Background on nonidiomatic ‘untrack’ and 'untracked'
Although Merriam-Webster’s Collegiate Dictionary series takes no notice of untrack prior to the 2003 Eleventh Collegiate, untracked as an adjective appears in Noah Webster, A Compendious Dictionary of the English Language (1806):
Untracked, a. not tracked or marked out, untrod
The larger American Dictionary of the English Language (1828) offered similar definitions:
UNTRACKED, a. 1. Not tracked; not marked by footsteps. 2. Not followed by the tracks.
The same definitions appeared in the 1847 edition of Webster’s, but untracked dropped out of the 1864 edition and did not reappear as a defined word in subsequent editions through the remainder of the nineteenth century.
A Google Books search for “untracked” turns up a number of instances of the word in this sense. One of the earliest is from Judith Drake, An Essay in Defense of the Female Sex: In a Letter to a Lady, fourth edition (1721, originally published in 1696):
I honour the Names and admire the Writings of Denham, Suckling, and d’Avenant ; I am ravish’d with the Fancy of Cowley, and the Gallantry of Waller ; I reverence the Fairy Queen ; am rais’d and elevated with Paradise Lost ; Prince Arthur composes and reduces me to a State of yawning Indifference ; and Mr. W--stl--y’s Heroicks lull me to Sleep. Thus all Ranks and Degrees of Poets have their Use, and may be serviceable to some body or other, from the Prince to the Pastry-Cook, or Past-board Box-maker. I should mention our Satyrists, but it would be endless to descend to every Particular : Of these Mr. Oldham is admirable ; and to go no farther, the inimitable Mr. Butler will be an everlasting Testimony of the Wit of his Age and Nation, and bid eternal Defiance to the Wits of all Countries, and future Ages, to follow him in a Path before untrack'd.
One relatively early instance of untrack as a nonidiomatic verb appears in “Inquiries and Answers” in The Cultivator and Country Gentleman (February 28, 1888), where it refers to resisting coming out of a (desirable) track:
Barn Doors.—I am repairing my barn door ; it now runs on a track. The entire front, 25 feet, divides in the middle, one behind another. The track is easily disordered. I saw in a last year’s paper a track described, formed thus—V. Can you give me a good arrangement which will not untrack easily, or other mode of arrangement? F. W. II, Roxbury, Mass.
Horses and ‘untrack’
In Google Books search results, idiomatic meanings of untrack begin to appear in publications from the late 1800s. The most prominent of these is untrack in connection with working with horses. From Charles Marvin, Training the Trotting Horse: A Natural and Improved Method (1892):
Manzanita was broken in her yearling form and showed great promise on the miniature track. If it was true that “lot-trotters” never amount to anything, we should not have taken the trouble to train Manzanita, but we did not pay any more attention to such “wise old saws” then than we do now. She kept on improving until I left for the East in 1883, but on my return the boys had a sorrowful story to tell about the mare whose future we had all built hopes upon. They assured me that she “was no good,” that she “could not untrack herself,” and to cap the climax, they pronounced her “foundered.”
{{ Hathi Trust finds an edition of Marvin's book from 1890 with the same paragraph in place. }}
From “Breeding for Performance---I. The Pedigree Element,” in The Country Gentleman (January 10, 1901):
He [the colt] is of good gait, but does not “train ion.” Up to a certain rate of speed, a little better than 2.80, he goes through the motions of a trotter just as one would want him to ; but beyond that limit he cannot cut loose, or to use a stable term, cannot “untrack himself.”
And the Morning Telegraph’s Racing Chart Book, covering horse races from February 4 1907 to June 19, 1907, uses the phrase “unable to untrack himself in the going” six times (as well as “unable to untrack himself” and “could not untrack herself” once each). The meaning in each case seems similar to what in modern U.S. idiom might be described by the phrase “kick into a higher gear.”
The use of this idiom continued in the 1910s and 1920s in the same sense. From Charles Van Loan, “Egyptian Corn,” in Old Man Curry: Race Track Stories (1919, though the story originally appeared in Collier’s Magazine in 1916):
"All right. To start with, I bought this hoss for little or nothing. Mostly nothing. I knew he was a freak. He couldn't begin to untrack himself till he had gone a mile, but after that it seemed like every mile he went he got better. I held a watch on him an' he ran four miles close enough to the record to show me that he had a chance in the Thornton Stakes.”
