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Author credit-assignment schemas: A comparison and analysis

Jian Xu

Sun Yat-sen University

Ying Ding

Indiana University

Min Song

Yonsei University

Tamy Chambers

Indiana University

2

Author credit-assignment schemas: A comparison and analysis

Jian Xu1, Ying Ding2*, Min Song3, Tamy Chambers2

1 School of Information Management, Sun Yat-sen University, Guangzhou, China, 2 Department of Information and Library Science, Indiana University, Bloomington, Indiana, United States of America, 3 Department of Library and Information Science, Yonsei University, Seoul, Korea

* E-mail: dingying@indiana.edu

Abstract

Credit assignment to multiple authors of a publication is a challenging task, due to the

conventions followed within different areas of research. In this study we present a review of

different author credit-assignment schemas, which are designed mainly based on author rank

and the total number of coauthors on the publication. We implemented, tested, and classified

15 author credit-assignment schemas into three types: linear, curve, and “other” assignment

schemas. Further investigation and analysis revealed that most of the methods provide

reasonable credit-assignment results, even though the credit-assignment distribution

approaches are quite different among different types. The evaluation of each schema based on

the PubMed articles published in 2013 shows that there exist positive correlations among

different schemas, and that the similarity of credit-assignment distributions can be derived

from the similar design principles that stress the number of coauthors or the author rank, or

consider both. In the end, we provide a summary about the features of each credit-assignment

schema in order to facilitate the selection of the appropriate one, depending on the different

conditions required to meet diverse needs.

Keywords: author credit, credit-assignment schema, coauthor evaluation, scientific

colalboration

Introduction

Scientific collaboration is becoming vital for triggering innovations and breakthroughs.

As a result, most scientific papers are now multi-authored (Wuchty, Jones, & Uzzi, 2007),

which has intensified the discourse regarding the fair evaluation of coauthor contribution.

This issue is non-trivial, as scientific credit assignment is essential to the recruitment and

promotion of scientists, as well as to the determination of awards and honors (He, Ding, &

Yan, 2012).

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Despite this, assigning credit to multiple authors remains a problematic task, as practices

vary among different research domains, and there exists no universally accepted means for

sharing credit of multi-authored papers (Abbas, 2013). While most papers rank authors

according to their contribution (Hu, Rousseau, & Chen, 2010), the assignment of a

corresponding author is often an exception to this practice. Corresponding authors are

primarily senior advisors responsible for directing research teams, including setting schedules,

assigning research tasks, and guiding experiments. Although they are ultimately responsible

for the research, and arguably the most prominent members of the research teams, such

authors are usually listed in the last position on a coauthor list (Frances Scientist, 2011).

Additionally, it is becoming routine, especially in biomedical publications, to see a note that

the first two (or three, or more) authors have made equal contributions to the publication (Li

et al., 2013). This has given rise to the phenomenon of “equal first authors” (Birnholtz, 2006).

It is also not uncommon to find publications identifying more than one corresponding author,

or for authors to be presented in alphabetical order. Add to all of this the practice of “gift”

authorship (Leash, 1997), and it is clear that it has become increasingly more complex to

measure how much an individual author may have contributed to a multi-authored paper.

Since authors are ranked in decreasing order according to their contribution in most

publications (Hu et al., 2010, Wager, 2009), many credit-assignment schemas do not take

situations of equal first authors, equal corresponding authors, alphabetically ordered coauthor

rank, and “gift” authorship into account, to keep the allocating process practical and simple.

In cases when there is no explicit declaration in the paper to determine the extents of

contributions of individual authors of a paper, credit-assignment policy that assigns credit to

authors of the paper plays an important role. Although authorship credit is routinely allocated

either by issuing full publication credit repeatedly to all coauthors or by dividing one credit

equally among all coauthors (Gauffriau & Larsen, 2005), which cause equalizing and

inflationary counting bias (Hagen, 2008), many other more reasonable credit-assignment

schemas are proposed to allocate credit according to the number of coauthors, the rank of

coauthors, or both.

Author-credit allocation schemas have been researched and categorized by a number of

researchers, but there is little consensus among them. Abbas (2013) categorized schemas into

three types: proportional (or arithmetic), geometric, and fractional (or equal). Jian and Xiaoli

(2013) held that author-rank-based schemas can be classified into three main types—namely,

arithmetic, geometric, and harmonic. Liu and Fang (2012), investigating ways to quantify

coauthor contribution, divided schemas into four types—first-author counting, normal (or

standard) counting, fractional counting, and uneven counting (inverse of author rank,

proportional or arithmetic counting, geometric counting, etc.). Here, we have classified

current credit-assignment schemas into three types, according to the distribution of coauthor

credit of a publication. In the first type, linear credit-assignment schemas, the distribution of

coauthor credit per publication is displayed as a straight line. In the second type, curve

credit-assignment schemas, the distribution of coauthor credit per publication is displayed as a

curve. The third type, “other” credit-assignment schemas, does not obey either a linear or

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curve distribution. As part of this third type we also include hyper-authorship schemas, as the

concept of hyper-authorship has become common in many research fields and presents unique

challenges to credit-assignment schemas. Since we focused on credit-assignment methods

based on coauthor rank and number of coauthors, citation-based credit assignment methods

(e.g., Hirsch, 2010, Tol, 2011, Carbone, 2011, and Hu et al., 2010) were not included in this

paper.

In total, we investigated 15 current credit-assignment schemas and compared their

features, based on our classification of them as having either a linear, curve, or “other”

distribution type. We also summarized the features of these credit-assignment schemas and

compared them based on a PubMed 2013 dataset. Results show that most methods can

provide reasonable allocation of every coauthor’s credit.

The rest of the paper is organized as follows. Section 2 reviews current credit-assignment

schemas according to our defined categories. Section 3 describes the detailed calculation

methods and parameter configurations of each credit-assignment schema. Section 4 contains a

comparison and evaluation of the credit-assignment schemas based on a PubMed 2013 dataset.

Section 5 discusses various features of the credit-assignment schemas and concludes this

research.

Literature Review

We divided author-credit-assignment schemas into three general categories—linear,

curve, and “other”—according to their coauthor credit-distribution patterns. In addition,

although hyper-authorship assignment schemas are generally included as part of the “other”

category, they are described as an independent type, since the average number of coauthors

per paper keeps rising, and ordinary credit-assignment schemas cannot deal with this situation

effectively.

Table 1 identifies the credit-distribution features of each credit-assignment schema

discussed in the following subsections. Unique codes were assigned to each to substitute for

the original names and will be used throughout the rest of this paper for referring to the

schemas.

Linear Credit-Assignment Schemas Just as their name implies, linear credit-assignment schemas (summarized in Table 1)

have features that create a coauthor-credit distribution pattern that is a straight line. These

schemas can be further divided into two groups—equal credit-assignment schemas and

ordinary linear credit-assignment schemas.

Equal credit-assignment schemas are a special type, which allocate the same credit to all

coauthors of a publication, and are suitable for papers in which all authors contribute equally.

Historically, most studies that count publications or citations have used normal (or standard)

counting schemas to allocate full credit to all contributors (Bayer & Folger, 1966; Chubin,

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1973; Hargens & Hagstrom, 1967) (Table 1, Credit01). However, since the number of

multi-authored publications has soared in recent years (Kaufmann, Annis, & Griggs, 2010),

this schema has tended to inflate the number of publications per author. Lindsey (1980)

proposed a fractional counting procedure, which—although still providing an even allocation

of the credit among coauthors—divides the credit for each publication by the number of

coauthors (Table 1, Credit02). Lindsey used this schema to count productions and citations,

and held that until it becomes possible to assess the relative contribution of collaborators,

equal allocation of credit seems the best solution.

Although both normal counting and fractional counting credit-assignment schemas have

been used in bibliometric studies for many years, more sophisticated linear credit-assignment

solutions have been developed, because equal credit-assignment schemas do not take into

account coauthor rank. Van Hooydonk (1997) assumed that an author's location on the

coauthor list of a multi-authored publication was an indication of his/her relative credit. As

such, he proposed a proportional method that assigned credit according to the rank of

coauthors as a proxy for their contribution (Table 1, Credit03). He did, however, note that this

schema could not be applied to publications that list authors in alphabetical order. More

recently, Abbas (2010) presented a generalized linear-weight schema for assigning weights to

multiple author publications called the Arithmetic: Type-2 schema (Table 1, Credit04). Unlike

other linear credit-assignment schemas, this schema allows for flexible weight-assignment

based on changing the weight decrement/increment parameter. He also compared his

proposed schema with existing schemas, including equal, arithmetic (Abbas, 2011), geometric,

and harmonic (Hagen, 2008, Hagen, 2010) schemas, arguing that arithmetic (Abbas, 2011)

and equal weight-assignment schema could be treated as special cases of the proposed

Arithmetic Type-2 schema.

Given that linear credit-assignment schemas allocate credit to coauthors based mainly on

coauthor rank and number of coauthors of a publication, they are a natural fit for calculating

coauthor credit when rank corresponds to author contribution. Additionally, linear

credit-assignment schemas are usually simple to calculate, and can be easily incorporated into

an author performance index by multiplying the number of citations to a multi-authored

publication by the weights of the individual authors. However, the shortcomings of linear

credit schemas are also obvious. First, equal credit-assignment schemas tend to either inflate

overall credit or simply ignore the differences in contribution among coauthors. Second, with

the increase in the number of coauthors, the absolute slope value of an ordinary linear

credit-assignment schema distribution pattern will decrease, to ensure that the lowest-ranked

coauthor still obtains positive credit. The consequence of doing so leads to diminished

differences between the main contributors and other contributors of a publication.

