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The next frontier in communications is teleoperation -- manipulation and control of remote environments. Compared to conventional networked applications, teleoperation poses widely different requirements, ultra-low latency (ULL) being the primary one. Teleoperation, along with a host of other applications requiring ULL communication, is termed as Tactile Internet (TI). A significant redesign of conventional networking techniques is necessary to realize TI applications. Further, these advancements can be evaluated only when meaningful performance metrics are available. However, existing TI performance metrics fall severely short of comprehensively characterizing TI performance. In this paper, we take the first step towards bridging this gap. To this end, we propose a method that captures the fine-grained performance of TI in terms of delay and precision. We take Dynamic Time Warping (DTW) as the basis of our work and identify whether it is sufficient in characterizing TI systems. We refine DTW by developing a framework called Effective Time- and Value-Offset (ETVO) that extracts fine-grained time and value offsets between input and output signals of TI. Using ETVO, we present two quantitative metrics for TI -- Effective Delay-Derivative (EDD) and Effective Root Mean Square Error. Through rigorous experiments conducted on a realistic TI setup, we demonstrate the potential of the proposed metrics to precisely characterize TI interactions.