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GitHub Sponsors: Exploring a New Way to Contribute to Open Source

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GitHub Sponsors, launched in 2019, enables donations to individual open source software (OSS) developers. Financial support for OSS maintainers and developers is a major issue in terms of sustaining OSS projects, and the ability to donate to individuals is expected to support the sustainability of developers, projects, and community. In this work, we conducted a mixed-methods study of GitHub Sponsors, including quantitative and qualitative analyses, to understand the characteristics of developers who are likely to receive donations and what developers think about donations to individuals. We found that: (1) sponsored developers are more active than non-sponsored developers, (2) the possibility to receive donations is related to whether there is someone in their community who is donating, and (3) developers are sponsoring as a new way to contribute to OSS. Our findings are the first step towards data-informed guidance for using GitHub Sponsors, opening up avenues for future work on this new way of financially sustaining the OSS community.
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GitHub Sponsors:
Exploring a New Way to Contribute to Open Source
Naomichi Shimada
Nara Institute of Science and
Technology, Japan
shimada.naomichi.sm3@is.naist.jp
Tao Xiao
Nara Institute of Science and
Technology, Japan
tao.xiao.ts2@is.naist.jp
Hideaki Hata
Shinshu University
Japan
hata@shinshu-u.ac.jp
Christoph Treude
University of Melbourne
Australia
christoph.treude@unimelb.edu.au
Kenichi Matsumoto
Nara Institute of Science and
Technology, Japan
matumoto@is.naist.jp
ABSTRACT
GitHub Sponsors, launched in 2019, enables donations to individ-
ual open source software (OSS) developers. Financial support for
OSS maintainers and developers is a major issue in terms of sus-
taining OSS projects, and the ability to donate to individuals is
expected to support the sustainability of developers, projects, and
community. In this work, we conducted a mixed-methods study of
GitHub Sponsors, including quantitative and qualitative analyses,
to understand the characteristics of developers who are likely to
receive donations and what developers think about donations to
individuals. We found that: (1) sponsored developers are more ac-
tive than non-sponsored developers, (2) the possibility to receive
donations is related to whether there is someone in their commu-
nity who is donating, and (3) developers are sponsoring as a new
way to contribute to OSS. Our ndings are the rst step towards
data-informed guidance for using GitHub Sponsors, opening up
avenues for future work on this new way of nancially sustaining
the OSS community.
CCS CONCEPTS
Social and professional topics Sustainability
;
Software
and its engineering Open source model.
KEYWORDS
GitHub Sponsors, Open Source, Sponsorship
ACM Reference Format:
Naomichi Shimada, Tao Xiao, Hideaki Hata, Christoph Treude, and Kenichi
Matsumoto. 2022. GitHub Sponsors: Exploring a New Way to Contribute
to Open Source. In 44th International Conference on Software Engineering
(ICSE ’22), May 21–29, 2022, Pittsburgh, PA, USA. ACM, New York, NY, USA,
12 pages. https://doi.org/10.1145/3510003.3510116
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©2022 Association for Computing Machinery.
ACM ISBN 978-1-4503-9221-1/22/05. . . $15.00
https://doi.org/10.1145/3510003.3510116
1 INTRODUCTION
Open source software (OSS) projects are often aected by economic
challenges, and soliciting donations is a common means of obtaining
funds for OSS projects. However, as pointed out by Staltz, many
OSS maintainers and developers do not generate enough income
to sustain their OSS projects [23].
In May 2019, GitHub introduced GitHub Sponsors [
33
], a service
which allows OSS developers to accept donations from other GitHub
users. While most OSS donation services in the past have targeted
projects, GitHub Sponsors is unique in that it allows users to donate
to individual OSS developers. GitHub advertises the service as “a
new way to contribute to open source”, in particular pointing out
the widespread dependence on OSS projects: “Sponsor the open
source software your team has built its business on. Fund the projects
that make up your software supply chain to improve its performance,
reliability, and stability.” Anyone who contributes to an OSS project
and lives in one of the 36 regions in which GitHub Sponsors was
available at the time of writing is eligible to become a sponsored
developer. Developers can join a waitlist, and once approved, a
‘Sponsor’ button will appear on their prole and they can dene
sponsorship tiers. As of now, GitHub matches contributions of up
to $5k during a developer’s rst year in GitHub Sponsors.
But who participates in GitHub Sponsors, what makes developers
more likely to receive sponsorship, and what challenges and benets
do GitHub Sponsors bring? To answer such questions, we conducted
a mixed-methods study of those who signed up for GitHub Sponsors
and those who contributed donations.
Existing work on donations in the context of OSS projects—
before the launch of GitHub Sponsors—reported that the activity
and popularity of a project on GitHub are positively correlated with
the likelihood of receiving donations, and projects that received
donations show a short-term increase in the number of commits
and a reduction in the time to resolve issues [
20
]. Krishnamurthy
et al. studied donations in SourceForge [
14
]. They reported that the
decision to donate is impacted by relational commitment with the
open source software platform, donation to projects, and accepting
donations from others. Furthermore, the length of association with
the platform and relational commitment aects donation levels.
Nakasai et al. studied the impact of donation badges on developers’
responses to Eclipse bug reports [
18
]. They reported that bug re-
ports from users who have donation badges used in Eclipse, take
less time to receive a reply from the developers than other bug
arXiv:2202.05751v1 [cs.SE] 11 Feb 2022
ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA Shimada et al.
reports. Compared to these studies which investigated donations to
projects, in this work, we study donations to individual developers,
enabled by GitHub Sponsors.
From our quantitative analysis, we nd that sponsored develop-
ers are more active than those looking for sponsorship unsuccess-
fully, and that many of the sponsors are active developers them-
selves, eectively building clusters of sponsorship. Distinguishing
sponsored developers from non-sponsored developers, the presence
of sponsorship in their development community is an important
factor. Our qualitative analysis also reveals benets and challenges
related to GitHub Sponsors. Developers typically do not have chan-
nels at their disposal to attract sponsors and communicate with
those who might be interested in donating, but on the other hand,
many donate to show appreciation, not expecting anything specic
in return.
Signicance of research contribution. Given the sustainability con-
cerns aecting many OSS projects that are depended on by millions,
understanding how sponsorship can provide the needed support
is a crucial step towards ensuring that we can continue to rely on
OSS projects. GitHub Sponsor’s focus on enabling sponsoring of
individual developers instead of projects is unique and has not been
studied before. Our work provides insights into the characteristics,
benets, and challenges of the early adopters of GitHub Sponsors.
