  In 1976, Alspach, Mason, and Pullman conjectured that any tournament $T$ of
even order can be decomposed into exactly ${\rm ex}(T)$ paths, where ${\rm
ex}(T):= \frac{1}{2}\sum_{v\in V(T)}|d_T^+(v)-d_T^-(v)|$. We prove this
conjecture for all sufficiently large tournaments. We also prove an
asymptotically optimal result for tournaments of odd order.
