' he got the drop on us '

The Ngram shows usage rising in about 1875 and then increasing in the early 1900s.

To get the drop on someone or something means to be at an advantage over it, particularly if you were competing over some outcome. This phrase's etymology is rather clouded, unfortunately. What scholars do know is that it appeared as a slang sometime around the middle of the 19th century. It appears to have originated with the quick-draw duels of the wild west, when two men would face each other in an empty street and try to be the first to draw their gun and shoot the other. The expression came to include the more general sense of a timely advantage by the turn of the 20th century. Around this same time another version appeared as get/have the jump on. Though this has the same general meaning, its connotation is more along the lines of having an advantage because you started the quickest.

Word Ancestry

Other references favour the idea that the fast drawing of a gun forces the opposing party to 'drop' their gun, and to hold their hands up in surrender. If so, it may be difficult, or impossible, to determine its first usage which would probably have been verbal and widespread before anything appeared in print that can be documented.

Early dictionary discussions of the origin of 'get the drop on'

Albert Barrère & Charles Leland, A Dictionary of Slang, Jargon & Cant, volume 1 (1889) offers the following explanation for the phrase "get the drop on":

Drop (American), to get the drop on a man, to forestall, get first advantage. This phrase alludes to a trick, practised in large cities upon unsuspecting strangers, called the drop game, which consists in pretending to find a pocket-book or purse full of notes, which a confederate has dropped upon the near approach of a likely victim. By specious representations the finder manages to obtain good money from the victim, who is said to be dropped on, the notes being, of course, counterfeit.

Also to have the drop on one.

When summoned to hold his hands up, he refused and attempted to draw his own revolver, with the result of having two bullets put through him. Finnigan commented on Calamity as a fool for not knowing when a man had the drop on him.—Century Illustrated Magazine.

Meanwhile, John Farmer, Americanisms—Old and New (1889) offers this treatment of the phrase:

DROP.——To GET THE DROP ON.—Generally speaking, to be in a position wherein one holds the life of another in hand ; literally to take one at a disadvantage before he can use his own weapon. Like most phrases of the kind, the idiom is being softened and otherwise modified, and is often used for "to get an advantage over."

I don't understand why Farmer thinks that his description of the expression's meaning presents something “literally”—but it seems clear that Farmer doesn't accept Barrère & Leland's view that the expression derives from the "drop game';" Farmer does devote considerable space to an entry for "drop game," and yet makes no attempt to tie "drop game" to the expression "get the drop on."

Isaac Funk, A Standard Dictionary of the English Language Upon Original Plans (1893) provides a rather precise definition of the phrase:

to get (or have) the d[rop], in a hostile encounter, to be first to get one's gun or pistol in position in readiness to fire.

*The recipe for a long life in this country was described as being very quick and getting 'the drop' on an antagonist; that is to say, being ready to shoot first.* W. H. Bishop Old Mexico [1883] pt. ii, ch. 31, p. 491.

This definition may reflect the meaning of the phrase as understood in 1893, but early occurrences of the expression don't require both parties to be armed; the point is rather than one party has a gun drawn or aimed while the other does not.

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Early instances of 'get the drop on' in the wild

J.E. Lighter, Random House Historical Dictionary of American Slang* notes an occurrence of the expression in William Simms, Mellichampe: A Legend of the Santee (1836):

"Adrat it, major, it did go agin me not to pull trigger ; but you see, major, 'twould ha' been mighty foolish now. More than once I had the drop on both of 'em, and could easy enough ha' brought down one or t'other with a wink ; but there was no fun in it, to think of afterward. I was only one shot, you see, sir, and quite too close to get away. ... It's no use, major, you know, to lose one for one, when one's all you’ve got."

The earliest match for the expression "get the drop on" that searches of the Elephind newspaper database turn up is from 1855. From "Chloroform Thief Caught," reprinted in the [Richmond, Virginia] Daily Dispatch (April 12, 1855), from an original story in the [New Orleans, Louisiana] Picayune (April 7, 1855) that included multiple specimens of contemporaneous U.S. thieves' slang such as "bogus," "shaved," "on the cross," "cases," "croak," and "frisking":

It was agreed that he [James Hall] should personate the Chief's servant at a hotel, but the mulatto said that they must be careful of one thing, and that was that they were not spotted by the Chief of Police, one James, who, he was informed, was a sharp fellow, and always on the look-out. This startled the Chief, who, at first, thought be was suspected; but seeing the fellow was perfectly in earnest, he carried on the joke, and said that it had cost him $50 to get the "drop" on that functionary, but that he knew him perfectly well, and would point him out.