2 RESEARCH QUESTIONS
In this work, we conduct an exploratory study of GitHub Sponsors,
a new approach to support developers. Although GitHub Sponsors
allows GitHub users to sponsor organizations as well as individuals,
this study only focuses on the sponsorship of individual developers.
Also, this study only targets sponsorship by individual developers
and does not cover sponsorship by organizations. The main goal of
the study is to gain insights into the use of GitHub Sponsors among
individuals. Based on this goal, we constructed three main research
questions to guide our study. We present these main questions and
sub-questions along with their motivation.
RQ1: Who participates in GitHub Sponsors?
RQ1.1 : What are the characteristics of sponsored developers?
RQ1.2 : What are the characteristics of sponsors?
The motivation of our rst main research question
RQ1
is to set
the stage for the rest of the paper by providing demographic infor-
mation of involved receivers (RQ1.1) and sponsors (RQ1.2).
RQ2:
What characteristics make developers more likely to receive
sponsorship?
For OSS developers who want to obtain sponsorship, we set this
second research question (
RQ2
) to identify the characteristics of
developers who are likely to obtain sponsorship.
RQ3:
What are developers’ perceived challenges and benets re-
lated to sponsoring?
RQ3.1 : Why are developers looking for sponsors?
RQ3.2 : What is the impact of (not) getting sponsorship?
RQ3.3 : Why are developers sponsoring?
To deepen our investigation of the answers to
RQ2
, we then ask the
corresponding ‘why’ questions for
RQ3
, again from both sides of
a potential donation: why are developers looking for sponsorship
(
RQ3.1
) and why are developers sponsoring (
RQ3.3
)? We assumed
that the main challenge related to sponsorship is not receiving
money, so we asked about this explicitly in RQ3.2.
3 RESEARCH METHODS
In this section, we describe our methods for data collection and
analysis.
3.1 Data Collection
This section describes the steps to identify GitHub users who are
participating in GitHub Sponsors, i.e., registered developers who
are asking for sponsors, and GitHub users who are donating to
developers.
Preparing repositories.
Since there is no direct way to get
the users who participate in GitHub Sponsors, we rst examined
repositories to get the list of contributing GitHub users. In order to
cover as many users involved in GitHub sponsorship as possible,
we collected a large number of GitHub repositories, i.e., repositories
that were created between 2008 and 2020 and had 10 or more stars
when we accessed them. We will discuss the limitations of this
threshold of 10 stars in Section 5.1. Access and cloning was done
between January and March 2021, and 1,210,041 repositories were
collected. We excluded 387 repositories with no commits, resulting
in 1,209,654 repositories.
Obtaining contributors.
The GitHub REST API was used to
retrieve the contributors from each of the repositories collected; due
to API limitations, the top 500 contributors from each repository
were retrieved. When we made requests via API between June
and July 2021, there were repositories for which we could not
get contributors because the repositories had been deleted or set
to private, for example. We obtained 1,695,015 contributors from
1,168,856 repositories. The limitations of the threshold of the top
500 contributors are also discussed in Section 5.1.
Identifying GitHub Sponsors participants.
In July 2021, We
used the GitHub GraphQL API to identify developers who can
be sponsored via GitHub Sponsors, i.e., developers who are seek-
ing sponsorship. From the 1,695,015 contributors, we identied
9,366 such developers. After analyzing each developer’s user pro-
le page for GitHub Sponsors and removing developers who had
deleted their prole, we identied 3,697 developers who had ob-
tained sponsors (
sponsored developers
) and 5,666 developers
who had not yet obtained sponsors (
non-sponsored developers
).
From the analysis of a user prole page, we can get the list of
sponsoring GitHub users including anonymous sponsors. Organi-
zation accounts were removed, and we identied a total of 17,458
non-anonymous individual sponsors. This includes sponsored and
non-supported developers.
Identifying primary programming languages.
Since we have
the list of contributors for all repositories we analyzed, we can ag-
gregate information about the repositories contributed to by each
developer. The primary language of the repositories can be retrieved
using the GitHub GraphQL API, so the most common primary lan-
guage of the repositories to which each developer contributed is
taken as the primary language of that developer. Note that this
is a rough estimate because we have not analyzed whether the
developer commits in that language or not. The primary languages
GitHub Sponsors:
Exploring a New Way to Contribute to Open Source ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA
Table 1: Survey participant demographics
sponsored non-sponsored sponsoring
years coding
less than 5 7 (4%) 4 (3%) 4 (6%)
5-9 44 (25%) 49 (38%) 17 (26%)
10-19 73 (41%) 47 (37%) 25 (38%)
20-29 33 (19%) 21 (16%) 10 (15%)
30 or more 20 (11%) 8 (6%) 10 (15%)
years on GitHub
less than 5 23 (13%) 18 (14%) 15 (23%)
5-9 98 (55%) 87 (67%) 37 (56%)
10 or more 56 (32%) 24 (19%) 14 (21%)
gender
male 157 (89%) 111 (86%) 60 (91%)
female 6 (3%) 8 (6%) 3 (5%)
non-binary, genderqueer, or gender non-conforming
8 (5%) 5 (4%) 2 (3%)
prefer not to say 6 (3%) 5 (4%) 1 (2%)
OSS contributions
full time 30 (17%) 15 (12%) 5 (8%)
part time 129 (73%) 96 (74%) 44 (67%)
other 18 (10%) 18 (14%) 17 (25%)
sum 177 (100%) 129 (100%) 66 (100%)
of developers identied in this way can be interpreted as the pro-
gramming languages of the ecosystems to which the developers
mainly contributed.
3.2 Survey
To understand how developers perceive GitHub sponsors
(RQ3)
, we
conducted a survey to get developer feedback on GitHub Sponsors.
In August 2021, we sent invitations to 2,000 randomly selected
sponsored developers, 2,000 non-sponsored developers, and 2,000
sponsors to participate in the survey, and received a total of 372
responses: 177 from sponsored developers, 129 from non-sponsored
developers, and 66 from sponsors. Table 1 presents an overview
of the demographics of our survey participants. Responses were
obtained from GitHub users with diverse years of experience. Most
of the respondents were male, but responses from other gender
minorities were also included. Most respondents’ contribution to
OSS is part time, but sponsored developers are more likely to be
full-time developers than others.
