Very good question, one I have been researching for a long time.
You could go on age, though the life of a LTO tape (for eg) is years, depending on how it is used. If you straem to an LTO (so writing >25ish MB/s) it will last years probably, providig it's not dropped, mis-handeled etc ...
If you don't get the data out quick enough, the drives will stop/start - known as shoeshining, this could wreak a tape in as little as 5 mounts, or it might not - it's unknown.
Some drives, such as storagetek, are designed to stop/start so this is not an issue.
YOu could count the no. mounts as a rough guide to tape useage (as the header is read so at least part of the tape has passed the heads on the dive, if you check the tape manufactures page, they will give figures such as max no mounts, no of full tape passes etc ..., so wrost case is each mount = 1 full tape pass, hence if no mounts=max no of tape passes then retire.
Not that simple though, re. section above on stop/start.
Generally, if tapes are rotated, age is not really an issue, as the shelf life is many years, depending on how they are stored (temp/humidity etc ...).
So, you could go on actually backup failures and errors (bit late by then I know), biut these can be difficult to work out as it could be the media or the drive.
So in answer to your question, there is no scientific way to work out your answer (sorry), without some specialist software.
(before anyone asks, I don't work for them) ...
Hi_stor make a product called storsentry (marketed through Imation). This software monitors tapes and drives at a low level (bit level) and using a combination of errors off the drive, clever functions and stats) predicts tape and drive failure, before you get errors.
Does it work - yep, I'm trialing it for my company and have visited a reference site to really see it in action, and it is the Daddy, so to speak.
Also, don't waste time researching other software, it is unique, no other company has yet come up with anything close.
Martin