In all four cases, the invading combatant found itself in a war which it was not in any immediate danger of losing, but where it perceived a potential for stalemate. It possessed considerable advantages in materiel, so it decided to open a second front in order to throw it's geopolitical opponents off-balance and seize the initiative, as well as employ its superior but idle resources. In three of the four cases, after some spectacular intitial successes, the foreign expeditions bogged down, turned, and eventually became a rout. In the fourth, it's still too early to tell yet.

I suppose there are counterexamples, you can prove anything you want with history, just like you can with statistics. But I can't think of any offhand.