significa collaborare o andare d'accordo - penso che sia un modo da dire più vecchio del baseball stesso,

https://www.merriam-webster.com/thesaurus/play ball
Synonyms of play ball
to participate or assist in a joint effort to accomplish an end
She refused to play ball with the investigators.
Synonyms for play ball
band (together), collaborate, concert, concur, conjoin, conspire, cooperate, join, league, team (up), unite
Words Related to play ball
connive affiliate, ally, associate, combine, confederate, hang together, interface
Phrases Synonymous with play ball
make common cause, pull together


Play ball definition and meaning | Collins English Dictionary
https://www.collinsdictionary.com/dictionary/english/play-ba...
Play ball definition: to do what someone has asked you to do, or to work with them in order to achieve... | Meaning, pronunciation, translations and examples




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Note added at 23 hrs (2021-09-11 08:42:44 GMT)
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un po' di storia del termine:

https://www.grammarphobia.com/blog/2013/04/play-ball.html

dice, tra le altre cose:
In fact, the phrase or various versions of it had been around for hundreds of years before any American stepped on the mound and threw the ball toward home plate.