as the sample of [@Svensson].

We also consider a theoretical curve for the LGRB event rate. [@form_rate_letter] estimated the LGRB progenitor rate using the [@diff_rate_letter] results in concert with SNe statistics via an approach patterned loosely off the Drake equation. Beginning with the cosmic star-formation history, [@form_rate_letter] took the expected number of broad-line Type Ic events that are in low metallicity host environments as potential LGRB progenitor candidates. They then adjusted this number by adding the contribution of broad-line Type Ic SNe in high metallicity host environments at a much reduced weighting of $\sim$$\frac{1}{30}$ (the @diff_rate_letter estimate on the relative suppression of LGRB formation in high metallicity environments). A comparison of this estimate of potential LGRB progenitor candidates to the observed LGRB rate corrected for instrumental selection effects (estimated by @Lien and @Graff), provided a combined estimate of the fraction of broad-line Type Ic SNe residing in metal poor environments that produce an LGRB and the fraction of such LGRBs that are beamed in our direction. Thus [@form_rate_letter] estimated that, in a low metallically environment, an aligned LGRB occurs out of approximately every 4000 $\pm$ 2000 broad-lined Type Ic Supernovae. Therefore if one assumes a semi-nominal beaming factor of 100 