Carpooling has the potential to transform itself into a mass transportation mode by abandoning its adherence to deterministic passenger-driver matching for door-to-door journeys, and by adopting instead stochastic matching on a network of fixed meeting points. Stochastic matching is where a passenger sends out a carpooling request at a meeting point, and then waits for the arrival of a self-selected driver who is already travelling to the requested meeting point. Crucially there is no centrally dispatched driver. Moreover, the carpooling is assured only between the meeting points, so the onus is on the passengers to travel to/from them by their own means. Thus the success of a stochastic carpooling service relies on the convergence, with minimal perturbation to their existing travel patterns, to the meeting points which are highly frequented by both passengers and drivers. Due to the innovative nature of stochastic carpooling, existing off-the-shelf workflows are largely insufficient for this purpose. To fill the gap in the market, we introduce a novel workflow, comprising of a combination of data science and GIS (Geographic Information Systems), to analyse driver GPS traces. We implement it for an operational stochastic carpooling service in south-eastern France, and we demonstrate that relaxing door-to-door matching reduces passenger waiting times. Our workflow provides additional key operational indicators, namely the driver flow maps, the driver flow temporal profiles and the driver participation rates.