Measuring the Quality of Experience (QoE) undergone by cellular network users has become paramount for cellular ISPs. Given its overwhelming dominance and ever-growing popularity, this paper focuses on the analysis of QoE for YouTube in mobile networks. Using a large-scale dataset of crowdsourced YouTube QoE measurements collected in smartphones with YoMoApp, we analyze the evolution of multiple relevant QoE-related metrics over time for YouTube mobile users. The dataset includes measurements from more than 360 users worldwide, spanning over the last five years. Our data-driven analysis shows a systematic performance and QoE improvement of YouTube in mobile devices over time, accompanied by an improvement of cellular network performance and by an optimization of the YouTube streaming behavior for smartphones.