This is something you'll probably need to develop on your own. The time to automate a test case is dependant on the detail of the test case, the skill of your automation team, and the complexity of your application. Automation should also involve a considerable amount of 'startup time' to develop your GUI map and any necessary function libraries before you even begin working on test cases.
The number(s) that seem to get tossed around by Mercury (and I'm not sure why as the previous post is right on) is that a "good" automator can be counted on to finish between 2 and 3 "complete" scripts per day. In my experience this is often low but then there have been places where due to the complexity of the test case it may take 2 to 3 days to do 1 script. There are many factors outside of automation that will affect this process-quality of the app currently, data availability, documentation quality, Subject Matter Expertise, environment issues, etc. If you're asking because management wants to trap you into a schedule and make projections..go low!!! make sure you specify all dependencies, like those mentioned above as well as automator skills and training. Also, make sure you decide what method you are going to employ when scripting and the need for standardization.
My estimate is it takes 10 times longer to automate a test than to execute it manually.
That includes scripting, debugging and testing the test. I assume that the test case is written up and the basic setup is done.
Any other numbers or ways to estimate?
In our company we category the functionality / test cases into three categories like Low / Medium / High. Accordingly we will estimate the time taken to automate. Like if the Low one will take .30mts then the Medium will take 1 hour etc., Not need the time should be same for every functionality, it depends on the functionality automate & your understanding of application. Above all your compatiability with WinRunner / any automation tool too.
Based on all those above factors we can estimate & categorise. We will be in a better position to estimate completion timelines of the entire automation suite. I would suggest to use MPP(Microsoft project Plan) Which will really help.