Defeated by Skill or Noise?

It is becoming clear to me that high level competitions in sports, including ours, have a problem. They demand a winner, even though having a winner is not strictly necessary. If two people tie for first place, they could both be granted a “win.” If there is money involved, there is already a procedure in place: if two people tie for second, they do not bother with a playoff, they simple take the second and third place monies and split them (basically they get 2.5 position money). So, in a two-way tie for first, the first and second place money could be split.

In archery this is not entirely doable, especially now that we emphasize “head-to-head shoot down rounds.” Unless two archers are competing for first place, then an archer needs to be declared a winner in all previous rounds, because in each of those one goes on to compete again and the other, as the saying goes, goes home.

In Olympic competition, ties are broken with a single shot with the winner determined by the arrow landing “closest to the center.” Because of some matches being decided by a very, very tiny distances, World Archery adopted a rule that if the two distances to the center do not differ by at least a millimeter (roughly 1/25th of an inch), then another arrow must be shot. It is only fair. Or is it?

This shoot-off procedure has the appearance of being “fair” but in actuality it is about as fair as a coin toss would be, that it is the outcome is determined by random factors, noise actually. It has the appearance of a decision based upon skill but is really a decision based upon chance.

Consider two spectacularly good Olympic Recurve archers who have tied in their match, each of them having shot three 10s in each of their ends. Wow! So, they shoot a “one arrow, closest to the center shoot off” and one archer is declared the winner. Actually both of those shots were tens also. If you look at the targets you would see a number of arrow holes in the 10-ring. Some of those holes would be closer to the center, others farther away. This is what “grouping” is all about. By executing shot after shot consistently, we end up with a bunch of arrows closely clustered together. Some are always farther from the center of the group and some are always closer. If you set up a shooting machine (We are partial to Hooter Shooters.) and fire away from 70 m, what do you think you’ll get? Some people think you would get arrow after arrow hitting dead center, but that is not what happens. You get a group just like an excellent group shot by a human archer; some of the shots are farther from the center of the group and some are closer. This is a result of normal variation (even when there is no wind, etc.). The arrows are not perfectly identical, the shooting machine settings are not perfectly identical, and 70 m is quite far away so the hit points “vary” normally.

So, this “noise” is a part of our sport, whether the arrows are shot by machines or by humans. And having a match decided by a 1 mm difference (about that ççfar apart) is having a match decided by noise. The differences from the center need to be greater than the noise in the two signals to be really fair, that is based upon skill.

Since we now have remote scoring at major events, a simple, easy procedure is to have the archer’s shoot arrows, one at a time, until the pressure causes one to shoot an arrow that scores less than the other. If the tie continues and continues, think of the drama!

In indoor compound competitions it is not unusual to have small herds of archers tie with perfect scores at the end of a tournament. These are shot off by score and then, in some cases by switching to “inside out scoring.” Usually if your arrow touches a higher scoring ring on the target, you get the higher score. In inside-out scoring, if you touch a lower scoring ring you get the lower score. The problem with this is that the ties often include X-counts (Yes, those guys are good!) and the X-ring on the Vegas target is only 3/4˝ (0.75˝) wide. A 25xx aluminum arrow is 25/64˝ (0.39˝) wide which is over half as wide as the X-ring. If another competitor is using a skinny carbon shaft, then he has much more room for the noise in his groups than the fat shafted archer does. (The fat shafts were adopted (as well as designed and sold) to take advantage of outside-in scoring.)

Again, a score-based shoot-off would be better. Imagine the final two or three competitors lined up in front of two target faces each. Each shoots an arrow. If still tied, they shoot another … and another. The drama is huge as is the pressure as these are one arrow shoot-offs. Once an archer falters, he is done. But the degree to which this happens needs to be based upon more than the noise (aka scatter) in an archer’s groups and inside-out scoring with fat shafts is just a quick way to determine a winner. Unfortunately this is not really a skill-based determination, just a luck of a coin toss determination dressed up like a skilled-based decision.

 

 

3 Comments

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3 responses to “Defeated by Skill or Noise?

  1. Thank you for sharing this. Very informative.

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  2. Marty

    I agree. Why switch horses in the middle of a stream? If for each end you award winner points, not cumulative scores, and then if there is a tie at the end of regulation play (multiple ends) they should play another end, then another if necessary. The whole idea of multiple attempts is to absorb both personal skill ability (internal variation) and the environment conditions (external variation) into a best result, a winner.
    Two reasons to NOT have a single shot tie-breaker:
    1. Suppose you have two very capable archers who can shoot a “X” nearly every time – one can do it 9.9 times out of 10, the other 9.5 times out of 10. Shooting 9 arrows each may not determine a winner, so shooting one arrow is less likely. but
    2. In any competition, while saying both archers are subject to the same environment, even small uncontrolled variations (luck, if you will) in that environment, such as wind, could play a large part in any single arrow’s flight – but much less than say, a baseball or a tennis ball – but it would be unlikely to favor one archer over another over multiple shots.
    In nearly every competition both of these are considered – in archery or golf, for example, everyone shoots in the same direction, either at the same targets or adjacent targets; in tennis or hockey, for example, opponents face each other and switch directions to account for any environmental conditions that may be favorable on one side.
    So, why would anyone decide that a one-arrow shoot-off is a good way to determine a winner? An archer who missis their target by 1/3 of an arrow diameter over 70 meters due to the uncontrolled environmental conditions, however small – a very slight momentary variation in the wind, for example – would lose a tied match. Given the two archers mentioned above who each can score an “X” at least 9 times out of 10, a “one-shot takes all” deciding a winner is not logical. This relies more on momentary luck favoring one over the other than each participant’s skill level.
    AND, if a one-arrow shoot-off is such a good idea, why not just start out that way?

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    • I saw an Olympic match (alternate shot) in which every time one competitor shot the wind would die down and when the other shot it would pick up. To be fair, both archers should shoot at the same time to ensure the same conditions. But fairness is not the primary criterion. TV interest is.

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