Etymology
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hat trick (n.)

in the sports sense, 1879, originally in cricket, "taking three wickets on three consecutive deliveries;" extended to other sports c. 1909, especially ice hockey ("In an earlier contest we had handed Army a 6-2 defeat at West Point as Billy Sloane performed hockey's spectacular 'hat trick' by scoring three goals" ["Princeton Alumni Weekly," Feb. 10, 1941]). So called allegedly because it entitled the bowler to receive a hat from his club commemorating the feat (or entitled him to pass the hat for a cash collection), but the term probably has been influenced by the image of a conjurer pulling objects from his hat (an act attested by 1876). The term was used earlier for a different sort of magic trick:

Place a glass of liquor on the table, put a hat over it, and say, "I will engage to drink every drop of that liquor, and yet I'll not touch the hat." You then get under the table; and after giving three knocks, you make a noise with your mouth, as if you were swallowing the liquor. Then, getting from under the table, say "Now, gentlemen, be pleased to look." Some one, eager to see if you have drunk the liquor, will raise the hat; when you instantly take the glass and swallow the contents, saying, "Gentlemen I have fulfilled my promise: you are all witnesses that I did not touch the hat." ["Wit and Wisdom," London, 1860]
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football (n.)

open-air game involving kicking a ball, c. 1400; in reference to the inflated ball used in the game, mid-14c. ("Þe heued fro þe body went, Als it were a foteballe," Octavian I manuscript, c. 1350), from foot (n.) + ball (n.1). Forbidden in a Scottish statute of 1424. One of Shakespeare's insults is "you base foot-ball player" [Lear I.iv]. Ball-kicking games date back to the Roman legions, at least, but the sport seems first to have risen to a national obsession in England, c. 1630. Figurative sense of "something idly kicked around, something subject to hard use and many vicissitudes" is by 1530s.

Rules of the game first regularized at Cambridge, 1848; soccer (q.v.) split off in 1863. The U.S. style (known to some in England as "stop-start rugby with padding") evolved gradually 19c.; the first true collegiate game is considered to have been played Nov. 6, 1869, between Princeton and Rutgers, at Rutgers, but the rules there were more like soccer. A rematch at Princeton Nov. 13, with the home team's rules, was true U.S. football. Both were described as foot-ball at Princeton.

Then twenty-five of the best players in college were sent up to Brunswick to combat with the Rutgers boys. Their peculiar way of playing this game proved to Princeton an insurmountable difficulty; .... Two weeks later Rutgers sent down the same twenty-five, and on the Princeton grounds, November 13th, Nassau played her game; the result was joyous, and entirely obliterated the stigma of the previous defeat. ["Typical Forms of '71" by the Princeton University Class of '72, 1869]
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