How do people here decide when to run discounts, what the % discount should be (e.g. 20%, 30%, 40% off your order), which items to discount, which customers to give discounts to, etc.? And after you run the discount, how do you know when it is successful vs. just reducing your margin? Is there a way to measure ROI? I’m starting to use Shopify and haven’t found any great resources on this yet.
Are there any apps that help run A/B tests for discounts, or automatically decide the % off?
Something like this app could probably help: https://apps.shopify.com/intelligems
It’ll allow you to A/B test with different product prices, and then once you find some trends, then you could make discount codes to handle the different prices, as needed.
There are a few A/B testing apps available on the app store: https://apps.shopify.com/search?q=A%2FB%20testing
Intelligems is indeed a great app for A/B testing but is very pricey. So it’s not appropriate for most stores.
If you’re interested, I just launched my free Shopify app Crowly: Automated Optimization. It’ll allow you to generate and optimize your products’ pricing and descriptions very quickly using real time customer data. Once the app has collected enough data you’ll be able to see what prices and descriptions have the revenue in per visitor.
We offer a free plan so there’s no commitment:
https://apps.shopify.com/crowly
If you have any other questions feel free to shoot me an email.
Would also love some feedback myself 
All the best,
-Ethan