You have to understand the following...
Automation will never find NEW bugs.
It will find bugs if your system is updated. It will find bugs if the system is down for whatever reason and you are sleeping in your bed and you have automation enabled overnight. It will send you an urgent email that you will read in the morning that the site was down for an hour or so.
It won’t find bugs that humans find through bug regression. It won’t find bugs in the system that require analysis and constant pounding. It won’t find hidden bugs. It will only find bugs that it is programmed to find.
That said... Automation is something that will help you concentrate on those hidden bugs. It will get a LOT of testing off your shoulder. Like multy browser, endless input of various combinations of data. Tidies tasks like create test data, companies, users, etc. Stress test, Load test, functionality. All that can be covered.
So success for an automated test would be the assurance that if a developer checks in code, you can be sure that a major part of the application is regressed at night when you are sound asleep. And you can be sure that it will find changes, defects which that update produced and nothing will be unnoticed unless you didn't write a test for it.