One of the many impacts of the COVID-19 crisis has been to highlight the role of quantitative models in our lives. Ideas associated with modeling, such as flattening the curve of disease transmission, are now regularly discussed in the media and among families and friends. Across the globe, we are trying to understand the numbers and what they mean for us.

Forward-looking models aren’t new. They have long played an important but unseen role in day-to-day life—for instance, in pricing homeowners’ insurance, anticipating the weather, and deciding how many iPhones to manufacture. However, in the COVID-19 pandemic, the scale of impact and the level of uncertainty have introduced new challenges—and notoriety—for modelers.

Used properly, models provide information that can present a framework for understanding a situation. But they aren’t crystal balls that state with certainty what will happen, and they don’t in themselves answer the difficult question of what to do. The eminent British statistician George Box summarized the point with his famous aphorism: “All models are wrong, but some are useful.” And he refined it by saying, “Since all models are wrong, the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad.”

This article explains how models can help us make sense of the world and why they behave the way they do (see sidebar “What is a model?”). We also discuss the most common modeling pitfalls and how to avoid them.

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