Furthermore, because the decreasing absolute slope value corresponds to an increased number

of coauthors, an extraordinary phenomenon may occur where the credit allocated to

lower-ranked coauthors may increase, then decrease as the number of coauthors increases.

This is inconsistent with common intuition.

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Curve Credit-Assignment Schemas Curve credit-assignment schemas (summarized in Table 1) all have features that result in

a coauthor credit-distribution depicted as a curved line. Similar to some linear

credit-assignment schemas, curve credit-assignment schemas allocate more credit, in general,

to top-ranked authors than to those ranked lower on coauthor lists. However, in these schemas,

the difference in credit between adjacent-ranked authors declines.

Academic careers become increasingly dependent on bibliometric evaluation to measure

research productivity, quality, and influence. Egghe, Rousseau, and Van Hooydonk (2000)

however, noted that employing a credit-assignment schema is no longer a purely academic or

mathematical problem. They presented a geometric method to assign credit to either authors

or countries (Table 1, Credit05). After using a real-world example to compare and evaluate

different counting methods, they concluded that some anomalies could be avoided by using a

geometric average instead of an arithmetic average. Sekercioglu (2008) proposed that the

rth-ranked coauthor could be considered to have contributed 1/r as much as the first author

(Table 1, Credit06). In this way, coauthors’ contributions could be standardized to sum to one,

regardless of the number of authors or how they are ranked. Hagen (2008) identified that

routine authorship credit-allocation methods that either issue full publication credit to all

coauthors or divide one credit equally among all coauthors systematically benefit secondary

authors at the expense of primary authors. He therefore proposed a harmonic counting method

to allocate credit according to author rank and number of coauthors, which would provide

simultaneous source-level correction for equalizing and inflationary bias (Table 1, Credit07).

Hagen (2013) would later compare this harmonic method to other credit-assignment schemas

(Lindsey, 1980; Liu & Fang, 2012; Trueba & Guerrero, 2004), using three independent

empirical datasets to show that the harmonic credit method explains most of the variations

usually identified in the empirical data. More recently, Abbas (2013) presented a polynomial

weight-assignment schema (i.e., Polynomial Weights Type-I and Polynomial Weights Type-II)

for assigning credit to multiple authors in a nonlinear way (Table 1, Credit08). The advantage

of this schema over equal-weight and geometrical-weight schemas is that the polynomial

weight can be varied depending upon the weight-control parameter. For example, when the

polynomial weight-control parameter is x=1, equal weights are given to all coauthors. When

the polynomial weight-control parameter is x=2, the result is a geometric weighted schema.

For this reason, polynomial weight is called “generalized geometric weight.”

Curve credit-assignment schemas are similar to linear credit-assignment schemas in that

they are easy to calculate, and the basic input parameters are only related to the number of

coauthors and their ranks in a publication. In general, curve credit-assignment schemas are

more reasonable than linear credit-assignment schemas, as top-ranked coauthors receive a

larger part of the credit—consistent with their assumed contribution. Additionally,

lower-ranked coauthors receive more intuitively reasonable credit than that given by linear

credit-assignment schemas. Still, such schemas do have a weakness, in that they seldom

consider situations of equal coauthor contribution or corresponding coauthor credit, which

would require that all coauthors receive as much credit as the first author. Furthermore, this

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type of schema is difficult to use in hyper-authorship situations, as when the number of

coauthors is larger than normal, low-ranked coauthors would be assigned a credit value close

to zero.

“Other” Credit-Assignment Schemas There also exist credit-assignment schemas that do not easily fit into either a linear or

curve-type distribution. These schemas are more independent than the previous schemas and

are not easily classified; therefore we have chosen to identify them in the “other”

credit-assignment schemas group (summarized in Table 1). Typically these schemas focus

more on the first author or corresponding author than either the linear or curve-type schemas.

They create specific rules to increase the credit assigned to main contributors, which changes

the basic linear or curve shape of credit-allocation distribution.

Cole and Cole (1973) proposed a simple credit-assignment schema called “first-author

counting,” and contended that only the first author should receive credit for a multi-authored

publication (Table 1, Credit09). Although it is simple to calculate, this schema greatly

overemphasizes the contribution of first author, while ignoring the contributions of the

remaining authors. Lukovits and Vinkler (1995) addressed this with the Corrected

Contribution Scores (CCS) equation, which calculated the individual contribution score of

each coauthor and which proved to be in good agreement with the questionnaire result. Later,

Trueba and Guerreo (2004) presented a credit-assignment schema base on the relative rank of

an author on the coauthor list, and applied it to a large sample of scientific references drawn

from the INSPEC commercial database (Table 1, Credit11). They compared the credit values

obtained with other values derived from earlier total-author-counting and

first-author-counting schemas (Cole & Cole, 1973) to argue that their schema measured credit

more effectively than comparable ones. Zhang (2009) also proposed a quantitative

credit-assignment schema that calculates the coauthor weight coefficient (Table 1, Credit11).

In his schema, first authors and corresponding authors are each allocated full credit, and one

credit is distributed over the remaining authors. He then applied this credit-allocation schema

to calculate weighted citation value by multiplying regular citations and weight coefficients.

The weighted citation value remains the same for the first and corresponding authors, but

decreases linearly for authors lower on the coauthor list.

Abramo, D Angelo, and Rosati (2013) more recently defined a rule to allocate the weight

of the rth coauthor. Under this rule, 40% of the publication is attributed to the first author, 40%

is attributed to the corresponding author, and the remaining 20% is divided among the

remaining coauthors (Table 1, Credit13). Based on this rule, they defined two types of

individual average yearly productivity measures at the individual level: a gross one, based on

publication counts, called weighted fractional output (WFO), and a more sophisticated

measure, based on field-normalized citations, called weighted fractional impact (WFI). They

derived these weight values based on interviews with top Italian professors in the life sciences.

However, they also mentioned that their work is not precisely concerned with establishing the

most appropriate value assignment for coauthor contribution.

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Flexibility appears to be the major merit of this kind of credit-assignment schema. By

defining simple and flexible rules, these schemas are easily calculated, and can be applied in a

variety of practical situations, in addition to providing valuable references to coauthor

credit-assignment practices. The weak point of this type of credit-assignment schemas is their

reliance on arbitrarily defined values, which results in overall assignment distributions that

are not as disciplined as either the linear or curve credit-assignment schemas.

Hyper-Authorship Credit-Assignment Schemas As identified in early studies, the number of coauthors per publication has continued to

rise (Price, 1963; Smith, 1958; Ioannidis, 2008), as co-authorship has evolved into

mega-authorship or hyper-authorship (Cronin, 2001; Kretschmer & Rousseau, 2001) in many

domains. This is especially in biology, medicine, and high-energy physics, where Birnholtz

(2006) found that articles listing 80 to 200 coauthors were quite common. In 2006 alone,

more than 100 papers had more than 500 coauthors, and one physics paper had a record 2,512

coauthors (King, 2007). With research groups growing larger and research questions

becoming more complex (Lawrence, 2007), this trend is likely to continue. As a result,

credit-assignment schemas need to address this new concept of hyper-authorship.

The difference between hyper-authorship credit assignment and normal multi-authorship

credit assignment is the large number of coauthors to be listed in the byline of a paper or in

the cover letter. Due to the extraordinary number of coauthors in these publications, many

credit-assignment schemas may fail when assigning credit to individual authors. For example,

the normal (or standard) counting schema (i.e., where each of the N authors is given full

credit) greatly inflates the overall credit when dealing with hyper-authorship publications,

while fractional counting (i.e., where each of the N authors receives a score equal to 1/N)

schemas assign very little credit to every coauthor, which sharply decreases allocated

credit—especially for major contributors. Similar problems also exist in some linear, curve, or

“other” credit-assignment schemas. However, there are a few credit-assignment schemas

claimed to have the potential to deal with hyper-authorship publications.

Tscharntke, Hochberg, Rand, Resh, and Krauss (2007) presented a “sequence determines

credit” approach (SDC), which assumes that the sequence of authors should reflect the

declining importance of their contribution (Table 1, Credit14). Their schema suggested that

the first author should get full credit, the second author half, the third one-third credit, the

fourth a quarter credit, and so forth, up to the tenth author, after which all remaining authors

would receive 5% credit. Liu and Fang (2012) contended that their method was suitable for

papers with a high number of authors. Their schema, the Combined Credit Allocation method

(CCA), was used to modify both the h-index and g-index (Table 1, Credit15). In comparison

with the Correct Credit Distribution Model (Lukovits & Vinkler, 1995), the Harmonic

allocation method (Hagen, 2008), the arithmetic schema (Van Hooydonk, 1997), the

geometric schema ( Egghe, Rousseau, & Van Hooydonk, 2000), and the fractional counting

schema (Price, 1981), they concluded that the assigned credit resulting from the normalized

Combined Credit Allocation method was between those of the Harmonic allocation method

and the fractional counting schema.

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While all hyper-authorship credit-assignment schemas can also be classified into other

credit-assignment schema groups based on their credit-distribution features, we acknowledge

them as different in that they all provided—or at least claimed—possible solutions to the

hyper-authorship credit-assignment problem.

We summarize the credit-distribution features of different credit-assignment schemas

mentioned above in Table 1. To facilitate further analysis, unique codes are substituted for the

original names of the credit-assignment schemas.