3.3 Qualitative Analysis
For the qualitative analysis of the survey responses, three of the
authors collaboratively took an initial look at all answers and dis-
cussed which themes were present in the data and how these themes
related to the research questions. One of the authors then formalised
this discussion into coding schemata. Three authors applied the
coding schemata to a random subset of the data, and one author n-
ished the annotation based on the encouraging kappa agreements.
We allowed multiple codes per answer. In all cases, the kappa agree-
ment was satisfactory after the rst pass, and we did not change
nor add codes during the process. We attribute this stability to the
fact that we had an initial discussion about all data, that most an-
swers were relatively short, and that this particular team of authors
have experience working together on qualitative data analysis from
previous research projects. We describe each coding schema in the
following questions.
Why are you looking for sponsors?
To answer
RQ3.1
, we
analyzed the reasons why OSS developers ask for donations. The
three raters independently labeled 29 answers from two groups
(from sponsored developers and non-sponsored developers). Then,
we calculated the kappa agreement of our coding schema from
three raters. Cohen’s kappa for this qualitative analysis is 0.7, which
indicates ‘substantial’ agreement [
26
]. The following list shows our
coding schema:
funding a particular feature/ product
: We used this code
if the respondent mentioned something in particular (other
than the OSS project itself) that they were planning to use
the donations for, e.g., “Fund hosting costs for hosted projects.
gauge interest/satisfaction
: Some respondents indicated
using sponsorship as a way to receive feedback from the
community, in particular to assess the community’s interest
in the project, e.g., “To measure the degree of satisfaction with
my OSS works.
motivation
: We used this code if respondents were aware
that receiving motivations would increase their motivation,
e.g., “It highly motivates me if I get money as donations for
my work.
recognition/ appreciation
: If respondents expressed that
they wanted to give the community a way to express ap-
preciation or recognition, we used this code, e.g., “Why not,
mostly. Mostly boils down to recognition for the work since the
monetary amounts are negligible.
nancial support in general terms
: In cases where re-
spondents gave a somewhat generic answer related to mak-
ing money, we used this code, e.g., “to fund my open source
work.
none
: For respondents who did not mention a reason in
response to the question, we used the code ‘none’.
not answered
: If the question was not answered, we coded
it as ‘not answered’.
Are you doing anything special to attract sponsors?
To get
a better understanding of what developers do to attract sponsors,
we analyzed the responses of the actions that developers men-
tioned in their survey responses. The three raters independently
coded 30 answers from two groups (from sponsored developers
and non-sponsored developers), achieving Cohen’s kappa of 0.91
or ‘almost perfect’ agreement [
26
]. The following list shows the
coding schema:
perks for sponsors
: For responses which mentioned a spe-
cic perk that was only available to sponsors of their work,
we used this code, e.g., “I oer short consulting sessions (just
a 30-60 minute video call) for higher tier sponsors.
social media
: We used this code if respondents mentioned
a specic social media site or social media in general, e.g.,
Twitter - tweet about my work.
ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA Shimada et al.
written content on GitHub
: Responses which mentioned
updating documentation to make their work more attractive
to sponsors, we used this code, e.g., “I’ve written out my goals
more publicly.
none
: If respondents did not mention any activities, we
coded the response as ‘none’.
not answered
: If the question was not answered, we coded
it as ‘not answered’.
How has having sponsors aected you and the projects
you are working on?/ How does the lack of sponsoring aect
you and the projects you are working on?
To answer
RQ3.2
,
we analyzed the responses to the above questions of the impacts
of (not) getting sponsorship to developers and OSS projects. Three
raters independently annotated 28 answers from two groups (from
sponsored developers and non-sponsored developers). The kappa
agreement is 0.79, interpreted as ‘Substantial’ [
26
]. Our coding
schema is as follows:
better project quality
: We used this code for responses
which mentioned a positive impact of sponsoring towards
specic quality attributes, e.g., “It’s made me feel a lot more
motivated towards adding more open source code, and paying
a higher level of attention to detail.
limited eort
: This code was used for responses which
mentioned a negative impact of the lack of sponsorship on
the eort they were willing or able to spend, e.g., “the projects
receive less attention due to the need to do paid work.
motivation
: Responses mentioning the impact of (lack of)
sponsorship on motivation received this code, e.g., “Some
pressure to nish the project.
satisfaction
: We used a similar category for responses re-
lated to satisfaction, e.g., “Just for my heart’s pleasure.
need other channels
: Responses which indicated that a
lack of sponsorship via GitHub Sponsors implied that they
used other sponsorship platforms fall into this category, e.g.,
I have people making contribution via other channels.
need other income
: Similarly, responses mentioning the
need to look for other income in the absence of GitHub
sponsorship were given its own code, e.g., “I have to work on
closed source and less interesting projects.
other
: For any answer to the question that did not t the
above categories, we used the code ‘other’.
none
: If respondents did not mention that there was any
impact, we coded the response as ‘none’.
not answered
: If the question was not answered, we coded
it as ‘not answered’.
Why are you sponsoring others?/ Why did you become
a sponsor?
To answer
RQ3.3
, we analyzed the responses of the
reasons why developers sponsor other OSS developers. Three raters
independently coded 30 answers from our survey, achieving kappa
of 0.62 or ‘substantial’ agreement [
26
]. The lower agreement can be
explained by 21 combinations of multiple codes being discovered
when coding reasons for sponsoring. Three raters achieved perfect
agreement in 15/30 cases (50%) and partial agreement in another
14/30 cases (47%), and completely disagreed only in 1/30 case (3%).
