> "this will improve our efficiency in performing Y by 80%"
Even if we took your example: Suppose it will improve the efficiency based on other, additional, work that would take a long while, and it is not trivial to understand why.
> "help us achieve our goal by reducing time wasted on Z."
Manager may well tell you:
* "I never allocate time for Z, only for concrete project goals. And nobody ever complains about wasting time on Z."
* "I don't know if you guys waste time on Z or not, but I definitely know that if I approve your request you will be wasting time on it, rather than implementing a new feature or fixing a bug."
Even if we took your example: Suppose it will improve the efficiency based on other, additional, work that would take a long while, and it is not trivial to understand why.
> "help us achieve our goal by reducing time wasted on Z."
Manager may well tell you:
* "I never allocate time for Z, only for concrete project goals. And nobody ever complains about wasting time on Z."
* "I don't know if you guys waste time on Z or not, but I definitely know that if I approve your request you will be wasting time on it, rather than implementing a new feature or fixing a bug."