Short answer: never, with two exceptions

Now to the long answer. When you use any points+cash or miles&money program, you are buying points if you don’t have enough or selling them if you have way too many of them. So, you’d usually calculate the points value and make a decision to use or not to use a program.

In case with British Airways Avios & Money there is a fluctuating chart of points value, so there may or may not be a good value. Same was for Hyatt for a while. Starting November 1 2018 Hyatt made a significant change, now points+cash program is always 50% of standard room points cost + 50% of standard room cash cost. So, if you think points have a good value, use all 100% of them, and if you don’t think they provide enough value, use all cash, there is no middle ground with two exceptions:

First: points show a great value, but you don’t have enough of them for 100%, so yeah, 50% will do it.

Second: Hyatt’s points+cash program rate does not require you to pay taxes, (but still requires to pay resort fees and other “fixed-sum” surcharges). So if taxes are exorbitant for some reason, getting rid of them by paying 50% in points could make sense.

Another note: Hyatt doesn’t offer Nth night free if you book with points, so its points program misses a huge incentive to hoard points unless they accumulate by natural causes.

And the last word: in my experience Hyatt points return the best value when used for room upgrades –