Our coding schema is as follows:
dependencies/ beneted otherwise
: We used this code
for responses which explicitly mentioned dependencies or
other benets, e.g., “My project uses their projects.
excellent work
: If respondents indicated that they spon-
sored because of excellent projects, we used this code, e.g.,
I want to contribute to great projects.
form of involvement
: Related to the previous point, if re-
spondents indicated that they see sponsoring as a form of
involvement, we used this code, e.g., “I had no more time to
help with coding, so I decided to sponsor.
fairness/ give back to community
: We used this code if
the main reason was related to fairness rather towards the
community, e.g., “If someone provides OSS software which I
daily use, I think it’s fair and important to pay a contribution.
set example
: Going a step further, some respondents men-
tioned that they sponsor to set an example for others, e.g., “I
want to set an example for other developers that large numbers
of even small supporters can make an impact on keeping the
OS community sustainable.
sustain project/ community
: If the response focused on
using sponsorship to sustain a project or the community as
a while, we used this code, e.g., “To help them sustain their
OSS software.
recognition/ appreciation
: If the responses mentioned rec-
ognizing a project or member of the community, or to show
appreciation, we used this code, e.g., “To praise their work,
and recognize their invested time.
motivation
: Some respondents explicitly mentioned target-
ing the motivation of developers with their donations, e.g.,
Because I understand how hard it is to stay motivated.
required to get access to features/ training
: If partici-
pants mentioned sponsoring in return for specic access, we
used this code, e.g., “It was required to access training videos.
generic help/ support
: Somewhat generic statements such
as “Help valuable users in community” received this code.
other
: If the response did not t any of these categories, we
coded it as ‘other’.
not answered
: If the question was not answered, we coded
it as ‘not answered’.
What are the eects of your sponsorship? Are the eects
as you expected?
Lastly, we analyzed the responses of the eects
of sponsoring, to the above questions. Three raters independently
coded 27 answers from our survey. The kappa agreement is 0.82
or ‘almost perfect’ [
26
]. We coded the responses according to the
following categories:
collective
: We used this code for responses which explicitly
mentioned that their contributions on their own would not
make a dierence while the collective might, e.g., “I do not
expect to aect anyone with 1 USD a month. The collective
does, but I personally don’t have a say necessarily, which is
good.
fund particular activities
: If respondents expected partic-
ular activities to take place in return for their sponsoring,
we used this code, e.g., “Maybe better handling of my les
Issues. Also to keep a project alive.
GitHub Sponsors:
Exploring a New Way to Contribute to Open Source ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA
Table 2: Primary programming languages of developers
sponsored non-sponsored GitHut
JavaScript 796 (22%) 1,240 (22%) (19%)
Python 450 (12%) 764 (13%) (16%)
PHP 352 (10%) 542 (10%) (6%)
C# 257 (7%) 334 (6%) (4%)
TypeScript 204 (6%) 317 (6%) (7%)
Go 203 (5%) 298 (5%) (8%)
Java 189 (5%) 373 (7%) (12%)
C++ 174 (5%) 294 (5%) (7%)
C 148 (4%) 180 (3%) (3%)
Ruby 130 (4%) 169 (3%) (7%)
other 794 (21%) 1,155 (20%) (11%)
sum 3,697 (100%) 5,666 (100%) (100%)
grateful/ motivated developers
: Responses related to the
motivation of the developers receiving sponsorship received
this code, e.g., “I’m not actually sure how to measure it. I just
hope that provides enough signal to them to feel motivated.
recognition as sponsor
: We used this code for responses
mentioning recognition of sponsors, e.g., “Yes, as part of
some sponsorships, we get our org some badges in their repo,
to showcase our support.
required to get access to features/ training
: If the in-
tended eect of sponsorship was to get access to certain
features, we used this code, e.g., “Getting involved in email
threads and invitations to beta testing.
satisfaction
: Responses from sponsors mentioning their
own satisfaction received this code, e.g., “I honestly don’t get
much out of sponsoring except personal satisfaction.
sustain project
: If the main eect was sustaining a partic-
ular project, we used this code, e.g., “That keep the product
alive and maintained.
none
: If respondents did not mention any eect, we coded
it as ‘none’.
not answered
: If the question was not answered, we coded
it as ‘not answered’.
4 RESULTS
We present the answers to our research questions in this section.
4.1 RQ1: Who participates in GitHub Sponsors?
To understand participants in GitHub Sponsors, we investigated
the characteristics of sponsored developers and sponsors.
RQ1.1: What are the characteristics of sponsored develop-
ers?
We measured the number of sponsors donating to the 3,697
sponsored developers in our dataset and found that 80% had eight or
fewer sponsors, and 1,355 (36%) had just one sponsor. 661 (17%) had
11 or more sponsors, and the developer with the highest number
of sponsors had 1,342 sponsors. The median was 2.
Primary programming languages.
The main programming
languages of the sponsored and non-sponsored developers iden-
tied by the method described in Section 3.1 are presented in Ta-
ble 2. It can be seen that many sponsored developers contribute to
9
22
1
10
100
1,000
non−sponsored
sponsored
(a) Number of repositories.
6,103 13,527
10
100
1,000
10,000
100,000
non−sponsored
sponsored
(b) Highest number of stars in
the repositories.
Figure 1: Comparison of repositories contributed to by spon-
sored and non-sponsored developers.
JavaScript, Python, and PHP repositories. Table 2 also shows the
percentage of pull request volume by language for Q4 2020 taken
from GitHut 2.0.
1
GitHut 2.0 is a web service that processes GitHub
data with Google’s BigQuery to visualize GitHub language statis-
tics.
2
In all three sets of data, the set of programming languages in
the top 10 is the same. This means that developers seeking spon-
sorship on GitHub Sponsors are in an ecosystem of programming
languages that are actively being used. JavaScript and Python are
at the top of the three lists in common. The other rankings for
sponsored and non-sponsored developers are almost the same, but
there are some dierences between these and the GitHut ranking.
Java, which is ranked third in terms of the volume of pull requests,
is ranked seventh in terms of the main language used by sponsored
developers. PHP, which ranks eighth in terms of the volume of
pull requests, is found in third place as the primary language of
sponsored developers. We can see that there is a dierence between
the activity level of each programming language, as measured by
the amount of pull requests, and the ecosystem of programming
languages that have a presence in GitHub Sponsors.
Contributions to repositories.
Figure 1a is a violin plot show-
ing the number of repositories with 10 or more stars contributed
to by sponsored and non-sponsored developers. The median val-
ues are 22 and 9, respectively. The median number of repositories
contributed to by the other 1,684,126 developers, excluding spon-
sored developers and non-sponsored developers (i.e., developers
who had set up sponsorship, but not received donations), was 1.
In this analysis of other developers, we excluded as many bot ac-
counts as possible using keywords such as ‘[bot]’, ‘-bot’, ‘Bot’, and
manual checks. Considering that most developers contribute to
only one repository, we can see that both developer groups (spon-
sored and non-sponsored) are active, contributing to several popular
projects, and especially sponsored developers contribute to many
such projects.
