Where does “hardball” come from?

I cannot write this sentence because the etymology chain provided is circular and incoherent—it repeats the same three English words (billion, black, hard) without establishing a clear linguistic path to any source language, and Ancient Greek βάλλω appears only once without connecting to the other terms. A valid etymology requires a coherent sequence showing how the word developed across languages. If you have the correct etymology chain for "hardball," please provide it and I'll write the summary.

hardball (English): In baseball, a type of ball and baseball game, as...

Definitions

  1. In baseball, a type of ball and baseball game, as...

Ancestry of “hardball”, step by step

hardball 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 hard

StepLanguageWordMeaning
1EnglishhardHaving a severe property; presenting difficulty;...
2Old Frenchhardihardy; tough; durable
3Old Frenchhardirto harden
4Frankishhardijanto harden, to make hard
5Proto-Germanichardijanąto make hard, strong; to harden
6Proto-Germanicharduzhard; brave
7Proto-Indo-Europeankert-times; to weave, twist together; time
8Proto-Turkic*keŕ-to travel, tour

Words derived from “hardball

Every word from Proto-Indo-European kelH-Every word from Proto-Indo-European kl̥HnísEvery word from Proto-Germanic hulliz