How does brawler ward work?

After seeing a post about it elsewhere I’ve been wondering how brawler ward actually works? What’s the formula?

This post on the subreddit is what got me thinking.
Check the comments.

When brawler works right it should multiply your melee by 4, but when you have any melee bonus, it only does times 3. Do you think that’s a bug?

Thanks, I haven’t found my answer yet, but that was very helpful.