Figure 1b is a violin plot showing the highest number of stars in
the repositories contributed to by sponsored and non-sponsored
1https://madnight.github.io/githut/#/pull_requests/2020/4
2https://github.com/madnight/githut
ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA Shimada et al.
7
1
10
100
1,000
(a) Number of repositories.
10
100
1,000
10,000
100,000
(b) Highest number of stars in
the repositories.
Figure 2: Repositories contributed to by sponsors.
0
100
200
300
400
0 5 10 15 20 25
# of developers sponsoring
Frequency
non−sponsored sponsored
Figure 3: Distribution of the number of developers spon-
sored by other sponsored or non-sponsored developers.
developers. The median values are 13,527 and 6,103, respectively.
We can see that sponsored developers contribute to repositories
with a higher number of stars than non-sponsored developers.
RQ1.2: What are the characteristics of sponsors?
Of the 17,458
sponsors we identied, 809 were sponsored developers themselves
and 446 were non-sponsored developers. Of the remaining 16,203
sponsors who had not sought sponsorship for themselves, 6,020
(37%) had not contributed to the repositories analyzed, while 10,183
(63%) were developers who had contributed to repositories with
10 or more stars. From this, we found that two-thirds of the spon-
sors of GitHub Sponsors were developers, not just users. Among
GitHub Sponsors participants, of the 16,203 GitHub users who were
only sponsoring, 80% were only sponsoring one or two developers.
Those who sponsored the most had sponsored 43 developers. The
median was one.
Contributions to repositories.
Figure 2 presents a violin plot
showing the number of repositories with 10 or more stars con-
tributed to by 10,183 sponsors (2a) and a violin plot showing the
highest number of stars in the repositories contributed to by the
same sponsors (2b). From these gures, we can see that these spon-
sors are active developers, comparable to the non-sponsored devel-
opers seen in Figure 1.
Sponsors among sponsored and non-sponsored develop-
ers.
Figure 3 shows the distribution of the number of developers
Figure 4: Largest network of sponsoring relationships
among sponsored developers. Nodes represent developers
and are color-coded by the top 10 major programming lan-
guages: JavaScript,Python,PHP,C#,TypeScript,Go,Java,
C++,C, and Ruby.
sponsored by other sponsored developers and non-sponsored de-
velopers. Most of them were sponsoring only a few developers, but
the maximum values were 25 and 22, respectively. We can see that
the sponsored developer group has more developers sponsoring
other developers than the non-sponsored developer group.
Sponsoring network of sponsored developers.
Of the 3,697
sponsored developers, 809 (22%) were also sponsors, suggesting
that developers are sponsoring each other. Therefore, we created
networks with developers as nodes and sponsorship relationships
as edges. Figure 4 shows the largest of these networks. The node size
corresponds to the total number of inputs (being sponsored) and
outputs (sponsoring) of the sponsorship. Developers whose primary
language is one of the top 10 major programming languages listed
in Table 2 are colored. In this network, we can see that developers
of the same major programming languages, such as JavaScript,
PHP, C#, and Ruby, have formed clusters. In particular, we nd that
developers whose primary language is PHP form the closest and
largest cluster, and they have a strong social network of donations
through GitHub Sponsors.
Summary
: Sponsored developers are more active than
non-sponsored developers, with JavaScript, Python, and
PHP being their top primary languages. About two-thirds
of the sponsors are also active developers, and the spon-
sored developers form clusters that sponsor each other.
GitHub Sponsors:
Exploring a New Way to Contribute to Open Source ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA
highest_stars@83.50 highest_stars@911.00
num_repos@12.50 num_repos_top_co_contributing@2.50
highest_stars@590.00 highest_stars@2034.50
num_repos_top_co_contributing@0.50
>
Figure 5: A decision tree for classifying sponsored and non-sponsored developers.
4.2 RQ2: What characteristics make developers
more likely to receive sponsorship?
To answer this research question, we employed a decision tree
to examine the characteristics that are important in separating
sponsored developers from non-sponsored developers. We also
present developer feedback on important factors to consider when
deciding who to sponsor.
Decision tree.
We use machine learning to nd useful charac-
teristics, or features, in the data. Because the relationship between
features and outcome could be nonlinear or the features may in-
teract with each other, we conducted the analysis with decision
trees rather than linear or logistic regression models. The following
features were measured for the outcome of having or not having
sponsors (sponsored/non-sponsored). These features were designed
based on the ndings from the
RQ1
results. Note that repositories
to be measured here had 10 or more stars.
highest_star
: Highest number of stars in the repositories
that developers contributed to. As seen in Figure 1b, spon-
sored developers are contributing to repositories with a high
number of stars.
num_repos
: Number of repositories that developers con-
tribute to. As seen in Figure 1a, sponsored developers are
contributing to many repositories.
num_own_repos
: Number of repositories contributed to
and owned by a developer. Owning and managing popular
projects might be a factor in getting sponsorship.
num_repos_top_contributing
: Number of repositories con-
tributed to that are ranked top in terms of commits. Making
top contributions to popular repositories might be a factor
in obtaining sponsorship.
num_repos_top_co_contributing
: Number of repositories
contributed to with the top number of commits and that have
at least one sponsor in the same repository. This does not
take into account who the sponsors in the same repository
are sponsoring. As seen in Figure 4, sponsored developers
form clusters of sponsoring relationships. The presence of
GitHub Sponsors participants as sponsors in the develop-
ment community might be a factor in obtaining sponsorship.
num_sponsoring
: Number of sponsored developers. As
seen in Figure 3, sponsored developers are sponsoring more
than non-sponsored developers.
Figure 5 shows the result of applying the decision tree using
scikit-learn
3
to the data of 9,363 developers, including 3,697 spon-
sored and 5,666 non-sponsored developers. The feature num_repos-
_top_contributing is found to be the most important, that is, the
existence of such repositories seems to be the most common char-
acteristic of sponsored developers. If that value was three or more,
most developers had obtained sponsors. If that value was one or two
and the feature highest_star was less than 590, more than half of the
developers have not attracted sponsors. If that value was zero, most
developers did not get sponsors. However, if the number of con-
tributing repositories is more than 13 and the feature highest_star
is more than 911, then more than half of those developers had ob-
tained sponsorship. We found that sponsored developers not only
contribute to the repositories with the most stars and contribute
to the most repositories, but they are also the top contributors to
the repositories where sponsoring developers are present. In other
words, whether or not the communities to which developers belong
have a habit of donating to OSS developers appears to be important
for whether or not the developers get sponsors.
