WHR required to gain purple:2724.646
WHR required to lose purple:2393.781
WHR required to gain blue:2415.052
WHR required to lose blue:2097.911
There are overlaps in the brackets, this is so that you don't change rank every game if you are right on the line between two ranks. It doesn't matter how long you stay there, the only way to rank up or down is to go over the threshold and be clearly inside the new bracket.
That's right! You can have 2 2400 WHR players, same skill, one silver, one purple. At this point, the rank colors have failed at their only job: to give people a rough estimate of how good a player is.
I frankly doubt that the "change rank every game if you are right on the line" is even a problem. Even if it is, it's nothing compared to the absurdity we have right now.