Tackling complex problems often requires coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of largescale, quantitative data. We analyze activity traces and success levels for ∼150,000 self-organized, online team projects. While larger teams tend to be more successful, the distribution of activity is highly skewed across the team, with only small subsets of members performing most work. This focused centralization in activity indicates that larger teams succeed not simply by distributing workload, but by acting as a support system for a smaller set of core members. High impact teams are significantly more focused than average teams of the same size, yet are more likely to consist of members with diverse experiences, and these members, even non-core members, are more likely to themselves be core members of other teams. This mixture of size, focus, experience, and diversity points to underlying mechanisms that can be used to maximize the success of collaborative endeavors. Massive datasets describing the activity patterns of large human populations now provide researchers with rich opportunities to quantitatively study human dynamics [1, 2], including the activities of groups or teams [3, 4]. With the rise in prominence of network science [5, 6] , much effort has gone into discovering meaningful groups within social networks [7, 8, 9, 10, 11, 12, 13, 14] and quantifying their evolution [15, 14] . Teams are increasingly important in research and industrial efforts [3, 4, 16] and small, coordinated groups are a significant component of modern human conflict [17, 18] . Recently, there has been much debate on the "group size hypothesis," that larger groups 1 arXiv:1407.2893v1 [cs.SI] 10 Jul 2014 are more robust or perform better than smaller ones [19, 20, 21, 22] . In scientific research, scholars have noted for decades that collaborative teams have been growing in size and importance [23, 24, 25, 26, 16] . Case studies show that leadership [27, 3, 28, 29] and experience [30, 31] are key components of successful team outcomes, while specialization and multitasking are important but potentially error-prone mechanisms for dealing with complexity and cognitive overload [32, 33, 34, 35] . New tools, including electronic sensor systems, can quantify team activity and performance [36, 4]. In all of these areas, large-scale, quantitative data can push the study of teams forward. Users of the Github web platform can form teams to work on real-world projects, primarily software development but also music, literature, design work, and more. A number of important scientific computing resources are developed through Github, including astronomical software, genetic sequencing tools, and key components of the Compact Muon Solenoid experiment's data pipeline Github provides rich public data on team activities, including when new teams form, when members join existing teams, and when a team's project is updated. These open collaborations evolve in an entirely self-organized manner and are not driven by hierarchical management as one may encounter at a commercial organization. Github also provides social media tools for the discovery of interesting projects. Users who see the work of a team can choose to flag it as interesting to them. This allows us to accurately quantify the impact of the team, in a manner analogous in many ways to citations of research literature. In this study, we analyze the memberships and activities of approximately 150,000 self-organized teams, as they perform real-world tasks, to uncover the blend of features that leads to success. To the best of our knowledge this is the largest study of real-world team performance to date. We present results that demonstrate (i) how teams distribute work activity across their members, (ii) the mixture of experiential diversity and collective leadership roles in teams, and (iii) how high-impact teams are different from other teams. To understand teams and the collaboration network between them, we began by characterizing their sizes and degrees of overlap. The distributions of team size M and teams per person k (Fig. 1A) both display truncation and significant rollover. Teams were relatively small, with only 0.46% of teams having M > 10 members. The dashed line indicates a pure power law P(x) ∼ x −3.5 and provides a guide for the eye. Such a high exponent emphasizes the degree of truncation we observed: while broader than a gaussian distribution, both M and k reflect underlying constraints on 1 For examples, see github.com/showcases/science. 2 See github.com/blog/1840-improving-github-for-science. with α = 3.5 near the steep distributions P(M) and P(k), and α = 1.5 near the broad distribution P(I). (B) Despite the overabundance of small teams, larger teams have significantly higher impact on average, with a 300% increase in I as M goes from 1 to 10. Errorbars here and throughout denote ±1.96 s.e. time and effort that prevent scaling. In contrast, the distribution of impact I, the number of times users flag a project as interesting (see Methods), was very broadly distributed. The shallower guide shows a power law with exponent 1.5. This broad distribution of I indicates the presence of significant preferential attachment [37, 38, 39] or rich-get-richer effects, as may be captured by a Simon model [40] . In the Supporting Information (SI) we reinforce these observations with a full statistical analysis, comparing multiple heavy-tailed models to the data. Despite the apparent drive towards smaller teams, there was a positive