View source for Author-level metrics

'''Author-level metrics''' are citation metrics that measure the [[Bibliometrics|bibliometric impact]] of individual authors, researchers, academics, and scholars. Many metrics have been developed that take into account varying numbers of factors (from only considering the total number of citations, to looking at their distribution across papers or [[Academic journal|journals]] using statistical or [[Graph theory|graph-theoretic]] principles). 

These quantitative comparisons between researchers are mostly done to distribute resources (such money and academic positions). However, there is still debate in the academic world about how effectively author-level metrics accomplish this objective.<ref name="hirsch">{{cite journal|last1=Hirsch|first1=J. E.|date=7 November 2005|title=An index to quantify an individual's scientific research output|journal=Proceedings of the National Academy of Sciences|volume=102|issue=46|pages=16569–16572|doi=10.1073/pnas.0507655102|pmc=1283832|pmid=16275915|arxiv=physics/0508025|bibcode=2005PNAS..10216569H|doi-access=free}}</ref><ref name=":0" /><ref name=":1" />

Author-level metrics differ from journal-level metrics which attempt to measure the bibliometric impact of academic journals rather than individuals. However, metrics originally developed for academic journals can be reported at researcher level, such as the author-level eigenfactor<ref name="wiley">{{cite journal |title=Author-level Eigenfactor metrics: Evaluating the influence of authors, institutions, and countries within the social science research network community |first1=Jevin D. |last1=West |first2=Michael C. |last2=Jensen |first3=Ralph J. |last3=Dandrea |first4=Gregory J. |last4=Gordon |first5=Carl T. |last5=Bergstrom |journal=Journal of the American Society for Information Science and Technology |year=2013 |doi=10.1002/asi.22790 |volume=64 |issue=4 |pages=787–801}}</ref> and the author impact factor.<ref name="nature">{{cite journal |title=Author Impact Factor: Tracking the dynamics of individual scientific impact |journal=Scientific Reports |doi=10.1038/srep04880 |first1=Raj Kumar |last1=Pan |first2=Santo |last2=Fortunato |year=2014 |volume=4 |page=4880|pmid=24814674 |pmc=4017244 |arxiv=1312.2650 |bibcode=2014NatSR...4E4880P }}</ref> 

==List of metrics==
{| class="wikitable sortable"
|-
! Name !! Description
|-
| '''{{vanchor|''h''-index}}''' ||Formally, if ''f'' is the function that corresponds to the number of citations for each publication, the [[H-index|''h''-index]] is computed as follows. First, we order the values of ''f'' from the largest to the lowest value. Then, we look for the last position in which ''f'' is greater than or equal to the position (we call ''h'' this position). For example, if we have a researcher with 5 publications A, B, C, D, and E with 10, 8, 5, 4, and 3 citations, respectively, the ''h''-index is equal to 4 because the 4th publication has 4 citations and the 5th has only 3. In contrast, if the same publications have 25, 8, 5, 3, and 3 citations, then the index is 3 because the fourth paper has only 3 citations.<ref name="hirsch"/>
|-
| '''{{vanchor|Individual ''h''-index}}''' ||An individual ''h''-index normalized by the number of authors has been proposed: <math>h_I = h^2/N_a^{(T)}</math>, with <math>N_a^{(T)}</math> being the number of authors considered in the <math>h</math> papers.<ref name=BatistaEtal2006>{{Cite journal |author=Batista P. D. |title=Is it possible to compare researchers with different scientific interests? |journal=Scientometrics |volume=68 |issue=1 |year=2006 |pages=179–89 |doi=10.1007/s11192-006-0090-4 |display-authors=1 |last2=Campiteli |first2=Mônica G. |last3=Kinouchi |first3=Osame |arxiv=physics/0509048 |s2cid=119068816 }}</ref>  It was found that the distribution of the ''h''-index, although it depends on the field, can be normalized by a simple rescaling factor. For example, assuming as standard the ''h''s for biology, the distribution of ''h'' for mathematics collapses with it if this ''h'' is multiplied by three, that is, a mathematician with ''h''&nbsp;=&nbsp;3 is equivalent to a biologist with ''h''&nbsp;=&nbsp;9. This method has not been readily adopted, perhaps because of its complexity. 
|-
| '''{{vanchor|Fractional ''h''-index}}''' ||To avoid incentivizing hyperautorship with more than 100 coauthors per paper it might be simpler to divide citation counts by the number of authors before ordering the papers and obtaining the ''fractional h-index'', as originally suggested by Hirsch. This index, also called h-frac, is not highly correlated with ''h''-index and is currently correlated with scientific awards.<ref name='h-frac'>{{cite journal |last1=Koltun |first1=V |last2=Hafner |first2=D |title=The h-index is no longer an effective correlate of scientific reputation. |journal=PLOS ONE |date=2021 |volume=16 |issue=6 |pages=e0253397 |doi=10.1371/journal.pone.0253397 |pmid=34181681 |pmc=8238192 |arxiv=2102.03234 |bibcode=2021PLoSO..1653397K |doi-access=free }}</ref>
|-
| ''' ''h''<sup>2</sup> ''' ||Three additional metrics have been proposed: ''h''<sup>2</sup> lower, ''h''<sup>2</sup> center, and ''h''<sup>2</sup> upper, to give a more accurate representation of the distribution shape. The three ''h''<sup>2</sup> metrics measure the relative area within a scientist's citation distribution in the low impact area, ''h''<sup>2</sup> lower, the area captured by the ''h''-index, ''h''<sup>2</sup> center, and the area from publications with the highest visibility, ''h''<sup>2</sup> upper. Scientists with high ''h''<sup>2</sup> upper percentages are perfectionists, whereas scientists with high ''h''<sup>2</sup> lower percentages are mass producers. As these metrics are percentages, they are intended to give a qualitative description to supplement the quantitative ''h''-index.<ref>{{cite journal |doi=10.1016/j.joi.2010.03.005 |title=The ''h'' index research output measurement: Two approaches to enhance its accuracy |year=2010 |last1=Bornmann |first1=Lutz |last2=Mutz |first2=Rüdiger |last3=Daniel |first3=Hans-Dieter |journal=Journal of Informetrics |volume=4 |issue=3 |pages=407–14 }}</ref>

