Upvote:12
Not as such. But there were stronger and weaker cohorts.
When a Roman legion of this period deployed for battle, the default formation was to arrange the cohorts in two rows from right to left. That is, the first and sixth cohorts would be on the right flank, while the fifth and tenth on the left. See the following illustration from Vox:
As you deduced, one would obviously want the strongest units guarding the flanks (and holding the centre). Which is exactly what the Romans did.
This is described in our main extant authority on the topic, De re militari, a Roman military treatise written by Vegetius in the late imperial period. This must have also been the ultimate source of those webpages (which appears to have copied the list from site to site since at least 2004), though they garbled it. According to Vegetius:
- But the First cohort exceeds the remainder in the number of soldiers and in rank, for it seeks out the most select men as regards birth and instruction in letter . . . It has 1,105 infantry, 132 cavalry classifiers, and is called a milliary cohort. This is the head of the legion; from it when there is to be a battle the First line begins being drawn up.
- The Second cohort has 555 infantry, 66 cavalry, and is called a quingenary cohort.
- The Third cohort similarly has 555 infantry, 66 cavalry, but it is customary to approve stronger men for this Third cohort because it stands in the centre of the line.
- The Fourth has 555 infantry, 66 cavalry.
- The Fifth has 555 infantry, 66 cavalry, but the Fifth cohort also needs strong soldiers because like the First on the right the Fifth is placed on the left wing.
- The Sixth cohort has 555 infantry, 66 cavalry; to it, too, recruits of proven ability should be assigned because the Sixth cohort stands in the Second line behind the eagle and images.
- The Eighth cohort has 555 infantry, 66 cavalry; it too needs brave men because it stands in the centre of the second line.
- The Ninth cohort has has 555 infantry, 66 cavalry.
- The Tenth cohort has 555 infantry, 66 cavalry, it also is accustomed to take good warriors because it holds the left wing of the second line.
Milner, M.P. (trans.). Vegetius: Epitome of Military cience. Liverpool University Press, 1996.
Clearly, there is no suggestion here that the cohorts were organised by some hierarchy of combat skills. Rather, Vegetius is saying that better soldiers were assigned with priority to the flanking and central cohorts. Just as you'd expect for these tactically important positions.
By the way, the specific wording of those internet cohort lists comes from the writings of the late Dr. Graham Webster, with a fair dose of filling in the blanks. Specifically, this passage (where Dr Webster was likewise paraphrasing Vegetius):
Vegetius . . . gives us some indication of their relative importance. In the front line the first cohort was placed on the right, the third in the centre and the fifth on the left, while between them were the second and fourth. Behind the first, in the second line, was the sixth, which he says should consist of the finest of the young men. The eighth was in the centre with selected troops and the tenth on the left flank also with good troops, the other two, the seventh and ninth, coming between. The weakest cohorts thus appear to be the ninth and seventh and the fourth and second, and it would be in the first of these two pairs that one might expect to find recruits in training.
Webster, Graham. The Roman Imperial Army of the First and Second Centuries AD. University of Oklahoma Press, 1998.