The next twelve matches for various versions of the phrase appeared in print during the period from 1865 to 1873. From The Vigilantes of Montana serialized in the [Virginia City] Montana Post (October 14, 1865):

The same evening, Tom [Caldwell] and his friend went over to the Cold Spring Ranche together, on the coach, and the entire particulars came out, in conversation. The driver finished the story by stating that he sat on his horse, ready to shoot Ives, if he should succeed in getting the "drop" on Caldwell.

From "Bold Robbery," in the [Plymouth, Indiana] Marshall County Republican (March 22, 1866):

A case of this kind is reported in the Montana Democrat of the 24th ult. [that is, February 24, 1866], which says, that as James Talbot, of Nevada, was on his way from Helena to Virginia City, he was robbed of 250 ounces of gold dust. Just before he reached Jefferson Bridge, two men on horseback approached him as he was riding along and said, "Jim, give us your money," presenting their revolvers at the same time, thus getting the "drop on him." Mr. Talbot, of course, had no alternative but comply.

From "A Trial for Murder in Nevada," in the Rockhampton [Queensland] Bulletin and Central Queensland Advertiser (March 1, 1870):

Lawyer: "Please state your conclusions in regard to the wounds of Mr. Roach on your first interview." Witness: "I kalkerlated his goose was about cooked." Lawyer: "Do you mean by that that you considered his condition as extremely critical?" Witness: "Wall, I made up my mind the fust time I seen him that he was bound to peg out." Lawyer: "Use a little plainer language, Mr. G. ; what shall we infer from your expression of 'pegging out/'" Witness: "I mean that I thought he'd pass in his checks less' an week." Lawyer (impatiently): "What did you tell Roach about his chances of recovery?" Witness: "I told him that I thought they'd get the drop on him this time." Lawyer (very short): "Did you think Roach would live or die of his wounds at your first visit?" Witness (indignantly): "I told yer I thought he was bound to go up when ye first asked me."

From "Local News: Homicide," in the Red Bluff [California] Independent (January 26, 1871):

Arriving at the house and finding Lansdale there he [Banks] ordered him away, making use of some very strong language. Lansdale left, and Banks busied himself about home for a while and then went into the field to attend to some stock. As he was returning Lansdale rose from behind a brush fence, with a revolver in hand, and said "You called me a s— of a b—, and you must take it back." To which Banks replied he did, and would not take it back; saying at the same time “You have got the drop on me, but I will prepare myself and give you satisfaction." They then separated.

From "Mexican Bandits," in the [San Francisco, California] Daily Alta California (May 14, 1871):

Finding himself surrounded by the desperate inhabitants of the cabin, he [Morse] sprang out of the door, and while on the porch Soto twice "got the drop on him," and he stepped round the corner of the house, where the fighting commenced in good earnest, if it had not been tolerably lively before. Each fired four shots, without effect; as often as Soto brought his pistol down to a level, Morse would drop and the ball pass over.

From Len Bourland, In Triple Peril; or, The Wizard of the Mines!: A Wild Romance of the Sierra Nevadas, serialized in the Red Bluff [California] Independent (July 13, 1871):

"By-the-by, I see no cause for alarm in the appearance of even a real man in this place, as I said before, and 1 will add, even a robber or two would not be very formidable adversaries, if they did not get the drop on us; I could hold a couple in check myself," he continued in a jocund tone.

From an untitled item in the Indianapolis [Indiana] Journal (February 27, 1872), reprinted from the San Francisco [California] Bulletin:

The conductor, as the [street] car neared the depot, started on his tour of [fare] collection, intending to start with the miner. Nut he was destined to meet with unexpected opposition in the pursuit of his legitimate business. He placed his hand in the side pocket of his coat to draw forth his nippers, when out came a formidable five shooter from the miner's hip pocket, accompanied with the exclamation, "Look hyar, stranger, I kim from the mountains, but yer can't get the drop on me!" The other passengers in the car, save a few ladies, smiled, explanations followed, and the gentleman from Nevada put up his weapon and paid his farr.

From "Facts and Fancies," in the [Memphis, Tennessee] Public Ledger (December 24, 1872):

A Wisconsin woman is known who, when she discovers a burglar beneath her bed, does not yell, but kneels and prays for him. This has worked well on one occasion, but her husband has purchased a horse pistol that carries a ball as large as a doughnut, and says "get the drop on him, next time, before you do anything else."

From an untitled item in the [Prescott, Arizona] Weekly Arizona Miner (February 22, 1873):

Some two months ago, a chief of the Pawnee Indians led his braves in the direction of the Sioux country, with the object of harvesting Sioux hair, but spotted Tail and his band got the drop on the Pawnees and raised the hair of several of them, besides capturing 75 of their ponies.