Table 1: Codes and credit-distribution features of different coauthor credit-assignment

schemas

Type Code Original Name Credit Distribution Feature

Linear

Credit01 Total author counting, normal counting, standard counting

Creditr-Creditr+1=0

Credit02 Fractional counting (Lindsey, 1980) Creditr-Creditr+1 =0

Credit03 Proportional counting (Van Hooydonk, 1997), Arithmetic: Type-1 (Abbas, 2011)

Creditr-Creditr+1=2/(N(N+1))

Credit04 Arithmetic: Type-2 (Abbas, 2010) Creditr-Creditr+1=α

Curve

Credit05 Geometric counting (Egghe et al., 2000) Creditr/Creditr+1=2

Credit06 (Sekercioglu, 2008) Creditr/Creditr+1=(r+1)/r

Credit07 Harmonic counting method (Hagen, 2008) Creditr/Creditr+1=(r+1)/r

Credit08 Polynomial Weights: Type-I (Abbas, 2013) Creditr/Creditr+1=1/x

Other

Credit09 First-author counting (Cole and Cole, 1973) Credit1=1, Others=0

Credit10 Corrected Contribution Scores, CCS (Lukovits and Vinkler, 1995)

First author is given extra credit. Parameter H adjusts the credit distribution among different authors;

Credit11 (Trueba and Guerrero, 2004) Extra credit is shared among the first, second, and last authors

Credit12 (Zhang, 2009)

First and last author are given 1 credit, while others obey Creditr-Creditr+1=2/((N+1)(N-2))

Credit13 (Abramo et al., 2013) First and last author are given major part of credit, while others divide the remaining credit equally.

Credit14 Sequence determines credit method, SDC (Tscharntke et al., 2007)

Curve type when r10; hyper-authorship assignment schema.

Credit15 Combined credit allocation method, CCA (Liu and Fang, 2012)

Extra credit shared between the first and last authors; parameter k adjusts the credit distribution among different authors; hyper-authorship assignment schema.

Note: N is number of coauthors listed on a publication and r is the coauthor rank on a publication.

From Table 1 we can see that linear credit-assignment schemas share a remarkable

feature: The difference between the credits allocated to authors of adjacent ranks is always a

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constant value. Curve-type credit methods also keep the ratio of credits between two adjacent

authors as a constant value, or an author-rank-dependent value.

The “other” type is not as disciplined as the linear or the curve type. In some methods of

this type, author ranks are divided into several parts, and author credits are calculated

separately using different formulas.

Since the two kinds of hyper-authorship assignment schemas (Credit14, Credit15) belong

to the “other” type, we did not list them in a separate hyper-authorship class. Instead, a

“hyper-authorship assignment schema” tag is added in their feature column.

Methodology

In this section, we discuss and provide descriptions of all major credit-assignment

schemas. Our analysis follows our classification schema, and is presented in the order

identified in Table 1; it uses the codes noted there for referring to the schemas.

Linear Credit-Assignment Schemas Linear credit-assignment schemas include equal credit-assignment schemas (normal

counting and fractional counting), the proportional schema, and the Arithmetic Type-2

schema.

Equal credit-assignment schemas (Credit01 and Credit02). These schemas assign the

same credit to all coauthors, and exist in two variations—normal counting and fractional

counting. The first, normal counting (Credit01), is defined as a schema in which each

coauthor receives full credit. If we let N be the number of coauthors of a publication, and r be

the rank of an author, then the schema can be described by the formula

01 1, 1 (1)rCredit r N=

where Credit01r is the normal counting credit value of the rth-ranked author. The second

equal credit-assignment schema (Credit02) is fractional counting. According to this schema,

full credit is distributed as an equal fraction to each coauthor (Lindsey, 1980). If we let N be

the number of coauthors of a publication, and r be the author rank, then the schema can be

described by the formula

102 , 1 (2)rCredit r N

N=

where Credit02r is the fractional counting credit value of the rth-ranked author. Given that

each of the N authors receives a score equal to 1/N, this counting method is sometimes called

an adjusted counting (Price, 1981) method.

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Proportional credit-assignment schemas (Credit03). Since the equal credit-assignment

schemas do not take coauthor rank into account, Van Hooydonk (1997) proposed a

proportional schema to accredit coauthors. If we let N be the number of coauthors of a

publication, and r be the rank of an author, then the schema can be described by the formula

2 (1 )103 , 1 r N (3)r

r

NCreditN

-=

where Credit03r is the credit value of the rth-ranked author. In this schema, coauthors are

assigned different credit value according to their coauthor rank. Top-ranked authors always

receive more credit than the other coauthors. Given an N value, the credit values assigned to

the authors form an arithmetic sequence.

Arithmetic: Type-2 schemas (Credit04). Abbas (2010) presented a generalized linear

credit schema—the Arithmetic Type-2 schema. In this schema, credits are assigned in a

linearly decreasing/increasing fashion depending upon the credit

decrement/increment-parameter. If we let N be the number of coauthors of a publication, and

r be the rank of an author, then the schema can be described in the formula

1 2 104 , 1 r N, 0 1 (4)

2r

N rCredit

N

- =

where Credit04r is the credit value of rth-ranked author. To make sure that the credit is a

positive number, the following condition must be satisfied:

2, N 2 (5)

( 1)N N

-

In this formula, the α, 0 ≤α≤ 1, is referred to as the credit decrement parameter,

because of its use in decrementing the credit from the first to last author. The lower the α

value, the lower the absolute value of the slope of the credit-assignment distribution line, and

vice versa. When the α is set to zero, this schema is equal to the Credit02 schema. This

schema, however, is more flexible than other linear credit-assignment schemas because of the

option to vary the weights assigned from first through last author by simply changing the

credit decrement parameter α.

Curve Credit-Assignment Schemas The significant feature of this type of schema is the fact that the credit difference

between adjacently ranked authors is not constant, but rather is a ratio. Curve

credit-assignment schemas include the geometric counting schema, the Sekercioglu schema,

the harmonic schema, and the Polynomial Weights Type-I schema.

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Geometric counting schema (Credit05). Egghe et al. (2000) first presented the

geometric method for assigning publication credit to either authors or countries. If we let N be

the number of coauthors of a publication, and r be the rank of an author, then the schema can

be described by the formula

205 , 1 r (6)

2 1

N r

r NCredit N

-

= -

where Credit05r is the credit value assigned to the rth-ranked author. This counting method is

normalized, and as a result the sum of all relative author credit values is 1. Before

normalizing, the score for the author at rank r was 2N-r. Note that in this schema, the ratio of

credits allocated to two adjacent authors is the constant number two. An individual author

always gets twice the credit as the author who follows him on the coauthor list.

The Sekercioglu schema (Credit06). Sekercioglu (2008) proposed that the rth-ranked

coauthor should be considered to have contributed 1/r as much as the first author to the

publication. If we let N be the number of coauthors of a publication, and r be the rank of an

author, then credit assigned to the rth author is defined as

106 , 1 r (7)rCredit N

r=

where Credit06r is the credit value of rth-ranked author. Coauthor credit can also be

normalized to sum to one, regardless of the number of authors or how those authors are

ranked. As such, the ratio of credits between the rth author and the r+1th author is: 1r

r

.

Harmonic counting method (Credit07). Hagen (2008) proposed that the harmonic

counting method, which assigns credit according to coauthor rank and number of coauthors,

could provide simultaneous source-level correction for both inflationary and equalizing biases.

If we let N be the number of coauthors of a publication, and r be the rank of an author, then

this method can be described by the formula

1/07 , 1 (8)

[1 1/ 2 1/ ]r

rCredit r N

N=

where Credit07r is the credit value of the rth-ranked author. Similar to the Credit06 schema,

the ratio of credits between the rth author and the r+1th author in this schema is also 1r

r

.

In fact, the harmonic counting method can be seen as a formula deformation of the Credit06

method.

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Polynomial Weights: Type-1 (Credit08). Abbas (2013) defined a weight-assignment

schema called Polynomial Weights Type-I. In this schema, if we let N be the number of

coauthors of a publication, r be the rank of an author, and x≤1 be a control parameter, then

this method can be described by the formula

1

1

1

1 for N=1

08 (9) for N>1,1 N

r

rN i

i

xCredit ar

x

-

-

=

ìï

= ïå

where Credit08ar is the credit value of the rth-ranked author. According to this formula, the

ratio of credits between the rth author and the r+1th author is 1/x. This means the ratio

depends on the x variable. The greater the value of x, the lower the ratio of credit between

adjacently ranked coauthors. When x=1, polynomial weights produce the same result as the

equal credit-assignment schemas. When x>1, the polynomial weight is called a Polynomial

Weights of Type II. In those cases, if we let x≥1, N be the number of coauthors of a

publication, and r be the rank of an author, then this method can be described by the formula

1

1

1 for N=1

08 (10) for N>1,1 N

N r

rN i

i

xCredit br

x

-

-

=

ìï

= ïå

where Credit08br is the credit value of rth-ranked author.

Other Credit-Assignment Schemas Different from either linear or curve credit-assignment schemas, the schemas in this

category do not obey disciplined line or curve distributions. These schemas assume main

contributors to a publication are the first, second, and corresponding authors, and that more

credit should be assigned to these authors despite their coauthor ranks. Types of

credit-assignment schemas in this category include the first-author counting schema, the CCS

schema, The Trueba and Guerrero schema, the Zhang schema, and the Abramo et al. schema.

First-author counting (Credit09). Cole and Cole (1973) proposed a schema in which

the first author receives full credit for a multi-authored publication, while all other coauthors

receive no credit. If we let N be the number of coauthors of a publication, and r be the rank of

an author, then this method can be described in the formula

1 for r=109 (11)

0 for 1 NrCredit

r

ì=

where Credit09r is the credit value of the rth-ranked author. The merit of this schema is that

the calculation process is very simple; however, it also overemphasizes the contribution of the

first author while ignoring the contributions of all other coauthors.

