Pass weight: the hidden variable in every attack.

The receiver is moving. Their stride length is roughly constant. Their contact window — the time inside which their planted foot can meet the ball cleanly — is around 300 milliseconds. Miss that window early and they overrun the ball; miss it late and they stretch, decelerate, or lose it to a defender.

A perfect pass is not delivered to the receiver. It is delivered to the point in space the receiver will occupy at the moment the pass arrives, at the velocity they can absorb.

Pass weight is a scalar you feel and a vector the engine calculates. It is the delivered velocity of the ball at contact, and it depends on:

• The initial strike velocity from the passer's boot.
• The angle of elevation (a rolled pass loses less to drag than a driven one).
• The surface friction of the pitch, which decelerates ground passes.
• Air drag, which scales with velocity squared.
• Distance to the interception point.

Change any one of these and the arrival velocity changes. A pass that was inch-perfect on a dry pitch is heavy on a wet one, because friction has dropped and the ball skids through faster than the receiver expected.

A receiver's control window depends on the direction of the ball relative to their stride. A pass arriving into stride — slightly ahead of the running foot — has a window near 500 ms. A pass arriving across the receiver's body has a window closer to 150 ms. This is why the same pass to the same player can succeed one match and fail the next: it is not the pass that changed; it is which of the receiver's feet was planted when the ball arrived.

Pass success  ≈  P(  v_arrival ∈ [v_min, v_max]
                   AND t_arrival ∈ [t_open, t_close]
                   AND θ_arrival ∈ [θ_left, θ_right] )

  v_arrival    ball velocity at receiver's plane
  t_arrival    ball's time to reach that plane
  θ_arrival    angle of the ball relative to receiver's stride

  Every "great pass" is a point inside this three-dimensional volume.

The best passers in the world are solving this equation in real time, under pressure, with a moving defender in the frame. The rest of us are pattern-matching. The engine lets you see the volume — and watch how the volume shrinks when the defender's lane closes.

A stationary passer inherits no momentum. A passer running at 6 m/s adds that velocity to the strike. If you don't model this, your engine turns every pass into a set piece and every attack into a series of standing kicks. Football is a moving game. The physics has to move too.