|-
| '''{{vanchor|Normalized ''h''-index}}''' ||The ''h''-index has been shown to have a strong discipline bias. However, a simple normalization <math>h/\langle h \rangle_d</math> by the average ''h'' of scholars in a discipline ''d'' is an effective way to mitigate this bias, obtaining a universal impact metric that allows comparison of scholars across different disciplines.<ref>{{cite journal |doi= 10.1016/j.joi.2013.09.002 |arxiv=1305.6339 |title= Universality of scholarly impact metrics |year=2013 |last1=Kaur |first1=Jasleen |last2=Radicchi |first2=Filippo |last3=Menczer |first3=Filippo |journal=Journal of Informetrics |volume= 7|issue= 4|pages= 924–32 |s2cid=7415777 }}</ref> 
|-
| '''{{vanchor|Author-level Eigenfactor}}''' ||Author-level Eigenfactor is a version of [[Eigenfactor]] for single authors.<ref>{{cite journal |last1=West |first1=Jevin D. |last2=Jensen |first2=Michael C. |last3=Dandrea |first3=Ralph J. |last4=Gordon |first4=Gregory J. |last5=Bergstrom |first5=Carl T. |title=Author-level Eigenfactor metrics: Evaluating the influence of authors, institutions, and countries within the social science research network community |journal=Journal of the American Society for Information Science and Technology |date=April 2013 |volume=64 |issue=4 |pages=787–801 |doi=10.1002/asi.22790}}</ref> Eigenfactor regards authors as nodes in a network of citations. The score of an author according to this metric is his or her [[Eigenvector centrality|eigenvector centrality]] in the network. 
|-
| '''{{vanchor|Erdős number}}''' ||It has been argued that "For an individual researcher, a measure such as [[Erdős number]] captures the structural properties of the network whereas the ''h''-index captures the citation impact of the publications. One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking." Several author ranking systems have been proposed already, for instance the Phys Author Rank Algorithm.<ref>{{cite web |author1=Kashyap Dixit |author2=S Kameshwaran |author3=Sameep Mehta |author4=Vinayaka Pandit |author5=N Viswanadham |url=http://domino.research.ibm.com/library/cyberdig.nsf/papers/2B600A90C54E51B18525755800283D37/$File/RR_ranking.pdf |title=Towards simultaneously exploiting structure and outcomes in interaction networks for node ranking |website=IBM Research Report R109002 |date=February 2009}}; see also {{cite conference |doi=10.1145/1871437.1871470 |title=Outcome aware ranking in interaction networks |book-title=Proceedings of the 19th ACM international conference on Information and knowledge management – CIKM '10 |year=2010 |last1=Kameshwaran |first1=Sampath |last2=Pandit |first2=Vinayaka |last3=Mehta |first3=Sameep |last4=Viswanadham |first4=Nukala |last5=Dixit |first5=Kashyap |isbn=9781450300995 |page=229}}</ref>
|-
| '''{{vanchor|i-10-index}}''' ||The i-10 index indicates the number of academic publications an author has written that have been cited by at least 10 sources. It was introduced in July 2011 by [[Company:Google|Google]] as part of their work on [[Google Scholar]].<ref>Connor, James; Google Scholar Blog. [http://googlescholar.blogspot.com/2011/11/google-scholar-citations-open-to-all.html "Google Scholar Citations Open To All"], Google, 16 November 2011, retrieved 24 November 2011</ref>
|-
