The issue is not that facts are overrated or that humans tend to make decisions based on emotions (true) but rather that humans tend to find it easier to understand if you explain logically to them how you are solving a problem they have before you get into the 'hard data' or logic.
For example, you have data that says building feature Y is better than building feature X because you have data from the number of support tickets and the fact that the tickets are growing because support is spending more time responding to this other issue leaving other tickets dangling.
An easier (IMHO) way to sell this would be something along the lines of - a) We see your stats are getting bad. I have a way of fixing this (the person is interested cos you are going to make them look good) b) I can see your people are getting burnt out, we can fix that issue for you
This gives an instant/emotional connection and gets the person's interest which then leads you to say - X% of the issues your team is dealing with is A and building this feature 'Y' means we automate that stuff and you no longer have to deal with it.