https://youtu.be/r5_ydLS4Tvg^This is David Morningstar video on Comanche style which is basically the figure-8.
Watch as the sling goes up and behind his back as is normal in the figure 8.
At this point he pulls into the throw. That's the beginning of the pitch. The previous portion is the wind up.
Notice how the sling lags behind the hand. It creates a lag angle.
And ideal lag angle creates less leverage causing the slinger to be able to pull against the weight of the projectile harder because there is less leverage at the moment of pulling.
This harder pull causes the sling to accelerate faster and more efficiently. A similar concept occurs with recurve bows. The tip is bent away from the direction of pull causing less leverage which stores more energy in the bows limbs.
The sling doesn't store energy though, therefore the effect of pulling harder into the throw is seen immediately by the sling accelerating faster towards the release.
Hope that makes sense.