Actually I am guessing more than two, but the modern test seems to have had two.
Max Hamilton (1963) And the Basic Test
A gentleman named Max Hamilton is credited with having invented the basic test. This test is to shoot bare shafts (only) into a target about two paces away. The first thing to look for is are the arrows straight into the target or are the nocks high or low. In the nock high case, one concludes that the nocking point of the arrow on the string is too high; in the nock low result, the nocking point is too low. The nocking point is adjusted and the test repeated until the nocks are level with the shafts.
Then one examines whether the arrows kick left or right (if they do, this is ignored until the nocking point position is corrected). If the nocks of the bare shafts are to the right, this indicates that the arrows are too stiff for the bow, if the nocks are leaning to the left, the arrows are too weak.
Today we have a great many ways of adjusting the bows to make a spine match and get the bare shafts flying straight from the bow. Back then the options were more limited. (I know people who sanded wood arrows to make them less stiff!)
Obviously, if the bare shafts are leaving the bow in a “straight” orientation, there is less for the fletches to correct.
Ed Eliason (1960s?) And the Modern Test
The modern test is attributed to Ed Eliason, one of the U.S.’s most accomplished archers.
This is the test we are all familiar with. At short distance (< five paces) three fletched and two bare shafts are shot. We look to see that the fletched shafts grouped and the bare shafts grouped. If they did not, then that test is scrapped and a “do over” is in order.
The test is interpreted according to the relative positions of the two groups. If the bare shafts are higher or lower than the fletched, the nocking point position needs adjusting. This is always done first. If the bare shafts hit to the right or left of the fletched group, then the arrows are too stiff (left) or too weak (right). (Note These are all for right-handed archers. If your archer is left-handed, you need to switch all lefts and rights.) Shafts that are just a tad too stiff or too weak may be able to be adjusted using cushion button pressure. If they are more than that, almost all modern bows have adjustable limb pockets that allow for draw weight changes (too stiff arrows need more draw weight, etc.). Arrows can adjusted, too. They can be cut shorter to stiffen them, for example.
More Than Two Inventors?
The reason that I think there were more than two people whose fingerprints are on this bow-arrow test is I have read and heard considerable information from trad shooters who describe tuning by shooting arrows into loose piles of dirt or sand. They were looking for the arrows entering the pile straight. If the nocks kicked left, right, high, or low, they made adjustments.
Adjustments to all wood bows involved sanding/scraping the limbs to drop the bow’s draw weight, cutting the limbs off a bit to raise the draw weight, changing the brace height, sanding the arrows to make them less stiff, I even know an archer who added layers of arrow lacquer to his arrows to make them heavier.
Since these “tests” of the bow-arrow system go quite far back in time, and are known today, I suspect they were background knowledge for people like Max and Ed. Before these “modern” tuning tests were invented, what did people do to tune their bows? I have to assume they did something. And that the “something” was informed by what people did in their past.