The growing demand for video streaming is straining the current Internet, and mandating a novel approach to future Internet paradigms. The advent of Information-Centric Networks (ICN) promises a novel architecture for addressing this exponential growth in data-intensive services, of which video streaming is projected to dominate (in traffic size). In this paper, we present a novel strategy in ICNs for adaptive caching of variable video contents tailored to different sizes and bit rates. Our objective is to achieve optimal video caching to reduce access time for the maximal requested bit rate for every user. At its core, our approach capitalizes on a rigorous delay analysis and potentiates maximal serviceability for each user. We incorporate predictors for requested video objects based on a popularity index (Zipf distribution). In our proposed model, named DASCache, we present delay queuing analysis for cached objects, providing a cap on expected delay in accessing video content. In DASCache, we present a Binary Integer Programming (BIP) formulation for the cache assignment problem, which operates in rounds based on changes in content requests and popularity scores. DASCache reacts to changes in network dynamics that impact bit rate choices by heterogeneous users and enables users to stream videos, maximizing Quality of Experience (QoE). To evaluate the performance of DASCache, in contrast to current benchmarks in video caching, we present an elaborate performance evaluation carried out on ndnSIM, over NS-3.