The default TrueSkill of a new player is 25, right?
That’s not fully correct. The TrueSkill value that is displayed in the leaderboard is the conservative estimate of a player’s skill, computed from two hidden parameters that are used to track a player’s skill: the mean skill μ and the skill uncertainty σ. The TrueSkill value is then μ-3*σ. What is correct is that a new player is assigned a mean skill of μ=25 and a skill uncertainty of σ=8.333. Thus, the TrueSkill of a new player is 25-3*8.333 = 0. Note that these two choices for μ and σ effectively mean that a new player’s skill can be anywhere from 0 to 50, representing a state of complete uncertainty about their skill.
