"Ultimate excellence lies
Not in winning
Every battle
But in defeating the Enemy
Without ever fighting."
-Sunzi: Master of War.
Every Halo game is very different from each other. Halo CE =/= Halo 2. Halo 2 =/= Halo 3, etc, etc...
And of course, the multi-player. Every game is different (especially Reach). Some games borrow mechanics from others, sure; but there is no definitive "formula" for Halo. If there was, it would re-use that "formula," and it would become a very monotonous mess game after game, just like Call of Duty.
Sure, Halo has its universal basics, such as "pick up gun. Shoot alien."
But if you think that as the "formula" of Halo, then you believe that's all Halo ever was, which it's not.