When it comes to assessing risk, there are few better laboratories than a football gridiron.
Thomas Matheson, an operations research and financial engineering (ORFE) major from the Class of 2025 and starting left guard on Princeton’s football team, devoted his senior thesis to the question of what coaches should do on a decisive fourth-down play, a team’s last chance to move the ball down the field or else turn over the ball to the other team.
Matheson hypothesized coaches were too conservative, conceding a chance to score in favor of leaving the other team in a worse position. He hypothesized that coaches could win more often with more aggressive plays. Not satisfied with his gut instinct, Matheson took the ORFE approach of testing his beliefs by applying data, studying hundreds of thousands of plays and employing machine learning technology to identify winning strategies.
Matheson’s research ended up showing the opposite of what he expected: Excessive aggression is not always the best play. Matheson, now a master’s student and football player at Boston College, found that coaches who tend to either punt or kick a field goal at key moments in a game, as opposed to using more aggressive tactics to score points, tended to win more often. He gained a newfound appreciation for coaches’ intuition to avoid costly aggression.
“Coaches are not too conservative in general. They might just be better at finding good spots to be aggressive,” Matheson said.
Navigating uncertainty using statistics and probability has been a winning strategy for Princeton’s Department of Operations Research and Financial Engineering for a quarter century. ORFE’s mouthful of a name befits a department dealing with complexity.
While the department’s research often finds use in economics and finance, ORFE faculty, students and alumni have also developed new approaches to managing sustainable energy, health care and transportation systems; and methods to improve artificial intelligence and robotics.
More than 25 years after its creation, ORFE’s mission of making good decisions in uncertain situations is more important than ever, and its researchers are employing new tools, namely machine learning, in that process.
Through it all, the department has stayed true to providing its students with foundational knowledge in statistics (collecting, analyzing and interpreting data), probability (how likely something is to happen) and optimization (making something the best it can be).
“In a way we are the intellectual owners of uncertainty on the campus of Princeton,” said Mete Soner, the Norman John Sollenberger Professor of Operations Research and Financial Engineering and current chair of the department. “That is our core: uncertainty and what you do with it.”
ORFE has enjoyed increasing popularity as a major because it equips students to build solutions to some of the world’s toughest and most interesting problems in business. Not only did Princeton’s valedictorians come from ORFE in both 2020 and 2021; it is consistently the second most popular major in the School of Engineering and Applied Science, behind computer science. This year it graduated 66 seniors, a number set to grow further based on the size of the current sophomore and junior classes. Eleven students completed ORFE Ph.D.’s this year, and the department currently has 47 graduate students.
An origin in bridging disciplines
Although ORFE was born in the fall of 1999, its roots go far deeper, tracing the rise, decline and resurgence of interest in statistics. In fact, it was the search for a home for statisticians at Princeton that led to the department’s creation.
Early work in that area included some of Princeton’s most legendary faculty, including John von Neumann, Alonzo Church, John Tukey and John Nash Jr., as well as a well-known graduate student, Alan Turing, who is often called the father of computer science.
In 1965, statisticians split off from the Princeton math department and formed the Department of Statistics. But when that department closed in 1985, the University encouraged departments in the natural and social sciences and engineering to invest in statistics as they saw fit.
By the mid-1980s, many of Princeton’s statisticians found their home in the civil engineering department. It may be hard today to envision what engineers who create buildings, roads and bridges have in common with finance experts. But both areas rely heavily on statistics, said ORFE department chair Soner.
According to the book “The New Princeton Companion”, civil engineering was home to the Basic Engineering program, which was started in 1938 to “meet the needs of students wishing to prepare for the administrative and economic aspects of an engineering career in industry or government.” This program became known as Engineering Management Systems and was later absorbed by ORFE.
In 1986, the Department of Civil Engineering added “and Operations Research” to its name. Nevertheless, by 1999, some of the operations research faculty wanted to move into financial engineering, defined as using math to solve problems in finance. It was a metaphorical bridge too far from the civil engineering department’s origins.
So, Operations Research and Financial Engineering was spun off into its own department in 1999; the remaining department was renamed Civil and Environmental Engineering, which it remains today.
The department began with seven faculty members and about 30 undergraduates, and today has 23 faculty members, including both professors and lecturers. ORFE is housed in Sherrerd Hall, described as a “deceptively simple glass cube” and “a study in light” when it was completed in 2008.
Math with a message
In the building’s central stairwell hangs a painting of Erhan Çinlar, who served as the department’s founding chair from 1999 to 2005. Based on a 2008 photograph, the picture shows him gesturing toward equations on a blackboard while holding a piece of chalk.
Çinlar, now an emeritus professor, was widely recognized for his pioneering research and his commitment to teaching and mentoring. For many years he taught an introductory class, “Probability and Stochastic Systems,” which alumni have credited with changing the way they view the world and approach decisions.
