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Take the initial thrower and receiver positions to be $(-a,0)$ and $(a,0)$, with counterclockwise angular velocity $\omega$. Interpret $v$ as the launch speed relative to the thrower. The ball inherits the thrower's tangential velocity, so in an inertial frame its initial horizontal velocity is $(v,-a\omega )$. The flight time across the diameter is $t_f\simeq 2a/v$. During that time the receiver moves approximately $+a\omega t_f$ sideways while the ball moves $-a\omega t_f$. Thus the transverse miss on a rotating platform isThe ball passes behind the receiver in the sense of rotation. Equivalently, in the rotating frame its transverse Coriolis acceleration has magnitude $2\omega v$ to leading order; integrating over $t_f$ gives $d=\frac{1}{2}(2\omega v)t_f^2$. Terms neglected here are higher order in $a\omega /v$. Specifying an initially radial launch velocity in the inertial frame instead would define a different throw and would lose the inherited tangential velocity.