TL; DR: Facebook shows a metric called the Relevance Score. This score is initially calculated after your first 500 impressions for your paid advertisements and will let you know how relevant an ad is to its target audience. We concluded to give a Facebook ad its best chance at life, we should analyze the best times for our past ads. Then, launch new ones in those windows to make the most of those first 500 impressions.
Understanding the Score
According to Facebook, Relevance Score is calculated based on the positive and negative feedback (scale from one to 10, 10 being the highest) they expect an ad to receive from its target audience.
View the score in Ads Manager by going to Campaigns and clicking Ads.
Example Ads with Relevance Scores

Source: Facebook
Why the Score Matters

Now for Some Examples
To figure out the best time or day to run your ad, you can analyze your ads performance and/or analyze your Business Page performance.
The below chart is from your Facebook Page’s Insights. So it gives a good review of the habits of those users who already follow your brand.

Below is a sample of one way to see what time of day is working best for your ad campaigns that are already running:

Using your Facebook Page traffic, you can also review the types of posts that people have engaged most with:

This graph shows the Relevance Score versus impressions. This one did really well initially by launching at a good time and has stayed in the 6 to 7 range.

Do you have good examples of success with the Relevance Score and your ad campaign? Be sure to share in the comments!
Resources from the Source: Facebook
The Ad Relevance Score
https://www.facebook.com/business/a/ads-relevance-score
Showing Relevancy Scores for Ads on Facebook
https://www.facebook.com/business/news/relevance-score
*According to Facebook: Relevance Score isn’t the only factor our ad delivery system considers. Bid matters too. For instance, if two ads are aimed at the same audience, there’s no guarantee that the ad with an excellent relevance score and low bid will beat the ad with a good relevance score and high bid.