Pick how hard and how high. Pick the field. Swing, and watch real drag and spin decide where it lands and who gets there. Then change one thing and swing again.
Three forces act on the ball. Gravity pulls it down. Drag pushes against its motion and grows with the square of speed, so a ball hit twice as hard feels about four times the drag. Backspin creates lift (the Magnus force), which is why a well-hit fly ball hangs and carries.
No air, no drag. After each swing we show how far the same ball would go in a vacuum. The gap between the two numbers is what the air did.
Thin air carries. At a mile high the air is roughly a fifth less dense, so there is less drag and less lift, and the drag drop wins. Same swing, more distance.
Fielders are a race against hang time. A fielder reacts, then runs. If he can cover the distance before the ball lands, it is an out. On ground balls the race is fielder plus throw against the runner going to first.
The sweet spot. Statcast calls launch angles from 8 to 32 degrees the sweet spot. Below 10 is a ground ball, 10 to 25 a line drive, 25 to 50 a fly ball, above 50 a pop-up.
This is a thinking toy, not a swing lesson. Kids must call the result before every swing. That is on purpose: guessing first, then seeing why the guess was wrong, is where the learning happens. The scientist score rewards good calls and changing one thing at a time, not big hits.
Best use: sit next to them. When a call is wrong, ask one question: what surprised you?
Ready to run a whole game with this physics under the hood? Try Skipper.
Note on certainty: this is a simplified model. Spin is estimated from launch angle. Fielders run at a steady speed. There is no sidespin, no bounce off the wall, and no bad hops. The typical exit velocity range shown for each field is a rough estimate, not a study. Use it to learn how the forces work, not to judge a player. The prediction study was with college physics students; we expect it to carry to kids, but that is not proven.