EPT(edit: I'll talk about two related approaches at the bottom of this post.)
It's based on the following observation: if you set out to measure people's skill level at anything, for example, measuring how far they can jump, you will find that the distribution of results typically follows the bell curve pretty closely (an effect that is explained by the Central Limit Theorem in statistics, but let's not go there).
Now, in long jumping the measure of skill is pretty well-defined, but the same phenomenon also occurs if you give them a set of questions that are designed to challenge their cognition. The number of questions answered correctly is again normally distributed, and if you score one standard deviation better than average, the test will tell you that you have an IQ of 115.
Philosophically, this is entering murky waters: is there really such a thing as brute cognition power - is intelligence not something more complex and multidimensional? Can it really be captured in a single number? Probably IQ is a gross oversimplification that has no counterpart in the real world. But people still find it a useful measure, for example it can help judge what type of school to send a child to. I think a good way to interpret an IQ score is as an aggregate score that measures roughly how good you are at the kind of tasks that the test focuses on.
So lets jump over these issues and assume we're happy with IQ as a measure of cognitive ability. A bunch of researchers took this idea and applied it to emotions and hey presto, we got this newfangled notion of "emotional intelligence", expressed in EQ. Let's jump on the bandwagon and do the same thing for Starcraft ability!
Now let's assume that your league placement is in line with your SQ: if you're in diamond, your SQ should be higher than the SQ of any old platinum dude, right? Under this assumption I can plot the bell curve for starcraft, where the leagues are now associated with particular SQ ranges.
![[image loading]](http://i.imgur.com/LINN4.png)
(Data taken from sc2ranks for the NA server. Grandmaster league, off on the right hand side, is too tiny to plot.)
From this graph we find that bronze level players have an SQ of at most 91, silver means 91-100, gold means 100-108, platinum is 108-117, diamond is 117-129, master is 129-150 and grandmaster level players have a genius level SQ of more than 150.
While we all know that bronze players are bad, there is still a distinction between plain bad and, well, completely retarded. The average bronze level player you'd meet on the street would have an SQ around 83, which is plain bad, but some of those people who lurk around the bottom of the bronze ladders... well, let's not talk about it.
On the other end of the spectrum the masters are doing pretty damn well. If your IQ were that high people'd call you gifted! Note though that most of the masters are near the low end of their SQ interval: the average master has an SQ of 133, only slightly better than a top diamond player. If you're progressing through master league, you would progress steadily up the ladder, meeting lots of people of comparable skill, until you come close to the very top where the skill level starts to ramp up dramatically. This is basically because people who are that good are starting to thin out. I am interested to learn if this prediction corresponds to the experience of you top level master players out there.
For those of us in the middle leagues, the skill level is distributed across the ladder much more smoothly, with each promotion corresponding to about 10 SQ points.
Hope there was anything in this post to interest you, please keep discussion friendly and please don't turn this thread into a discussion about merits/drawbacks of IQ.
Related posts
Two posts are quite related to this one. The first is Excalibur_Z's analysis of the league system
http://www.teamliquid.net/forum/viewmessage.php?topic_id=195273.
It provides detailed information on the inner workings of the league system, including the numbers of players that are kept in each league by the league system. In contrast, in this post I don't use any knowledge about the league system at all, just numbers from sc2ranks. It is nice to see that my results roughly seem to match Excalibur_Z's values. Note that according to his post, people are assigned to leagues based on their hidden MMR performance score, which is the game's estimate of skill level. That seems reasonable, but in my story I only needed to assume that people in higher leagues are better.
Darmousseh's post http://www.teamliquid.net/blogs/viewblog.php?id=183608, also has a lot in common with mine, but makes a different argument.
I still don't understand how both these people could respond to my post within five minutes...
