I answered a question similar to this here but I'll repost it below.

The "points system" you are describing is very historically accurate. Technically, it was called the "Adjusted Service Rating score" and decided which troops in the European and Mediterranean Theaters of Operations would be sent home as part of Operation Magic Carpet, the mass demobilization as World War II drew to a close, or be retrained for the invasion of Japan.

In immediate postwar Europe, U.S. units were divided into four categories, with men transferred in and out of them as needed. Empty slots left by men sent home because of points were to be filled by transfers or new replacements.

Category	Explanation
I	Those units to be retained as occupational troops
II	Those units to be transferred to an active theater, either directly or indirectly through the United States, or transferred to the United States to be placed in strategic reserve
III	Those units to be converted or reorganized (to include necessary activations and inactivations) and upon completion thereof to fall under Category I or II
IV	Those units to be demobilized

In order to be sent home, a man needed to accumulate 85 points as you have noted. Many soldiers earned well over 140 points; this just rounded down to 85. No points were given for age or marital status.

Criteria	Points
1 month of military service	1 point each
1 month of military service overseas (in addition to total time in service)	1 point each
Combat award (Medal of Honor, Distinguished Service Cross, Distinguished Service Medal, Legion of Merit, Silver Star Medal, Distinguished Flying Cross, Soldier's Medal, Bronze Star Medal, Air Medal, Purple Heart) or campaign participation credit	5 points each
Having a dependent child under the age of eighteen	12 points each

Many men complained bitterly that the allowed list of combat awards did not contain the Combat Infantryman Badge. Men who had three or more dependent children under eighteen were eligible for immediate repatriation and discharge regardless of the amount of points they had earned.

As an example, a man who served for three years in the Army, including one and a half years overseas, had a child under 18, and fought in the Northern France, Ardennes-Alsace, Rhineland and Central Europe Campaigns, earning a Bronze Star Medal and two Purple Hearts would have:

36 (months in service) + 18 (months overseas) + 12 (dependent under 18) + 5 (Northern France) + 5 (Rhineland) + 5 (Ardennes-Alsace) + 5 (Central Europe) + 5 (Bronze Star Medal) + 5 (Purple Heart) + 5 (Purple Heart) =

101 points, enough to go home!

Category I, II, and III units would contain no men who had earned 85 or more points, while Category IV units would exclusively be made up of men who had earned 85 or more points. The units to be shipped to the Pacific were to contain those troops "least eligible" for discharge. Many veteran divisions that had not yet returned home were whittled to absurdly low levels by the reduction of the ASR score down to 75 points (and resultant transfers of personnel) in September 1945; the 88th Infantry Division was down to only 1,200 men! There were also gripes that the system unfairly rewarded rear-echelon troops; infantrymen didn't get additional points for risking their lives daily, besides points for medals, which all troops could get.

Campaigns in chronological order:

Campaign	Dates
Egypt-Libya	11 June 1942 - 13 February 1943
Air Offensive, Europe	4 July 1942 - 5 June 1944
Algeria-French Morocco	8 - 11 November 1942
Tunisia	17 November 1942 - 13 May 1943
Sicily	9 July - 17 August 1943
Naples-Foggia	9 September 1943 - 21 January 1944
Anzio	22 January - 24 May 1944
Rome-Arno	22 January - 9 September 1944
Normandy	6 June - 24 July 1944
Northern France	25 July - 14 September 1944
Southern France	15 August - 14 September 1944
North Apennines	10 September 1944 - 4 April 1945
Rhineland	15 September 1944 - 21 March 1945
Ardennes-Alsace	16 December 1944 - 25 January 1945
Central Europe	22 March - 11 May 1945
Po Valley	5 April - 8 May 1945