Recent HST observations of a large sample of globular clusters reveal that every cluster contains between 40 and 400 blue stragglers. The population does not correlate with either stellar collision rate (as would be expected if all blue stragglers were formed via collisions) or total mass (as would be expected if all blue stragglers were formed via the unhindered evolution of a subset of the stellar population). In this paper, we support the idea that blue stragglers are made through both channels. The number produced via collisions tends to increase with cluster mass. In this paper we show how the current population produced from primordial binaries decreases with increasing cluster mass; exchange encounters with third, single, stars in the most massive clusters tend to reduce the fraction of binaries containing a primary close to the current turn-off mass. Rather their primaries tend to be somewhat more massive (~1-3 M_sun) and have evolved off the main sequence, filling their Roche lobes in the past, often converting their secondaries into blue stragglers (but more than 1 Gyr or so ago and thus they are no longer visible as blue stragglers). We show that this decline in the primordial blue straggler population is likely to be offset by the increase in the number of blue stragglers produced via collisions. The predicted total blue straggler population is therefore relatively independent of cluster mass, thus matching the observed population. This result does not depend on any particular assumed blue straggler lifetime. ; Comment: 7 pages, 6 figures; MNRAS in press