| '''{{vanchor|RG Score}}''' ||''ResearchGate Score'' or ''RG Score'' is an author-level metric introduced by [[Company:ResearchGate|ResearchGate]] in 2012.<ref>{{cite news |title="Professoren der nächsten Generation" {{!}} NZZ |url=https://www.nzz.ch/digital/researchgate-rg-score-1.17536449 |access-date=25 May 2020 |work=Neue Zürcher Zeitung |language=de}}</ref> According to ResearchGate's CEO Dr. Ijad Madisch, “[t]he RG Score allows real-time feedback from the people who matter: the scientists themselves.”<ref>{{cite news |last1=Knowles |first1=Jamillah |title=ResearchGate Releases RG Score - Klout for Boffins |url=https://thenextweb.com/insider/2012/08/10/researchgate-introduces-rg-score-like-klout-boffins/ |access-date=26 May 2020 |work=The Next Web |date=10 August 2012 |language=en-us}}</ref> RG Score has been reported to be correlated with existing author-level metrics and has an undisclosed calculation methodology.<ref name="doi10.1002/asi.23236">{{Cite journal| doi = 10.1002/asi.23236| title = ResearchGate: Disseminating, communicating, and measuring Scholarship?| journal = Journal of the Association for Information Science and Technology| volume = 66| issue = 5| pages = 876–889| year = 2014| last1 = Thelwall| first1 = M.| last2 = Kousha| first2 = K.| url = http://www.scit.wlv.ac.uk/~cm1993/papers/ResearchGate.pdf| citeseerx = 10.1.1.589.5396| s2cid = 8974197| access-date = 2018-07-30| archive-url = https://web.archive.org/web/20180218233038/http://www.scit.wlv.ac.uk/~cm1993/papers/ResearchGate.pdf| archive-date = 2018-02-18| url-status = live}}</ref><ref>{{cite journal|last1=Yu|first1=Min-Chun|title=ResearchGate: An effective altmetric indicator for active researchers?|journal=Computers in Human Behavior|date=February 2016|volume=55|pages=1001–1006|doi=10.1016/j.chb.2015.11.007}}</ref><ref name=Kraker>{{cite journal |last1=Kraker |first1=Peter |last2=Lex |first2=Elisabeth |title=A Critical Look at the ResearchGate Score as a Measure of Scientific Reputation|journal=Proceedings of the quantifying and analysing scholarly communication on the web workshop (ASCW’15) |date=2015 |url=https://graz.pure.elsevier.com/en/publications/a-critical-look-at-the-researchgate-score-as-a-measure-of-scienti |language=en}}</ref><ref name="Jordan">{{cite conference|first=Katy|last=Jordan|title=Exploring the ResearchGate score as an academic metric: Reflections and implications for practice|conference=Quantifying and Analysing Scholarly Communication on the Web (ASCW'15)|year=2015}}</ref> Two studies reported that RG Score seems to incorporate the journal impact factors into the calculation.<ref name=Kraker/><ref name="Jordan"/> The RG Score was found to be negatively correlated with network [[Centrality|centrality]] – users that are the most active on ResearchGate usually do not have high RG scores.<ref>{{cite journal|last1=Hoffmann|first1=C. P.|last2=Lutz|first2=C.|last3=Meckel|first3=M.|title=A relational altmetric? Network centrality on ResearchGate as an indicator of scientific impact|journal=Journal of the Association for Information Science and Technology|date=2016|volume=67|issue=4|pages=765–775|doi=10.1002/asi.23423|s2cid=7769870|url=https://www.alexandria.unisg.ch/240735/1/Hoffmann_Lutz_Meckel-2015-Journal_of_the_Association_for_Information_Science_and_Technology.pdf}}</ref> It was also found to be strongly positively correlated with Quacquarelli Symonds university rankings at the institutional level, but only weakly with [[Company:Elsevier|Elsevier]] SciVal rankings of individual authors.<ref name="CHB">{{cite journal|last1=Yu|first1=Min-Chun|title=ResearchGate: An effective altmetric indicator for active researchers?|journal=Computers in Human Behavior|date=February 2016|volume=55|pages=1001–1006|doi=10.1016/j.chb.2015.11.007}}</ref> While it was found to be correlated with different university rankings, the correlation in between these rankings themselves was higher.<ref name="doi10.1002/asi.23236" />
|-
