Semi related: what kind of process do you have that makes you feel confident pushing 40x a day? Do you run some kind of automatic analysis that helps you automate the push completely? What if you know that HEAD has a regression that shouldn't be pushed?
We have a lot of automation and infrastructure in place to give us that confidence. We have an extensive test suite of hundreds of thousands of tests, linting and static checks that run on CI, a deploy automation tool that automatically merges and deploys on green (https://shopify.engineering/successfully-merging-work-1000-d...) and a canary deploy system where we quickly detect regressions that might have escaped our systems to that point. We have a lot of posts about those systems written up in our engineering blog, as well.