  The constituent counting ruling (CCR) has been found to hold for numerous
hard, exclusive processes. It predicts the differential cross section at high
energies and fixed $\cos \theta_{c.m.}$ should follow $\frac{d \sigma}{dt} \sim
\frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in
the reaction. Here we provide an in-depth analysis of the reaction $\gamma p
\rightarrow \omega p$ at $\theta_{c.m.}\sim 90^\circ$ using CLAS data with an
energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in
other reactions. We argue for a stringent method to select data to test the CCR
and utilize a Taylor-series expansion to take advantage of data from nearby
angle bins in our analysis. Na\"{i}vely, this reaction would have $n=9$ (or
$n=10$ if the photon is in a $q\bar{q}$ state) and we would expect a scaling of
$\sim s^{-7}$ ($s^{-8}$). Instead, a scaling of $s^{-(9.08 \pm 0.11)}$ was
observed. Explanations for this apparent failure of the na\"{i}ve CCR
assumptions are examined.
