Well I bought an on peak one as I did not know the times!
It would have been just my luck to get caught and have a fine to pay - I argued with the bus driver on the last leg of my journey as it is!
The off peak times for all railway companies vary and are nor made clear on their web sites. Check which company you are traveling with before you book a ticket. e.g Cross Country after 9.30 no other restriction at the moment. Virgin varies depending on the route.
I used to work for National Rail Enquiries before they decided that customers would be better served from India rather than Newcastle, and quoting fares was a nightmare. Some journeys would have over thirty different fares, depending on time of travel, advance booking and availability. Return fares between Manchester and London varied between £20 and £200.