Reading through the Oregon Vehicle Code, Oregon Revised statutes (ORS) and Oregon DMV site and was unable to find mention of a points system for moving violation convictions.

The Oregon Driver Manual states that if you get a ticket for violating any rule or the road the offense is termed a traffic violation and you will be required to pay a fine if you plead guilty or no contest.An Oregon driver who is over 18 and has 3 traffic convictions or 3 accidents, or a combination that totals 3, in an 18 month period, the DMV will restrict your driving privileges for 30 days

If a traffic offense is considered serious, such as a DUI and reckless driving, you will be charged with a traffic crime. Punishment for a crime includes a jail sentence. The OR DMV can revoke your driving privileges for 5 years if you are convicted of 3 or more traffic crimes or 20 or more traffic violations within a 5 year period.

According to the Oregon DMV, a motorist's driving record includes reports of convictions for traffic violations and crimes, suspensions, revocations and cancellations of your driving privileges. It does not mention points for violations. So if you believe Oregon has a points system, contact the OR DMV to find out how long the points stay on your record.

Regarding car insurance and your driving record, under Oregon law an auto insurance company can use only the last 3 years of your driver's history to determine premiums.