The same short-story collection includes two other instances of the same idiom: “He can’t untrack himself : runs like he was all bound up somehow!” [from “A Morning Workout,” first published in Collier’s Magazine in 1916] and “There’s a sweet combination for you! A horse that can’t untrack himself, a jockey that never rode a winner, and a half-witted grocer!” [from “The Last Chance,” first published in Collier’s Magazine, August 28, 1915]. Van Loan even applies the idiom to baseball, in “Mister Conley” (by 1916), reprinted in Score by Innings: Baseball Stories (1919):
Shag put everything between his spikes and his shoulders into one terrific swipe, and he caught that slow ball square on the end of his bat—wham! It came down toward third base, level as a sunbeam and buzzing like a bee. I didn't have time to untrack myself or turn my head — just time to think, "There goes the ball game!" — when out of the corner of my eye I saw Conley make a lunge into the air with his glove.
Back to the horses: From Sherwood Anderson, “I Want to Know Why,” in The Smart Set (November 1919):
What had happened was that both these horses are the kind it makes my throat hurt to see. Middlestride is long and looks awkward and is a gelding. He belongs to Joe Thompson, a little owner from home who only has a half dozen horses. The Mullford Handicap is for a mile, and Middlestride can’t untrack fast. He goes away slow and is always way back at the half, then he begins to run and if the race is a mile and a quarter he’ll eat up everything and get there.
And much later, in “Saddling a Horse” in Boys’ Life (October 1949), the following (somewhat different) explanation of untracking appears:
Another precaution is to untrack your horse. This means walking him. The saddle may feel okay until he takes a step. Then it may pinch, which can cause a cow pony to act like a rodeo bronc. Better to untrack your horse than yourself, cowboy.
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UPDATE (11/25/2014): I found a slightly earlier first instance of "untrack himself" in the Library of Congress newspaper archives, from "A Bad Day for the Races" in the Washington [D.C.] Star (May 2, 1889):
About Seadrift's chances, the public seem to think his race in the Analostan stakes was a fluke, and expected the tables to be turned yesterday by Cotton & Boyle's colt Carroll, but he didn't like the going and was beaten from the start; he could hardly untrack himself.
UPDATE (7/24/2020): Another early instance appears in "Riley in the Bay Ridge" in the New York Tribune (June 19, 1891):
Merry Monarch then shot out and won in a romp by three lengths; Airplant second, the same distance before Fremont. Georgia could not "untrack" herself, and was last all the way.
And from "Speedy Our Dick: He Won the Exciting Four Furlong Pace" in the San Francisco [California] Call (June 2, 1893):
James L went to the front after the start and set the pace around to and up the backstretch. At the half he was leading Alexander Button Jr., Jim C.Neva and Menlo Fallis, who seemed unable to untrack himself, following, strung out in the order named.
UPDATE (10/24/2020): Also intriguing is this instance from "A Novel Trial for Colts," in from the New York Sun (February 19, 1888):
Mr. C. J. Hamlin, the owner of Village Farm, in Erie county, and of Belle F., the fastest mare on the strictly racing track, has special confidence in the produce of unraced stallions. He thinks that the extreme exertion of training and trots must unfit a horse as a sire compared with one that has never been required to stand the pressure of exhausting campaigns. ...
It must be said that this theory regarding the particular qualities of untracked horses is not new. Many turfmen of experience and judgment would say that between the great and proven racer and his untried brother they would for breeding purposes take the brother.
Here, however, untracked seems to mean "never run in a serious, formal race on an actual race track"—which doesn't seem applicable to the instances of reflexive use of untrack from the same period.
‘Untrack’ without a horse in sight
A somewhat different early sense the term arises in Francis Halsey, The Literary Digest History of the World War, volume 4 (1919):
On the twelfth of October (1917), for the first time since he started his Flanders offensive, Haig had for a time to cease operations. It was not German guns that stopt him, but a more than usually heavy rainfall, which turned an already swampy region, over which men were supposed to pass, into a veritable quagmire from which they could not untrack themselves. In the early hours of the morning of October 12, a drive had been started which extended from near the Houtholst Wood, where at several points the British gained ground over fronts ranging up to a thousand yards, but here rain intervened and fighting ceased.
A Google Books search doesn’t find any other instances of this usage, which seems to use untrack as a synonym for extricate, until 1944, when this sentence appears in “Pending in Congress” in Electrical World [combined snippets]:
Congress failed last week to untrack itself from the fiscal year-end snarl which has piled up appropriations bills in conference committees, and as a result, had made virtually no progress early this week on any of the bills of interest to the electric power industry.
A somewhat similar sense of untrack—though closer in meaning to “get out of a habitual pace or pattern” appears in Factory Management and Maintenance, volume 103 (1945):
Quality vs. Speed The first lesson and every succeeding one recognizes that the motion pattern at slow speed may be quite different from the pattern at production speed; that the operator who has learned a slow pattern must later learn the fast pattern at the same time he tries to untrack himself from the slow one.
Non-horse-related instances of untrack from the period 1920–1934, including several involving boxing (starting in 1921), U.S. football (1934), businessmen baffled by the effects of Prohibition (1933), and the messianic savior of the Ghost Dance legend (1933).
