Different indices have been proposed in the literature to characterize headway regularity. These metrics aggregate the headway variability for a service, but none can be directly associated with a specific driver. This paper seeks to understand drivers' influence on a service's regularity. To do so, we propose four regularity indices related to a driver's performance and use the Hierarchical Clustering Analysis method to generate a classification of drivers according to their contribution to the headway regularity during the operation of a service. We characterize each class based on the driver's attributes such as age, years of experience as a driver, and years in the bus company, and those attributes associated with the operation, such as number of services per day and period of the day. The results show consistency in the classification obtained, with nearly 90% of drivers remaining in the same regularity classes regardless of the index.