| '''{{vanchor|Field-weighted Citation Impact}}''' ||Field-weighted Citation Impact (FWCI) is an author-level metric introduced and applied by [[Scopus]] SciVal.<ref>{{cite web |last1=Cooke |first1=Bec |title=Guides: Research Metrics: Field-Weighted Citation Impact |url=https://libguides.usc.edu.au/researchmetrics/researchmetrics-field-weighted-citation-impact |website=libguides.usc.edu.au |language=en}}</ref> FWCI equals to the total citations actually received divided by the total citations that would be expected based on the average of the considered field. FWCI of 1 means that the output performs just as expected for the global average. More than 1 means that the author outperforms the average, and less than 1 means that the author underperforms. For instance, <math>1.55</math> means <math>55</math>% more likely to be cited.<ref>{{cite web |title=Snowball Metrics Recipe Book |url=https://www.snowballmetrics.com/wp-content/uploads/snowball-metrics-recipe-book-upd.pdf |date=2012}}</ref><ref>{{cite web |last1=Tauro |first1=Kiera |title=Subject Guides: 6. Measure Impact: Field-Weighted Citation Impact |url=https://canterbury.libguides.com/impactmeasure/fieldweighted |website=canterbury.libguides.com |language=en}}</ref> 
|-
| '''{{vanchor|''m''-index}}''' ||The ''m''-index is defined as ''h''/''n'', where ''h'' is the ''h''-index and ''n'' is the number of years since the first published paper of the scientist;<ref name="hirsch"/> also called ''m''-quotient.<ref>{{cite web |url=http://www.harzing.com/pop_hindex.htm |title=Reflections on the ''h''-index |author=Anne-Wil Harzing |date=2008-04-23 |access-date=2013-07-18}}</ref><ref>{{cite journal |pmid=21507617 |year=2011 |author1=von Bohlen und Halbach O |title=How to judge a book by its cover? How useful are bibliometric indices for the evaluation of "scientific quality" or "scientific productivity"? |volume=193 |issue=3 |pages=191–96 |doi=10.1016/j.aanat.2011.03.011 |journal=Annals of Anatomy}}</ref>
|-
| '''{{vanchor|''g''-index}}''' ||For [[G-index|''g''-index]] is introduced in 2006 as largest number of top <math>g</math> articles, which have received together at least <math>g^2</math> citations.<ref name="Egghe">{{cite journal
 |last1=Egghe |first1=Leo
 |year=2006
 |title=Theory and practise of the ''g''-index
 |journal=Scientometrics
 |volume=69 |issue=1 |pages=131–152
 |doi=10.1007/s11192-006-0144-7
|hdl=1942/981
 |s2cid=207236267
 |hdl-access=free
 }}</ref>
|-
| '''{{vanchor|''e''-index}}''' ||The ''e''-index, the square root of surplus citations for the ''h''-set beyond ''h''<sup>2</sup>, complements the ''h''-index for ignored citations, and therefore is especially useful for highly cited scientists and for comparing those with the same ''h''-index (iso-''h''-index group).<ref>{{cite journal |doi=10.1371/journal.pone.0005429 |title=The e-Index, Complementing the ''h''-Index for Excess Citations |year=2009 |editor1-last=Joly |editor1-first=Etienne |last1=Zhang |first1=Chun-Ting |journal=PLOS ONE |volume=4 |issue=5 |page=e5429 |pmid=19415119 |pmc=2673580|bibcode=2009PLoSO...4.5429Z |doi-access=free }}</ref><ref>{{cite journal |doi=10.1016/j.bbrc.2009.07.091 |title=Citation analysis: Maintenance of ''h''-index and use of e-index |year=2009 |last1=Dodson |first1=M.V. |journal=Biochemical and Biophysical Research Communications |volume=387 |issue=4 |pages=625–26 |pmid=19632203}}</ref>
|-