Developer feedback.
In the survey described in Section 3.2, we
asked how important the following criteria were when deciding
who to sponsor. The criteria are based on our insights gained from
answering RQ1. The respondents were asked to choose from the
following options: very important, somewhat important, a little bit
important, not important at all, or don’t care.
(a)
They are major contributors to OSS projects that are impor-
tant to me.
(b) They inspire me.
(c) We are contributing to the same OSS projects.
(d) We know each other outside the OSS community.
Figure 6 shows the distributions of the responses. As expected,
being a major contributor to an important OSS project (a) was a very
important criterion. In terms of the criterion of inspirational (b),
the majority of responses were positive, including ‘very important’,
‘somewhat important’, and ‘a little bit important’. Because of the
individual sponsorship, personal attractiveness seems to be impor-
tant. Frequent responses to the criterion of contributing to the same
project (c) were ‘a little important’, ‘not important at all’, and ‘don’t
care’. It is not an important criterion for everyone, but it shows that
some people do care about it. This can be considered as support
3https://scikit-learn.org/
ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA Shimada et al.
(d) We know each other outside of the OSS
community.
(c) We are contributing to the same OSS projects.
(b) They inspire me.
(a) They are major contributors to OSS projects
that are important to me.
100 50 0 50 100
sponsoring
non−sponsored
sponsored
sponsoring
non−sponsored
sponsored
sponsoring
non−sponsored
sponsored
sponsoring
non−sponsored
sponsored
Percentage
Don't care
Not important at all
A little bit important
Somewhat important
Very important
Figure 6: Distribution of the number of developers spon-
sored by other sponsored or non-sponsored developers.
for the importance of the feature num_repos_top_co_contributing
as revealed by the decision tree analysis. Being an acquaintance (d)
is mostly considered ‘not important at all’ or ‘don’t care’.
Summary
: In addition to being a top contributor to pop-
ular repositories, we found that it is important to have
developers sponsoring others in the development commu-
nity. Our survey revealed that being a major contributor to
an important OSS project and being inspirational were par-
ticularly important criteria in determining who to sponsor.
4.3 RQ3: What are developers’ perceived
challenges and benets related to
sponsoring?
To address this research question, we conducted qualitative analyses
of the survey results, as described in Section 3.3.
RQ3.1: Why are developers looking for sponsors?
Table 3
shows the result of our coding, separately for sponsored devel-
opers and non-sponsored developers. From all 306 answers, the
majority referred to nancial support in general terms, accounting
for 100 sponsored and 83 non-sponsored developers, respectively.
Some sponsored developers started to accept donations to receive
recognition/ appreciation of their works and eort, accounting for
37 answers. Among the reasons, to gauge interest/ satisfaction is
a special reason related to the growth of OSS development. Devel-
opers consider GitHub Sponsors as a way to assess how the OSS
community responds to their works. Some developers see GitHub
Sponsors as a potential opportunity to become full-time OSS de-
velopers. For example, one respondent stated that “I have enough
money with my full time job, but I love contributing to OSS and
giving to the community. Sponsors are mainly a way for me to see
Table 3: Why are you looking for sponsors?
sponsored non-sponsored
nancial support in general terms 100 83
recognition/ appreciation 37 12
funding a particular feature/product 24 15
motivation 15 8
none 9 3
gauge interest/ satisfaction 8 5
not answered 7 8
Table 4: Are you doing anything special to attract sponsors?
sponsored non-sponsored
none 106 103
written content on GitHub 36 10
social media 24 5
perks for sponsors 11 4
not answered 7 8
Table 5: How has having sponsors aected you and the
projects you are working on?/ How does the lack of spon-
soring aect you and the projects you are working on?
sponsored non-sponsored
none 74 41
motivation 65 0
better project quality 18 0
satisfaction 14 0
not answered 14 10
other 1 3
limited eort 0 61
need other income 0 19
need other channels 0 1
how much interest my projects get from the community. If it became
self-sustaining some day, I could consider working full time on OSS.
Are you doing anything special to attract sponsors?
Table 4
shows the distribution of the codes across answers from sponsored
developers and non-sponsored developers. From all 306 answers,
the majority of developers indicated no specic activities to attract
sponsors, accounting for 106 and 103 respectively. Other actions
included specic perks for sponsors and advertising on social media
and/or the social coding platform itself.
RQ3.2: What is the impact of (not) geing sponsorship?
Ta-
ble 5 shows the results of the qualitative analysis. We found that
most of the sponsored developers (74) have not been aected by
having sponsors. The second most frequently mentioned impact
is motivation, accounting for 65 developers. For example, one re-
spondent pointed out: “It makes me feel bad when I ignore open pull
requests or bug reports for too long, and causes me some anxiety as to
whether it’s really okay for me to ask for money, even though I make
it very clear that sponsoring me won’t make development faster or
make me work on it full-time.” For non-sponsored developers, being
GitHub Sponsors:
Exploring a New Way to Contribute to Open Source ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA
Table 6: Why are you sponsoring others?/ Why did you be-
come a sponsor?
sponsored non sponsoring
dependencies/ beneted otherwise 22 11 22
recognition/ appreciation 22 13 17
generic help/ support 11 7 14
sustain project/ community 8 4 3
excellent work 7 6 5
fairness/ give back to community 7 3 5
motivation 5 4 4
set example 5 0 1
not answered 4 4 9
form of involvement 2 0 4
other 0 1 1
required to get access to features/ training 0 0 1
able to dedicate only limited eort is the most common impact from
not having sponsors, accounting for 61 developers.
RQ3.3: Why are developers sponsoring? Table 6 presents the
results. From the responses of 180 developers who indicated that
they were sponsoring, we found that having dependencies on the
code written by the receivers of the sponsorship and recognition/
appreciation are the most frequently mentioned reasons for all
dierent roles of OSS developers.
What are the eects of your sponsorship? Are the eects
as you expected?
