Raby and Wingerter have performed an interesting poll of heterotic orbifold vacua. 12% of their vacua have $\sin^2 \theta_W = \frac 38$ while none of them exceeds this value. $\frac 38$ is an upper bound! Among those that saturate the bound, 89% embed the hypercharge within an SU(5) group and can thus be interpreted as SU(5) GUT models.
I personally don't think that vacua that belong to a certain minority are excluded. On the other hand, if there were a plausible argument - supported by some experimental data - that some numbers always satisfy some inequality, like that $\frac 38$ is the maximum value of $\sin^2 \theta_W$, then it could be viewed as an insight.
Other Interesting arXiv Papers (Week Ending 18 May 2013)
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