“We make lots of decisions under uncertainty, and he really helped dispel some of the bad intuition we as human beings have about probability,” said Kemal Askar, a 1998 graduate in civil engineering and operations research who took several courses with Çinlar. Nearly three decades later, Askar said he continues to be guided by Çinlar’s message that “it’s not just about coming up with a mathematical solution and being really good with the numbers. You need to then be able to convey those ideas and win people over.” Askar, now a managing director of global rates at Deutsche Bank, serves on ORFE’s academic advisory council.
From fiction to finance
The department “prepares its students to excel in any domain where quantitative thinking is valued,” said Nicholas Johnson, Princeton’s 2020 valedictorian — the University’s first Black valedictorian as well as the first ORFE concentrator to receive this honor.
A strong grounding in probability also “prepares students to be leaders in their careers,” said Johnson, “because real-world decision-making is very rarely black and white. That’s something I’ve experienced a lot since graduating from Princeton.” Johnson completed a Ph.D. in operations research at the Massachusetts Institute of Technology last year and is now working in quantitative finance and helping to build a computer vision startup.
ORFE faculty members tend to be more grounded in mathematics than finance, Soner said. In fact, about two-thirds of the department’s faculty have no formal training in finance, he said. Nevertheless, about half of its B.S.E. graduates go into the financial industry, even including those whose senior theses had nothing to do with finance, he said. Many also go on to work at large consulting firms. A lot of students start their careers at quantitative trading firms, he said. Those firms rely on mathematical and statistical models that help point out good trades.
“We teach risk management,” Soner said. “That is exactly what I want to teach my students, how to manage the risk of their portfolios, their positions. That is extremely valuable.”
The department’s emphasis on managing uncertainty and risk has led to some interesting uses. Some recent senior theses have sought to advance the performance of Shariah-compliant investment portfolios, model the global semiconductor market, optimize the placement of patients in hospitals, and quantify rates of intergenerational economic mobility.
Katy Milkman, a 2004 ORFE graduate and one of the department’s best-known alumni, also earned a certificate in American studies. Her senior thesis combined her interests to pose some unusual questions: How did the editors of The New Yorker magazine influence the short fiction pieces published over the course of a decade? Did editorial shifts impact which types of stories were published? Did authors write about characters who resembled them demographically?
Her study found that authors were indeed “autobiographical” in how they approached their works, although authors from underrepresented groups were more likely to stretch and write from the point of view of someone from a majority group. She also found there were major changes in the kinds of pieces that were published when the fiction editor changed, but not when the editor-in-chief changed.
Milkman has called her thesis a transformative experience and said her ORFE education was crucial to setting her on a career path to use insights from economics and psychology to help people make positive behavioral change such as saving money, exercising, and doing better in school. She is now the James G. Dinan Endowed Professor of Operations, Information and Decisions at the Wharton School of the University of Pennsylvania, and a member of ORFE’s advisory council.
ORFE, she said, is inherently interdisciplinary. “I’ve never fit in any narrow category myself, and it made me feel comfortable sitting in the boundary between things.”
Making machines learn, before it was called AI
The department’s courses “are agnostic in the sense of applications. We teach statistics, probability and optimization” using diverse examples from finance and economics, and decision and data sciences, said Ronnie Sircar, Eugene Higgins Professor of Operations Research and Financial Engineering, who chaired the department from 2018 to 2024. “Whatever the next big thing is, these tools will be valuable,” he added, noting that an increasing number of students are now pursuing data science and AI theory.
Sircar and professor René Carmona received a five-year grant from the U.S. Department of Energy to explore ways to optimize the integration of renewable energy into the power grid, and are now working to commercialize their team’s software. The project requires a large amount of data from the electrical grid, which is then processed, modeled and simulated using machine learning to predict electricity prices, customer demand and renewable energy production.
“Machine learning” is a term most people relate to nowadays, but ORFE researchers have been using that sort of technology for several decades, said Carmona, the Paul M. Wythes ’55 Professor of Engineering and Finance. Back then, he said, it was referred to as high-dimensional data analysis. There has been a quantum leap in computing power, memory size and performance of the computer implementations of neural network models. Still, there are applications of paramount importance to the mission of ORFE for which the use of machine learning remains problematic and requires more research, he said. The scarcity of historical data to train neural networks for stock trading is a case in point.
The enduring importance of foreseeing failures
Over the quarter century since ORFE was founded, the field of operations research has given rise to some amazing advances, said John Mulvey, one of the department’s founding faculty members and still an active professor. For instance, air travelers are subjected less often to planes circling the runway as the aviation industry gets better at managing potential disruptions, he said, and Amazon is really good at making sure your package arrives by the promised time.
In a way, the department’s melding of finance with other areas of engineering anticipated recent developments in the financial industry, said Mulvey. Just as civil engineers predict potential failures as they weigh tradeoffs when designing bridges, financial engineers try to learn from problems in finance to build better solutions going forward, he said. For instance, being able to foresee the cause of a bank failure can inform steps to avoid it. Individuals need to protect themselves from a market crash, and universities can study how to protect their endowments, he said.
“The heart of the matter is, how do you make decisions under uncertainty? The world’s more and more uncertain nowadays,” Mulvey said, adding, “we were surprised it became so important to the world.”
