We consider the complexity of a single-sided AdS black hole as modelled by an end-of-the-world brane. We compute the complexity using a modified replica trick corresponding to the "quenched geodesic length" in JT gravity. The late time behaviour of complexity shows a saturation to a constant value of order $e^{S_0}$ following a period of linear growth. Furthermore, we show that our approach leads to an improved result for the variance of complexity, namely it being time-independent at late times.

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