By 1942, Billboard magazine had started using the word in the context of recently released recordings, with the sense “catch on.” From "Talent and Tunes on Music Machines," in Billboard (September 5, 1942):
Here is a cute novelty tune that hasn't managed to untrack itself nationally but has done quite well over the radio and might still catch on in the machines if given a proper chance.
Dwindling usage of reflexive ‘untrack’
The American Dialect Society (1948), in what appears to be a glossary of horseracing terms, identifies untrack as being exclusively a reflexive verb [combined snippets]:
untrack (himself) : v. reflexive only. Of a horse : to show a burst of speed. Conversely, a horse which cannot untrack himself is floundering in the going. Usually used in a humorous sense.
That the term continued to have that form and meaning at least as late as 1977 is clear from this item from Chronicle of the Horse, volume 40 (1977):
TO "UNTRACK HIMSELF"
A racing fan recently asked the Questions & Answers Column of the Daily Racing Form what is meant by when it is stated that a horse is unable to "untrack himself," which elicited the following answer: "Bascially [sic] the phrase means that a horse does not have his action.
But beyond that date, Google Books finds only six matches for the reflexive untrack—and just one in the context of horses, which suggests that the phrase in that form had fallen out of general use.
Emergence of ‘get/gets/got untracked’
The earliest Google Books match for “gets untracked” is from the same Sherwood Anderson short story cited earlier. From ““I Want to Know Why” in The Smart Set (November 1919):
Then when the barrier goes up he is off like his name, Sunstreak. It makes you ache to see him. It hurts you. He just lays down and runs like a bird dog. There can't anything I ever see run like him except Middlestride when he gets untracked and stretches himself.
The next Google Books occurrence is in Gene Fowler, Shoe the Wild Mare (1931):
Cripps tells the Commissioner: 'I got some stuff in the Cat's eye by mistake and it's stung him for a while. He'll get untracked pretty soon.' Terry goes in again, groping, and the crowd razzing. He has to clinch so he can get the Strudel spaced.
And the first instance not related to horses is from a review of Bright Boy, in Billboard (March 11, 1944):
Only his dumb and ingenuous roommate catches on to his secret — that his shell isn't as thick as it seems — and that underneath he's just a kicked-around, hurt kid who can't get untracked. There's a nice girl in it, too, who falls in love with the nice roommate, and an understanding headmaster and a professor who knows kids.
Somehow, from these or earlier modest beginnings, “get/gets/got untracked” has emerged to eclipse (almost totally) the reflexive “untracked himself/herself/themselves” in idiomatic usage in the United States. The sports examples in the opening question are typical of today’s usage.
Early days of ‘get on track’
The earliest instance that a Google Books search finds of the phrase “on track” in what might be a relevant sense is from William Sims, The Kinsmen: or The Black Riders of Congaree (1841):
I’m going to leave you now, Muggs, but you’ll see an old man coming here to look after a horse about midday. Give him a drink, and say to him that you don't know nothing about the horse, but there's a hound on track after something that went barking above, three hours before. That'll sarve his purpose, and mine too : and now, God bless you, old boy, and remember I’m your friend, and I can do you better sarvice now than any two Black Riders of the gang.
Here, of course, the phrase is not being used figuratively and does not involve a racetrack, but describes a dog following a track (or trail) of some animal or person. The same situation is present in Isaac Scribner, Laconia: or, Legends of the White Mountains and Merry Meeting Bay (1855):
“I think,” said Wenane, “that the young Forest Queen had better stay at home for some days, while I look about the woods and get on track of the dogs.”
Here, though, the “dogs” are people, and the tracking is being done by Wenane (a Pequakett warrior). To similar effect is this instance from “The Half-Breed Colony of Illinois,” in Odd-Fellows’ Casket and Review (July 1859):
I owed 'em an old grudge, and I cum back to Kaintuck to fight 'em — some of these boys cum from the settlement and some we picked up. We got on track of the Ingins, at this camp, jist by accident, yesterday, and we followed 'em till last night, and it was dark We know 'd we was close on 'em, and we thought we 'd take 'em afore mornin', but it got tarnal dark.
The earliest metaphorical use of the phrase in a Google Books search is from “A Returned Californian,” California Illustrated (1852), describing the pursuit of a prospect for gold:
This was precisely our case. We had got our "lead" almost opened, and if we should step out, some one would step in, and get the fortune. This we were not disposed to do. We had got on track, and were determined not to give way to any one.
Also figurative is this instance from Samuel Bartlett, ”Restorationist Views among Universalists,” in Lectures on Modern Universalism (1856):
Mr. Chapin never replied to my inquiry. But not long afterwards, being in New York, I went to the Universalist Book-store, kept at the entrance of his church, and inquired for Restorationist books. The clerk, in response, pulled out from a miscellaneous pile of dingy pamphlets, a treatise purporting to have been written by Jeremy White, chaplain to Oliver Cromwell, and published (after his death) in the year 1707, one hundred and forty nine years ago! “But have you nothing else?” “Nothing,” was the answer ; and I thought I could understand why I never received a reply from Mr. Chapin, to my inquiry.
