No, water is not a miraculous element - no more for us than for Naaman. Just as water was the means God chose for cleansing Naaman's leprosy, it is the means He chose for cleansing our iniquities.
Why did He choose water instead of something else? Or why did He choose baptism instead of a shower or a splashing from a fire hose? He didn't tell us. (Though He does explain to us some aspects of baptism - as in Romans 6, for instance.) Rather, He simply commands, and we either believe and obey, or disbelieve (Mark 16:16).
Does this mean we're concocting some sort of "formula", as you put it? Well, was Elisha concocting some formula for Naaman? Let's look at that story again, and see if perhaps there are some similarities between our attitude and Naaman's:
Then Naaman went with his horses and chariot, and he stood at the door of Elisha’s house. And Elisha sent a messenger to him, saying, “Go and wash in the Jordan seven times, and your flesh shall be restored to you, and you shall be clean.”
But Naaman became furious, and went away and said, “Indeed, I said to myself, ‘He will surely come out to me, and stand and call on the name of the Lord his God, and wave his hand over the place, and heal the leprosy.’ Are not the Abanah and the Pharpar, the rivers of Damascus, better than all the waters of Israel? Could I not wash in them and be clean?” So he turned and went away in a rage.
And his servants came near and spoke to him, and said, “My father, if the prophet had told you to do something great, would you not have done it? How much more then, when he says to you, ‘Wash, and be clean’?” -
II Kings 5:9-13
What if Naaman had gone to Damascus and dipped seven times in the Abanah or the Pharpar? Would his leprosy have been cured?
What if he had dipped four times in the Jordan instead of seven?
What if he'd had his servants splash him seven times with buckets of water from the Jordan?
And finally, what if a leper today dips seven times in the Jordan?