| '''{{vanchor|''c''-index}}''' ||The ''c''-index accounts not only for the citations but for the quality of the citations in terms of the collaboration distance between citing and cited authors. A scientist has ''c''-index ''n'' if ''n'' of [his/her] ''N'' citations are from authors which are at collaboration distance at least ''n'', and the other (''N'' − ''n'') citations are from authors which are at collaboration distance at most ''n''.<ref>{{cite journal |author1=Bras-Amorós, M. |author2=Domingo-Ferrer, J. |author3=Torra, V | year = 2011 | title = A bibliometric index based on the collaboration distance between cited and citing authors | journal = Journal of Informetrics | volume = 5 | issue = 2 | pages = 248–64 | doi = 10.1016/j.joi.2010.11.001 |hdl=10261/138172 }}</ref>
|-
|-
| '''{{vanchor|RA-index}}''' ||The RA-index accommodates improving the sensitivity of the ''h''-index on the number of highly cited papers and has many cited paper and uncited paper under the ''h''-core. This improvement can enhance the measurement sensitivity of the ''h''-index. <ref>{{Cite journal|last=Fatchur Rochim|first=Adian|date=November 2018|title=Improving fairness of ''h''-index: RA-index|journal=DESIDOC Journal of Library & Information Technology|volume=38|issue=6|pages=378–386|doi=10.14429/djlit.38.6.12937|doi-access=free}}</ref>
|-
| '''{{vanchor|''L''-index}}''' ||''L''-index combines the number of citations, the number of coauthors, the age of publications into a single value, which is independent of the number of publications and conveniently ranges from 0.0 to 9.9.<ref>{{cite journal |last1=Belikov |first1=Aleksey V. |last2=Belikov |first2=Vitaly V. |title=A citation-based, author- and age-normalized, logarithmic index for evaluation of individual researchers independently of publication counts |journal=F1000Research |date=22 September 2015 |volume=4 |pages=884 |doi=10.12688/f1000research.7070.1| pmc=4654436|doi-access=free }}</ref> With ''c'' as number of citations, ''a'' as number of authors and ''y'' as number of years, ''L''-index is defined by the formula: 
:<math>L=\ln\left({\sum_{i}{\frac{c_i}{a_i y_i}}}\right)+1</math>
''L''-index is automatically calculated by the Exaly database.<ref>{{cite web |last1=Engine |first1=exaly Search |title=exaly Search Engine |url=https://exaly.com |website=Free database of papers and journals |access-date=20 May 2022 |language=en}}</ref>
|-
| '''{{vanchor|''s''-index}}''' ||An ''s''-index, accounting for the non-entropic distribution of citations, has been proposed and it has been shown to be in a very good correlation with ''h''.<ref>{{cite journal |last1=Silagadze |first1=Z. K. |title=Citation entropy and research impact estimation |year= 2010|pages=2325–33 |volume=41 |issue=2010 |journal=Acta Phys. Pol. B |arxiv=0905.1039 |bibcode=2009arXiv0905.1039S}}</ref>
|-
| '''{{vanchor|''w''-index}}''' || ''w''-index is defined as follow: if ''w'' of a researcher's papers have at least <math>10w</math> citations each and the other papers have fewer than <math>10(w+1)</math> citations, that researcher's ''w''‐index is ''w''.<ref>{{cite journal |last1=Wu |first1=Qiang |title=The w-index: A measure to assess scientific impact by focusing on widely cited papers |journal=Journal of the American Society for Information Science and Technology |date=2009 |volume=61 |issue=3 |pages=609–614 |doi=10.1002/asi.21276|arxiv=0805.4650 |s2cid=119293304 }}</ref>
|-
| '''{{vanchor|Author Impact Factor}}''' || Author Impact Factor (AIF) is the Impact Factor applied to authors.<ref name="nature"/> The AIF of an author <math>X</math> in year <math>y</math> is the mean number of citations given by papers published in year <math>y</math> to papers published by <math>X</math> in a period of <math>\Delta y</math> years before year <math>y</math>. Unlike the h-index, AIF is able to capture trends and variations of the impact of the scientific output of scientists over time,  which is a growing measure taking into account the whole career path.
|}

