Industry 4.0 and Industrial Internet of Things projects work towards adoption of standard IT technologies for real-time control networks in industrial automation. For this the IEEE 802.1 Time-Sensitive Networking (TSN) Task Group has developed and continues to develop a set of standards. One of these standards is the IEEE 802.1AS clock synchronization protocol. IEEE 802.1AS can be used to enable time-triggered communication as well as to coordinate distributed actions in industrial networks. In this paper we study the synchronization quality of IEEE 802.1AS and we are interested in whether the clocks can be synchronized with sufficiently low error such that the protocol can be used for demanding industrial automation applications. In particular, we study the protocol behavior in large-scale networks while considering critical implementation details. We report analytical worst-case results as well as probabilistic results based on simulations, that show that implementation details such as the PHY jitter and the clock granularity have a big impact on the time synchronization precision.