Table 7 shows the distribution of the codes. From
all 180 answers, the majority of OSS developers have not observed
any impact of their sponsorship. Other sponsors mentioned grate-
ful/motivated developers, accounting for 13, 7, and 14 answers,
respectively. One interesting theme mentioned in the responses is
related to the collective of open source developers. For example,
one respondent stated: “No - It is dicult to know who to sponsor -
and many people don’t accept sponsorships. I wish folks who did not
need money could gather and re-distribute money (i.e., ow through).
Summary
: Our qualitative analysis revealed several bene-
ts and challenges related to GitHub Sponsors, as perceived
by its participants. While developers are hoping to receive
nancial support after signing up for GitHub Sponsors,
the majority of developers does not do anything specic to
attract sponsors. Sponsorship can aord funded developers
more time to improve project quality, but those not receiv-
ing sponsorship tend to look elsewhere for money. The
impact of sponsoring is not always clear to those making
the donations, but many donate out of appreciation, not
expecting anything specic in return.
5 DISCUSSION
In this section, we describe the threats to validity that aect our
study, and we discuss implications and future work.
Table 7: What are the eects of your sponsorship? Are the
eects as you expected?
sponsored non sponsoring
none 31 20 27
not answered 13 8 16
grateful/motivated developers 13 7 14
satisfaction 8 4 1
recognition as sponsor 2 1 2
fund particular activities 2 0 2
collective 2 0 0
sustain project 1 4 3
required to get access to features/ training 0 0 2
5.1 Threats to validity
Subjects are early adopters. GitHub sponsorship started in 2019
and at this point, all participants are early adopters. There are not
many developers who have obtained sponsors yet, which is a threat
to the external validity of our empirical study. Therefore, it is im-
portant to note that the ndings of this study are not generalizable
to all open source developers, but rather results for early adopters.
Sponsored developers in less-starred repositories. As explained in
Section 3.1, this study identies users involved in GitHub Sponsors
among developers who have contributed to repositories with 10 or
more stars. Assuming that most sponsored developers contribute
to popular repositories with a high number of stars, we targeted
these repositories, but did not consider sponsored developers who
only contribute to repositories with a low number of stars. To
examine the magnitude of the threat to external validity posed by
this limitation, we analyzed a sample of repositories with fewer
than 10 stars in the same way. Due to the large number of less
popular repositories on GitHub, it is not possible to retrieve all
repositories with 9 or fewer stars from the API. We used the list of
repositories from RepoReapers, which examined 1,857,423 GitHub
repositories for curating engineered software projects [
17
], and
investigated the star counts of all repositories in July 2021. We
identied 1,338,533 repositories that had a star count of 9 or less.
From the developers who contributed to repositories with 9 or
fewer stars, we excluded those who also contributed to repositories
with 10 or more stars, indicated in Section 3.1. We obtained 450,884
contributors who contributed only to repositories with 9 or fewer
stars. Among these contributors, we identied seven sponsored
developers. We manually investigated the proles of these seven
people, and found that four had changed their GitHub account
names, and that their accounts before the change were among
the contributors to repositories with 10 or more stars. Since there
were only three sponsored developers out of the 450,884 developers
who only contributed to repositories with 9 or fewer stars in the
approximately 1.3 million repositories surveyed, we can conclude
that the threat related to targeting contributors to repositories with
10 or more stars is small.
Up to 500 contributors from a repository. When retrieving the con-
tributors from a repository, only the top 500 developers with the
most commits could be retrieved due to API limitations. However,
a large repository can have more than 500 contributors. Due to this
ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA Shimada et al.
limitation, developers who are not in the top 500 committers for
at least one repository with 10 or more stars are not included in
our analysis. To examine the eect of this limitation, we measured
the highest commit rank in repositories with 10 or more stars con-
tributed to by each developer. The median and maximum values
for sponsored developers were 1 and 351, respectively, while the
median and maximum values for non-sponsored developers were
1 and 435, respectively. Most sponsored and non-sponsored devel-
opers in our analysis contribute to at least one repository with 10
or more stars where they are the main committer, so the threat to
external validity from the top 500 limit seems small.
Response biases. Recall bias can occur in survey research. This
means that respondents answer only what they remember and not
necessarily what was most important to them in the past. Therefore,
we tried to collect spontaneous responses and asked respondents
to answer most of the questions in an open-ended format.
5.2 Implications and Future Work
GitHub Sponsors advertises their service as enabling “a new way to
contribute to open source.” While donating to open source projects
is not necessarily new, our study conrms that some sponsors do
indeed see sponsorship as an alternative to contributing code, e.g.,
I had no more time to help with coding, so I decided to sponsor.
Most of the sponsors are active developers themselves, i.e., would
likely have the technical skills to contribute in other ways as well.
However, if they do not have sucient time, sponsorship can be an
eective way for them to show their support and appreciation.
A unique feature of GitHub Sponsors is its focus on enabling
sponsorship for individual developers instead of entire projects.
A side eect of this focus is that the social network of individual
developers becomes an important determiner for whether they will
be able to attract funding: our study identied several clusters in the
network of sponsoring relationships among sponsored developers.
While we only investigated sponsorship by individual developers,
organizational sponsorship is an important aspect that should be
analyzed in future studies.
Developers who had signed up for receiving sponsorship seemed
unsure what they could do to attract sponsors. It might be worth
for GitHub to simplify the current sponsorship tier system which
seems too complex for developers who are only looking for small
donations to stay motivated. Expectations around what one gets in
return for sponsorship are not always clear. From the perspective of
sponsors, we identied a wide range of reasons for giving, from sus-
taining the entire OSS community to expecting particular features
to be implemented. These expectations are not always perfectly
matched with the reasons that developers enabled GitHub Sponsors
in the rst place.
A recent trend related to expectations and sponsorship is ‘spon-
sorware’,
4
a “a release strategy for open-source software that en-
ables developers to be compensated for their open-source work
with fewer downsides than traditional open-source funding models.
In those cases, expectations are made very explicit and software
is not released until sponsorship has been obtained. This strategy
stands in contrast to sponsors giving to show appreciation or to do
4https://github.com/sponsorware/docs
something good for the OSS community in general. Future work
will have to investigate whether sponsorware has the potential to
disrupt the current OSS model.
6 RELATED WORK
There are many factors that aect the sustainability of OSS projects.
