Joseph Randle Police Report -- Snapped After Losing at Beer Pong ... Extremely Violent

More sad and disturbing details in the arrest of ex-Cowboys running back Joseph Randle -- cops say a beer pong game was at the center of the violent incident that culminated with JR hitting people with his car.

TMZ Sports obtained a police report in which cops say they spoke with several witnesses who claim 24-year-old Randle attended a housewarming party in Wichita, KS on Feb. 21st and played a game of beer pong.

But an argument broke out about who won the match -- with Randle pushing the opposing player onto the balcony of the home. The other man apologized and the situation was briefly diffused.

Randle then went downstairs and continued acting aggressive -- so the party hosts asked him to leave.

Instead, cops say Randle ran back upstairs and attacked party guests -- until several people wrangled Randle and literally pushed him out of the home.

One of the hosts followed Randle outside and asked him to leave -- instead, Randle got in the car and punched it in his direction ... striking the man at somewhere between 20 and 30 mph.

The man was thrown over the top of the car. When others came to assist the victim Randle struck again ... hitting 2 more people.

One of the female victims was hospitalized after losing consciousness several times from the attack.

Randle was eventually arrested and hit with a slew of charges including aggravated battery, threats, possession of marijuana and interfering with law enforcement.