by Plasma_Wolf » 03 Feb 2013, 11:32
Go to Leaderboards -> Global and Matchmaker.
There you have the ratings of all players (or of the ones who recently played, I'm not really sure).
At the time of writing, there are over 4800 players on that leaderboard. I've done a rough estimate, one that is bounded above.
The first 450 players have a rating of 1500 or higher. I've given them a rating of 2300 (which is about the highest at the moment), that'll hugely boost the average up, but only for the ones with a rating > 1500.
The players 451 to 2100 have a rating of between 815 and 1500, I've given them all a rating of 1500. This is a middle zone that will allow me to choose a nice upper bound for the ones with a rating less than 1500. In checking whether the average is more or less than 1500, I can easily omit these players (but I won't).
The players 2100 to 4800 all have a rating of 815 or less, so I've given them a rating of 815, as upper bound.
The average then is (450*2300+1650*1500+2700*815)/4800 ~= 1190. As all input values were upper bounds, the value of 1190 is also an upper bound. The actual average is probably about 800 (if not less).
The claim that the average would be 1500 is already plausible at best if you see that the maximum is far less than 3000 and the minimum is negative. The trueskill rating theoretically ranges from 0 to 3000, but in reality no one will get to 3000.