A team needs 14.5 points out of 28 to win the Ryder Cup outright.

If the match finishes 14–14 , it’s a tie and the team that already holds the Ryder Cup keeps it (they “retain” the Cup), even though the other side has matched their score.

At a glance:

  • Total points available: 28.
  • Points to win the Ryder Cup: 14.5.
  • If it’s 14–14: defending champions retain the trophy.

So the “magic number” you’re looking for is 14.5 points.

TL;DR:
To answer “how many points to win the Ryder Cup” in one line:
You need at least 14.5 points out of 28 to win; at 14 points , you only retain the Cup if you’re the defending team.

Information gathered from public forums or data available on the internet and portrayed here.