14

Corrected Contribution Scores (CCS) (Credit10). Lukovits and Vinkler (1995)

developed the Corrected Contribution Scores (CCS) to calculate the individual contribution

score of coauthors listed on multi-authored papers. The CCS is primarily based on

calculations of the Minimum Contribution Score (ICS) and the Maximum Contribution Score

(ACS). The Minimum Contribution Score (ICS) for the first authors of papers with any

number of coauthors is equal to the share calculated by the linear fractional authorship model

(i.e., 0.50; 0.33; 0.25; 0.20; 0.16 for two, three, four, five, and six-authored papers,

respectively). The ICS value for all other coauthors is 0.1. The Maximum Contribution Score

(ACS) of any coauthor, except for the first author, is equal to the share calculated by the linear

fractional-authorship model. The first author ACS score however, is assumed to be unity. The

Uncorrected Mean Contribution Score (UMS) value for the first author (UMS(1)) and

remaining coauthors (UMS(k)) can be calculated as an arithmetic mean of the ICS and ACS.

If we let N be the number of coauthors of a publication, and r be the rank of an author, then

according to the CCS, coauthor credit can be described by the formula

1

1 for r=1

210 (12)

for 1 N2

1 1 1 1 100where F= [ + + ] and T=

2

r

N

i

N

NFCredit

r Tr

rFT

N

N T i H=

ìïï

= ï

ï

-å

where Credit10r is the credit value of the rth-ranked author and the tuning parameter H is the

percent value of their contribution threshold.

The Trueba and Guerrero schema (Credit11). Trueba and Guerrero (2004) presented

a schema to credit authorship according to relative author rank on a coauthored publication. If

we let N be the number of coauthors of a publication, and r be the rank of an author, then this

schema can be described by the formula

1

2

3

2 1 2(1-f)+c f for r=1

( 1) 3

2 2(1-f)+c f for r=2

( 1) 311 (13)

2 2(1-f)+c f for r=N

( 1) 3

2 2 2(1-f) for 3 r N-1

( 1) 3

r

N

N N

NCredit

N

N N

N r

N N

ì ï

ïï

ï ï=

ï ï ï

- ï ï

where Credit11r is the credit value of the rth-ranked author. Here the tuning parameter f

determines the proportion of extra credit to be shared among the first, second, and last authors,

15

according to the coefficients c1 + c2 + c3 = 1 and c1≥ c2≥ c3. After some trials, Trueba

and Guerrero found that f=1/3, c1=0.6, c2=c3=0.2 gave satisfactory test results.

The Zhang schema (Credit12). Zhang (2009) proposed a quantitative schema to

calculate coauthor weight coefficients. Considering a paper of five authors, with the last being

the corresponding author, the weight coefficient for the first and corresponding authors is 1.

Contributions of the second, third, and fourth authors are proportional to 4, 3, and 2; hence,

the coefficients are 4/9, 3/9 and 2/9, respectively, where 9=4+3+2. If we let N be the number

of coauthors of a publication, and r be the rank of an author, then this schema can be

described by the formula

1 for r=1 or r=N

12 (14)2( 1) for 2 N-1, N 4

( 1)( 2)rCredit N r r

N N

ìï

= - ï -

where Credit12r is the credit value of the rth-ranked author. There exists a special case when

Credit122=0.7 and N=3, based on the extrapolation of Credit122 when N = 4, in which, by

this definition, the sum of credit for the authors who are neither first nor corresponding is 1.

The Abramo et al. schema (Credit13). Abramo et al. (2013) defined the following

credit-assignment schema and combined it with other factors, such as citations received by

the publication and the number of work years of each researcher, to evaluate the average

yearly researcher productivity. If we let N be the number of coauthors of a publication, and r

be the rank of an author, then this schema can be described by the formula

1 for N=1

0.5 for N=2

13 (15)0.4 for r=1 or r=N, N>2

0.2 for 2 N-1, N>2

2

rCredit

rN

ìïïï

= ïï ï -

where Credit13r is the credit value of the rth-ranked author. These credit values are assigned

based on the results of interviews with top Italian professors in the life sciences. The values,

however, could be changed to suit different research practices and different national contexts.

Hyper-Authorship Credit-Assignment Schemas The two schemas that offer a solution to hyper-authorship credit assignment include the

sequence-determines-credit (SDC) schema and the combined credit allocation (CCA) schema.

Sequence-determines-credit (SDC) schema (Credit14). Tscharntke et al. (2007)

created the sequence-determines-credit approach (SDC) to assign credit based on coauthor

sequence. If we let N be the number of coauthors of a publication, and r be the rank of an

author, then this schema can be described by the formula

16

1 for r 10

14 (16)

0.05 for 10rCredit r

r

ìï

= ï

where Credit14r is the credit value of the rth-ranked author. Given this formula it is noticeable

that this method is equal to the Credit06 schema when r10. Although the sum of credits

assigned to hyper-authors is bigger than 1, it is a feasible choice, as top-ranked authors are

assigned credit based on a declining curve, while lower-ranked authors are assigned relatively

reasonable credit, based on a straight line.

Combined credit allocation (CCA) schema (Credit15). Liu and Fang (2012) proposed

a credit-assignment schema to identify coauthor contribution. First the order of coauthors

must be rearranged to allow the corresponding author to tie for the first rank. Then, if we let N

be the number of coauthors of a publication, and r be the rank of an author, the normalized

credit-assignment schema can be described by the formula

Credit15r=

N

-1

k r-(1-

1

k)

i=1

N1st-rankåN

1st-rank

N-

1

k i-(1-

1

k)

i=1

N

å when crediting first author and corresponding author(s)

N-

1

k r-(1-

1

k)

N-

1

k i-(1-

1

k)

i=1

N

å when crediting other author(s)

ì

ïïïï

ïïïï

(17)

where Credit15r is the credit value of the rth-ranked author. The CCA has an additional

parameter k to adjust the credit distribution among different authors. A higher k enlarges the

credit allocation gaps between authors in a manner that favors the authors ranked near the

start of a coauthor rank, and vice versa. Before normalization, when k=1 is the fractional

counting (Credit02), then Creditr = 1/N; if k=∞, then Creditr = 1/r, whose normalized form

is a harmonic counting method (Credit07); When k is a finite natural number greater than 1,

then the credit-assignment method result is between those of these two methods. CCA

successfully avoids the defect in arithmetic counting schemas, where the first-author credit

decreases rapidly, and the last-author credit initially increases and thereafter decreases slowly

when the author number increases. The schema also avoids the defect of nearly unchanged

credit assignment and having the first few authors receive most of the credit in geometric

counting, when the number of authors increases.

17

PubMed Evaluation

To further analyze the difference between these 15 schemas, we calculated

coauthor credit based on the PubMed articles published in 2013 which has 406,203

articles and 2,084,921 distinct authors. After excluding single-authored papers, the

final number of articles decreases to 362,052, with 2,047,236 unique authors. All

author credits are calculated based on 15 different credit-assignment schemas. Taking

Credit09 as the baseline method, the top 100 ranked author list which ends up with

111 authors due to the reason that some authors share the same rank are generated (see

Appendix A).

Comparison of Linear Credit-Assignment Schemas By definition, linear credit-assignment schemas have straight-line distributions. This is

exemplified in Figure 1, which shows the distribution for each of the four linear

credit-assignment schemas using a paper with five coauthors.

Figure 1: Linear credit-assignment schema (Credit01, Credit02, Credit03, and Credit04)

distributions for a paper with five coauthors

All linear credit-assignment schemas have distributions that are equal or form an

arithmetic progression. The difference between the distributions yielded by these schemas is

most noticeable in their slope. Credit01 at the top of Figure 1 is a horizontal line because it

assigns each coauthor full credit, which inflates the total amount of credit. Credit02 is also a

18

horizontal line, as it assigns each coauthor an equal portion of the credit (in this case 0.2); it

can be regarded as the normalized transformation of Credit01. Given the proportional nature

of both Credit03 and Credit04, it is appropriate to see in Figure 1 their similar decreasing

slope. Given the visual analysis presented in Figure 1, it could be deduced that an increase in

number of coauthors would cause linear credit-assignment schemas to either inflate the total

credit, or decrease the absolute value of the slope, to allow the lowest-ranked author to retain

positive credit, at the cost of reducing the difference between primary and secondary

contributors.

Comparison of Curve Credit-Assignment Schemas By definition, curve credit-assignment schemas have curved-line distributions, which are

usually downward-sloping. This is exemplified in Figure 2, which shows the distribution for

each of the four curve credit-assignment schemas using a paper with five coauthors.

Figure 2: Curve credit-assignment schemas (Credit05, Credit06, Credit07, Credit08) for a paper with five coauthors (Note: The credits of authors under Credit08 correspond to the value of x=0.5,

which is used in the analysis of (Abbas, 2013)’s study.)

Given the depiction in Figure 2, curve credit-assignment schemas appear more intuitively

reasonable than linear credit-assignment schemas, as the difference between lower-ranked

coauthors is small while major coauthors receive most of credit. The curve of Credit06 is

greater than those of other schemas because its definition does not take the normalization

process into account. Credit05 and Credit08 coincide because parameter x of Credit08 is set to

0.5. By using this setting, Credit08 is exactly the transformation of Credit05, while they

19

remain different in definition. As a result, if x in the Credit08 schema is set to something other

than 0.5, the curves of these two schemas would not coincide.

Comparison of “Other” Credit-Assignment Schemas “Other” credit-assignment schemas are a collection of different credit-assignment

schemas that assign credit to authors based on the needs of differently ranked coauthors. In

Figure 3, the distributions of five “other” assignment schemas are displayed, characterizing a

paper with five coauthors.

