Richard Steckel, a professor at Ohio State, did a study on the height of Northern Europeans from 900-1200 and found the average height for men of 68.3 inches compared to 69+ today. This same group 'shrank' to 65.8 by the 1700s.

He attributes:

• A Little Ice Age hit about 1300 AD decreasing temperature 2-3 degrees which caused growing seasons to shrink which caused less food to be available. It also reduced the activity of this population.

• An increasing movement to cities increased the transmission of disease

His background is as an economist but I liked this quote:

"Average height is a good way to measure the availability and consumption of basic necessities such as food, clothing, shelter, medical care and exposure to disease, Height is also sensitive to the degree of inequality between populations."

As famine and plague became more prevalent in the late Middle Ages, humans in Northern Europe didn't grow as tall as they had in previous centuries.

Taking the 4th century Roman writer Vegetius at his word, with a hefty pinch of salt given that he's talking about a much earlier period, the minimum height requirement of the first legionary cohorts was between 70 and 72 Roman inches, although later recruiters sometimes had to take what thry could get. Given that the roman inch, the uncia, was equivalent to about 0.971 modern inches, you've got an ideal legionary, intentionally recruited for his height, with a minimum height of 67.97 to 69.912 modern inches; call it 5'8" to 5'10". Ideally we'd be looking at an analysis of legionary skeletal remains for the best answer, but this gives you some idea.

Vegetius - De Re Militari
Smith, Sir William; Charles Anthon (1851) A new classical dictionary of Greek and Roman biography, mythology, and geography partly based upon the Dictionary of Greek and Roman biography and mythology New York: Harper & Bros. Tables p 1025.