From "Humorous," in the Dallas [Texas] Herald (April 12, 1873):

"You've got the drop on me," as the criminal on the scaffold said to the Sheriff,

From a letter dated April 24, 1873 from Vallejo, California, to the Sonoma [California] Democrat (May 10, 1873):

Outsiders have a dread of Vallejo; yet I do not think out people fear to walk the streets, although when the wind blows hard, which it frequently does at this point, the coat-tails of our citizens are often blown to the one side or the other, and then is revealed to the eyes of the astonished looker-on a pearl-handled bowie-knife or a silver-mounted sixshooter. This don't mean that our people are particularly BLOOD-THIRSTY, But then they don’t intend to let any one get the "drop on 'em."

And from "How They Fight Out West, A Duel to the Death. A Western Feud. Two Desperadoes. The Revolver and the Bowie," a story datelined "Medicine Lodge, I[ndian] T[erritory], July 5," in the Boston [Massachusetts] Pilot (August 16, 1873):

"Look out for him. He is a hard man to get the drop on. He caught Mike, you know." ... "I don't want to drop on him," replied McCluskey. "I'll give him an equal show. I'll fight him fair and square with pistol and knife. But I want a good man to back me up and see fair play. Who can I get?"

The breakdown of these thirteen newspaper matches is as follows: the earliest one is from New Orleans, Louisiana; the next three originated in Montana and or Nevada; five of the remaining nine are from California; one is from Arizona, one is from Dallas, Texas; one is from Memphis, Tennessee; and one (the latest) is from "Indian Territory" (evidently, Oklahoma).

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Early figurative instances of 'get the drop on'

Christine Ammer, The American Heritage Dictionary of Idioms (2013) has this entry for "get the drop on":

get the drop on Also get or have the jump on. Achieve a distinct advantage over someone, especially through early or quick action; get a head start. [Example omitted.] The first of these slangy examples dates from the mid-1800s and originally alluded to pointing one's gun at someone before he pointed his at you. It was transferred to more general use by about 1900.

Ammer may be right about the gun-pointing origin of the expression, but figurative use of the phrase clearly began much earlier than 1900. We've already seen examples of this from New Orleans in 1855 and San Francisco in 1872, and a Google Books search turns up several other nineteenth-century matches of this sort.

From the subhead of "Humors of the Pueblo Bar," in Chicago Legal News (May 2, 1874), in which some lawyers played a prank (not involving weapons) on a local judge:

"Getting the Drop" on a Chief Justice

From David Locke, Nasby on Inflation (1875):

Mackey and Burns started one [a bank] with Mackey ez President and Burns ez Cashier with them and a ... carpenter ez the Board of Direkters. They hev got the drop on us by requirin the officers to give bonds, wich they accomplished by hevin Mackey sign Burns', Burns sign Mackey's, and both sign the ... carpenter's.

And from "Running Water," in Brotherhood of Locomotive Engineer's Monthly Journal (October 1880):

I bought a nice new suit of clothes down town, and the water chased me a whole square to get on the suit, but I got it on first; but the water got the drop on me and beat me after all, for it got on my suit, and I told him that suit was mine, and I looked him square in the face, and I 'spose I looked mad, and the water ran like a whitehead and finally fell in the mud, and I was glad of it.

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Conclusions

The early regional sources of instances of "get the drop on"—which tend heavily toward locations west of the Mississippi River—offer little support for the Barrère & Leland hypothesis that the expression originated in reference to a prototypical Eastern big-city scam. Indeed, John Bartlett, Dictionary of Americanisms, second edition (1859) specifies that the "drop game" was primarily an East Coast phenomenon:

DROP GAME. A trick practised by the light-fingered gentry of New York and other eastern cities on their country cousins. ...

Although the association between "get the drop on" and preemptively pointing a gun at someone goes back to the earliest (1836) instance of the phrase that I'm aware of, none of those early instance explain what the "drop" literally refers to. Since the expression occurs very often in situations where the gun is not actually fired, it is difficult to conclude that the dropping refers to "dropping the hammer" of the gun or, alternatively, to "dropping the target" by shooting it. For the time being, at least, the nature of the original "drop" that the person in the advantageous position obtains in getting the drop on someone remains a mystery.

In the mid 19th century, plays were all the rage. About then, the works of the Greek playwrite Aeschylus were newly translated to English and published. Aeschylus is often called the "Father of Tragedy", and reportedly died when a Golden Eagle tried to break open a turtle shell by dropping it on a "rock", which turned out to be the playwrite's bald head. In case you're wondering, reputable ornithology sources (e.g., Cornell Labs) report that some Golden Eagles really do hunt turtles in this manner. So I'm just speculating, but I wonder if the new translations made some buzz about Aeschylus, and the phrase "getting the drop on someone" arose from this buzz. After all getting the advantage over someone when they're not paying attention sounds a bit like the Eagle and Aeschylus.