What is the one single most important metric brands should use to measure customer engagement online? and why?

There are at least5 important metrics to measure customer engagement online and it is in the order of its level of importance:

1. Response Time: The faster the response the sooner you will be able to converse with your customer. This is the first and foremost thing to do with any customer to keep them satisfied, retain the brand image and thus gives a chance for you to do the next step.
2. Problem resolution and time taken to resolve it: The customer satisfaction is also directly proportional to the time taken to resolve a particular issue. The faster the company fixes the issue with accurate remedies, the higher the satisfaction rate of the customer and vise versa. This also shows the commitment of the company towards the customers.
3. Cross verifying with the customers about the remedy suggested: Most of the times we stop our conversation after providing the solution or remedy. However, checking if the proposed remedy or solution worked with the customer leads to building better understanding of the customer and check if they have any other doubts in their mind like "he/she did not resolve the problem now and how can I expect him to solve my issues in the future?". Its always a safe bet to recheck with the customer and if the issue is resolved, the information can be used to reassure the customer if the customer comes back with another issue again.
4. Seek for customer experience rating: This is a very important step to analyse if the customer is actually satisfied or not. Usually it is recommended to seek the rating without the customer support personnel being involved. The rating matrix may vary from company to company. This activity also gives an opportunity to stay much longer in customers mind and build better brand image.Remember happy customers tend to respond and unhappy customers tend to share their experience on social media.
5. Finally the volume of customer handling: It is crucial step where we have to allocate the customer support resources during the spike of the customer approaching based on each online media and resolve the issue faster. It is also recommended to provide a time say8 AM to6 PM for the customers to reach you.