and significant relationship (p < 10 −10 , rank correlation ρ = 0.0845) between the size of a team and its success, with 300% greater impact on average for teams of size M = 10 compared to solos with M = 1 (Fig. 1B) . Larger teams tend to also have higher impact but, while the trend was highly significant, ρ indicates that there remains considerable variation in impact that is not captured by team size alone. Our next analysis reveals an important relationship between team focus and success. Unlike bibliographic studies, where teams can only be quantified as the listed coauthors of a paper, the data here allow us to measure the intrinsic work or volume of contributions from each team member to the project. For each team we measured the contribution w r of a member to the team's ongoing project, how many times that member updated the project (see Methods). Team members were ranked by contribution, so w 1 counts the work of the member who contributed the most, w 2 the second heaviest contributor, and so forth. The total work of a team is W = M r=1 w r . We found that the distribution of work over team members showed significant skew, with w 1 often more than 3 2-3 times greater than w 2 ( Fig. 2A and SI) . This means that the workloads of projects are predominantly carried by a handful of team members, or even just a single person. Larger teams perform more total work, and the heaviest contributor carries much of that effort: the inset of Fig. 2A shows that the fraction of work carried by the rank one member falls slowly with team size, and is typically far removed from the lower bound of equal work among all team members. See SI for more details. This focus in work activity indicates that the majority of the team serves as a support system for a core set of members. Does this arrangement play a role in whether or not teams are successful? We investigated this in several ways. First, we asked whether or not a team was dominated, meaning that the lead member contributed more work than all other members combined (w 1 /W > 1/2). High impact "top" teams, those in the top 10% of the impact distribution, were significantly more likely to be dominated than average teams, those in the middle 20% of impact ( Fig. 2B ). Given that it requires more effort to dominate a larger team than a smaller one, the fact that dominated teams were so prevalent in the high-impact regime emphasizes a strong need for workload focus. Next, we moved beyond the effects of the heaviest contributor by performing the following analysis. For each team we computed its effective team size m, directly accounting for the skew in workload (see Methods for full details). This effective size can be roughly thought of as the average number of unique contributors per unit time and need not be a whole number. For example, a team of size M = 2 where both members contribute equally will have effective size m = 2, but if one member is responsible for 95% of the work the team would have m ≈ 1.22. Figure 2C shows that (i) teams are effectively much smaller than their total size would indicate, for all sizes M > 1, and (ii) top teams are significantly smaller in effective size (and therefore more focused in their work distribution) than average teams with the same M. Further, impact is significantly, negatively correlated with m, for all M (Fig. 2D ). More focused teams have significantly higher impact that less focused teams, regardless of total team size. Focused work activity appears to be a crucial factor of success. Further analyses revealed the importance of team composition and its role in team success. The teams being studied are self-organized, and therefore it seems reasonable for successful teams to have evolved the key ingredients of success in an emergent fashion. Are there distinguishable patterns for who joins a team? Are successful teams more likely to be comprised of narrowly focused specialists? Will their members have longer histories of team projects? Team members do not perform their work in a vacuum, they each bring experiences from their work histories. Often members of one team belong to other teams at the same time. We investigated these facets of a team's composition by exploring (i) how many projects team members have worked on, (ii) how diverse are the other teams that members belonged to, and (iii) how many team members were "leads" of other teams. Experience E, the average number of other projects that team members have worked on (see Methods), was significantly related to impact. However, the trend was not particularly strong (see SI) and, as we later show via combined modeling efforts, this relationship with impact was entirely explainable by the teams' other measurable quantities. It may be that the past volume of work does not contribute much to the success of a team, but this seems to contradict previous studies on the importance of experience and wisdom [30, 31] . To investigate, we turned to a (Fig. 3) . Even small teams seem to have benefitted greatly from diversity: high-D duos averaged nearly eight times the impact of low-D duos. The relationship between D and I was even stronger for larger teams (Fig. 3 inset), implying that larger teams can more effectively translate this diversity into success. Even if the raw volume of experience a team has does not play a significant role in the team's success, the diversity of that experience is a key component of team impact. Considerable attention has been paid recently to collective leadership, where decision-making structures emerge