The SImple Synchronization Protocol (SISP) has been designed for tiny sensors to offer a wireless synchronization service to the network. SISP is completely distributed with a flat architecture. Nodes broadcast a SYNC message periodically that contains the value of their view of a shared clock counter. Every time a SYNC message is received, nodes update their shared clock by averaging it with the clock value embedded in the message. This protocol converges in practice very well, and requires a small amount of energy as SYNC messages can be sent every second only. Moreover, computations are basic, perfectly fitting the tiny sensor platforms needed for the Internet of Things. Its distributed operations enable the network to adjust seamlessly to the appearance or disappearance of other nodes. This paper concentrates on the convergence analysis of this promising protocol. Convergence time and synchronization accuracy are determined analytically, by simulations and by experimenting a real sensor platform. All results show that this protocol offers an accuracy in the order of a few tens of microseconds. Moreover, our analytical derivations capture very well an upper bound on the synchronization accuracy.