Figure 3: Other credit-assignment schemas (Credit09, Credit10, Credit11, Credit12, and Credit13) for a paper with five coauthors (Note: The credits of authors under Credit10 correspond to a value of H=10, which is used in analysis of (Lukovits and Vinkler, 1995); the credits of authors under Credit11

correspond to a value of f=1/3 ,c1=0.6, c2=0.2, c3=0.2, used in analysis of (Trueba and Guerrero, 2004)).

As depicted in Figure 3, Credit09 presents a unique distribution, which is explained by

the fact that it assigns full credit to the first author and nothing to the remaining coauthors.

The distributions of Credit11, Credit12, and Credit13 all descend as author rank increases, but

go up for the lowest-ranked author because they all assign additional credit to corresponding

authors. The distribution of Credit12 is higher than the others since it is not normalized.

Although the distribution of Credit10 looks like a curve-type distribution, it is classified as

“other” because it requires two different formulas to calculate the credits of first and

subsequent authors.

20

Comparison of Hyper-Authorship Credit-Assignment Schemas Hyper-authorship is quite common in the biomedical field. As such, our Pubmed dataset

contains a good sampling of these types of publications. Table 2 shows the count of

hyper-authorship papers in the 2013 PubMed article dataset, delineated by the number of

authors on the paper.

Table 2: Counts of hyper-authorship papers in the 2013 PubMed dataset

Number of coauthors ≥10 ≥30 ≥50 ≥100 ≥200 ≥500 ≥1000

Number of papers

42350 888 231 74 42 20 9

Note: Total number of papers is 362,052.

To analyze the distribution character of the two hyper-authorship credit-assignment

schemas, we used a paper with 100 coauthors. Additionally, a representative schema

(Credit04, Credit07, and Credit11) was selected from each type to highlight the comparison

and serve as a combined baseline schema.

Figure 4: Comparison of (a) two hyper-authorship credit-assignment schemas (Credit14, Credit15) and (b) typical linear, curve, other schemas (Credit04, Credit07 and Credit11) for a paper with 100 coauthors. (Note: Credits of authors under Credit11 correspond to parameter values of f=1/3, c1=0.6, c2=0.2, and c3=0.2, used in analysis of (Trueba and Guerrero, 2004); credits of authors under

Credit15 correspond to the parameter value of k=3, used in analysis of (Liu and Fang, 2012). Figure 4a is an overall figure of credit distribution under 5 schemas. Figure 4b shows partial distributions, which cover author

rank from 20 to 90, to illustrate details of every schema in the middle part of the credit distribution.)

From Figure 4, it is clear that the credit distribution of Credit14 drops sharply when

author rank increases from 1 to 10, after which the curve becomes a horizontal line with a

constant value of 0.05. Conversely, Credit15 is displayed as a curve that slowly decreases and

coincides with Credit11 in the middle and end of its distribution.

Compared to other methods, the advantage of Credit15 is its parameter k, which can

adjust the credit assignment ratio between authors, and takes the designation of a

corresponding author into account. Although Liu and Fang (2012) claim that their method is

21

suitable for papers having a wide range of numbers of coauthor, it seems in practice there is

no remarkable difference between the Credit15 schema and other typical schemas. In general,

Credit14 may be a more suitable assignment schema for hyper-authorship, even though the

total credit distribution is larger than 1. Credit14 employs a combination of different

assignment schemas (Credit06 when r10),

which correspond to the different credit-assignment needs of different distribution sectors,

which is more sensitive in hyper-authorship papers.

Correlation and PCA Analysis among Credit-Assignment Schemas Taking Credit09 as the baseline method, a Spearman correlation (Spearman, 1904)

analysis was conducted for each credit schema, using the top 100 ranked authors from the

2013 PubMed article dataset. The results show that all schemas are highly correlated, at a

confidence level of 0.01 or 0.05.

Figure 5: A Corrgram (Friendly, 2002) of Spearman’s rank correlation coefficient analysis among all schemas based on top 100 ranked authors order by Credit09. (Note: Variables were ordered by PCA. Gray intensity increases uniformly as correlation value increases. In the lower triangle of Figure 5, correlations are shown by intensity of shading; in the upper triangle: by pie-chart symbols.

22

The parameter values for the different schemas are: x=0.5 in Credit08, H=10 in Credit10, f=1/3, c1=0.6, c2=0.2, and c3=0.2 in Credit11, and k=3 in Credit15.)

As shown in Figure 5, Credit06, Credit14, and Credit12 achieve the highest

Spearman-rank correlation coefficient (r>=0.93, P

23

Table 3: Spearman correlation analysis based on top 100 ranked authors order by

Credit01, Credit02 and Credit09 respectively.

Type Code Order by Credit01 Order by Credit02 Order by Credit09

Linear

Credit01 1.000 0.554 0.883

Credit02 0.482 1.000 0.511

Credit03 0.347 0.510 0.588

Credit04 0.392 0.430 0.518

Curve

Credit05 0.289 0.429 0.879

Credit06 0.371 0.457 0.953

Credit07 0.339 0.479 0.754

Credit08 0.289 0.429 0.879

Other

Credit09 0.126 0.060 1.000

Credit10 0.349 0.433 0.676

Credit11 0.400 0.761 0.737

Credit12 0.507 0.673 0.927

Credit13 0.414 0.698 0.877

Credit14 0.368 0.459 0.953

Credit15 0.423 0.817 0.653

In order to further understand the correlation between these credit schemas, the same

rank counts in different segments are listed in Table 4. Most of the schemas share similar

authors in segment ranks 1-18; after that, the number of similar authors between Credit09 and

other schemas decreases as author rank increases. This indicates that regularly top-listed

authors (e.g., the top 18 authors) have a better chance of getting similar value in all credit

schemas. Besides this difference, the increasing number of tied listing situations has an

influence on the count results. However, the most correlated schemas (such as Credit06 and

Credit14) get a higher count score than most of the other schemas in each segment of Table 4

and Table 5, which is consistent with the analysis results of Figure 5.

Table 4: Segmented counts of top-100-ranked authors based on Credit09

Credit 09 Rank 1-18

(RecNum:18)

Rank 19-40

(RecNum:22)

Rank 41-72

(RecNum:32)

Rank 73-111

(RecNum:39)

Credit01 6 (33%) 0 (0%) 2 (6%) 0 (0%)

Credit02 6 (33%) 5 (23%) 6 (19%) 9 (23%)

Credit03 9 (50%) 7 (32%) 7 (22%) 5 (13%)

Credit04 9 (50%) 3 (14%) 5 (16%) 5 (13%)

Credit05 12 (67%) 11 (50%) 14 (44%) 12 (31%)

Credit06 14 (78%) 12 (55%) 29 (91%) 9 (23%)

Credit07 11 (61%) 7 (32%) 7 (22%) 11 (28%)

Credit08 12 (67%) 11 (50%) 14 (44%) 12 (31%)

Credit10 11 (61%) 6 (27%) 8 (25%) 7 (18%)

Credit11 11 (61%) 9 (41%) 9 (28%) 11 (28%)

Credit12 8 (44%) 2 (9%) 1 (3%) 0 (0%)

24

Credit13 9 (50%) 4 (18%) 3 (9%) 0 (0%)

Credit14 14 (78%) 12 (55%) 29 (91%) 9 (23%)

Credit15 10 (56%) 5 (23%) 5 (16%) 4 (10%)

Note: The segments are not separated evenly because tied ranking cases are not uncommon in schema ranking lists.

Table 5: Segmented cumulative counts of top-100-ranked authors based on Credit09

Credit 09 Rank 1-18

(RecNum:18)

Rank 1-40

(RecNum:40)

Rank 1-72

(RecNum:72)

Rank 1-111

(RecNum:111)

Credit01 6 (33%) 9 (23%) 19 (26%) 28 (25%)

Credit02 6 (33%) 14 (35%) 28 (39%) 46 (41%)

Credit03 9 (50%) 23 (58%) 42 (58%) 66 (59%)

Credit04 9 (50%) 20 (50%) 42 (58%) 62 (56%)

Credit05 12 (67%) 32 (80%) 56 (78%) 82 (74%)

Credit06 14 (78%) 30 (75%) 72 (10%) 82 (74%)

Credit07 11 (61%) 26 (65%) 52 (72%) 73 (66%)

Credit08 12 (67%) 32 (80%) 56 (78%) 82 (74%)

Credit10 11 (61%) 26 (65%) 49 (68%) 75 (68%)

Credit11 11 (61%) 24 (60%) 41 (57%) 66 (59%)

Credit12 8 (44%) 20 (50%) 37 (51%) 46 (41%)

Credit13 9 (50%) 18 (45%) 31 (43%) 47 (42%)

Credit14 14 (78%) 30 (75%) 72 (100%) 82 (74%)

Credit15 10 (56%) 16 (40%) 35 (49%) 52 (47%)

Note: The segments are not separated evenly because tied ranking cases are not uncommon in schema ranking lists.

Discussion and Conclusion

Current author credit-assignment schemas routinely rely on two methods—total author

counting, where full authorship credit is issued repeatedly to all coauthors; and fractional

counting, where one credit is divided equally among all coauthors. However, total counting

tends to cause inflationary bias, while fractional counting can result in equalizing bias (Egghe

et al., 2000; Gauffriau & Larsen, 2005). Nonetheless, there are other options to improve both

the fairness and accuracy of the credit assignment process. Different credit-assignment

schemas for coauthors, which were mainly based on author rank and number of coauthors in a

publication, were reviewed. We classified each schema as either linear, curve, or other,

depending on their distributions. Our results show that most credit-assignment schemas obey

basic principles, and can give a reasonable credit value to every coauthor, although the credit

assignment distribution can vary quite a lot between linear, curve, and “other” assignment

schemas.

