"If there's doubt there is no doubt. " If in doubt anti-ice. The time interval between making the decision NOT to anti-ice and taking off is indeterminate, as is the fickleness of the weather. The next decision is if you need to de-ice first. Sitting at the end of the rwy wondering if this takeoff is going to be safe, or should we have anti-iced, is not healthy. It is not possible to see the wings from the cockpit. Delays? It's better to be 10 minutes late on departure than 20 years early upstairs.
I do understand the technicalities in your question, but it is not an exact science. However, there are solid guidelines and legal boundaries.