris-
ingly well. The goal was to improve
the method used to evaluate the raw
download figures. Indeed, the proposed
model will still undercount the same
areas that the raw download figures
undercount, but the undercounting will
be proportional across disciplines and
less severe.
It is important when evaluating wheth-
er approximations are “acceptable” to
keep the goal in mind. The goal is a
reduction in undercounting, and under-
counting is much more severe for long
half-life journals with short electronic
runs available.
For example, look at a journal with
a very long half-life, Mathematische An-
nalen. According to JCR, this respected
mathematics journal has a half-life of >
10 years with an electronic run of nine
years. The ISI database does not give the
exact half-life; however, only 24.2 percent
of citations are from articles published be-
tween 1994 and 2003. Using least-squares
minimization, the “ISI half-life” is 23.2
years. Math. Ann. moves from a $46 CPU
in table 4 to a $23 CPU in table 5 and to a
$17 CPU in table 6.
As time passes, the electronic runs of
journals will increase, and there will be
sufficient year-to-year raw download fig-
ures to make reasonable extrapolations.
Thus, the model for adjusting downloads
that this article proposes will become less
urgent.
542 College & Research Libraries November 2005
Notes
1. Marisa Scigliano, “Serial Use in a Small Academic Library: Determining Cost-effective-
ness,” Serials Review 26 (2000): 43–52.
2. JCR Glossary. Available online at h p://jcr4.isiknowledge.com/www/help/hjcrgls2.htm.
[Accessed 27 February 2005].
3. Lawrence A. Coleman, “Exponential Growth and Decay,” Macmillan Encyclopedia of Physics,
vol. 2 (New York: Simon and Schuster Macmillan, 1996), 533.
4. Endre Száva-Kováts, “Unfounded A ribution of the ‘Half-Life’ Index-Number of Literature
Obsolescence to Burton and Kebler: A Literature Science Study,” Journal of the American Society for
Information Science 53 (Nov. 2002): 1098–1105.
5. R. E. Burton and B. A. Green Jr., “Technical Reports in Physics Literature,” Physics Today
(Oct. 1961): 35–37. “While the phrase ‘literature half-life’ has been applied to this figure, it more
properly should be referred to as the median age.”
6. Helmut M. Artus, “‘Halbwertzeit wissenschaftlicher Literatur ’—Naturgesetz oder
Forschungsartefakt?” Nachrichten für Dokumentation 34 (Apr. 1983): 79–86. He also claims: “Ein
bloß quantifizierendes Vorgehen reicht nicht aus, um das gleichermaß en kognitive wie soziale
Phänomen ‘Literaturnutzung’ in den Griff zu bekommen.” “A purely quantitative procedure is
insufficient to come to terms with the cognitive and likewise social phenomenon of ‘literature use.’”
(Translated by Robert L. Kusmer, Associate Librarian, University Libraries of Notre Dame.)
7. Leonard Roth, “On the Projective Classification of Surfaces,” Proceedings of the London
Mathematical Society, Second Series 42 (1937): 142–70.
8. Andrew J. Sommese, “Hyperplane Sections of Projective Surfaces I—The Adjunction Map-
ping,” Duke Mathematical Journal 46 (1979): 377–401.
9. Ming-Yueh Tsay, “Library Journal Use and Citation Half-life in Medical Science,” Journal
of the American Society for Information Science 49 (Dec. 1998): 1283–92.
10. Ibid., 1286.
11. Diane Schmidt and Elizabeth B. Davis, “Biology Journal Use at an Academic Library: A
Comparison of Use Studies,” Serials Review 20 (summer 1994): 45–63.