The formation of blue stragglers is still not completely understood, particularly the relationship between formation environment and mechanism. We use a large, homogeneous sample of blue stragglers in the cores of 57 globular clusters to investigate the relationships between blue straggler populations and their environments. We use a consistent definition of "blue straggler" based on position in the color-magnitude diagram and normalize the population relative to the number of red giant branch stars in the core. We find that the previously determined anticorrelation between blue straggler frequency and total cluster mass is present in the purely core population. We find some weak anticorrelations with central velocity dispersion and with half-mass relaxation time. The blue straggler frequency does not show any trend with any other cluster parameter. Even though collisions may be expected to be a dominant blue straggler formation process in globular cluster cores, we find no correlation between the frequency of blue stragglers and the collision rate in the core. We also investigated the blue straggler luminosity function shape and found no relationship between any cluster parameter and the distribution of blue stragglers in the color-magnitude diagram. Our results are inconsistent with some recent models of blue straggler formation that include collisional formation mechanisms and may suggest that almost all observed blue stragglers are formed in binary systems.