===Additional variations of ''h''-index===

There are a number of models proposed to incorporate the relative contribution of each author to a paper, for instance by accounting for the rank in the sequence of authors.<ref>{{cite journal | last1 = Tscharntke | first1 = T. | last2 = Hochberg | first2 = M. E. | last3 = Rand | first3 = T. A. | last4 = Resh | first4 = V. H. | last5 = Krauss | first5 = J. | year = 2007 | title = Author Sequence and Credit for Contributions in Multiauthored Publications | journal = PLOS Biology | volume = 5 | issue = 1| page = e18 | doi = 10.1371/journal.pbio.0050018 |pmc=1769438 | pmid=17227141 | doi-access = free }}</ref> A generalization of the ''h''-index and some other indices that gives additional information about the shape of the author's citation function (heavy-tailed, flat/peaked, etc.) has been proposed.<ref>{{cite journal |last=Gągolewski |first=M. |author2=Grzegorzewski, P. |year=2009 |title=A geometric approach to the construction of scientific impact indices |journal=Scientometrics |volume=81 |issue=3 |pages=617–34 |doi=10.1007/s11192-008-2253-y |s2cid=466433 }}</ref>  Because the ''h''-index was never meant to measure future publication success, recently, a group of researchers has investigated the features that are most predictive of future ''h''-index. It is possible to try the predictions using an online tool.<ref>{{cite journal |doi=10.1038/489201a |title=Future impact: Predicting scientific success |year=2012 |last1=Acuna |first1=Daniel E. |last2=Allesina |first2=Stefano |last3=Kording |first3=Konrad P. |journal=Nature |volume=489 |issue=7415 |pages=201–02 |pmid=22972278 |pmc=3770471|bibcode=2012Natur.489..201A }}</ref> However, later work has shown that since ''h''-index is a cumulative measure, it contains intrinsic auto-correlation that led to significant overestimation of its predictability. Thus, the true predictability of future ''h''-index is much lower compared to what has been claimed before.<ref>{{cite journal |doi=10.1038/srep03052 |title=On the Predictability of Future Impact in Science|year=2013 |last1=Penner |first1=Orion |last2=Pan |first2=Raj K. |last3=Petersen | first3=Alexander M. |last4=Kaski | first4=Kimmo | last5= Fortunato | first5=Santo |journal=Scientific Reports |volume=3 |issue=3052|page=3052 |pmid=24165898 |pmc=3810665|bibcode=2013NatSR...3E3052P|arxiv=1306.0114 }}</ref> The ''h''-index can be timed to analyze its evolution during one's career, employing different time windows.<ref>{{cite journal|last=Schreiber|first=Michael|date=2015|title=Restricting the ''h''-index to a publication and citation time window: A case study of a timed Hirsch index|journal=Journal of Informetrics|volume=9|pages=150–55|doi=10.1016/j.joi.2014.12.005|arxiv=1412.5050|s2cid=12320545}}</ref>

==Criticism==

Some academics, such as physicist [[Biography:Jorge E. Hirsch|Jorge E. Hirsch]], have praised author-level metrics as a ''"useful yardstick with which to compare, in an unbiased way, different individuals competing for the same resource when an important evaluation criterion is scientific achievement."''<ref name="hirsch" /> However, other members of the scientific community, and even Hirsch himself<ref>{{Cite journal|last=Hirsch|first=Jorge E.|date=2020|title=Superconductivity, What the H? The Emperor Has No Clothes|journal=Physics and Society|volume=49|pages=5–9|arxiv=2001.09496|quote=I proposed the H-index hoping it would be an objective measure of scientific achievement. By and large, I think this is believed to be the case. But I have now come to believe that it can also fail spectacularly and have severe unintended negative consequences. I can understand how the sorcerer’s apprentice must have felt. (p.5)}}</ref> have criticized them as particularly susceptible to [[Social:Gaming the system|gaming the system]].<ref name=":0">{{cite journal |last1=Peter A. |first1=Lawrence |title=The mismeasurement of science |journal=Current Biology |date=2007 |volume=17 |issue=15 |pages=R583–R585 |doi=10.1016/j.cub.2007.06.014 |pmid=17686424 |s2cid=30518724 |url=https://www.cell.com/current-biology/pdf/S0960-9822(07)01516-3.pdf}}</ref><ref name=":1">{{cite journal |last1=Şengör |first1=Celâl. AM |title=How scientometry is killing science |journal=GSA Today |date=2014 |volume=24 |issue=12 |pages=44–45 |doi=10.1130/GSATG226GW.1 |url=https://www.geosociety.org/gsatoday/archive/24/12/pdf/i1052-5173-24-12-44.pdf}}</ref><ref name=":2">{{cite journal |last1=Seppelt |first1=Ralf |title=The Art of Scientific Performance |journal=Trends in Ecology and Evolution |date=2018 |volume=11 |issue=33 |pages=805–809 |doi=10.1016/j.tree.2018.08.003 |url=https://doi.org/10.1016/j.tree.2018.08.003 
|pmid = 30270172|s2cid=52890068 }}</ref>

