There is infact a pattern. Heres what I notice. The first person to join the server is a red color. Which is usaly the host or server admin. Then the 2nd player is yellow, the 3rd is purple, and the rest of the player colors arent random either. Its a certain pattern but I forgot the pattern order. Also if enough people join a server. The game will run out of player colors and will make all of them a grey color. In this screenshot you can see most of the colors are grey
And I REALLY want someone to make a mod to allow you to asign someone a certain color. That would have so much potenial.