Page 233 - Becoming Metric Wise

224 Becoming Metric-Wise

7.8.2 Payback Times: A Variation on the Success Index
Instead of determining whether a given article has reached a certain
threshold, a more dynamic approach would be determining how long it
takes for an article to reach the threshold. This idea precedes the concept
of a success index. It was proposed by Liang and Rousseau (2008) for
journals and is referred to as the yield period or the payback time. The
term “payback time” refers to the idea that a journal uses resources from
the science system (as shown by its lists of references) and that it takes a
certain time to pay back (through received citations) to the science system
what had been taken. Liang and Rousseau (2008) studied yearly issues of
Science and Nature, leading to so-called yield sequences. They determined
not only the time to reach a number of citations equal to the number of
used references, but also the time to reach twice, thrice, .. . this number. It
was observed that at least for these journals, payback times tended to
become shorter over the years. Another variation on the success index and
the idea of a payback time would be to consider the percentage of articles
in a given set that already reached the threshold after a given time t.
7.8.3 Success Multipliers (Rousseau & Rousseau, 2016)

Instead of a binary score leading to a success index, we can also determine
the fraction of the threshold reached by an article at any given moment.
For instance, if the threshold is 20 citations and an article has obtained 14
citations, a value 0.7 can be associated with it. Similarly, if an article received
30 citations, it receives a value of 1.5. The values 0.7 and 1.5 are then referred
to as multipliers. An article’s multiplier reflects the relative number of citations
received by that article compared to the threshold value that is used.
The success multiplier of a set of articles is simply the sum of the
scores of all articles in the set, generalizing the success index of a set of
articles. When using success multipliers it is still possible to separate an
elite set from the other ones, but this division is not as clear-cut as in the
0-1 case. Further, an average score is created by dividing this general score
by the total number of articles. When the number of references is used as
a threshold this leads to the formula:
n
1 X c j
(7.14)
n r j
j51
Here n is the number of publications under consideration, c j is the num-
ber of citations received by article j (over a given citation window) and r j is