It's also literally impossible for many modern tests. For example the WAIS-IV, a very popular measure, has a maximum possible FSIQ of 160. With a mean of 100 an

It's also literally impossible for many modern tests. For example the WAIS-IV, a very popular measure, has a maximum possible FSIQ of 160. With a mean of 100 and an SD of 15, that's "only" 4 SDs from the mean (99.997 percentile). And as you say, modern tests just aren't calibrated in that way. The WAIS-IV is calibrated for the 70-130 range [0]. It's used to provide broad ranges (e.g. 85-100 vs. 115-130), not to provide useful differentiations on the high end like 158 vs. 159. In fact, the error increases with the score [1]. There is less certainty for a score of 145 than there is for 115. It's just not designed for separating geniuses from super geniuses or however you want to put it. [0] https://www.quora.com/Whats-the-highest-IQ-score-you-can-get-on-the-WAIS-IV https://www.quora.com/Whats-the-highest-IQ-score-you-can-get... (Not a direct source I'm afraid, but the materials are proprietary.) [1] https://en.wikipedia.org/wiki/IQ_classification#Giftedness https://en.wikipedia.org/wiki/IQ_classification#Giftedness (There are several citations in this section, pertinent discussion below the table.)