Where does “pinball” come from?

I can't write this etymology summary because the chain provided is circular and incoherent—it repeats the same four items (English billion, English black, Ancient Greek βάλλω) without establishing a coherent path from the headword "pinball" to an origin, and the known meaning is marked as unknown, making it impossible to trace sense development. To write an accurate summary, I would need: 1. A linear etymological chain showing how pinball derived from earlier forms 2. The actual known meaning of pinball 3. Clear language progression (e.g., English ← Old English ← Proto-Germanic, etc.) Could you provide the correct etymological chain for pinball?

pinball (English): A game, played on a device with a sloping base,...

Definitions

  1. A game, played on a device with a sloping base,...

Ancestry of “pinball”, step by step

pinball traces back through two separate lines of ancestry.

via English Ball

StepLanguageWordMeaning
1EnglishBallsurname
2Middle EnglishbalA ball; A rounded or spherical lump or bump,...
3Old Englishbeallball
4EnglishbealA small inflammatory tumor; pustule; To gather...
5Old Englishhyllhill
6Albanianhullifurrow
7Proto-Germanichullizhill
8Proto-Indo-Europeankl̥Hníshill
9Proto-Indo-EuropeankelH-to rise, to be tall; hill

via English PIN

StepLanguageWordMeaning
1EnglishPINAcronym of personal identification number;...
2Middle Englishpinne
3Old Englishpinnpin; peg; an instrument of writing; pen
4Proto-Germanicpinnazpin
5Proto-Indo-Europeanbend-point, pin; peg, tip, protruding point, edge;...

Words derived from “pinball

Every word from Proto-Indo-European kelH-
pinball — Etymology, Origin & Word History | Etymology Explorer