Logistic Regression: Is it viable to use data that is outdated?
Your thinking is sensible. Indeed, in a perfect world, your training data should be completely representative of the data you'll encounter. However, in practice, you often find that "unrepresentative" data may still have some value.

Ultimately, whatever you do is good if it improves your model, so if using "outdated" data helps, then do it!

Here is what you could experiment with:


Let the data speak


You could compare models using more or fewer data and it might give you an idea of the ideal cutoff point.


Implement "time decay"


Maybe, 1870 data is useful but likely, it's less useful than 1871 and even less useful than last year's. You could weight your training instance based on how old they are so that your recent data points have a bigger impact.


Create time-insensitive features


By this I mean, you could find a way to turn your problem such that the number of playoffs team doesn't matter. Instead of a binary "playoff/no playoff", your problem could be to instead rank your teams, then you can select the playoffs team based on the cutoff at this specific year.

You could also add how many playoff teams there are as a feature so that the learning algorithm is aware of how many spots there are.