Fireball
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No, an elf is definitely needed. It's almost the only ranged unit (if you consider archers). And tigers might not even make it and end up as real meat. Especially if the opponent has a slowing effect (like Order).
Many players (especially beginners, but not only) believe that if there's no ranged unit in the army, life is meaningless. But Necromancers, for example, feel perfectly fine without ranged units.
Now, about elves. The Speed buff of Nature greatly enhances tigers, as mentioned above. And in a battle against a hero, elves have many disadvantages:
-against Necromancers, they deal very little damage, and they require another stack to quickly eliminate Vampires.
-Order has Dispel, but the main thing is that you can't "outrange" Order, even with archers.
-facing Chaos is dangerous even with a very high-damage, low-health stack. One cast is enough.
-Life will either have a large number of ranged units or rush forward, and then the elves are very easy to kill or block (with angels, for example).
In short, in my opinion, for a battle against a hero with an army, tigers are better than elves (and they also move faster on the map and don't require as much wood). In general, in Heroes 4, it's much harder to protect ranged units from melee units than in Heroes 3 or 5. Therefore, in a serious battle, they can be quickly destroyed