Introduction

I often see posts or comments in this sub with references to IQ, like "200 IQ play" or "70 IQ jungler". I thought that this was not very precise, since you can actually find out what your LoL IQ is. IQ is found by taking the percentile you got in a test, assuming that the test results of people will be normally distributed, and finding the corresponding IQ value. For example if I scored in the top 21% in an IQ test, I would score and IQ value1 of 112. Similarly, if you rank Gold 1 in soloqueue, you will be around the top 21% of ranked League of Legends players2, and your League Equivalent IQ (LEIQ) will be 112. Following this approach, we can Assign a LEIQ value to each tier. In this post I will be doing that, while discussing the underlying assumptions.

Method

The first thing we need is the cumulative player count in the ranked tiers from different regions. These were retrieved from OP.gg2, from EUW, NA and KR. These regions should be somewhat representative, but if someone knows how to get the same numbers from China, please tell me. The results are shown in figure 1:

Figure 1

As can be seen on the above figure, the numbers seem to be somewhat normally distributed, which is the assumption behind the IQ system. We also see that there is not a big difference in the distribution of ranks between these three regions. Thus we will be using the sum of the regions going forward.

An IQ of 100 is defined as the 50% percentile, and the percentile at various IQ values is defined by the standard deviation (sigma) of the IQ system, which sometimes differs. We will use sigma = 15, which means that at an IQ of 115 (one sigma), you will roughly be in the top 16%, and at an IQ of 130 (two sigma), you will roughly be in the top 2%3.

To find the mean of the rank, which would be where 50% have higher rank, and 50% have lower, I fitted the rank distribution in LoL to a cumulative normal distribution. The results are shown on figure 2.

Figure 2

We see that the data seems overall to fit a normal distribution (cumulative), but at Dia IV, and Plat I, II and IV, there are noticeable deviation from the normal distribution. It might be hard to judge from figure 2, but the points at the highest rank are actually very close to the fit. My fit concludes that the mean is right between Gold IV and Silver I. This means that if you at these ranks, your LEIQ would be very close to 100. The fit also reveals that the standard deviation is 4.223 ( ± 0.126) divisions. So 4.223 divisions higher than the mean, between Silver 1 and Gold IV would be around Plat IV. This should mean that Plat IV players have an LEIQ of around 115, and similarly Dia IV would be a LEIQ of 130.

Results

Now that we have a method of finding LEIQ, we can make a table that shows the LEIQ for each Rank:

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RankPercentileLEIQ
Iron IV99.759.0
Iron III99.462.6
Iron II98.866.1
Iron I97.869.7
Bronze IV96.373.2
Bronze III93.976.8
Bronze II90.580.3
Bronze I85.983.9
Silver IV79.987.4
Silver III72.691.0
Silver II64.294.5
Silver I55.198.1
Gold IV45.7102
Gold III36.5105
Gold II28.0109
Gold I20.6112
Platinum IV14.5116
Platinum III9.80119
Platinum II6.30123
Platinum I3.87126
Diamond IV2.26130
Diamond III1.25134
Diamond II0.66137
Diamond I0.33141
Master0.16144
Grandmaster0.072148
Challenger0.031151

Discussion

It should be noted that the data is only from LoL players who have placed in ranked solo queue this season. One would expect the players who play ranked to be generally more skilled than the players who do not play ranked, but this just means that LEIQ is a measure of your IQ relative to other people who play LoL regularly, and not a comparison to those who don't play a lot.

Perspectives

So where is this usefull? Well I often see people calling each other stupid etc in soloqueue, even in high ranks. This seems weird to me since a 140 IQ person wouldn't call another stupid just because his IQ is 130. So ask yourself "at what IQ would I call someone stupid", and then realise what ranks that apply to.

Another thing to note is how skilled a true 200IQ play would be, since challenger LEIQ is "only" 150.

Also I didn't actually expect the rating to be so normally distributed, which was a nice surprise since this makes the comparison to IQ more valid.

1:

Percentile to IQ table.