Researchers have argued that retaining newcomers is a way to
sustain OSS projects [
10
,
24
], and Steinmacher et al. [
24
] found
that 20% of newcomers became long-term contributors. Hata et
al. [
9
] suggest ways to incentivize developers to code and nally
make projects sustainable (they assumed projects that can attract
and retain coding contributors), which include that OSS projects
should prepare documentation and make innovations to reduce
code writing cost, and employ developers. Previous research [
25
]
showed that organizational sponsorship aects development ac-
tivity over time. According to GitHub’s representative survey [
6
],
OSS development highly relies on voluntary contributions (23% of
respondents indicated they contribute to open source as part of
their professional work). But recently, researchers found that the
number of employees paid to work (they assumed work during
weekdays from 9am—5pm as paid work) on OSS projects is increas-
ing [
21
]. Moreover, Atiq and Tripathi [
1
] explored how developers
perceive asymmetry in compensation in OSS projects, and found
that OSS projects that are distributed unequally may fail if they are
mismanaged. These researches point out that the nancial benets
are a factor to sustain OSS projects.
6.1 Donation
Donations become a common way for obtaining these nancial
benets [
3
]. Nakasai et al. [
18
,
19
] analyzed donations in the Eclipse
projects, and found that benets to donors and presenting badges
could motivate donations. Krishnamurthy and Tripathi [
14
] found
that commitment to an OSS platform contributes to the decision
to donate. Moreover, donations decrease response time to bug re-
ports of donors, and new releases are triggers of donations. Besides
that, Overney et al. [
20
] conducted a mixed-methods empirical
study on the prevalence of donations, characteristics of projects
requesting and receiving donations, and reasons for asking for do-
nations in OSS projects. They found only 0.2% of
npm
packages and
0.04% of GitHub repositories ask for donations and the commonly
used donation platforms are
PayPal
and
Patreon
. The projects
asking for and receiving donations tend to be more active, more
mature, and more popular. The authors also qualitatively analyzed
donation information (e.g.,
README.md
les and donation prole
pages) and identied four reasons for asking for donations in OSS
projects: Engineering (48%), Community (18%), Project expenses
(13%), and Personal (9%). In addition, Yukizawa et al. [
28
] promoted
new strategies that applied social proof and legitimization of paltry
contributions tactics to help OSS projects attract donations.
6.2 Bounty
Financial benets are an important extrinsic motivation to sustain
OSS projects [
1
]. Bounties are another way of obtaining these nan-
cial benets [
3
]. Unlike donations, bounties are used to motivate
specic developers (i.e., bounty hunters) for tasks which are not
of their primary interest by providing monetary incentives [
8
,
13
].
GitHub Sponsors:
Exploring a New Way to Contribute to Open Source ICSE ’22, May 21–29, 2022, Pisburgh, PA, USA
Several studies investigated the eectiveness of bounty programs
on disclosing vulnerabilities [
4
,
16
,
29
]. Similar to Kanda et al. [
11
],
Zhou et al. [
32
] conducted an exploratory analysis on bounty back-
ers and bounty hunters in the bounty issues addressing process of
OSS projects from the
Bountysource
platform. They found that
backers prefer to support implementing new features rather than
xing bugs, and bounty issues that are likely to be addressed by
hunters tend to be in more popular and mature OSS projects. More-
over, the timing of proposing bounties is the most important factor
in this process [
31
]. Zhou et al. [
30
] also found that questions with
bounty are likely to attract more trac on Stack Overow. Despite
the advantages of bounties, they could also lead to disadvantages:
winner-take-all property, disturbing the software development pro-
cess, short-termism, alienating volunteer developers, bypassing
existing leaders in the development community, attracting devel-
opers who lack project context, or redening the priorities of the
project in favor of the bounty [13].
6.3 Motivation
The motivation of OSS developers has been studied for decades.
Lakhani and Wolf [
15
] grouped this motivation into three groups: 1)
enjoyment-based intrinsic motivations, 2) obligation/community-
based intrinsic motivations, and 3) extrinsic motivations. They
found that being paid and feeling creative on OSS projects does
not have a signicant negative impact on project eort, contrary
to ndings on the negative impact of extrinsic rewards on intrin-
sic motivations [
2
]. Besides that, Roberts et al. [
22
] argued that
OSS developers being paid to participate leads to above-average
contribution levels, while intrinsic motivations do not signicantly
impact average contribution levels. Hars and Ou et al. [
7
] classied
motivations of OSS developers into internal and external factors.
They showed that external factors (e.g., building human capital,
self-marketing, peer recognition, and personal needs) have greater
weight. Von Krogh et al. [
27
] reviewed the literature on the motiva-
tion of OSS developers until 2009. They identied ten motivation
categories grouped into intrinsic motivation, internalized extrinsic
motivation, or extrinsic motivation. Gerosa et al. [
5
] investigated
shifts in the motivation of OSS developers via a survey, and found
that developers contribute to OSS projects for extrinsic factors, but
continue contributing because of intrinsic factors. While nancial
benets are common for experienced contributors, payment and
money are still not common motivators. Moreover, the study of
Krishnamurthy et al. [
12
] found that intrinsic and extrinsic motiva-
tions positively aect OSS developers’ intention to accept monetary
rewards.
7 CONCLUSION
To understand the potential of GitHub Sponsors in helping the open
source community attract and retain developers, we conducted
a mixed-methods study of 1,695,015 contributors from 1,168,856
repositories, focusing on sponsored developers, non-sponsored
developers, and sponsors. We identied dierences between those
successful in attracting sponsorship and those still waiting for their
rst sponsor. The fact that developers are often clustered in terms
of their sponsorship relationships implies that being connected to
sponsors and other sponsored developers can have an impact on
whether the search for sponsors is successful. While the impact
of sponsorship is not always clear, and some sponsors were left
disappointed that their donations did not have the intended eect,
most sponsors contribute as a token of appreciation and recognition
and/or for the good of the open source community.
8 DATA AVAILABILITY
Our online appendix contains the lists of studied repositories on
GitHub, the dataset for the network diagram for answering RQ1,
the features of sponsored and non-sponsored developers for RQ2,
the features of sponsors for RQ2, and survey material and coding
of responses for RQ3. The appendix is available at at https://github.
com/NAIST-SE/GHSponsors and https://doi.org/10.5281/zenodo.
6017901.
9 ACKNOWLEDGMENTS
This work has been supported by JSPS KAKENHI Grant Numbers
JP20H00587 and JP20H05706.
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