Understanding Bike‑Share Demand with a Simple Probabilistic Model

The city’s bike‑share system is a popular way to move around, but figuring out how many bikes people will need at different times and places is tricky. A new approach looks at the data from Madrid’s dock‑based network, BiciMad, and turns it into a clear model that can predict demand and spot problems. First, the method treats each bike ride as an event with two parts. The length of a trip is described by a Gamma curve, while the number of trips that happen each hour follows a Negative Binomial pattern. These two parts are linked to the time of day, whether it’s a weekday or weekend, and how much rain there is. By combining these statistical pieces with real patterns of where people usually start or finish rides, the model can create realistic fake data that mimics real usage.

The fake data is useful for many things. It gives a baseline of what normal demand looks like, including how uncertain that prediction is. When the model’s 95 % confidence bands matched real data almost perfectly, it showed that the math was sound. The same framework also helped find mistakes in the official records: a 2019 data set had wrong timestamps, and the model’s predictions flagged these errors before they were fixed. Unlike heavy simulation tools that try to predict every bike’s movement, this framework stays simple and easy to understand. It is meant for planners who want a quick way to test how changes—like adding new stations or closing some docks—might affect demand, and for data teams who need a quick check that the underlying records are correct. Overall, the approach shows that with standard probability tools you can build a transparent model for bike‑share demand. It keeps uncertainty in view, helps spot data glitches, and gives a useful starting point for future improvements.

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