Are Averages Misleading? The Ergodicity Trap: The Use of Averages in Predicting School Performance

Context

Educators, administrators, and policymakers frequently depend on average test scores to evaluate school performance, allocate educational resources, and shape policy decisions. Yet, this widespread reliance on averages may obscure more than it reveals. Specifically, when it comes to forecasting the future success of individual schools, mainly on high-stakes assessments, averages can become unhelpful and dangerously misleading. This article explores the concept of ergodicity and its implications for educational assessment, arguing that most school systems are non-ergodic and therefore incompatible with predictive models based solely on historical averages.

The Fallacy of Averages in Educational Forecasting 

Look at the usual performance prediction process: school administrators use midterm scores to anticipate end-of-year outcomes. Let's say that if the state midterm average in math is 70, and historically, that has correlated with meeting minimum proficiency standards, some districts assume that any school reaching 70 at midterms is on track. However, suppose the passing requirement for midterm tests is 75 in certain schools or districts due to curriculum pacing, resource gaps, or testing frameworks. In that case, reliance on the state average leads to false confidence and insufficient preparation. Some say, “big mistake.”

This example highlights a critical flaw in the conventional model: it assumes that all schools operate under the same trajectory of performance and response. It ignores the unique dynamics, histories, and local factors that shape student outcomes within each institution.

Introducing Ergodicity: 

A Perspective from Complex Systems 

The notion of ergodicity originates in statistical physics but has profound implications in education, economics, and system dynamics. A system is ergodic if the average outcome of a group over time is equal to the average outcome of one entity observed over the same period. In simple terms, group averages can reliably stand in for individual predictions in an ergodic system.

However, most real-world systems—including educational ones—are non-ergodic. A non-ergodic system means that the experience of a single school over time can significantly diverge from the average experience of many schools in a single year. The assumption that a school will achieve at the average state-level performance overlooks variability, shocks, and compounding effects unique to that institution.

Why Schools Are Non-Ergodic Systems

 

Schools are deeply affected by factors that change over time—teacher turnover, funding shifts, leadership transitions, demographic changes, neighborhood dynamics, and external shocks like pandemics or policy reforms. These variables create individualized pathways that deviate from the state or district average. Therefore, a school’s performance trajectory is not a simple function of its current score relative to an average, but a product of many interdependent, evolving conditions.

Moreover, the learning process is itself non-linear. Gains are not uniformly distributed across time or students. Interventions that work for one school may have a limited or delayed impact in another. Test scores may spike or drop due to local, contextualized causes that are invisible in aggregate metrics.

The Risks of Misapplying Averages in Decision-Making 

When policymakers use averages to plan instructional interventions, deploy resources, or enforce accountability measures, they risk implementing strategies that do not suit everyone. For underperforming schools, this could mean interventions arriving too late. For high-performing schools, it might result in complacency or underfunding. Most dangerously, systemic reliance on ergodic assumptions could reinforce inequality by penalizing schools whose unique conditions make them outliers.

The limitations of averages are not an argument against data but a call for deeper analysis. Recognizing non-ergodicity in schools compels us to use individual time-series data, analyze local variance, and adopt predictive models sensitive to temporal and structural shifts.

Toward a New Predictive Way 

To move beyond the ergodicity trap, educational forecasting must evolve:

Individualized Trajectories: Schools should be assessed based on their own historical performance trends, not against static group averages.

Dynamic Modeling: Incorporate system dynamics and complexity science into predictive analytics. This includes feedback loops, threshold effects, and nonlinear progression.

Context-Aware Interventions: Tailor strategies based on each school’s specific challenges and assets, informed by qualitative and quantitative data.

Scenario Planning: Rather than treating projections as certainties, use probabilistic forecasting that accounts for a range of possible futures.

Finally 

Average scores may be comforting in their simplicity, but they are often illusions of stability in complex systems like education. By embracing the concept of ergodicity and recognizing the non-ergodic nature of school systems, we can design more accurate forecasts and effective policies. Such a shift demands that we treat each school not as a datapoint on a curve but as a living, evolving system worthy of individualized understanding and support. Only then can we move toward equity-informed, performance-driven reform that truly meets the needs of all learners.

References

Peters, O. (2019). The ergodicity problem in economics. Nature Physics, 15, 1216–1221. https://doi.org/10.1038/s41567-019-0732-0

Taleb, N. N. (2018). Skin in the game: Hidden asymmetries in daily life. Random House.

Mason, M., & Wilson, M. (2006). Complexity theory and education: The new paradigm. Educational Philosophy and Theory, 38(2), 211–226. https://doi.org/10.1111/j.1469-5812.2006.00217.x

Mehta, J., & Fine, S. (2019). In Search of Deeper Learning: The Quest to Remake the American High School. Harvard University Press.

Senge, P. M. (2006). The Fifth Discipline: The Art and Practice of the Learning Organization. Doubleday.

Bryk, A. S., Gomez, L. M., Grunow, A., & LeMahieu, P. G. (2015). Learning to improve: How America’s schools can get better at getting better. Harvard Education Press.

National Research Council. (2011). Incorporating 21st Century Skills into K-12 Education: A Guide for Policymakers. The National Academies Press.

Kamenetz, A. (2015). The Test: Why Our Schools Are Obsessed with Standardized Testing–But You Don’t Have to Be. PublicAffairs.

Additional Source:

Ergodicity economics — a history, Ole Peters: https://ergodicityeconomics.com/2024/02/05/ergodicity-economics-a-history-2/

Final Remarks

This article and analysis result from a compilation of references and notes from various theses, authors, media, and academics, gathered by a group of friends from “Organizational DNA Labs.” We employed AI platforms, including Gemini, Storm, Grok, Open-Source ChatGPT, and Grammarly, to expedite research and ensure clarity and logical flow. Our additional goal in using these tools was to verify information across multiple sources and validate it through academic databases and collaborations with equity firm analysts.

The provided references and notes offer a comprehensive list of our sources. As a researcher and editor, I have meticulously ensured proper citation and recognition of all contributors. The primary content stems from our compilation, analysis, and synthesis of these materials. Our summaries and inferences reflect a commitment to expanding and disseminating knowledge. While high-quality sources inform our perspective, the final conclusion represents our current views and understanding of the discussed topics, which are subject to change through continuous learning and literature reviews within this business field.