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Loops are irregular structures which connect two secondary structure elements in proteins. They often play important roles in function, including enzyme reactions and ligand binding. Despite their importance, their structure remains difficult to predict. Most protein loop structure prediction methods sample local loop segments and score them. In particular protein loop classifications and database search methods depend heavily on local properties of loops. Here we examine the distance between a loop's end points (span). We find that the distribution of loop span appears to be independent of the number of residues in the loop, in other words the separation between the anchors of a loop does not increase with an increase in the number of loop residues. Loop span is also unaffected by the secondary structures at the end points, unless the two anchors are part of an anti-parallel beta sheet. As loop span appears to be independent of global properties of the protein we suggest that its distribution can be described by a random fluctuation model based on the Maxwell-Boltzmann distribution. It is believed that the primary difficulty in protein loop structure prediction comes from the number of residues in the loop. Following the idea that loop span is an independent local property, we investigate its effect on protein loop structure prediction and show how normalised span (loop stretch) is related to the structural complexity of loops. Highly contracted loops are more difficult to predict than stretched loops.