Here is some background on the antecedents of the pinball machine, which includes Billiards, Croquet, and Bagatelle.
Billiards came about in the 15th century in Northern Europe or modern day France. Billiards was a popular game among European nobility.  It was a common enough game by the 1600’s that it came to be found referenced in some of Shakespeare works.  The modern day billiards table comes about in the 1850’s. Billiards is considered an antecedent of pinball because it is the antecedent of Bagatelle. Billiards goes through a decline in the 1930’s during the depression; then has resurgence in the 1950’s.  Billiards has multiple ways of being played but it all boils down to the concept of using a cue stick to hit one ball in order to knock the other balls into the various pockets around the frame of the table.
Croquet came into being during the 19th Century and quickly immigrated to English speaking nations. It was a popular garden party game. It’s popularity can even be seen as it features in works of literature such Lewis Carroll’s Alice in Wonderland. Croquet is perceived to be an antecedent of Pinball by croquet’s feature of hitting the balls into pegs and through hoops in order to score points. 
“Pinball is a game derived from the French billiard table game Bagatelle, where a player tries to get a ball past wooden pins into holes.” Bagatelle was very popular among 1700 french nobility.  Bagatelle reached It’s peak of popularity from 1770 to 1850. It is when Montague Redgrave adds a spring launcher to the board of a Bagatelle game, that it becomes the modern-day version of pinball.  Though these games vary greatly in design, their concept is the same. The table is set up at an angle and the ball is shot up the board with a cue stick similar to billiards and goes through the various features on the board in order to score points. 
(1) The Billiard Shop, “History of Billiards (or Pool),” accessed March 16, 2017, http://www.thebilliardshop.com/history-of-pool-and-billiards.
(2) William Shakespeare, Cleopatra and Anthony, Spark Notes: No Fear Shakespeare, accessed April 24, 2017, http://nfs.sparknotes.com/antony-and-cleopatra/page_96.html, 2.5.3.
(3) Robert R. Craven, “Billiards, Pool, and Snooker Terms in Everyday Use,” American Speech 55, no. 2 (Summer 1980): 93 – 100.
(4) United States Croquet Association, “Croquet in America: From Backyard Game to Worldclass Sport,” accessed March 16, 2017, http://www.croquetamerica.com/croquet/history/.
(5) Karen Sternheimer, Pop Culture Panics: How Moral Crusaders Construct Meanings of Deviance and Delinquency (New York: Routledge, 2015), 52.
(6) Rick Sherin, “A Mere Bagatelle: From Marbles to Pinballs and Beyond.” Play Stuff Blog, January 13, 2014, accessed March 16, 2017, http://www.museumofplay.org/blog/play-stuff/2014/01/a-mere-bagatelle-from-marbles-to-pinball-and-beyond/.
(7) Redgrave, Montague. 1871. Improvement in bagatelles. U.S Patent 115,357. Issued May 30, 1871.
(8) James Masters, “Bagatelle – History and Useful Information,” accessed March 16, 2017. http://www.tradgames.org.uk/games/Bagatelle.htm.
J. L. Magee, A little game of bagatelle, between Old Abe the rail splitter & Little Mac the gunboat general. (Cartoon).Philadelphia, PA, 1864. From Library of Congress. The Alfred Whital Stern Collection of Lincolniana, accessed February 21, 2017, https://www.loc.gov/resource/lprbscsm.scsm0337/.