Drag the balls, the leave crosshair, or the dot on the circle edge to resize it. Click a pocket to change it. Arrow keys nudge; hold shift for bigger steps.
Anchor shot
A true 20° cut to a corner, object ball 24 in out, cue ball 36 in back, centre ball, no leave required. 20° rather than half-ball because throw peaks near 30°, which would tie the unit of difficulty to ball condition.
Placing it sets the balls, the pocket, the tip and the speed, and turns the leave off. Speed goes to 2.35 m/s: the anchor's 0.80 was fixed under a model in which speed had no effect, and under this one the pot probability falls with speed, so 0.80 now picks out a single speed. At that speed the shot reads 1.00, which is what the anchor is for.
Leave
With no leave required, this is the pot-only difficulty — the cue ball may finish anywhere.
A circle, not a rectangle: the real tolerance is elongated toward your next ball, which this model does not know about, so claiming no direction is the honest choice.
Cushions
The cushion nose meets the ball above its centre, so the rail pushes the ball down into the cloth while friction at the contact pushes it up. Slip at that contact turns as the ball is spun up, so the impact is integrated rather than solved: compression runs until the ball stops approaching, then the rail gives back energetic restitution squared of the work it took, and friction is charged on top of that. Rail friction is measured at 0.18 to 0.22 for cloth-covered rubber.
The ball leaves a cushion pointed closer to the rail normal than it arrived, then swings back out and past it as the cloth turns its new sidespin into travel. It also loses about 40% of its speed doing so, because the impact has to reverse the ball's own rolling. Both come out of the impact rather than being set by a slider.
There is no speed dependence here, and that is a claim, not an omission: an impulsive contact with dry friction is scale-free, so the same shot struck harder rebounds along the same line. Any speed dependence you see on the table comes from the cloth.
A path that ends in a pocket is a scratch, and a scratch loses the turn, so it fails the pot as well as the leave — "pot only" means potted and not scratched. Cushion nose height is not modelled.
Stroke
Tip height is follow and draw. Side is english — it squirts the cue ball, which the aim compensates for.
Equipment
Total aim error is fixed at 0.1307° by the anchor. Pivot length only changes how much of it is attributed to squirt, so it does not move the score.