The math behind it
this is where we geek out on basketball forces
The math behind the perfect basketball shot involves various concepts from physics and geometry, such as projectile motion, parabolic trajectory, and optimization. We are looking for the perfect combination of angle, velocity, and release point to maximize the chance of the ball going through the hoop. Here are the key factors to consider:
Projectile motion: When a basketball is shot, it follows a parabolic trajectory due to the force of gravity acting upon it. The equations of motion for the horizontal (x) and vertical (y) positions of the ball are:
x(t) = x0 + v0x * t y(t) = y0 + v0y * t - (1/2) * g * t^2
where x0 and y0 are the initial positions, v0x and v0y are the horizontal and vertical components of the initial velocity, t is the time, and g is the acceleration due to gravity (approximately 9.81 m/s^2).
Launch angle: The angle at which the ball is released (θ) is crucial for the success of the shot. Research has shown that a release angle between 45 and 55 degrees is optimal for most players. This angle determines the initial velocity components:
v0x = v0 * cos(θ) v0y = v0 * sin(θ)
where v0 is the initial velocity and θ is the launch angle.
Release point: The height at which the ball is released (h) is another essential factor. A higher release point increases the chances of the shot being successful because it reduces the effect of the defender's reach and minimizes the ball's trajectory deviation.
Optimization: To find the perfect trajectory, we can use optimization techniques to maximize the likelihood of the ball going through the hoop. This involves finding the ideal combination of launch angle, initial velocity, and release height while considering factors like the player's height, arm length, and shooting style. This can be achieved by solving a system of equations or using numerical methods, such as the gradient descent algorithm.
In other words the math is tough. Can we calculate what should be the perfect angle or release point for a particular individual. We can but we also need to take into consideration other aspects of the game. This is where Edge and Flow Analytics sees a gap in the math. We consider the Edge part to be a combination of the Math and the Conditioning of the athlete where the flow now becomes environmental variables such as noise, consistency of the last 12 shots, amongst a myriad of other ingest points not only can we calculate the optimal shot trajectory for a particular player we can create workout plans that move from edge to flow and allow your athletes/teams to be in the edge flow space more often. Imagine creating a practice that allowed your athletes to perform in this space more than other teams……