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Compare a controlled change
Basketball Arc starts the ball from the same position for every shot and has no wind or random shot term. Angle and power determine the launch. That makes it a useful place to change one input while holding the other fixed. The lab simulates two separate shots, draws their complete paths, and checks whether each earns a basket. It imports the same launch and collision functions as the game rather than substituting a generic projectile calculator.
Worked comparison: 66° at three power settings
| Angle | Power | 1/60-second steps | 1/120-second steps |
|---|---|---|---|
| 66° | 96 | Miss | Miss |
| 66° | 98 | Basket | Basket |
| 66° | 100 | Basket | Miss |
At power 96, both tested simulations miss. At 98, both score. At 100, the result changes with the step size. The 98-power shot contacts the rim before scoring; it is not evidence of a completely clean arc. Treat these as controlled observations of this implementation, not a claim that adding power always helps.
Why the smooth curve is not the whole test
Gravity bends the flight, but the backboard, two rim contact points and floor can change the velocity. A basket requires a downward crossing of the hoop opening under the game’s scoring check. Passing above the target, overlapping a rim, or reaching the right horizontal distance does not by itself earn two points. The plotted path includes rebounds until the shot finishes; follow it in time order from the lower-left launch rather than treating every segment near the hoop as a fresh shot.
What the two step sizes reveal
The engine advances the ball and resolves contacts in discrete steps. This lab compares 1/60-second and 1/120-second intervals. Near a rim or backboard boundary, changing when a contact is detected can change the later path and the result. If the columns disagree, you have found a sensitive setting. Agreement at these two intervals is useful evidence, but does not establish the same result at every live frame duration. The live game uses frame timing, so a repeated result here is not a guarantee for every device.
Use the experiment to diagnose a miss
Begin with the supplied 66°/96 and 66°/98 comparison. Hold angle constant and describe what changed: the first approach, the rebound, or the downward passage through the opening. Next compare 66°/98 with 60°/98 to change angle alone. Do not conclude that one variable caused a difference after changing both at once. If you are testing live rounds, record the displayed settings and whether the ball scored; a recollection that a shot “looked almost right” is weaker evidence.
What this lab deliberately does not predict
It does not fit real-world basketball, assign a success probability, search for an unbeatable setting or simulate network latency. The court coordinates are game units, not metres. It reports one deterministic outcome for each setting and step size. A made shot earns two points, but a round still requires at least five baskets from ten shots. Use the practice guide to plan a controlled ten-shot session and to separate learning attempts from a score attempt.
Updated 4 October 2026. Original calculations and teaching examples; method and limits.