from the mass of the group instead of being imposed via a top-down hierarchy [27, 29] . The open collaborations studied here have the potential to display collective leadership due to their volunteer-driven, self-organized nature. The heaviest contributor to a team is most likely to occupy such a leadership role. Further, since teams overlap, a secondary member of one team may be the "lead," or heaviest contributor to another. This poses an interesting  Figure 4: Teams with more leads have higher impact than teams of the same size with fewer leads. A lead is someone who contributes more work to at least one team he or she belongs to than any other members of that team. question: Even though teams are heavily focused, are teams more successful when they contain many leads, or few? A team with many leads will bring considerable experience, but its members may also lack the time and resources necessary to dedicate their attention to the team. The answer was overwhelming the former. We measured L, the number of team members who are the lead of at least one team (1 ≤ L ≤ M, see Methods), and found that teams with many leads have significantly higher impact than teams of the same size with fewer leads (Fig. 4) . Despite the limited support a team member can provide when he or she is occupied with other work, successful teams tend to arrange their members in exactly this fashion. Of course, the strong focus in work activity (Fig. 2 ) is likely interrelated with these observations. However, we will soon show that both remain significantly related to impact in combined models. Expanding on this observation, Table 1 illustrates the extreme case of teams with a single lead (L = 1) compared with teams comprised entirely of leads (L = M). The latter always displayed significantly higher impact than the former (MWU test, see table), independent of team size, underscoring the correlations displayed in Fig. 4 . Often the difference was massive: teams of size M = 7, for example, averaged more than 1200% higher impact when L = 7 than when L = 1. The best groups are sets of diverse leads. These results on focused work, experiential diversity, and leadership amplify our primary finding on team focus, and augment important existing research [30, 3, 4, 42, 29, 41] . We have found that a team does best when it is optimized along all three of these dimensions. Of course, it is necessary to explore the joint effects of quantities, which we will do with linear and nonlinear modeling. a When M ≥ 8, the number of teams with L = M is too small (N < 20) for us to conclude the difference in I is significant. One important aspect of the individual team measurements is that they do not exist in isolation. For example, successful teams also have high work activity (high W). This can correlate with effective team size m since the potential inequality between team members can grow as their total activity grows. In other words, we need to see how our team measures relate to impact together. To understand the relative effects of these team composition measures, we performed two analyses. First, a linear regression model of impact as a function of all explored measures is shown in Table 2 . Not only did this regression allow us to determine whether a variable was significant or if it is merely confounded by the other measures, but the coefficients (on the standardized variables) let us measure the relative strengths of each variable. Team size M, effective team size m, and lead number L play the strongest roles in team impact, and all three are significant in the presence of the other variables. The coefficient on m was negative while for M it was positive, further underscoring our result that, while teams should be big, they effectively should be small. Next, the total work W done on the project, followed by the diversity D of the team, were also significant measures related to impact. Finally, overall team experience E was not significant in this model (p > 0.1). We conclude that, while I and E are correlated by themselves, the effects of E are entirely explained by the other quantities. Second, we applied a nonlinear modeling technique called symbolic regression [43] . Symbolic regression evolves families of equations to best fit data. Our goal was to find equations of the form I = f (M, m, W, E, D, L). The overall 8 Table 2 : Combined robust regression model on team im- Num. of leads, L 0.1283 ± 0.003642 < 10 −270 a Variables are standardized for comparison such that a coefficient β x implies that increasing a variable x by one standard deviation σ x corresponds to a β x σ I increase in I, holding other variables fixed. best model, in terms of balancing complexity and accuracy, was In this equation, impact increases when M, W, D, and L increase, and decreases when m increases; experience E has no effect. In fact, E never appeared in any discovered model (see SI). This aligns well with the linear model. (How the second term contributes to changes in I depends on the magnitudes of W vs. L and D, so we performed a variable sensitivity study of this and all other discovered equations; see SI.) The collaborations under study are open and ongoing in that users can monitor the course of a team's project. The impact of the team may grow over time, as it makes improvements or progresses towards its goals. It is then natural to ask, are skilled team members attracted to join a successful, high impact project, or does their presence cause the team to later attract impact? To understand this, we conducted an