Heroes of Might and Magic V [Game Discussion]

But for some reason, when my troops attack the enemy's phantoms, it's always a "miss," but when their troops attack mine, they take down my units immediately. Does the probability of eliminating a phantom unit depend on the hero's level?

You're exaggerating about phantoms/ghosts. It's more effective to attack them with magic. The probability of hitting (and thus destroying) a phantom is close to 100% (although "magic fist" and archers have a chance to miss). With a physical attack, the probability of hitting is 1/3. This doesn't mean that every third attack is effective (see the relevant section on mathematics). This applies to version 3.1; in version 1.6, the probability of a physical hit is lower.