Foiled thus to get on track of Restorationism, I followed Mr. King's suggestion and turned to the Quarterly Review. I examined all the numbers of that periodical for the years 1855 and 1856, without finding article or paragraph, that distinctly advocates punishment beyond the grave.
Significantly, almost all of these early occurrences of “on track” in the sense of “on the trail” are followed by of. This distinctive feature of the usage continues well into the twentieth century.
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UPDATE (10/24/2020): One interesting early literal usage of "get on track" appeats in the context of bicycle racing. From "Walthour Will Ride on Monday Night," in the Salt Lake [City, Utah] Tribune (July 28, 1907):
In case of a puncture or accident to wheel, or a fall, each man is given sixteen laps to remount and get on track.
Notably, "get on track" is one of two phrases in the quoted sentence that omits an article where one might normally appear—the other being "accident to wheel." The literal meaning of "get on track" here is "get back on the race track."
Did ‘get on track’ influence ‘get untracked’?
In the second half of the nineteenth century, a number of instances “on track” where track refers to “railroad track” appear in the clipped diction of official fatality reports, such as these from “Lehigh Valley Railroad Report,” in Reports of the Several Railroad Companies of Pennsylvania for 1862 (January 1863):
Aug. 18. Stranger run over by iron train near Hope’s station and killed—was lying on track, and supposed to be asleep when the train came along. When seen in the afternoon he was drunk.
…
Aug. 21. Samuel Arnold, walking on track a short distance above Bethlehem was struck by passenger train and killed.
Sept. 16. A man, unknown, walking on track a short distance below Laury’s, was struck by engine and severely injured.
But the first instances of “on track” used metaphorically, without trailing and without trains, appear surprisingly late—and seem to originate from aeronautics.
From Elbert Blackburn, Basic Air Navigation (1944) [combined snippets]:
After the plane has leveled off and picked up normal cruising speed, the drift must be checked again. The heading should be altered as required in order to stay on track; in the beginning of the flight, nothing is more important. There is very little that you can do to improve the ground speed; your duty is largely fulfilled when you have made sure that every mile of ground speed is being made good toward the destination. The immediate objective is always to improve the compass headings. As the flight progresses, the question of distance made good and the ground speed will become of increasing importance.
From Western Aerospace, volume 25 (1945) [combined snippets]:
Hold the heading of the airplane and "feel out" the edges of the null until its center is seen, by checking the azimuth readings, to be at 210°. Now, since we figured 10° of drift in the first place, as soon as we get back on track we will automatically put on a 10° drift correction, turning to a new heading of 65°.
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When we get back on track we will receive the null. That’s it. Apparently we didn’t have sufficient correction on when Amarillo went off the air, since we drifted off course to the right again, so this time we put on 5° more correction for a total of 15°.
From U.S. Department of the Air Force, “Instrument Flying Techniques and Procedures” (1952) [combined snippets]:
The procedure for intercepting a desired magnetic bearing is the same as simple tracking except that the angle of interception required (to get on track) is usually greater. To intercept a magnetic bearing, the position of the aircraft in relation to the station and the magnetic bearing must be determined.
One of the first uses of the idiom in fiction involves a drunk about to be set "back on track" with a slap. From James Henderson, Cargo of Fear (1947):
I stood up, raised my right hand to sting him back on track with a slap across the face. Automatically my eyes swept the surroundings, a habit you pick up flying if you don't want to get jumped.
In any event, "get on track" as a figurative way of saying "get on plan" seems to have emerged during World War II, whereas "get untracked" in the sense of "achieve full speed or productivity" goes back to the immediate aftermath of World War I. It's hard to see how "on track" can have influenced acceptance of "untracked."
Provisional answers
Untrack in the sense of "escape from a slump" seems to have evolved from untrack in the sense of "go at maximum speed," which was used idiomatically in racehorse training at least as early as 1889.
I haven’t been able to uncover the logic of the original expression “untrack himself [or herself].” My best guess is that the track in untrack is conceived of as a rut, or otherwise as a constraining factor that needs to be escaped for best performance—but I haven’t found any confirmation of this conjecture. The possibility that “get untracked” arose from a mishearing of "get on track" seems extremely unlikely, given the time frames for the two expressions.
None of the early instances of the idiomatic use of untracked that I found through Google Books searches are from publications outside North America. As far as I can tell, "get untracked" isn't used in British English, but perhaps commenters from the UK (or from other English-speaking countries outside the United States) can update the status of the idiom in their country.