25

The evaluation of each schema based on the PubMed articles published in 2013 shows

that there exist positive correlations between different schemas, and that the similarity of

credit-assignment distributions can be derived from the similar design principles that stress

the number of coauthors or the author rank, or consider both. Table 6 summarizes the features

of each credit-assignment schema in order to facilitate the selection of the appropriate one,

depending on the different conditions required to meet diverse needs. For example, if the first

author and corresponding author factors need to be emphasized under a certain condition,

then all the linear and curve type credit-assignment schemas should not be applied since they

do not take these two factors into account; if equalizing and inflationary counting bias needs

to be avoided, then Credit01, Credit02, Credit06, Credit12, and Credit 14 should be excluded;

if you want to set up the credit allocation gaps among coauthors, then Credit04, Credit08 and

Credit 15 should be the best candidates.

Table 6: Features of different credit-assignment schemas

Type Code CR CN FA CA In Eq Parameter Feature

Linear

Credit01 N N N N Y Y None

Credit02 N Y N N N Y None

Credit03 Y Y N N N N None

Credit04 Y Y N N N N Parameter α controls the slope of the distribution line

Curve

Credit05 Y Y N N N N None

Credit06 Y N N N Y N None

Credit07 Y Y N N N N None

Credit08 Y Y N N N N Parameter x control the ratio of credits between adjacent-ranked coauthors

Other

Credit09 N N Y N N N None

Credit10 Y Y Y N N N Parameter H is the percentage value of their contribution threshold

Credit11 Y Y Y Y N N Parameter f determines the proportion of extra credit to be shared among the first, second, and last authors

Credit12 Y Y Y Y Y N None

Credit13 N Y Y Y N N None

Credit14 Y N N N Y N None

Credit15 Y Y Y Y N N Parameter k adjusts credit allocation gaps among coauthors

Note: CR, CN, FA, and CA stand for the requirement for information about coauthor ranks, number of coauthors, first author, and corresponding author, respectively. Eq and In represent equalizing and inflationary counting bias. Value “Y” in column CR and CN means the credit schema needs corresponding information as input. Value “Y” in column FA or CA means the credit schema take first author or corresponding author into account. Value “Y” in column Eq or In means credit schema will cause certain kind of counting bias. Value “N” describes the opposite condition in each case.

26

Author credit assignment is a complicated issue. In our future work, we want to focus on

how to identify and measure the social and disciplinary differences about the coauthorship to

better understand the credit allocation among coauthors. For instance, whether there exist

significant differences on author’s position within or across disciplines and specialties;

whether the corresponding author’s position and coauthors in the alphabetical order link to

disciplinary practices; whether there is a correlation between the alphabetical order or the

position of corresponding author and the type of document; and whether there exists an

association between the position of author in the coauthor list and his/her seniority. From our

initial experiment on PubMed dataset in the latest 20 years, the mean positions of the top 20

authors ranked by Credit09 in their articles showed overall increasing trends (see Appendix

B). The increasing average number of coauthors of articles, and the status of the top

20 ranked authors changing from being the first authors to being the corresponding

authors could be the hidden reasons. The more detailed analysis will be carried on in

our future research.

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29

Appendix A: Credits and Ranks of top 100 ranked authors order by Credit09

Author Code Credit

09 Rank

09 Credit

01 Rank

01 Credit

02 Rank

02 Credit

03 Rank

03 Credit

04 Rank

04 Credit

05 Rank

05 Credit

06 Rank

06 Credit

07 Rank

07 Credit

08 Rank

08 Credit

10 Rank

10 Credit

11 Rank

11 Credit

12 Rank

12 Credit

13 Rank

13 Credit

14 Rank

14 Credit

15 Rank

15

A001 20 1 35 1 6.28 9 9.42 5 8.55 5 13.45 1 26.67 1 11.17 2 13.45 1 10.46 3 9.68 2 26.45 1 9.23 2 26.67 1 8.15 3

A002 20 1 21 6 7.00 4 10.33 2 10.33 3 11.71 2 20.50 2 11.18 1 11.71 2 11.52 1 9.47 3 20.70 5 8.20 6 20.50 2 7.95 6

A003 17 3 17 15 6.93 7 9.63 3 10.40 2 10.52 3 17.00 4 10.15 4 10.52 3 10.62 2 8.62 5 17.00 8 7.90 7 17.00 4 8.09 5

A004 16 4 18 11 7.25 3 9.62 4 10.21 4 10.33 5 16.83 5 10.04 5 10.33 5 10.46 4 8.69 4 17.40 7 7.90 7 16.83 5 8.43 2

A005 15 5 18 11 3.73 37 5.90 10 5.38 16 8.55 6 16.50 6 7.29 6 8.55 6 6.94 7 6.17 8 16.64 9 6.27 11 16.50 6 5.00 14

A006 14 6 14 22 1.80 292 3.17 79 2.70 122 7.05 7 14.00 8 5.18 19 7.05 7 4.49 30 4.31 26 14.00 14 5.60 13 14.00 8 3.19 63

A007 12 7 13 30 3.15 53 4.97 21 4.64 23 6.63 10 12.50 10 5.92 11 6.63 10 5.81 11 4.97 17 12.60 17 4.90 18 12.50 10 4.60 18

A008 11 8 12 36 3.15 53 4.87 22 4.64 23 6.21 14 11.50 12 5.63 14 6.21 14 5.60 17 4.75 18 11.60 24 4.50 24 11.50 12 4.22 26

A009 11 8 11 46 4.00 26 5.83 11 6.00 10 6.48 11 11.00 13 6.24 8 6.48 11 6.50 8 5.27 15 11.00 26 4.60 22 11.00 13 4.65 16

A010 10 10 10 57 2.45 134 3.93 38 3.68 57 5.32 20 10.00 16 4.76 25 5.32 20 4.69 27 3.96 33 10.00 32 4.00 34 10.00 16 3.73 41

A011 10 10 10 57 1.12 1133 2.00 290 1.68 428 5.02 23 10.00 16 3.53 62 5.02 23 2.96 106 2.94 94 10.00 32 4.00 34 10.00 16 2.19 181

A012 10 10 11 46 5.00 13 6.67 8 7.33 6 6.76 9 10.50 15 6.70 7 6.76 9 7.09 6 5.77 11 10.70 28 5.00 16 10.50 15 5.31 11

A013 9 13 9 89 3.08 59 4.53 25 4.63 25 5.22 22 9.00 19 4.96 22 5.22 22 5.11 20 4.18 29 9.00 40 3.80 45 9.00 19 3.67 42

A014 9 13 9 89 4.33 21 5.83 11 6.50 9 5.90 15 9.00 19 5.88 12 5.90 15 6.28 9 5.02 16 9.00 40 4.40 26 9.00 19 4.61 17

A015 9 13 26 3 10.00 1 10.83 1 11.17 1 10.38 4 17.17 3 10.21 3 10.38 4 10.21 5 9.92 1 22.10 3 8.60 3 17.17 3 9.54 1

A016 9 13 11 46 1.68 328 2.65 133 2.47 160 4.83 27 9.37 18 3.76 52 4.83 27 3.42 76 3.14 76 9.19 38 3.73 49 9.38 18 2.58 122

A017 9 13 9 89 2.48 131 3.83 44 3.73 54 4.94 25 9.00 19 4.49 29 4.94 25 4.48 31 3.76 40 9.00 40 3.70 51 9.00 19 3.27 59

A018 9 13 9 89 2.25 160 3.60 50 3.38 71 4.80 29 9.00 19 4.32 33 4.80 29 4.27 39 3.60 47 9.00 40 3.60 56 9.00 19 3.22 61

A019 8 19 8 116 4.00 26 5.33 16 6.00 10 5.33 18 8.00 32 5.33 16 5.33 18 5.71 13 4.56 20 8.00 63 4.00 34 8.00 32 4.00 30

A020 8 19 8 116 0.80 4479 1.45 643 1.20 1767 4.00 45 8.00 32 2.73 120 4.00 45 2.24 215 2.28 171 8.00 63 3.20 84 8.00 32 1.58 477

A021 8 19 9 89 3.00 64 4.17 29 4.17 35 4.71 31 8.33 27 4.55 28 4.71 31 4.69 26 3.93 34 9.00 40 3.60 56 8.33 27 3.40 52

A022 8 19 9 89 1.80 295 2.87 104 2.60 133 4.26 39 8.33 27 3.65 53 4.26 39 3.48 71 3.04 82 8.33 59 3.27 81 8.33 27 2.46 136

A023 8 19 10 57 2.13 177 2.92 98 2.62 132 4.48 36 8.60 25 3.80 50 4.48 36 3.56 67 3.33 64 9.04 39 3.72 50 8.60 25 3.16 67

A024 8 19 10 57 2.83 83 4.03 31 3.95 42 4.74 30 8.70 24 4.46 30 4.74 30 4.50 29 3.82 37 8.84 49 3.45 64 8.70 24 3.65 43

A025 8 19 8 116 1.60 377 2.67 130 2.40 163 4.13 43 8.00 32 3.50 67 4.13 43 3.33 85 2.90 98 8.00 63 3.20 84 8.00 32 2.29 165

