For a sequence $u_j:\Omega\subset \R^n\to \R^m$ generating the Young measure $\nu_x, x\in\Omega$, Ball's Theorem asserts that a tightness condition preventing mass in the target from escaping to infinity implies that $\nu_x$ is a probability measure and that $f(u_k)\rightharpoonup\langle\nu_x,f\rangle$ in $L^1$ provided the sequence is equiintegrable. Here we show that Ball's tightness condition is necessary for the conclusions to hold and that in fact all three, the tightness condition, the assertion $\Vert\nu_x\Vert=1$, and the convergence conclusion, are equivalent. We give some simple applications of this observation.