Along with enhanced mobile broadband and ultra-reliable low latency communication, massive connectivity has been one of the key requirements for enabling technologies of 5G. For IoT, low power consumption and wide area coverage for end devices (ED) are important figures of merit, for which LoRa, SigFox and Narrow Band-IoT are dominant technologies. In this letter, we analyze LoRa systems for increasing average system packet success probability (PSP) under unslotted ALOHA random access protocol. The lower bound for average system PSP is derived by stochastic geometry. And it is shown that the average system PSP can be maximized by properly allocating spreading factor (SF) to each traffic, which also maximizes connectivity of EDs. We formulate an optimization problem for maximizing the average system PSP to propose a sub-optimal SF allocation scheme to each traffic. Analysis on PSP is validated through simulations, and comparison with existing schemes reveals that our proposed scheme achieves the highest PSP and so the maximum connectivity.