Work in bibliometrics has demonstrated multiple techniques for the manipulation of popular author-level metrics. The most used metric ''h''-index can be manipulated through self-citations,<ref name="10.1007/s11192-017-2330-1">{{cite journal|author=Gálvez RH|date=March 2017|title=Assessing author self-citation as a mechanism of relevant knowledge diffusion|journal=Scientometrics|volume=111|issue=3|pages=1801–1812|doi=10.1007/s11192-017-2330-1|s2cid=6863843}}</ref><ref>{{Cite journal|author=Christoph Bartneck & Servaas Kokkelmans|last2=Kokkelmans|year=2011|title=Detecting ''h''-index manipulation through self-citation analysis|journal=Scientometrics|volume=87|issue=1|pages=85–98|doi=10.1007/s11192-010-0306-5|pmc=3043246|pmid=21472020}}</ref><ref>{{Cite journal|author=Emilio Ferrara & Alfonso Romero|last2=Romero|year=2013|title=Scientific impact evaluation and the effect of self-citations: Mitigating the bias by discounting the ''h''-index|journal=Journal of the American Society for Information Science and Technology|volume=64|issue=11|pages=2332–39|arxiv=1202.3119|doi=10.1002/asi.22976|s2cid=12693511}}</ref> and even computer-generated nonsense documents can be used for that purpose, for example using [[Software:SCIgen|SCIgen]].<ref name="ike-antkare">{{cite report|url=http://rr.liglab.fr/research_report/RR-LIG-008.pdf|title=Ike Antkare one of the great stars in the scientific firmament|author=Labbé, Cyril|date=2010|publisher=Joseph Fourier University|work=Laboratoire d'Informatique de Grenoble RR-LIG-2008 (technical report)}}</ref> Metrics can also be manipulated by [[Coercive citation|coercive citation]], a practice in which an editor of a journal forces authors to add spurious citations to their own articles before the journal will agree to publish it.<ref name="science1">{{cite journal|last1=Wilhite|first1=A. W.|last2=Fong|first2=E. A.|year=2012|title=Coercive Citation in Academic Publishing|journal=Science|volume=335|issue=6068|pages=542–3|bibcode=2012Sci...335..542W|doi=10.1126/science.1212540|pmid=22301307|s2cid=30073305}}</ref><ref name="nature2">{{Cite journal|last=Noorden|first=Richard Van|date=February 6, 2020|title=Highly cited researcher banned from journal board for citation abuse|journal=Nature|volume=578|issue=7794|pages=200–201|doi=10.1038/d41586-020-00335-7|pmid=32047304|bibcode=2020Natur.578..200V|doi-access=free}}</ref> 

Additionally, if the ''h''-index is considered as a decision criterion for research funding agencies, the [[Game theory|game-theoretic solution]] to this competition implies [[Academic authorship#Growing number of authors per paper|increasing the average length of coauthors' lists]].<ref>{{cite journal|author1=Rustam Tagiew|author2=Dmitry I. Ignatov|year=2017|title=Behavior mining in h-index ranking game|url=http://ceur-ws.org/Vol-1968/paper6.pdf|journal=CEUR Workshop Proceedings|volume=1968|pages=52–61}}</ref> A study analyzing >120 million papers in the specific field of biology showed that the validity of citation-based measures is being compromised and their usefulness is lessening.<ref>{{cite journal |last1=Fire |first1=Michael |last2=Guestrin |first2=Carlos |title=Over-optimization of academic publishing metrics: observing Goodhart’s Law in action |journal=GigaScience |date=1 June 2019 |volume=8 |issue=6 |doi=10.1093/gigascience/giz053}}</ref> As predicted by [[Philosophy:Goodhart's law|Goodhart's law]], quantity of publications is not a good metric anymore as a result of shorter papers and longer author lists.

