An Archer’s Quandary: Reading Targets and Arrow Scores (Part 1)

This is a quandary all archers face when they are approaching a high level of expertise. It actually occurs all of the time, although when groups are larger it is harder to see and often goes unnoticed. Here is an example:

“You are shooting a 300 round indoors (10-0 scoring a la Vegas) and you have shot 10s and 9s only for the first eight ends. Then in the ninth end, you shoot a ten and then two 8s. Is something wrong?”

Well, what do you think?

If you think there is a problem, well, you are wrong.

If you think it is not a problem, you are also wrong.

I did not give you enough information to tell which it was.

You see, it depends on who is shooting and what is “normal” for them. If that were me, then I could tell you eights are normal … for me … and that seven ends of all 9s and 10s was not normal. But I have known archers for whom this would have indicated a problem of some sort. One of my archery club colleagues in California kept shooting perfect 300 scores on the NFAA five-spot target. (I noticed that because I was trying to shoot my first such score.) I asked him when was the last time he didn’t shoot a 300 score, and he couldn’t remember. It had been years, he said. The 5-ring on that target is equivalent in size to the 9-ring on the 40 cm indoor target, so shooting all 10s and 9s on that target was “normal” for him. (It was not normal for me.)

Also, what your thinking would have been if I had told you one of those 8s came in the fourth end and the other in the eighth end? If you thought the two eights were a problem in the first scenario, are they indicative of a problem when spread out, too? Most would say “no.”

We all seem to think that a string of good shots should continue, but this is an illusion, one of the so-called “gambler’s illusions” which includes winning streaks, basketball players “hot hands,” and many other phenomena.

When Brady Ellison shot his most recent world record for an indoor 600 Round, he shot is lone 9 in an otherwise perfect round (599/600) on his thirtieth arrow (out of 60). How would you feel if he had shot his nine on the first arrow? Or his last arrow? (Oh, he came so close!) The score would be the same, but the feelings are different. In one scenario we think he made a good recovery and a strong comeback. In another, we can tell stories of how the pressure got to him and he crumpled on his last shot. In all three, same score, same WR.

What we have to be aware of is our own propensity to see patterns, whether they do or do not exist. Consider the idea of “streaks.” These go against what we are taught is the “law of averages” which is properly named the “law of large numbers.” We are told that if we are gambling, winning more than a few hands in a row is not normal. We think that wins and loses should be mixed evenly. None of these are true.

We are told and believe that if you flip a coin often enough you will end up with half  of the flips being “heads” and half “tails.” People have actually undertaken experiments in which they flipped coins 10,000 times or more to check this “law.” To the contrary I remember reading an article in Scientific American magazine a very long time ago described an experiment in which a computer was programmed to simulate flipping a coin. They expected the law of large numbers/averages to show a 50:50 distribution of heads and tails in short order and then stay that way forever. Contrary to ordinary thinking, starting with ten heads or ten tails in a row is not at all impossible, but however it began, the totals would rapidly approach a 50:50 distribution and then stay there. But this is not what they saw. They saw a 50:50 distribution of heads and tails in short order and then they had a long streak in which heads flips dominated creating a number of head flips greater than the number of tail flips, then this “streak” was followed by a long stretch of 50:50 flips, but then there was a longish streak of tails creating a number of tail flips greater than the number of head flips, followed by a 50:50 stretch. This continued, as far as they could tell, forever.

The length of the 50:50 stretches was, in total, the vast majority of the tosses. But the long stretches of mostly heads or mostly tails (winning streaks?) resulted in almost no time being spent at exactly 50:50. This behavior is not governed by luck as a computer does not operate via luck, it is the ordinary nature of random events. All of these things are “streaky” by nature and not consistent as we would expect.  (BTW, the 10,000 coin toss experiment came out 5,067 heads, 4,933 tails.)

Now, clusters of archery shots are not random events, but if one were to shoot a long stretch of all 10s and 9s, and then shoot two 8s, would that be a sign of something going wrong or not? We are conditioned to see patterns, especially if they are negative. (I can’t tell you how often I have had the thought “Here we go again” while shooting, but it is not a small number.) The problem is you can’t tell, because the stretches are not predictive.

But wait, “What do we do? You haven’t said!”

Look for my next post.