Attack Luck
In war.app classic games that use Random Combat, you can double-tap a completed attack/transfer order in the orders list to reveal more information about it. It will show the offense luck and defense luck.
The offense luck is the difference between how many armies the attacking armies killed and how many they would have killed assuming an average roll. For example, 100 will kill on average 60, so if they kill 61 the luck is +1.
Defense luck is the same thing for the defense roll, but from the defender's perspective. For example, 100 defending would, on average, kill 70, so if they kill 68 the defense luck is -2.