Passengers are not allowed to drink or visibly carry alcohol on ScotRail services between 9pm and 10am.
The ban was introduced in July 2012 in a bid to combat anti-social behaviour.
New figures from British Transport Police (BTP) show they dealt with just four incidents related to alleged breaches of the ban last year, with three people reported to the procurator fiscal.
From the introduction of the ban until the end of December 2012 there were nine reported incidents with six people reported to prosecutors.
Superintendent John McBride, of BTP in Scotland, welcomed the low number of alleged offences.
He said: "The message that anti-social behaviour at stations and on trains is unacceptable is clearly being heeded by those who use the rail network. We will continue to support ScotRail in ensuring everyone can travel and work without encountering unwelcome or unwarranted disorderly behaviour."
Jacqueline Taggart, customer services director at ScotRail, said: "This is welcome news and demonstrates that the vast majority of rail passengers respect - and welcome - the ban. I would like to thank people for their co-operation in this regard.
"We remain committed to working with BTP to support our customers and staff in this important area. 2014 is an important year for Scotland and, as a major transport operator, we take our contribution very seriously."