Just wanted to share an article I wrote about how to achieve an accurate realistic semi-transparent shadow. This is useful for pictures with a transparent background, but you still want to add an accurate ground shadow that includes indirect lighting effects.
In the article I use a fairly simple Suzanne render: https://blendergrid.com/learn/articles/compositing-transparent-background-renders-for-the-web
I also recored a video walk-through of the compositing that was done: https://youtu.be/kDaDvCt9Mj0
Thanks for sharing I will have to watch your video a few times ti catch on plus read your site. - I like this book
Color Right from the Start: Progressive Lessons in Seeing and Understanding Color Hardcover – April 1, 1994
It goes into how the eye sees color but also has much information on color pigments.
Thanks! If you have any questions about it, feel free to shout 
Something I forgot to mention is using a “shadow catcher”, which is way easier. But I didn’t do that in this situation because I wanted a fully accurate shadow including indirect lighting.