# Athletes Bio-Passport: Horners Histograms

Histograms are a graphical technique that allows us to see the shape of a distribution of data. Any data set is assumed to have some distribution, for example, a “normal” distribution is the name for the shape that we describe as a “bell-curve” (see Figure 1). This is the distribution that many natural phenomena (such as human characteristics like height, weight, etc. appear in) — the majority of specimens are somewhere around the median value, and there are a few individuals on either side of the median that represent the extremes of the population (sometimes called the “tails”). It is reasonable to assume that something like Hemoglobin (Hg) is normally distributed throughout a population of humans, with a handful of individuals with extraordinarily high levels, and a handful of individuals with extraordinarily low levels, but with most folks clustered around the median value.

**Horners Distributions for Hemoglobin & Reticulocytes**

Figures 2 & 3 show the histogram distributions for Chris Horners bio-passport values for Hg (Figure 2) and R% (FIgure 3). It is quite interesting to note that the Hg plot seems to conform to a “normal” distribution quite nicely with values clustered about a median of 14.6. What this graph describes is that of the 39 Hg values recorded in the Horner Bio-Passport dataset, 17 of those values (nearly half) fall between 14.4-14.8, with the aforementioned median value of 14.6. Only 5 values (12 %) fall below 13.6 or above 15.6. But, “normal distribution” and “looks normal to me” are two entirely different ideas – “looks normal” would require a sense of what we “should” expect if nothing was amiss – or if the athlete were not trying to manipulate their values (through legal means or otherwise).

**Reticulocytes**

Horner’s R% has a much different distribution, with the median value of 0.7 NOT coinciding with the peak. There appears to be a peak of R% values about 0.5 and another about 0.8 – we might describe this as a “bi-modal” or “two peak” distribution. However, this is not to say that an individuals Hg or R% *should be normally distributed*. I don’t honestly know, though I would say that it might be reasonable to speculate that the Hg level would be more likely to be normal than the R%, since the R% is a kind of “2nd order” function, since it changes in reaction to fluctuations in the Hg level (actually, it responds to fluctuations in O2 levels, which are a function of Hg).

- Ashenden, et. al. Standardization of Reticulocyte Values in an Antidoping Context. http://ajcp.ascpjournals.org/content/121/6/816.full.pdf