Ah, thanks! I knew about the levels and uncertainty; I just didn't realize it was also called "mean skill".

But now I'm confused why WW puts 3 pleases before asking you to use it instead of level. Is it vastly preferred in some circles?

i am going to oversimplify here, but basically mean skill is a more accurate measure for skill for people on the top end of the leaderboard (or who have a ton of games played) and the isotropic level is a better measure for less skilled or newer players.

That's patently false. The mean skill is the best guess you have for the skill of anyone. BY DEFINITION.

You could say it's the most accurate guess. To say that it's the best guess really depends on what you're trying to accomplish with your guess.

What are you trying to accomplish with your guess?

Hey WanderingWinder, I missed the response earlier, sorry about that.

First a disclaimer. I'm an algebraist by trade, not a statistician. I also don't know the details of how the True Skill system works. My guess is that it's effectively the following. Your "skill" is considered probabilistically. That is, in the most encompassing sense, the best and most accurate "guess" of your skill is really a probability distribution. You can't exactly totally order probability distributions in a meaningful way, and so these distributions are distilled to a mean and a standard deviation. Your mean skill in the mean, and your level is the mean minus some multiple of the standard deviation perhaps.

Now, if the probability distribution which best describes your skill is normal, then sure, mean skill is the best single number estimate in a reasonable sense. However, if your distribution is bimodal, for instance, then the mean skill may extremely unlikely to be your actual skill, but rather is roughly the average of two other skills which are likely. As an example from the recent US election, Nate Silver presented his prediction of the electoral vote split via a probability distribution. The two most likely outcomes, by his model, were that Obama would win 304 or 332 electoral votes (I may be slightly off, by this principle I'm illustrating is the same). The mean of this distribution? It was about 314 if I recall correctly, but his model gave a VERY low probability of Obama getting precisely 314 electoral votes. This illustrates how the mean is often a terrible guess in and of itself.

Now, if you have a reason to believe that the underlying distribution is normal, then the mean skill would be a fair choice for best guess. But it certainly isn't by definition, as illustrated above. Now, I imagine that True Skill probably assigns a new user a default distribution, and then updates the distribution in a Bayesian manner each night based on the results of the day. Maybe True Skill only assigns normal distributions? In this case, I suppose by a quirk of the system, yes the mean skill would always be the "best" guess.