The latency value comes from the need to accurately reproduce what happens when recording to tape, including its non-linearities and non-causal behavior. To achieve this, the signal must be processed up to 1882 samples in advance. In other words, a sample at time N can be influenced by what occurred at N – 1882. The dynamic behavior of tape depends heavily on the material passing through it—transients, processing, and more. What you record onto tape directly affects what you hear on playback.
A tape machine and all of its components (machine, tape, and heads) form a non-causal system. This means the output signal depends on the current state of the system, so the same input doesn’t always produce the same output; it also depends on what has previously been recorded.
A good analogy is a spring reverb: the spring reacts differently to the same input depending on how it was excited before. Many systems are inherently non-causal, but they are usually modeled as causal systems because it is simpler—same input, same output, every time. The latency here is the unavoidable by-product of authentically replicating every part of a real tape machine: the input electronics, record head, tape, repro head, and even the output electronics.
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