Network Coding-based Epidemic Routing (NCER) facilitates the reduction of data delivery delay in Delay Tolerant Networks (DTNs). The intrinsic reason lies in that the network coding paradigm avoids competitions for transmission opportunities between segmented packets of a large data file. In this paper, we focus on the impact of transmission competitions on the delay performance of NCER when multiple data files exist. We prove analytically that when competition occurs, transmitting the least propagated data file is optimal in the sense of minimizing the average data delivery delay. Based on such understanding, we propose a family of competition avoidance policies, namely the Least Propagated First (LPF) policies, which includes a centralized, a distributed, and a modified variants. Numerical results show that LPF policies can achieve at least 20% delay performance gain at different data traffic rates, compared with the policy currently available.