A026 8 19 9 89 4.08 24 5.37 15 5.96 13 5.37 17 8.33 27 5.37 15 5.37 17 5.73 12 4.61 19 8.40 56 4.00 34 8.33 27 4.53 19

A027 8 19 8 116 2.64 98 3.88 40 3.96 41 4.62 34 8.00 32 4.32 34 4.62 34 4.41 32 3.64 46 8.00 63 3.40 66 8.00 32 3.05 73

A028 8 19 8 116 1.95 245 3.06 87 2.93 103 4.31 38 8.00 32 3.77 51 4.31 38 3.68 55 3.15 74 8.00 63 3.30 73 8.00 32 2.54 126

A029 8 19 8 116 4.00 26 5.33 16 6.00 10 5.33 18 8.00 32 5.33 16 5.33 18 5.71 13 4.56 20 8.00 63 4.00 34 8.00 32 4.23 25

A030 7 30 8 116 0.69 6001 1.05 2280 0.89 3656 3.56 71 7.25 45 2.25 199 3.56 71 1.73 441 1.94 254 7.22 100 2.87 123 7.25 45 1.53 528

A031 7 30 8 116 2.00 194 2.90 100 2.75 113 3.80 58 7.25 45 3.48 69 3.80 58 3.46 73 3.00 89 8.00 63 3.20 84 7.25 45 2.90 90

A032 7 30 8 116 1.49 585 2.23 179 2.03 265 3.62 65 7.20 47 3.05 102 3.62 65 2.87 111 2.62 120 8.00 63 3.20 84 7.20 47 2.38 154

A033 7 30 7 209 2.00 194 3.10 85 3.00 85 3.85 56 7.00 49 3.56 59 3.85 56 3.59 60 2.98 91 7.00 105 2.80 129 7.00 49 2.62 117

A034 7 30 8 116 2.50 109 3.43 61 3.25 77 4.18 40 7.50 43 3.89 44 4.18 40 3.87 47 3.41 58 8.00 63 3.30 73 7.50 43 2.84 95

A035 7 30 9 89 3.67 38 4.67 23 5.00 20 4.81 28 7.83 39 4.76 26 4.81 28 4.98 22 4.20 28 8.70 52 3.80 45 7.83 39 4.04 28

A036 7 30 7 209 2.48 133 3.54 52 3.71 55 4.15 42 7.00 49 3.88 45 4.15 42 3.99 45 3.29 70 7.00 105 3.10 99 7.00 49 3.17 66

A037 7 30 8 116 4.00 26 5.00 20 5.50 15 5.00 24 7.50 43 5.00 21 5.00 24 5.29 18 4.42 24 8.00 63 4.00 34 7.50 43 4.00 30

A038 7 30 7 209 2.58 101 3.70 46 3.88 45 4.17 41 7.00 49 3.99 41 4.17 41 4.13 44 3.37 61 7.00 105 3.10 99 7.00 49 3.12 71

A039 7 30 7 209 3.50 41 4.67 23 5.25 18 4.67 32 7.00 49 4.67 27 4.67 32 5.00 21 3.99 32 7.00 105 3.50 60 7.00 49 3.50 46

30

Author Code Credit

09 Rank

09 Credit

01 Rank

01 Credit

02 Rank

02 Credit

03 Rank

03 Credit

04 Rank

04 Credit

05 Rank

05 Credit

06 Rank

06 Credit

07 Rank

07 Credit

08 Rank

08 Credit

10 Rank

10 Credit

11 Rank

11 Credit

12 Rank

12 Credit

13 Rank

13 Credit

14 Rank

14 Credit

15 Rank

15

A040 7 30 7 209 3.17 50 4.33 26 4.75 21 4.48 37 7.00 49 4.42 32 4.48 37 4.70 25 3.77 39 7.00 105 3.30 73 7.00 49 3.45 50

A041 6 41 9 89 3.17 51 3.83 44 3.92 43 4.10 44 7.17 48 4.03 35 4.10 44 4.15 40 3.66 45 8.70 52 3.50 60 7.17 48 3.56 45

A042 6 41 6 295 2.50 109 3.47 60 3.75 46 3.73 61 6.00 61 3.63 54 3.73 61 3.81 49 3.08 79 6.00 152 2.80 129 6.00 61 2.91 89

A043 6 41 6 295 1.20 933 2.00 216 1.80 356 3.10 107 6.00 61 2.63 140 3.10 107 2.50 160 2.18 184 6.00 152 2.40 199 6.00 61 1.85 302

A044 6 41 6 295 1.01 1336 1.73 392 1.51 528 3.05 112 6.00 61 2.46 164 3.05 112 2.26 203 2.03 229 6.00 152 2.40 199 6.00 61 1.62 431

A045 6 41 6 295 0.69 6007 1.22 1464 1.04 2413 3.02 113 6.00 61 2.12 231 3.02 113 1.79 414 1.78 316 6.00 152 2.40 199 6.00 61 1.54 518

A046 6 41 7 209 1.37 650 2.10 199 1.92 320 3.13 105 6.20 57 2.71 123 3.13 105 2.59 144 2.27 172 6.14 144 2.45 198 6.20 57 1.81 322

A047 6 41 6 295 2.00 194 2.97 94 3.00 85 3.45 78 6.00 61 3.26 89 3.45 78 3.35 83 2.75 112 6.00 152 2.50 171 6.00 61 2.31 162

A048 6 41 10 57 1.67 329 2.54 138 2.28 175 3.94 52 7.83 39 3.15 95 3.94 52 2.88 110 2.71 116 7.52 94 2.64 158 7.83 39 2.21 180

A049 6 41 20 9 4.20 23 6.00 9 5.60 14 6.78 8 13.00 9 5.86 13 6.78 8 5.64 15 5.33 13 12.22 19 3.33 72 13.00 9 4.39 20

A050 6 41 6 295 3.00 64 4.00 32 4.50 26 4.00 46 6.00 61 4.00 36 4.00 46 4.29 34 3.42 52 6.00 152 3.00 102 6.00 61 3.34 53

A051 6 41 6 295 3.00 64 4.00 32 4.50 26 4.00 46 6.00 61 4.00 36 4.00 46 4.29 34 3.42 52 6.00 152 3.00 102 6.00 61 3.45 48

A052 6 41 6 295 2.39 141 3.32 76 3.59 63 3.70 63 6.00 61 3.53 61 3.70 63 3.67 56 3.00 88 6.00 152 2.80 129 6.00 61 2.68 111

A053 6 41 6 295 1.75 300 2.70 115 2.63 129 3.31 94 6.00 61 3.08 100 3.31 94 3.11 98 2.58 124 6.00 152 2.40 199 6.00 61 2.38 152

A054 6 41 6 295 2.83 83 3.83 41 4.25 32 3.90 53 6.00 61 3.88 46 3.90 53 4.13 41 3.31 66 6.00 152 2.90 115 6.00 61 2.89 93

A055 6 41 6 295 3.00 64 4.00 32 4.50 26 4.00 46 6.00 61 4.00 36 4.00 46 4.29 34 3.42 52 6.00 152 3.00 102 6.00 61 3.00 77

A056 6 41 6 295 2.83 83 3.83 41 4.25 32 3.90 53 6.00 61 3.88 46 3.90 53 4.13 41 3.31 66 6.00 152 2.90 115 6.00 61 3.00 82

A057 6 41 6 295 3.00 64 4.00 32 4.50 26 4.00 46 6.00 61 4.00 36 4.00 46 4.29 34 3.42 52 6.00 152 3.00 102 6.00 61 3.45 48

A058 6 41 6 295 2.42 136 3.40 63 3.63 61 3.68 64 6.00 61 3.57 58 3.68 64 3.74 53 3.03 84 6.00 152 2.70 152 6.00 61 3.03 75

A059 6 41 6 295 1.50 428 2.40 156 2.25 179 3.20 102 6.00 61 2.88 112 3.20 102 2.85 121 2.40 145 6.00 152 2.40 199 6.00 61 1.95 259

A060 6 41 6 295 2.00 194 3.00 88 3.00 85 3.43 79 6.00 61 3.27 88 3.43 79 3.38 78 2.76 110 6.00 152 2.40 199 6.00 61 2.40 145

A061 6 41 6 295 1.20 933 2.00 216 1.80 356 3.10 107 6.00 61 2.63 140 3.10 107 2.50 160 2.18 184 6.00 152 2.40 199 6.00 61 1.72 377

A062 6 41 6 295 2.33 143 3.33 70 3.50 66 3.62 66 6.00 61 3.52 63 3.62 66 3.68 54 2.98 91 6.00 152 2.60 160 6.00 61 2.75 104

A063 6 41 6 295 1.20 933 2.00 216 1.80 356 3.10 107 6.00 61 2.63 140 3.10 107 2.50 160 2.18 184 6.00 152 2.40 199 6.00 61 1.72 377

A064 6 41 6 295 1.20 933 2.00 216 1.80 356 3.10 107 6.00 61 2.63 140 3.10 107 2.50 160 2.18 184 6.00 152 2.40 199 6.00 61 2.04 226

A065 6 41 6 295 2.17 169 3.13 82 3.25 77 3.54 73 6.00 61 3.38 74 3.54 73 3.50 69 2.86 100 6.00 152 2.60 160 6.00 61 2.42 143

A066 6 41 11 46 3.67 38 4.33 26 4.33 31 4.57 35 8.17 30 4.45 31 4.57 35 4.51 28 4.13 30 10.10 31 3.80 45 8.17 30 3.79 40

A067 6 41 6 295 0.66 7726 1.17 1542 0.99 3172 3.02 114 6.00 61 2.09 242 3.02 114 1.74 439 1.75 329 6.00 152 2.40 199 6.00 61 1.29 869

A068 6 41 6 295 0.01 2028700 0.02 1958600 0.01 2022703 3.00 115 6.00 61 0.86 5401 3.00 115 0.09 1351226 1.21 1040 6.00 152 2.40 199 6.00 61 0.23 583624

