Because the $\mathrm{S}_{\mathrm{N}} 1$ reaction goes through a flat carbocation, we might expect an optically active starting material to give a completely racemized product. In most cases, however, $\mathrm{S}_{\mathrm{N}} 1$ reactions actually give more of the inversion product. In general, as the stability of the carbocation increases, the excess inversion product decreases. Extremely stable carbocations give completely racemic products. Explain these observations