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176   Becoming Metric-Wise


          journals covered by the database. As a mathematical formula DCP can be
          written as follows:
                                                      n
                                   r 1 1 r 2 1 ::: 1 r n  1  X
                           DCP 5                 5       r j          (6.17)
                                         n          n
                                                     j51
             In this formula, n denotes the number of publications in the journal’s
          subject field; r j denotes the number of references in the j-th publication
          that appeared in the three preceding years in journals covered by the data-
          base. Such reference items are called active references.


          6.12.2 The New SNIP Indicator
          Waltman et al. (2013) pointed out that the original SNIP indicator had
          some properties which a good indicator is not supposed to have, namely:
          1. It may happen that an additional citation leads to a decrease of the
             SNIP-value.
          2. Nonconvexity: if two journals merge (are considered as one whole)
             then one would expect a new SNIP-value between the original two
             SNIP-values. However, this does not have to be the case. This is a
             convexity issue, see also Ramanana-Rahary et al. (2009) for a discus-
             sion of convexity issues in scientometric evaluations.
             For these reasons Waltman et al. (2013) proposed a revised SNIP index.
          Its most significant modifications with respect to the original one are:
          •  Database citation potential (DCP)-values are calculated as harmonic
             rather than arithmetic averages.
          •  The calculation of DCP values takes into account not only the num-
             ber of active references in citing publications but also the proportion
             of publications with at least one active reference in citing journals.
          •  The distinction between DCP and RDCP is abandoned, in other
             words the median DCP value does not play a role anymore.
             We provide now some details about the new SNIP. The basic formula
          is SNIP 5 RIP/DCP in which the RIP-value of a journal is the same as
          in the original version. The DCP-value is a harmonic mean:
                                    1          n
                             DCP 5                                    (6.18)
                                    3   1  1  1  1 ::: 1  1
                                       p 1 r 1  p 2 r 2  p n r n
          where the r j ’s have the same meaning as before, namely the number of
          references in the j-th publication. The p j ’s are new entities. Consider the
          jth publication in the subject field of a journal and consider then all pub-
          lications that appeared in the same journal and the same year as the
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