Using a story of credit allocation gone wrong, we introduce some of the challenges that come with assigning credit to collaborative work in science, espeically given the historicial emphaisis on individual acheivement in our field. We explore traditional methods for indicating ownership of scientific work, particularly the ordering of authors on a paper. While this method for understanding who should get the lion’s share of the credit for a discovery is usually effective, it is complicated by discipline-specific variations in the order of authorship. We also look at how alphabetical ordering of authorship in some fields further complicates the picture, how “guest authors” and “ghost authors” reflect flaws in the credit allocation system, and how bias affects the process adversely. We end with a discussion of the alarming colloboration penalty women economists experience, which illustrates the mishaps that can and do occur as a result of the existing system.

Citations reflect the cumulative nature of science, where new research builds on previous discoveries. While citations have been previously used to condense and signal knowledge, they have been employed more recently to gauge the scientific impact of a particular paper or discovery. Groundbreaking work, the thinking goes, should be highly cited by other scientists. In Part III, we explore how scientific impact is quantified, focusing less on the producers of science and more on the work that is produced.

To provide a framework for understanding the importance of team assembly, we open the chapter with a story about teams of chickens. This leads into a discussion about the “too much talent” effect in a range of arenas. We then discuss the role that diversity plays in scientific teamwork. Studies show that diversity among team members – whether ethnic, international, or institutional – promotes the team’s effectiveness, with ethnic diversity offering the largest boost in impact of the resulting paper. We also define collective intelligence and explore that factors that lead to highly intelligent teams. Finally, by mapping the larger networks team members are involved in, we’ve identified four types of links that influence group effectiveness. By varying the proportion of these types of links within a network, we can see how certain coauthorship patterns will impact a team’s success. Taken together, these results show a strong correlation between a team’s composition and the quality of the work it produces. We end by discussing super-ties, or extremely close working relationships that become scientific partnerships, which yield surprising citation and productivity premiums.

The random impact rule allows us to build a null model of a career. Using the null model, we can examine what a scientific career looks like when its driven by chance alone. We call this the R-model. But the R-model only accounts for differences in productivity, not differences in ability or talent. In response to this discrepancy, we create the Q-model, which assumes that the impact of papers we publish is determined by two factors, luck and a Q parameter unique to each person. We can then calculate how a person’s highest impact paper is expected to change with productivity. We find that the Q-model’s predictions are in excellent agreement with real world data. In fact, the Q parameter alone seems sufficient to explain what differentiates one scientist from another. We also find that it remains relatively stable over the course of a career. We then show how we calculate the Q factor for individual scientists, how we can use their Q factor to predict their impact, and how doing so provides a more accurate forecast of a scientist’s future impact than the h-index can. In the case of great scientists, we see that the Q factor turns luck into a consistently high impact career.

We begin by detailing Einstein’s “miracle year,” during which he published four major discoveries. We discuss the debate over the existence of hot streaks in sports, and ask if a hot-streak phenomenon exists in science. To address this question, we look at the relative timing of hit works during a career, which is captured mathematically by a normalized joint probability. We find that hit works are more likely to colocate than they would by chance, indicating that hot streaks do occur. So while the timing of each highest impact work is random, the relative timing of top papers in a scientist’s career shows a high degree of temporal clustering. To account for these patterns, we introduce a slight variation to the Q-model – a brief period of elevated impact. We call this the “hot-streak model.” The model shows us that hot streaks are ubiquitous across creative careers, that they usually occur only once, and that they occur randomly. We then discuss the implications of these findings for scientists and science administrators, using the life of John Fenn as an example of how the hot-streak model can provide a hopeful framework for scientists still waiting for their big break.

We illustrate some of the challenges of credit allocation in science by discussing the Thomas theorem –often seen as the orgin of the “self-fulfilling prophecy” – which, ironically given its subject matter, has been repeatedly cited as the work of W. I. Thomas alone. Thomas’ coauthor and wife, Dorothy Swaine Thomas, has never received the credit she deserved for the discovery. This raises this issue of how biases affect credit allocation in science, since our perception of who deserves credit is reinforced by the Matthew effect. We tend to give disproportionate credit to renowned scientists over unknowns, making coauthoring with eminent scientists risky. Many of these problems arise because credit is allocated collectively in science, based on the community’s perception of who is responsible for a discovery. While that perception is often correct, there are plenty of instances where the community gets it wrong. We describe how a collective credit allocation algorithm, which was created using cocitation patterns, can capture how the community assigns credit and predict who will get credit for a discovery. We then discuss the algorithm’s implications for individual scientists.

