The noun handicap dates back to the mid-17^th century and originally denoted a sort of game in which one person claimed an article belonging to another and offered something in exchange, an umpire being chosen to decide the difference of value between the two articles, to be made up in money by the owner of the less valuable one; the word handicap was probably derived from the phrase hand in (the) cap as used of this game, which a certain J. S. Coyne described in Notes and Queries (London) of 23^rd June 1855:

The handicap, or “hand i’ the cap,” was originally played by three persons in the following manner:—A. wishes to obtain some article belonging to B., say a horse; and offers to “challenge” his watch against it. A. agrees; and C. is chosen to “make the award;” that is, to name the sum that the owner of the article of lesser value shall give with it in exchange for the more valuable thing. The three parties then put down a certain stake, and the arbitrator makes his award. If A. and B. are both satisfied with the award, the exchange is made between the horse and the watch, and the arbitrator takes up the stakes. Or, if neither be satisfied with the award, the arbitrator also takes the stakes; but if A. be satisfied, and B. not, or vice versa, the party who declares himself satisfied gets the stakes. It is therefore the object of the arbitrator to make such award as will cause the challenger and the challenged to be of the same mind; and considerable dexterity is required for this. The challenge having been made as stated between A.’s horse and B.’s watch, each party holding a piece of money puts his hand into a cap or hat (or into his pocket), while C. makes the award. After recapitulating the various excellences, and expatiating on the value of the articles, he makes his award in as rapid and complex a manner as possible: thus, he might say the owner of the “superior gold lever watch shall give to the owner of the beautiful thoroughbred grey horse, called ‘Seagull,’ the watch and fifteen half-crowns—seven crowns—eighteen half-guineas—one hundred and forty groats—thirteen pounds—seventeen shillings and twenty-five farthings. Draw, gentlemen!” A. and B. must instantly draw out, and open their hands. If money appears in both, the award is made; if money be in neither hand, or only in one, the award is off, and the stakes go as I have described. Very frequently, neither A. nor B. are sufficiently quick in their mental calculations to follow the arbitrator; and not knowing on the instant the total of the various sums in the award, prefer being “off,” and therefore draw “no money.” This is the true handicap. The application of the term to horse-racing has arisen from one or more persons being chosen to make the award between parties who put down equal sums of money on entering horses for a race.

This game is very old; it was mentioned under the name of newe feire (= new fair) in The vision of William concerning Piers Plowman, an alliterative poem from the late 14^th century attributed to William Langland:

(Copyright © President and Fellows of Harvard College)
Clement the cobbler cast off his cloak
And named it for sale at the ‘new fair’ game.
Hick the horse dealer heaved his hood after
And bade Bart the butcher be on his side.
There were chapmen chosen the goods to appraise;
Whoso hath the hood should have amends for the cloak.
Two rose up quickly and whispered together
And priced these pennyworths apart by themselves.
They could not in their conscience agree on a value,
Till Robin the roper arose for the truth
And named himself umpire to avoid a debate
And to settle this business betwixt them three.
Hickey the hostler he had the cloak,
In covenant that Clement should the cup fill
And have Hick hostler’s hood and hold himself served;
And whoso sooner repented should arise after
And give to Sir Glutton a gallon of ale.
     original text:
Clement the Cobelere caste of his cloke,
And at the newe feire nempned it to selle.
Hikke the Hakeneyman hitte his hood after,
And bad Bette the Bocher ben on his syde.
Ther were chapmen ychose this chaffare to preise:
Whoso hadde the hood sholde han amcndes of the cloke.
Tho risen up in rape and rouned togideres,
And preised the penyworthes apart by hemselve.
Thei kouthe noght by hir conscience acorden in truthe,
Til Robyn the Ropere arise the[i by]sou[ght]e,
And nempned hym for a nounpere, that no debat nere.
Hikke the Hostiler hadde the cloke
In covenaunt that Clement sholde the cuppe fille
And have Hikkes hood the Hostiler, and holden hym yserved;
And whoso repented rathest shoulde aryse after
And greten Sire Gloton with a galon ale.

The word handicap also denoted a card game described in Tavern anecdotes and sayings; including the origin of signs, and reminiscences connected with taverns, coffee-houses, clubs, etc., etc. (London, 1875), an edited, expanded and annotated version by Charles Hindley (died 1893) of the book originally written by William West (1770-1854), bookseller and antiquarian:

Handicap.—A game at cards not unlike Loo, but with this difference—the winner of one trick has to put in a double stake, the winner of two tricks a triple stake, and so on. Thus: If six persons are playing, and the general stake is 1s., and A gains three tricks, he gains 6s., and has to “hand i’ the cap” or pool 3s. for the next deal. Suppose A gains two tricks and B one, then A gains 4s. and B 2s., and A has to stake 3s. and B 2s. for the next deal.

The term handicap match was applied in the 18^th century to a match between two horses, the arrangement of which was made in accordance with the game of handicap, the umpire deciding in this case the extra weight to be carried by the better horse, and the parties drawing to declare whether the match should be ‘on’ or ‘off’; this was explained in The Sporting Magazine; or Monthly Calendar of the Transactions of the Turf, the Chace, and every other Diversion interesting to the Man of Pleasure and Enterprize (London) of February 1793:

A handy cap match is for A B and C to put an equal sum into a hat; C, which is the handy capper, makes a match for A and B, which, when perused by them they put their hands into their pockets, and draw them out closed; then they open them together, and if both have money in their hands the match is confirmed, if neither have no money it is no match. In both cases the handy capper draws all the money out of the hat; but if one has money in his hand, and the other none, then it is no match; and he that has money in his hand is entitled to the deposit in the hat.
If a match is made without the weight being mentioned, each horse must carry ten stone.

The New English Dictionary (Oxford, 1901), as the Oxford English Dictionary was known, stated:

Such matches are recorded as early as 1680, but the term ‘handicap’ does not appear.

By the late 18^th century, handicap race, or simply handicap, had come to denote a race with more than two horses and without a betting game about the umpire’s decision, i.e. a horse race in which an umpire (the handicapper) decides what weights have to be carried by the various horses entered, according to his judgment of their merits, in order to equalise their chances.

In the 19^th century, the word handicap was extended to any contest in which inequalities are artificially evened out, which led to its use in the sense of the disadvantage imposed on superior contestants—whence the main modern meaning: disadvantage, disability.