Cool idea, although it's not exactly how I'd do it. One: it's another of these big table-based mechanics from the old days, which generally turn out to be unnecessary, and requires another page of paper at your table just for this. Two: The game-world target that Len presents has just 4 rings, as opposed to real-world targets with 5. Third: Len doesn't include any points-scoring system (which wouldn't be bad if the target was the same as real-world, but it isn't, so it's unclear to what resource we should turn).
A Second ShotSo here's my take on it. An initial, maximally-concise option would be this: just have the archers roll d20's and add their attack bonuses, and add the totals all up as their "points" (however many rolls you like). That's in line with the core mechanic and requires nothing to look up or memorize, really. However, maybe that's a little too abstract.
A more concrete option would be this: Say in-game targets are the same as real-world ones, viewed by Imperial scoring rules -- the targets have five concentric regions on them: white, black, blue, red, and gold, for point values 1-3-5-7-9 respectively (in Metric scoring the regions are subdivided into two halves each, for point-values from 1 to 10). Roll an attack as normal against the target, and for each +5 increment, say that an improved scoring region has been hit (i.e., each smaller region has +5 better armor class).
Based on our model of archery for D&D from last week (link), the effective AC for a large, immobile tournament target is approximately 10 (base AC) + 4 (size) + 6 (immobile) = 20. Note that this exactly cancels out the normal "Target 20" requirement for a hit, so we can simplify matters by just looking at the raw roll from the player, d20 + attack bonus (including level, Dexterity, equipment, etc.) and not even bothering with the normal AC or to-hit requirement. Say the levels of success are then as follows, for convenience:
Again, this is just standard real-world archery scoring. I would have each archer in the competition shoot perhaps 12 times (real-world tournament have contestants shoot 2-3 dozen arrows per round, but you'll probably have other players at the table waiting to do something). Also: this is at very short range (10 yards; Lakofka sets his at 40 feet) -- if you run a longer-range competition at a distance of 20, 40, or 80 yards (as in real life), then subtract a penalty of -4 from the attack roll for each doubling increment of range. (Optional simplification: just say hits are one ring worse per range increment.)
So I think that mechanic is pretty attractive, and you can probably memorize it for use without any table lookups -- Just make a standard attack roll for each archer, and remember that each increment of 5 is an improved hit location (with real-world Imperial scoring of 1-3-5-7-9 points). Easy!