In real world it's usually hard to precisely quantify this improvement ahead of time and so managers might over weigh the probability that your efforts fail to materialize the win. In the end you need a manager that is comfortable enough with risks, has the same expectation of success as you, and trusts you personally. So as usual, you need a good manager.
People often just don't think about "how long does it take to do X?"
At one startup I worked at the CEO wanted to try "hackathon" style development and have us try to knock something out in two hours.
This was a system that had a back end written in Scala and a front end using Typescript and React. I told the CEO that it took 20 minutes to go from zero to docker images ready to run (I knew because I kept notes) so at best we could do six iterations in that time. The CTO said, "No way it takes that long".
I stepped back at this point and we all agreed we'd go ahead and see what happens.
It really took 18 minutes.
Whenever I've felt pressured and "under the gun" I've taken notes about what the process is and where the time actually goes.
