The latest figures show that British Transport Police were called to deal with 43 alcohol-related crimes on the company's trains in the six months to the end of October this year, compared to 66 for the same period in 2012.
However, while the total number of drink-related offences is down by 34% year-on-year, the number of assaults linked to alcohol has barely changed - going from nine in the period from May 1 to October 31 last year to eight for the same six months this year.
The bulk of offences were minor public order incidents, such as threatening and abusive behaviour or being drunk and incapable. These fell from 55 to 30 year-on-year.
However, it appears that staff working in railway stations have seen less of a benefit from the ban, with non-train alcohol offences actually increasing 7% from 168 to 180. These included 20 assaults and 140 minor public order incidents.
A spokesman for RMT, which represents rail workers, welcomed the decline in alcohol-related crime on trains. He said: "If the net effect has been a decline in alcohol-related crimes then that's a good thing.
"I would wonder whether the lack of Old Firm matches has played a part in it. It'd be interesting to know what effect that has had and what happens when they do come back.
"Most of the incidents our staff deal with are pretty run-of-the-mill - drunk people swearing at staff, being abusive and so on. But we are seeing fewer people taking bottles on board the trains."
One Saturday in December saw around one-dozen incidents reported to police by members across Scotland, he said.
They included two drunk females swearing at staff in Argyle Street station in Glasgow, a male passenger assaulted on a train at Uphall and a drunk and incapable female at Edinburgh Waverley station. There was also an ambulance requested for a drunk male with a facial injury in Glasgow, a male behaving "inappropriately" on a train near Perth, and a male reported for an assault around midnight outside the Burger King in Glasgow Central station.
The spokesman said that these incidents were "all depressingly familiar". However, he said there were "no assaults with weapons, which is good".
ScotRail is responsible for 95% of train services in Scotland, running 2000 routes a day. It launched its ban on July 20 last year, with the sale and consumption of alcohol on board forbidden between 9pm and 10am. Drunk passengers can also be prevented from boarding.
British Transport Police said it was confident that the travelling public were safer than ever.
They point to overall crime figures - not restricted to those which are alcohol-related - which show that total violent offences dropped by 15%, from 197 in the six months to the end of October 2012 to 167 for the same six-month period this year.
Anti-social behaviour offences have fallen 56% in the last ten years, while total recorded crime has halved despite a growth in passenger numbers of 36%.
Chief Superintendent Ellie Bird, divisional commander for BTP in Scotland, said: "The figures represent less than one alcohol-related incident per day across the whole of the Scottish rail network.
"It is worth noting that with passenger figures in excess of 83 million British Transport Police has delivered a further reduction in crime and offences on the network for a ninth consecutive year. So the chance of becoming a victim of crime on Scotland's railway remains very low."
Steve Montgomery, ScotRail's managing director, said: "These new figures show our pioneering alcohol ban is making a real difference in creating an ever safer and friendlier environment for customers using Scotland's railways.
"It is particularly pleasing that offences on trains have dropped by more than a third while passenger numbers continue to grow."
Robert Samson, of commuters' champion Passenger Focus, added: "This small improvement in the crime figures will be welcomed by passengers. However, we know they want to see the continuation of both a visible staff and police presence at stations and on trains."