Baseball Savant Pitch Trajectory a la Alan Nathan

pitch-trajectory.py

def get_xz_at_y(row, y_target=0.0):
    """
    Given a row of Baseball Savant pitch data and a target y (distance from plate),
    return the (x, z) location of the pitch at that y.
    
    Converted this via Gemini and the Alan Nathan spreadsheet 
    https://view.officeapps.live.com/op/view.aspx?src=https%3A%2F%2Fbaseball.physics.illinois.edu%2FTrajectoryCalculator-new-3D-May2021.xlsx&wdOrigin=BROWSELINK
    If you're using pandas and numpy, you should be good to go. Sorry, I'm not good at dependencies and docs GIGGLECHAD     
        
    Parameters
    ----------
    row : pd.Series
        Must contain release_pos_x, release_pos_y, release_pos_z,
        vx0, vy0, vz0, ax, ay, az.
    y_target : float
        Distance from plate in feet (default 0 = front of home plate).
    
    Returns
    -------
    (x, z) : tuple of floats
    """
    # Initial conditions
    x0, y0, z0 = row["release_pos_x"], row["release_pos_y"], row["release_pos_z"]
    vx0, vy0, vz0 = row["vx0"], row["vy0"], row["vz0"]
    ax, ay, az = row["ax"], row["ay"], row["az"]

    # Solve quadratic: y(t) = y_target
    # (1/2)ay t^2 + vy0 t + (y0 - y_target) = 0
    coeffs = [0.5 * ay, vy0, y0 - y_target]
    roots = np.roots(coeffs)

    # Select the positive, real root (time going forward)
    t_candidates = [r for r in roots if np.isreal(r) and r >= 0]
    if not t_candidates:
        return None, None  # no valid solution
    
    t = min(t_candidates)  # earliest valid time
    
    # We did this on 9/10/2025 and the randos in chat are unstabledeus hectorhsc trevin_flick queuemina jasminsc16 et al 
    # Compute x, z at time t
    x = x0 + vx0 * t + 0.5 * ax * t**2
    z = z0 + vz0 * t + 0.5 * az * t**2

    return float(x), float(z)