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It is not disappointment, bad luck or bad parenting. It is arithmetic, it happens in both directions, and it is the reason every “predict your child’s IQ” calculator you have seen is quietly lying to you.
One generation to the next
The dotted line is where the child would land if nothing regressed. The solid line is where they actually land — and the shape on the right is how wide “actually” is.
| Midparent | Expected child | 95% range | Pull toward 100 |
|---|---|---|---|
| 70 | 82 | 57–107 | +12 |
| 85 | 91 | 66–116 | +6 |
| 100 | 100 | 75–125 | ±0 |
| 115 | 109 | 84–134 | −6 |
| 130 | 118 | 93–143 | −12 |
| 145 | 127 | 102–152 | −18 |
Two parents averaging 130 have children who, on average, score 118 — 12 points closer to the population average. But the honest answer is a range: 93 to 143. Only about 17 in 100 of those children will score above 130.
The model, in full: midparent = (A + B) ÷ 2; expected child = 100 + 0.6 × (midparent − 100); residual SD = 12.8 points, so the 95% range is ±25. These are population averages drawn from twin and family studies. They vary by population and environment and say nothing about any individual child.
Regression to the mean is not a force pulling families back to average. It is what happens when you select on a measurement that contains anything other than the thing being passed on.
Any very high score is partly real ability and partly a good day — favourable questions, sharp concentration, a lucky guess or two. The ability part is passed on. The good day is not. Selecting parents because their score was high guarantees you have selected some of that luck along with it.
Each parent passes on half their genes, in a combination neither of them had. The specific arrangement that made a parent exceptional is unlikely to reassemble in the same way. The child inherits the average tendency far more reliably than the extreme.
Two parents averaging 70 have children expected around 82 — pulled up by the same twelve points. This is the half of the effect that never appears in headlines, and it is the reason regression is a statistical property rather than a story about disappointing families.
An expected score of 118 is still around the 88th percentile — comfortably above average, and higher than roughly seven out of eight people. Regression moves a family’s children toward the middle; it does not move them to it. Both facts are true at once, and dropping either one produces a misleading page.
Read this table from the top and from the bottom. The arrows point the same way — inward — and that is the entire content of the idea.
| Midparent | Expected child | 95% range | Direction of pull |
|---|---|---|---|
| 70 | 82 | 57–107 | ↑ up 12 points |
| 85 | 91 | 66–116 | ↑ up 6 points |
| 100 | 100 | 75–125 | no pull — already there |
| 115 | 109 | 84–134 | ↓ down 6 points |
| 130 | 118 | 93–143 | ↓ down 12 points |
| 145 | 127 | 102–152 | ↓ down 18 points |
Look at any row’s range. At midparent 130 it runs from 93 to 143 — fifty points, wider than the entire span most people would call “average to gifted”. A calculator that answers “118” and stops has thrown away the only honest part of the result. Every competitor in this category does exactly that, which is why their output looks confident and means almost nothing. If you take one thing from this page, take the width of the range rather than the number in the middle of it.
Usually above average, but usually not as high as the parents. Two parents averaging IQ 130 have children whose scores centre around 118 — still roughly the 88th percentile, but twelve points closer to the population average. Only about 17 in 100 of those children score above 130. This is regression to the mean, and it is a statistical certainty rather than a comment on any particular family.
Only as a very wide range. The expected value is 100 + 0.6 × (midparent − 100), but the 95% interval around it is roughly ±25 points. For midparent 130 that is 93 to 143 — a fifty-point span. Any calculator that gives you a single number without that range is presenting a guess as a measurement.
When you pick people because they scored unusually high or unusually low, their next measurement — or their children’s — tends to land closer to average. That is because an extreme score usually combines real ability with a favourable set of circumstances, and only the ability part carries over. Nothing causes the pull; it is what selecting on an imperfect measurement does.
Yes, symmetrically. Two parents averaging 70 have children expected around 82 — pulled up by the same twelve points that pulls a 130 midparent down to 118. The effect has no preferred direction; it always moves toward the middle from wherever you started.
No — the opposite. Regression to the mean is what you observe when a trait is substantially heritable but not perfectly so, and when the measurement itself carries error. If IQ were not inherited at all, the expected child score would simply be 100 regardless of the parents. The fact that midparent 130 predicts 118 rather than 100 is the inheritance showing up.
Possibly, especially if the first score was unusually high. The same logic applies to one person tested twice: an extreme first result tends to be followed by a less extreme second one. Before treating any change as real, check it against the margin of error on the comparison tool — most retest differences do not clear it.
A predicted score spans fifty points. A measured one comes with a percentile and a confidence range you can actually use.
