"ivory ball used in the game of pool," by 1871, from pool (n.2) + ball (n.1).
Entries linking to pool-ball
pool n.2
game similar to billiards, 1848, originally (1690s) the name of a card game played for collective stakes, from pool "collective stakes of players in a game," which is from French poule "stakes, booty, plunder," literally "hen," from Old French poille "hen, young fowl," from Vulgar Latin *pulla, fem. of Latin pullus "young animal," especially "young fowl," from PIE root *pau- (1) "few, little."
Perhaps the original notion is from jeu de la poule, supposedly a game in which people threw things at a chicken and the player who hit it, won it, which speaks volumes about life in the Middle Ages. The notion behind the word, then, is "playing for money." The connection of "hen" and "stakes" is also present in Spanish polla and Walloon paie.
By 1868 it came to mean "combination of a number of persons, each staking a sum of money on the success of a horse in a race, a contest in a game, etc., the money to be divided among the successful bettors," thus also "collective stakes" in betting. The sense of "common reservoir of resources" is from 1917. Meaning "group of persons who share duties or skills" (typist pool, etc.) is from 1928. From 1933 as short for football pool in wagering.
Pool shark is from 1898. The phrase dirty pool "underhanded or unsportsmanlike conduct," especially in politics (1951), seems to belong here now, but the phrase dirty pool of politics, with an image of pool (n.1) is recorded from 1871 and was in use early 20c.
ball n.1
"round object, compact spherical body," also "a ball used in a game," c. 1200, probably from an unrecorded Old English *beal, *beall (evidenced by the diminutive bealluc "testicle"), or from cognate Old Norse bollr "ball," from Proto-Germanic *balluz (source also of Dutch bal, Flemish bal, Old High German ballo, German Ball), from PIE root *bhel- (2) "to blow, swell."
The meaning "testicle" is from early 14c. (compare ballocks). Ball of the foot is from mid-14c. The meaning "rounded missile used in warfare" is from late 14c.
The meaning "a game played with a ball" is from mid-14c. The baseball sense of "pitch that does not cross the plate within the strike zone" is by 1889, probably short for high ball, low ball, etc.
Ball-point pen is by 1946. Ball of fire when first recorded in 1821 referred to "a glass of brandy;" as "spectacularly successful striver" it is attested from c. 1900. Many phrases are from sports: To have the ball "hold the advantage" is from c. 1400. To be on the ball is from 1912; to keep (one's) eye on the ball in the figurative sense is by 1907, probably ultimately on golf, where it was oft-repeated advice. Figurative use of ball in (someone's) court is by 1956, from tennis.
The head must necessarily be steady, for it is most important that you should keep your eye fixedly on the ball from the moment that the club-head is lifted from the ground until the ball is actually struck. "Keep your eye on the ball," should be your companion text to "Slow back." [Horace G. Hutchinson, "Hints on the Game of Golf," 1886]
Once a meeting is over, someone will be expected to do something. Make sure it is someone else. This is known as keeping the ball in their court. [Shepherd Mead, "How to Get Rich in TV Without Really Trying," 1956]