Beyond the reference curve
Khamis-Roche places every athlete on a population reference curve. But athletes do not all traverse that curve at the same speed. Here is how repeated measured tests unlock a personalised trajectory.
The population growth rate curve
This is the rate of height gain, in cm per year, across adolescence for a general population. The spike around age 13 to 14 is Peak Height Velocity (PHV), the point of fastest growth in the pubertal spurt. Every Khamis-Roche assessment takes an athlete's height, weight, and parental heights and places them somewhere on this curve.
The population growth rate curve
This is the rate of height gain, in cm per year, across adolescence for a general population. The spike around age 13 to 14 is Peak Height Velocity (PHV), the point of fastest growth in the pubertal spurt. Every Khamis-Roche assessment takes an athlete's height, weight, and parental heights and places them somewhere on this curve.
A consistent measurement history
This athlete has had four stadiometer tests, one every three months. Each dot is a real measurement, and their position on the curve at each test reflects their biological age at that point. Notice they're already tracking above the reference line at every test date. They are moving through the growth curve faster than average.
Without velocity data, follow the reference
The standard Khamis-Roche projection, shown as a dashed line, continues forward from the athlete's current biological age at the same pace as the reference. It is a reasonable population-level estimate. The problem is it assumes every athlete moves through the curve at the same rate. These four tests suggest that assumption is wrong for this athlete.
Inter-test velocity reveals individual tempo
The height gained between each test tells us how fast this athlete is actually moving through the curve. Their velocity ratio works out to c = 1.35, meaning they're progressing 35% faster than the reference. PHV arrives earlier than the K-R line predicts, and the rate drops off faster afterwards. That gap between the red fork and the dashed line is where load management decisions start to matter.
More tests, narrower band
With only one inter-test interval, the band is wide. You can tell which direction the projection is going, but you cannot trust the magnitude yet. Four intervals, roughly a year of quarterly testing, changes that. The band narrows because each new measurement either confirms the velocity estimate or corrects it. Two or three tests gives you a direction. Four gives you something you can actually act on.
What this means in practice
Measure consistently
Stadiometer or careful home measurements every three to four months give enough signal to compute a reliable velocity estimate. Two tests at least 90 days apart is enough to activate the projection.
The fork activates automatically
Once an athlete has two eligible measured tests at least 90 days apart, the personalised fork appears on their Rate Timing graph. No extra input needed. It builds in the background as tests accumulate.
K-R always runs unchanged
The personalised fork is additive. It does not replace the Khamis-Roche assessment. Every athlete still gets a full maturation report regardless of their measurement history.
How the projection is built
The system runs two complementary methods in parallel, each contributing something the other cannot do alone.
Khamis-Roche predicts adult height from a single measurement using height, weight, and parental heights. It places the athlete on a population reference percentile and produces a maturation stage, a biological age, and a percentage of predicted adult height. This works from the very first test. No longitudinal history is required.
The velocity layer activates once an athlete has two or more stadiometer or home-measured tests at least 90 days apart. By comparing how fast the athlete actually grew between tests against how fast the reference curve grows at that same age, the system estimates a personal tempo factor. An athlete moving through puberty faster than the reference has a factor above 1. Slower than average gives a factor below 1. This factor then adjusts where on the reference curve the athlete is projected to be at any future age, shifting PHV earlier or later accordingly.
Why use a population reference rather than fitting a model to the athlete alone? Statistical models like SITAR, used in research settings, fit a mean growth curve to a full longitudinal cohort and estimate individual deviations from it. They require many measurements per person to be stable and cannot produce maturity or adult-height estimates from a single test. For academy use, where an athlete might arrive with one measurement and no history, a population reference anchors the system from day one while the velocity layer personalises it over time.
A note on reference data. The population growth curves used here are derived from CDC reference data using LMS values to calculate every percentile. Like all cross-sectional references, these curves slightly underestimate the true height of the growth velocity spike at PHV compared to longitudinal datasets such as the Berkeley Growth Study. The velocity factor is calculated as a ratio against this same reference, so both the observed velocity and the expected velocity share the same baseline. The relative signal, whether an athlete is ahead of or behind their own reference trajectory, is preserved. What this means in practice is that the direction and timing of the personalised projection are sound, while the absolute peak height of the velocity spike shown on the graph may be modestly conservative.
The confidence band reflects two sources of uncertainty. Before PHV, where the growth curve is rising steeply, a small difference in timing produces a large difference in projected rate, so the band is wider. After PHV, the trajectory is more predictable and the band narrows. With a single inter-test interval the band uses a conservative fixed width. With each additional measured test the band tightens as the velocity estimate becomes more consistent.
This approach draws on the SITAR model (Cole et al. 2010) and is supported by findings in Monasterio et al. (2026), which showed SITAR correctly classifies 80 to 84% of athletes as pre, circa, or post-PHV from incomplete growth records, compared to roughly 60% for cross-sectional maturity offset equations. The Khamis-Roche method (1994) forms the single-test foundation, with adult height predictions consistent in accuracy with skeletal age assessments that require radiographs.