Responding to "Perhaps from the ticket number?"
If the boarding pass has the ticket number on it, then as Doc mentions in comments, these are issued sequentially and can possibly be used to determine the rough date, however it requires a little research. Although BA boarding passes don't have ticket numbers on them (apart from mobile ones), they're the ones I have most of so I used those.
I took a sample of about 15 ticket numbers together with the issue date and plugged into a spreadsheet. I divided the difference in ticket number by the difference in days between two tickets. Over the last two years the average increment in ticket number per day ranged from 37000 to 44000. That would be more than sufficient to determine the right year for a given ticket number given one reference ticket with known date. You would need to perform a similar test for the airlines you have BPs for.
You can look at the barcode boarding pass standard here. There doesn't appear to be any other useful field that would indicate the year. This is somewhat surprising following the update of the standard to incorporate digital signatures, as that means that a boarding pass issued one year, will pass the digital signature test on the same day every subsequent year.