I think the shadow buffer represents only cast shadows. The shadowed side of an object is something different.
If you want a hard black and white shading on the ball, set its color to white and set its "Diffuse Falloff" to 0.
(The "Intensity" of the Klieg light must be 100%)
If you want to eliminate the darkness from the ground, where it isn't illuminated by the Kleig light, set its Ambiance Color to white and set its Ambiance Intensity to 100.
That should get you all white except for the shaded portion of the ball.
Does that get you what you want?