A069 6 41 6 295 1.82 289 2.73 112 2.73 120 3.38 83 6.00 61 3.11 97 3.38 83 3.15 94 2.61 121 6.00 152 2.50 171 6.00 61 2.32 160

A070 6 41 6 295 3.00 64 4.00 32 4.50 26 4.00 46 6.00 61 4.00 36 4.00 46 4.29 34 3.42 52 6.00 152 3.00 102 6.00 61 3.00 77

A071 6 41 6 295 2.83 83 3.83 41 4.25 32 3.90 53 6.00 61 3.88 46 3.90 53 4.13 41 3.31 66 6.00 152 2.90 115 6.00 61 3.31 54

A072 6 41 7 209 1.18 985 1.80 357 1.62 468 3.06 111 6.14 60 2.53 157 3.06 111 2.36 185 2.19 183 7.00 105 2.80 129 6.14 60 2.17 183

A073 5 73 5 1033 1.45 600 2.23 179 2.18 239 2.76 137 5.00 118 2.55 151 2.76 137 2.58 145 2.14 201 5.00 254 2.00 293 5.00 118 1.93 265

A074 5 73 5 1033 0.36 113463 0.67 6621 0.54 56222 2.50 189 5.00 118 1.53 659 2.50 189 1.15 2144 1.31 850 5.00 254 2.00 293 5.00 118 0.87 4139

A075 5 73 5 1033 0.68 6033 1.19 1525 1.02 2426 2.53 180 5.00 118 1.89 347 2.53 180 1.65 543 1.57 529 5.00 254 2.00 293 5.00 118 1.36 772

A076 5 73 6 295 2.50 109 3.13 82 3.25 77 3.40 82 5.50 95 3.29 87 3.40 82 3.38 80 2.94 95 6.00 152 2.80 129 5.50 95 2.65 115

A077 5 73 6 295 2.83 83 3.50 56 3.92 43 3.48 75 5.33 107 3.52 63 3.48 75 3.75 52 3.10 77 6.00 152 2.90 115 5.33 106 3.00 82

A078 5 73 8 116 3.00 64 3.33 70 3.33 73 3.57 69 6.17 58 3.55 60 3.57 69 3.62 57 3.34 62 8.00 63 3.40 66 6.17 58 3.29 56

A079 5 73 5 1033 1.83 260 2.67 117 2.75 113 2.95 122 5.00 118 2.85 116 2.95 122 2.97 104 2.41 142 5.00 254 2.10 266 5.00 118 2.22 177

A080 5 73 6 295 0.91 3077 1.52 539 1.33 1292 2.66 156 5.33 107 2.12 233 2.66 156 1.93 346 1.74 333 5.22 241 2.03 289 5.33 106 1.49 620

A081 5 73 5 1033 1.10 1153 1.80 350 1.65 446 2.62 160 5.00 118 2.27 195 2.62 160 2.20 219 1.89 262 5.00 254 2.00 293 5.00 118 1.65 416

A082 5 73 5 1033 1.83 260 2.67 117 2.75 113 2.95 122 5.00 118 2.85 116 2.95 122 2.97 104 2.41 142 5.00 254 2.10 266 5.00 118 2.16 192

A083 5 73 7 209 2.12 184 2.90 99 2.98 102 3.30 96 5.83 89 3.10 98 3.30 96 3.15 93 2.65 119 5.76 220 2.35 240 5.83 89 2.65 113

A084 5 73 5 1033 2.33 143 3.17 80 3.50 66 3.24 98 5.00 118 3.21 91 3.24 98 3.42 77 2.74 113 5.00 254 2.40 199 5.00 118 2.81 98

31

Author Code Credit

09 Rank

09 Credit

01 Rank

01 Credit

02 Rank

02 Credit

03 Rank

03 Credit

04 Rank

04 Credit

05 Rank

05 Credit

06 Rank

06 Credit

07 Rank

07 Credit

08 Rank

08 Credit

10 Rank

10 Credit

11 Rank

11 Credit

12 Rank

12 Credit

13 Rank

13 Credit

14 Rank

14 Credit

15 Rank

15

A085 5 73 5 1033 1.10 1153 1.80 350 1.65 446 2.62 160 5.00 118 2.27 195 2.62 160 2.20 219 1.89 262 5.00 254 2.00 293 5.00 118 1.65 416

A086 5 73 5 1033 0.83 3270 1.43 656 1.25 1343 2.54 177 5.00 118 2.04 254 2.54 177 1.87 376 1.69 421 5.00 254 2.00 293 5.00 118 1.35 787

A087 5 73 5 1033 0.57 10013 1.03 2323 0.86 4080 2.51 188 5.00 118 1.78 417 2.51 188 1.51 672 1.48 607 5.00 254 2.00 293 5.00 118 1.06 1821

A088 5 73 5 1033 1.00 1347 1.67 464 1.50 533 2.58 166 5.00 118 2.19 212 2.58 166 2.08 290 1.81 301 5.00 254 2.00 293 5.00 118 1.43 673

A089 5 73 5 1033 2.50 109 3.33 64 3.75 46 3.33 85 5.00 118 3.33 77 3.33 85 3.57 61 2.85 102 5.00 254 2.50 171 5.00 118 2.50 130

A090 5 73 5 1033 2.50 109 3.33 64 3.75 46 3.33 85 5.00 118 3.33 77 3.33 85 3.57 61 2.85 102 5.00 254 2.50 171 5.00 118 2.73 105

A091 5 73 5 1033 1.05 1254 1.73 371 1.58 500 2.60 165 5.00 118 2.23 202 2.60 165 2.14 278 1.85 277 5.00 254 2.00 293 5.00 118 1.54 517

A092 5 73 6 295 2.75 95 3.63 49 4.04 38 3.60 68 5.50 95 3.57 57 3.60 68 3.80 50 3.10 78 5.60 226 2.60 160 5.50 95 3.26 60

A093 5 73 5 1033 1.58 382 2.40 156 2.38 165 2.82 133 5.00 118 2.66 138 2.82 133 2.73 128 2.24 174 5.00 254 2.00 293 5.00 118 1.96 256

A094 5 73 5 1033 0.00 2039727 0.00 2029281 0.00 2036052 0.00 2041914 5.00 118 0.60 56938 2.50 191 0.02 2004447 1.00 2458 5.00 254 2.00 293 5.00 118 0.11 1201302

A095 5 73 6 295 1.34 669 2.08 200 1.93 315 2.89 130 5.50 95 2.50 161 2.89 130 2.41 175 2.13 209 5.60 226 2.10 266 5.50 95 1.69 389

A096 5 73 5 1033 0.63 8027 1.11 2015 0.94 3360 2.51 186 5.00 118 1.84 390 2.51 186 1.59 594 1.52 571 5.00 254 2.00 293 5.00 118 1.11 1619

A097 5 73 5 1033 0.49 105729 0.80 4640 0.74 52020 2.57 168 5.00 118 1.59 597 2.57 168 1.22 1884 1.40 703 5.00 254 2.00 293 5.00 118 1.10 1641

A098 5 73 5 1033 2.50 109 3.33 64 3.75 46 3.33 85 5.00 118 3.33 77 3.33 85 3.57 61 2.85 102 5.00 254 2.50 171 5.00 118 2.73 105

A099 5 73 6 295 1.48 586 2.27 175 2.14 246 2.94 127 5.50 95 2.62 145 2.94 127 2.57 146 2.23 175 5.60 226 2.10 266 5.50 95 1.86 296

A100 5 73 5 1033 0.76 4683 1.32 1364 1.14 1873 2.53 179 5.00 118 1.97 322 2.53 179 1.78 422 1.63 441 5.00 254 2.00 293 5.00 118 1.40 704

A101 5 73 5 1033 1.20 933 1.93 300 1.80 356 2.65 158 5.00 118 2.36 177 2.65 158 2.31 192 1.96 246 5.00 254 2.00 293 5.00 118 1.59 475

A102 5 73 5 1033 1.67 355 2.50 142 2.50 142 2.86 131 5.00 118 2.73 121 2.86 131 2.82 123 2.30 157 5.00 254 2.00 293 5.00 118 2.02 232

A103 5 73 6 295 2.33 143 2.97 94 3.00 85 3.30 95 5.50 95 3.17 94 3.30 95 3.23 90 2.83 108 6.00 152 2.70 152 5.50 95 2.62 116

A104 5 73 5 1033 1.10 1153 1.80 350 1.65 446 2.62 160 5.00 118 2.27 195 2.62 160 2.20 219 1.89 262 5.00 254 2.00 293 5.00 118 1.64 420

A105 5 73 5 1033 2.50 109 3.33 64 3.75 46 3.33 85 5.00 118 3.33 77 3.33 85 3.57 61 2.85 102 5.00 254 2.50 171 5.00 118 2.50 130

A106 5 73 7 209 2.40 140 3.10 85 3.30 76 3.18 103 5.50 95 3.19 93 3.18 103 3.36 82 2.76 110 5.44 233 2.33 241 5.50 95 2.40 146

A107 5 73 5 1033 0.93 2942 1.57 501 1.40 1199 2.56 173 5.00 118 2.13 229 2.56 173 2.00 307 1.76 326 5.00 254 2.00 293 5.00 118 1.43 670

A108 5 73 5 1033 1.42 619 2.20 185 2.13 247 2.74 138 5.00 118 2.53 158 2.74 138 2.55 154 2.12 211 5.00 254 2.00 293 5.00 118 1.75 347

A109 5 73 5 1033 2.50 109 3.33 64 3.75 46 3.33 85 5.00 118 3.33 77 3.33 85 3.57 61 2.85 10