5G has loudly ambitioned to achieve extremely low la-tency in mobile networks. To this aim, we have recently introduced two novel latency-aware caching heuristics, LAC and LAC+ and we showed through simulations in Information-Centric Networks their good performance figures. In this paper, we present an insight on their operations: a mathematical analysis of these caching systems led us to novel results that we validate in simulation. The advantages of these algorithms come (i) on one side from the fact they are distributed and lightweight and (ii) from the ability to quickly adapt to content popularity and network congestion, with no signaling nor explicit coordination between the network nodes. In this paper we provide analytical bounds of latency aware caching policies and evaluate their performance by network simulations. The proposed mechanisms can halve the mean and standard deviation of content delivery time with respect to approximations of LFU as leave a copy probabilistically.