The expression “to get the drop on a person” means: To have a marked advantage; literally, to have a person covered with a gun before that person is able to draw his own weapon.
According to Mary A. Jackson’s Memoirs of Stonewall Jackson (1895 ), this phrase originated during the War between the States.
At least, she wrote: “They had seventy-three pieces of artillery, one battery being siege guns or thirty pounder Parrotts, but the elevated position of McLaws and Walker gave them decidedly the drop, not only on the big guns but on the whole Federal line.”
Nevertheless, long before her Memoirs were written, back in 1869 in fact, the traveler, Alexander K. McClure, wrote in his Three Thousand Miles through the Rocky Mountains: “So expert is he with his faithful pistol, that the most scientific of rogues have repeatedly attempted in vain to get ‘the drop’ on him.”
And, for that matter, I think it most likely that the literal phrase was in use during the famous days of the Forty-Niners, or possibly much earlier.