experiment using a subset of the teams under study. Each of these n = 962 teams formed at approximately the same time, and each was actively updated with multiple members (M > 1) at the end of our data window. This ensures that these teams have comparable lifespans, and their entire evolution was available to us. We tracked the times when new members joined the team, and when I increased (someone from the greater community flagged the project as interesting). ) than teams that form after achieving impact (∆T > 0), independent of team size. The solid line denotes the average trend. by the team in our data window. For each team we measured ∆T , the average of the times when members join minus the average of the times when impact was received. If ∆T > 0, the team tends to receive success earlier than new members; for ∆T < 0, the team tends to grow in membership before success. Teams showed a strong trend towards membership formation predating success, with high impact teams almost always gaining members well before they gain their success (Fig. 5) . Teams with ∆T < 0 have a significantly higher median impact I = 8 compared to I = 3 for teams with ∆T > 0 (MWU test, p < 10 ). The average trend shown in Fig. 5 is not present in a randomized null model (see SI.) One explanation for this phenomenon is that the members of high impact teams are more capable of estimating a team's future potential than other users, and so can anticipate the best teams to join. Of course, establishing causality is difficult: a confounding factor may have caused the team members to join the team and then later caused the project to become popular. But this result does indicate that one argument is unlikely, success does not bring the team. There has been considerable debate concerning the benefits of specialization compared to diversity in the workplace and other sectors [32, 34] . Our discoveries here show that a high-impact team forms a diverse support system for a specialist core, indicating that both specialization and diversity contribute to innovation and success. Team members 10 should be both specialists, acting as the lead contributor to a team, and generalists, offering ancillary support for teams led by another member. This has implications when organizations are designing teams and wish to maximize their impact. Teams tend to do best on average when they maximize M (Fig. 1B) while minimizing m (Fig. 2D ) and maximizing D (Fig. 3) and L (Fig. 4) . The negative relationship between effective team size m and impact I (as well as the significantly higher presence of dominated teams among high impact teams) further belies the myth of multitasking [33, 34] and supports the "surgical team" arguments of Brooks [44] . Focused work activity, often by even a single person, is a hallmark of successful teams. This focus both limits the cognitive costs of task switching, and lowers communication and coordination barriers, since so much work is being accomplished by one or only a few individuals. Of course, some tasks are too large for a single person or small team to handle, necessitating the need for megateams of hundreds or even thousands of members. Our results indicate that such teams may be most effective when broken down into large numbers of small, overlapping groups, where all individuals belong to a few teams and are the lead of at least one. Doing so will help maximize the experiential diversity of each sub-team, while ensuring each team has someone "in charge". An important open question is what are the best ways to design such pervasively overlapping groups [13] , a task that may be project-or domain-specific but which is worth further exploration. Dataset. Public Github data covering 1 January 2013 to 1 April 2014 was collected from githubarchive.org in April 2014. These activity traces contain approximately 110M unique events, including whenever users create, join, or update projects. Projects on Github are called "repositories". A team is the set of users who can directly update ("push to") a repository. Activity or workload W is measured by the number of pushes. Users on Github can bookmark projects they find interesting. This is called "stargazing". We take the maximum number of stargazers for a team as its measure of success or impact I. To avoid abandoned projects, studied teams have at least one stargazer (I > 0) and at least two updates per month on average (151542 teams). To mitigate outlier effects when averaging and modeling (excluding Fig. 1A) , projects above the 99th percentile of I and the 99.99th of W were removed. Since very few teams have M > 10, those teams were not studied. This leaves N = 148272 teams. A total of 275387 unique users participated in these teams. where the sum and union run over the M members of the team. Note that D ∈ [1/M, 1). Someone is a lead when, for at least one team they belong to, they contribute more work to that team than any other member. A non-lead member of team j may be the lead of team k j. The number of leads L k in team k is: where L i j = 1 if user i is the lead of team j, and zero otherwise. The first sum runs over the M k members of team k, the second runs over all teams j. Acknowledgments We thank Josh Bongard, Brian Tivnan, and Paul Hines for useful discussions, and we gratefully
Larger groups are also able to gain more success in collaborative efforts such as software development REF .
Understanding the group dynamics and success of teams
R. Soc. open sci. 2016 3 160007
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