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In this work we study the dynamics of spinning binary black hole systems in the strong field regime. For this purpose we extract from numerical relativity simulations the binding energy, specific orbital angular momentum, and gauge-invariant frequency. The goal of our work is threefold: First, we extract the individual spin contributions to the binding energy, in particular the spin-orbit, spin-spin, and cubic-in-spin terms. Second, we compare our results with predictions from waveform models and find that while post-Newtonian approximants are not capable of representing the dynamics during the last few orbits before merger, there is good agreement between our data and effective-one-body approximants as well as the numerical relativity surrogate models. Finally, we present phenomenological representations for the binding energy for nonspinning systems with mass ratios up to q=10 and for the spin-orbit interaction for mass ratios up to q=8 obtaining accuracies of ≲0.1% and ≲6%, respectively. [ABSTRACT FROM AUTHOR]