Here we discuss the growing dominance of teams in science. Importantly, this shift toward collaborative work is not unique to fields where experimental challenges are becoming more complex and expensive. Rather, we see a universal rise in team science even in “pencil and paper” disciplines like mathematics and sociology. We find that teams tend to produce more impactful science, garnering more citations than solo-authored work at all points in time and across all disciplines. What has driven the shift toward collaboration in science? The increasing complexity and expense of scientific experimentation forces communities to share resources and knowledge effectively. Additionally, the ever-broadening body of knowledge has made specialization necessary, which means that each person has command of a small piece of a larger puzzle. We also discuss what we call “the death of distance” created by advancing technologies, which has made collaboration easier both among institutions and across international borders. While the advantages of these types of collaboration are clear, there are some potential drawbacks which we detail here.

Here we introduce Part IV, where we will discuss the work at the frontiers of the science of science, the future of the discipline, and how knowledge of the doings of science may change how science is done.

In this chapter we define and detail the Matthew effect, exploring the role that status plays in success. We use the absence and presence of Lord Rayleigh’s authorship on a paper to introduce the idea of reputation signaling, and look at how reputation signaling plays out in randomized control experiments. We then discuss the implications of reputation signaling for both single and double-blind review processes. We find that the Matthew effect applies not just to scientists themselves, but also to their papers through a process known as preferential attachment. To see how an author’s reputation affects the impact of her publications, we look at how her citation patterns deviate from what preferential attachment would predict. We also explore the drivers behind the Matthew effect, asking whether status alone dictates outcomes or whether it reflects inherent talent.

Here we outline our aims for the book and provide a definition for the science of science. We also identify our audience – scientists and students, science administrators, and policymakers, and those already working on science of science research. We explain that the book is structured into four parts: The Science of Career, The Science of Impact, The Science of Collaboration, and an Outlook on the future of the science of science.

We introduce Part II by sharing the story of the LIGO experiment which validated Einstein’s theory of general relativity and which many consider to be the “discovery of the twenty-first century.” While Einstein’s discovery was made by a single scientist, the LIGO experiment involved the contributions of over 1,000 authors. These two discoveries, made 100 years apart, speak to the changing nature of science, where 90% of papers now are written by teams. In Part II we will explore the implications of collaborative work, the benefits and challenges of working in teams, and the factors that help and hinder team effectiveness.

Here we explore peer effects in science, outlining the ways in which scientists affect each other’s outcomes and behavior. In particular, we look at the influence of star scientists on their colleagues, showing that both the productivity of a department and the quality of future faculty increases after a luminary is hired. We detail the negative affect that a star scientist’s death can have on her colleagues, effects which speak to the power of the “invisible college” that binds scientists together in shared interests and ideas. Lastly we outline examples of how changes to the invisible college can have far-reaching impact, demonstrating the highly connected nature of science.

The exponential growth of science has continued, virtually uninterrupted, for decades. What does this mean for contemporary scientists? With the scientific literature doubling every 12 years, the practice of science is characterized by immediacy: 80 to 90 percent of all scientists who have ever lived are alive now. That means that science is becoming more competitive. If one invididual doesn’t make a discovery, someone else likely will. We explore the implications of this growth and competition for scientists from a training and employment standpoint, finding that it is increasingly difficult to earn a PhD and to locate a job in academia after a doctorate is earned. That doesn’t mean that making it as a scientist is impossible – the dearth of jobs in academia has led to a shift toward industry, where many scientists thrive. We end the chapter by asking if new discoveries require more effort than they did in the past. We can answer this question by comparing the growth rate of the workforce compared with the growth rate of producitivity, finding that there is relative stability in individual productivity over a wide range of disciplines.