Visualizing Volatility: Why the Negative Binomial Model Belongs in Hotel Forecasting

Forecasting in hospitality is never one-size-fits-all. The data shifts daily. Some patterns are smooth and consistent. Others are sharp, unpredictable, and driven by events outside our control. What matters isn’t choosing a flashy model—it’s understanding what your data is doing and applying the method that fits that behavior.

The chart compares two models that are often used to forecast count-based events like hotel bookings: the Poisson distribution (red line) and the Negative Binomial distribution (purple bars). Both models assume discrete outcomes. Both are grounded in probability theory. And both are useful.

Poisson Regression is not wrong. In fact, it's highly effective when the data meets its core assumption—that the mean and the variance are equal. Many booking patterns fit this. Weekdays, shoulder seasons, periods of steady demand—Poisson handles those well. That’s why it’s been widely used in both travel and airline forecasting (Leeuwen & Koole, 2021).

But what do you do when the variance is no longer equal to the mean?

That’s where Negative Binomial comes in. It adds a dispersion parameter—essentially allowing the model to account for variability that grows independently of the average. In hospitality, this is a common reality. Demand might average 15 rooms, but with pickups ranging from 5 to 30 depending on the day. No group behaves the same way. Campaigns don’t convert equally.

Volatility isn’t an exception. It’s part of the cycle.

This is not a theoretical problem. It’s operational.

A 10-room variance on a 40-room property changes labor, rate, and revenue. Overforecast and you bleed costs. Underforecast and you miss compression. The tools you use must reflect that volatility, not smooth it over.

Historically, the Negative Binomial distribution was developed to address exactly this kind of data. In the late 19th century, statisticians like Wilhelm Lexis and John Venn used it to model events like deaths, accidents, and insurance claims—areas where irregularity was normal and precision mattered (Lexis, 1879; Venn, 1880). Today, it’s widely used in epidemiology, risk modeling, and retail forecasting. Hospitality should be no different.

In practice, applying the Negative Binomial model to hotel forecasting allows you to do three important things:

• Predict the expected number of bookings

• Quantify how much that number might swing

• Plan commercial actions around both the volume and the risk

This matters most on days when volatility is likely—weekends, campaign days, school holidays, or any period with compressed lead time. These are the moments when traditional assumptions break, and flexibility becomes a competitive advantage.

What the visual comparison shows is simple but powerful: while Poisson gives you a tight, centered estimate, the Negative Binomial reflects the wider, more realistic spread of outcomes. It doesn't discard the central forecast—it expands your visibility around it.

Forecasting isn’t about being perfect. It’s about being prepared.

When variance behaves, Poisson works. When it doesn’t, Negative Binomial lets you stay grounded in data instead of gut feel.

That’s the difference between reacting and anticipating.

References:

• Hilbe, J. M. (2011). Negative Binomial Regression. Cambridge University Press.

• Leeuwen, R. van, & Koole, G. (2021). Demand forecasting in hospitality using smoothed demand curves. arXiv.