[[Biography:Leo Szilard|Leo Szilard]], the inventor of the [[Physics:Nuclear chain reaction|nuclear chain reaction]], also expressed criticism of the decision-making system for scientific funding in his book "The Voice of the Dolphins and Other Stories".<ref name="szilardbook">{{cite book |title=The Voice of the Dolphins and Other Stories |date=1961 |publisher=Simon and Schuster |location=New York}}</ref> Senator J. Lister Hill read excerpts of this criticism in a 1962 senate hearing on the slowing of government-funded [[Medicine:Cancer research|cancer research]].<ref>{{cite book |last1=Committee |first1=United States Congress Senate Appropriations |title=Labor-Health, Education, and Welfare Appropriations for 1962, Hearings Before the Subcommittee of ... , 87-1 on H.R. 7035 |date=1961 |pages=1498 |url=https://books.google.com/books?id=B7tgSd4ZDBsC&pg=PA1498 |language=en}}</ref> Szilard's work focuses on metrics slowing scientific progress, rather than on specific methods of gaming:
<blockquote>
''"As a matter of fact, I think it would be quite easy. You could set up a foundation, with an annual endowment of thirty million dollars. Research workers in need of funds could apply for grants, if they could mail out a convincing case. Have ten committees, each committee, each composed of twelve scientists, appointed to pass on these applications. Take the most active scientists out of the laboratory and make them members of these committees. And the very best men in the field should be appointed as chairman at salaries of fifty thousand dollars each. Also have about twenty prizes of one hundred thousand dollars each for the best scientific papers of the year. This is just about all you would have to do. Your lawyers could easily prepare a charter for the foundation. As a matter of fact, any of the National Science Foundation bills which were introduced in the Seventy-ninth and Eightieth Congress could perfectly well serve as a model."''

''"First of all, the best scientists would be removed from their laboratories and kept busy on committees passing on applications for funds. Secondly the scientific workers in need of funds would concentrate on problems which were considered promising and were pretty certain to lead to publishable results. For a few years there might be a great increase in scientific output; but by going after the obvious, pretty soon science would dry out. Science would become something like a parlor game. Somethings would be considered interesting, others not. There would be fashions. Those who followed the fashions would get grants. Those who wouldn’t would not, and pretty soon they would learn to follow the fashion, too."''<ref name="szilardbook"/>
</blockquote>

==See also==
*[[Academic age]]
*[[Philosophy:Goodhart's law|Goodhart's law]]
*[[Scientometrics]]

==References==
{{Reflist}}

==Further reading==
*{{cite book |isbn=978-3319000251 |url=https://books.google.com/books?id=8DK6BQAAQBAJ&q=author-level%20metrics&pg=PA181 |title=Opening Science: The Evolving Guide on How the Internet is Changing Research ...  |date=2013-12-16 |access-date=2015-08-16|last1 = Bartling|first1 = Sönke|last2 = Friesike|first2 = Sascha| publisher=Springer }}
*{{cite book |isbn=978-1107653603 |url=https://books.google.com/books?id=WnIhAwAAQBAJ&q=author-level%20metrics&pg=PA152 |title=The Handbook of Journal Publishing |author=Sally Morris |author2=Ed Barnas |author3=Douglas LaFrenier |author4=Margaret Reich |date=2013-02-21 | publisher=Cambridge University Press |access-date=2015-08-16}}
*{{cite book |isbn=978-3319097848 |url=https://books.google.com/books?id=3pY9BQAAQBAJ&q=author-level%20metrics&pg=PA267 |title=Incentives and Performance: Governance of Research Organizations |date= 7 November 2014|access-date=2015-08-16|last1 = Welpe|first1 = Isabell M.|last2 = Wollersheim|first2 = Jutta|last3 = Ringelhan|first3 = Stefanie|last4 = Osterloh|first4 = Margit| publisher=Springer }}
*{{cite book |isbn=978-3319103761 |url=https://books.google.com/books?id=oP05BQAAQBAJ&q=author-level%20metrics&pg=PA90 |title=Measuring Scholarly Impact: Methods and Practice  |date= 6 November 2014|access-date=2015-08-16|last1 = Ding|first1 = Ying|last2 = Rousseau|first2 = Ronald|last3 = Wolfram|first3 = Dietmar| publisher=Springer }}

{{Academic publishing}}

[[Category:Academic publishing]]
[[Category:Citation metrics]]
[[Category:Game theory]]

{{Sourceattribution|Author-level metrics}}