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.

https://www.reddit.com/r/borderlands3/comments/fy3r1f/melee_damage_bonuses_dont_work_how_they_seem/
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.