Understanding Prediction Error in Height Calculations

Introduction

Growth tools like Khamis–Roche estimate a child's likely adult height and help us understand where they sit on their growth journey. They are powerful, but they are never perfect — and that is exactly how good science behaves.

Instead of saying "your child will be 178 cm", the model gives a most likely value with a range around it. That range is the error band.

Why Predictions Have Error

Even with careful measurement, three main sources of uncertainty remain:

1. Biological variation

Children grow at different speeds. Genetics, hormones, sleep, illness, training load, and nutrition all contribute. Two children who look identical on paper today can still end up at different adult heights.

2. Measurement variation

Small differences in technique — even 3–5 mm in standing height or sitting height — can shift calculations. That impact is bigger earlier in growth, when there is still a lot of development to come.

3. Model uncertainty

Growth equations are built from large samples of real children. They describe what is typical in a population, not a guaranteed path for one child. This is why we talk about probabilities and ranges, not certainties.

How Error Changes With Maturity

Error is not a fixed number. It depends on how far through growth a child is.

The table below is illustrative, based on typical ranges seen in the research and in practice.
Individual children and populations will vary.

Turning % Error into Centimetres

If a boy has a predicted adult height of 180 cm and the current error band is 3.5%, we can convert that percentage into a height range:

Absolute error (cm) = 0.035 × 180 = 6.3 cm

So the prediction:

• 180 cm with ±6.3 cm error

means his adult height is most likely somewhere between 173.7 cm and 186.3 cm.

If he eventually finishes at 178 cm or 184 cm, the prediction hasn't "failed" — he is still inside the expected band.

How Often Should You Re-Test?

Re-testing every 3–6 months is usually enough to:

• Smooth out one-off measurement noise
• Let MatCalc track the trend rather than a single point
• Show when an athlete is approaching, passing through, or moving away from their Peak Height Velocity (PHV) window

During very rapid growth, you might choose to monitor a little more closely, but the priority is consistent, careful measurement, not testing every week.

How MatCalc Uses Error Bands

MatCalc is built to show uncertainty clearly and responsibly:

• It displays % of predicted adult height alongside other indicators of maturity
• It uses shaded confidence bands rather than just a single line
• It reacts to patterns over time, not isolated measurements
• It uses error-aware logic when highlighting possible "growth risk windows" for training load

The aim is not to label children as "early", "on time", or "late" and stop there. It is to give context that supports smarter planning, safer training, and realistic expectations.

For Parents

• Treat every prediction as a guide, not a verdict
• Focus on how the curve changes from test to test
• Talk to your child's coach or a health professional if you are worried — growth tools do not replace medical advice

For Coaches

• Use maturity information to plan and individualise training, not to gate-keep selection
• Expect more uncertainty around PHV — this is a time for careful load management, open communication, and patience
• Remember that two athletes with similar data can still follow slightly different paths

Summary & Important Note

Growth and maturation models always include error — and that is exactly what makes them honest. Used well, error bands:

• Help parents and coaches understand where a child might be on their growth journey
• Encourage a focus on trends, not single numbers
• Support safer, more realistic planning around training and development

Important:
The information provided by MatCalc is for education and planning. It is not a medical device and does not replace consultation with a qualified health professional if you have concerns about a child's growth or health.