  The Park-Pham theorem (previously known as the Kahn-Kalai conjecture), bounds
the critical probability, $p_c(\mathcal{F})$, of the a non-trivial property
$\mathcal{F}\subseteq 2^X$ that is closed under supersets by the product of a
universal constant $K$, the expectation threshold of the property,
$q(\mathcal{F})$, and the logarithm of the size of the property's largest
minimal element, $\log\ell(\mathcal{F})$. That is, the Park-Pham theorem
asserts that $p_c(\mathcal{F})\leq Kq(\mathcal{F})\log\ell(\mathcal{F})$. Since
the critical probability $p_c(\mathcal{F})$ always satisfies
$p_c(\mathcal{F})<1$, one may ask when the upper bound posed by Kahn and Kalai
gives us more information than this--that is, when is it true that
$Kq(\mathcal{F})\log\ell(\mathcal{F}) < 1$? There are many situations where
this occurs, as well as many situations where this is not the case. In this
short note, we provide a number of necessary conditions for this to happen
together with some easy-to-compute conditions that are sufficient to ensure it.
