How Good Is Good

by Barry Clasper Originally Printed in Zip Coder Magazine

In a recent article, Bill Heimann did an excellent job of delineating the difference between high quality and high level dancing. I would like to take the liberty of summarizing the main points of Bill's article (or at least what I perceived to be the main points) so that I can use them as a springboard for my own remarks. Bill made the following points:

  1. Good dancers are usually recognized as such by other dancers.

  2. Most dancers aspire to be in the group that is so recognized.

  3. Bill discussed the criteria he uses in evaluating how well or how poorly a dancer performs. In point form, they were:

    1. Number of mistakes - better dancers make fewer mistakes.

    2. Command of fundamentals - better dancers have a superior grip on certain fundamental elements which form the basis of a large number of calls and concepts - examples are circulate, rotate, trade, hinge, roll, etc.

    3. Ability to help - how much assistance is the dancer capable of offering to others in the square?

    4. Adaptability - better dancers can adapt to a situation that represents a logical extrapolation of known material without having to be taught or walked through.

    5. Ability to handle distortions - can the dancer handle distorted setups that are legal at the level being danced?

    6. Precision - better dancers make precise formations and adopt precise facing directions.
    7. Ability to recognize the unright - better dancers realize when something does not make sense, when a formation cannot be correct, and therefore a mistake has been made.

    8. Ability to recover - when good dancers make a mistake, or find themselves in a situation they do not understand, they can adjust so as to keep the square moving.

    9. Confidence - how confident is the dancer that he or she knows what they are about?

  4. The above characteristics are level-independent. They transcend the material associated with any given Callerlab program. Thus, it does not follow that any given C4 dancer is necessarily a better dancer than any given A2 dancer, simply by virtue of their habitual dance level. It is entirely possible for an A2 dancer to be a better dancer than a C4 dancer, despite the fact that the C4 dancer probably knows more calls.

  5. Because the square dance movement has not done a good job of articulating the characteristics that contribute to good dancing, a great many people mistakenly assume that there is a direct correlation between the level somebody dances and how well they dance. They assume that attendance at a higher level dance indicates that someone must be a better dancer.

  6. Since we all wish to be well-regarded by our peers, this mistaken idea that dance level is synonomous with dancing ability fosters an inappropriate compulsion to advance through the levels.

  7. The equation between dance-level and prestige has resulted in an unfortunate decline in the average levels of dance skill exhibited at the Advanced and Challenge levels.

Since my purpose is not to review Bill's article, but rather to expand upon it, I offer these points merely to refresh your memory. If you have not yet read Bill Heimann's article, I heartily recommend that you do so.

In reading Bill's article, the first thing that struck me was that Bill's list of good dancer criteria actually consisted of a single point, with a number of supporting elements. Most of Bill's criteria were in fact specific instances of his first point - better dancers make fewer mistakes. I think that better dancers make fewer mistakes because they have a good grasp of fundamentals, are adaptable, can deal with distorted setups, are precise, recognize errors, and know how to recover. Further, dancers who make few mistakes tend to be confident and are more liable to be able to help others. Therefore, I think that Bill's list actually boils down to a single point: better dancers make fewer mistakes.

While I do not wish to argue that a low error rate represents the only virtue a good dancer need possess, it seems clear that the level of error exhibited by dancers must represent the single most important criterion in evaluating how well they dance. This being so, I think it might be instructive to examine dancer performance from this point of view. How many mistakes is it reasonable for a competent dancer to make in the course of an evening? How many sequences out of a tip is it reasonable to expect a square to execute successfully?

First, we need to define what we mean by mistake. I'm not talking about momentary hesitations or false starts. I'm referring to those killer mistakes that cause squares to crumble. I call these fatal errors. I define a fatal error as follows:

An incorrect action (or inaction) which:

  1. if left uncorrected, would result either in the square breaking down or an incorrect resolution, and
  2. is not recovered by the perpetrator before it damages the square.

So my question is, How many such errors is it acceptable for a competent dancer to make?

In pondering this, it quickly became evident to me that there is no easy answer. It is easy to say 2. or 17. or 89, but without a supporting rationale, the number itself has no meaning. The underlying premise in our concern with dancing errors is the fact that mistakes contribute directly to broken squares and broken squares result in dancers being transformed into spectators who watch the other squares dance. Our problem is that we consider the proportion of time spent spectating to be growing to unacceptable levels. This line of thought splits my original question into two:

  1. For what portion of the total dance time is spectating acceptable?
  2. How do mistakes influence spectator time?

The first question is a matter of personal judgement, but the second is open to analysis. Perhaps if we undertake the analysis we will be better positioned to make the judgement required for the first question. First we need to quantify our terms in a way that makes analysis possible.

Since we are concerned with the number of mistakes dancers make, it is useful to quantify that as an error rate using the number of sequences danced as a base. For instance, if a dancer makes fatal errors at the rate of 1 error every 5 sequences, it follows that he or she dances faultlessly 4 out of 5 sequences. In other words, you could say that the dancer executes without error 80% of the sequences called. This value can also serve to express the probability of that dancer executing any given sequence successfully. Henceforth, I will refer to such a dancer as an 80% dancer.

Now let's examine how well dancers with various probabilities for dancing error-free might be expected to do. Let's suppose that each of the dancers in the square dance 90% of the sequences without fatal error. A mark of 90% is usually considered pretty good in school. In dancing terms that means that you blow one sequence in ten. We are interested in is the probability of 8 dancers, each with a 90% probability of dancing error-free, making it through a sequence without any one of them making an error. Statistics tells us that the formula for this calculation is to take the product of all the probabilities. Therefore, a square composed entirely of 90% dancers could expect to make:

.9 x .9 x .9 x .9 x .9 x .9 x .9 x.9 = .43 = 43%

LESS THAN HALF of the sequences

Or in other words, they would be standing around more than half of the time. I do not think many would be prepared to argue that spectating for more than half of the time is satisfactory. Let's look at this from another angle. Suppose we apply our 90% number to the entire square instead of the individual dancers? How well do the dancers have to dance in order for a square to make 90% of the sequences? We need a number n such that:

n x n x n x n x n x n x n x n = 0.9

If you work it out, it turns out that n = 0.987 or 98.7%. In order for the entire square to make 90%, each individual needs to be dancing at 98.7%.

This seems like a very high performance level. After all, in school only genius level students get 98.7%. When you consider that the average 2-1/2 hour dance comprises 7 or 8 tips each containing 10 or 12 sequences, 98.7% represents, at most, one mistake per night. Perhaps attempting to achieve a 90% level of success for the square is shooting too high. However, we have already seen that 90% dancers will stand for more than half their time on the floor, so it is clear that whatever value we use will have to be higher than that. By now many of you will be saying to yourselves, But that doesn't make sense. I've danced in squares with totally incompetent dancers, and we still got most of the sequences. These numbers can't be right. And, of course, they are not. What the above calculations overlook is the fact that many, if not most, mistakes are corrected before the square dissolves. In fact, when dancers know one another well, many mistakes are anticipated and prevented before they are made. That is, there are dancers in the square who not only dance their own parts flawlessly, they also correct at least some of the mistakes of others.

Another way of looking at this is to say that dancers who correct others are, in effect, dancing higher than 100%. They are dancing 100% of their own parts, plus some parts that should be executed by other dancers. For instance, let's assume we had a square composed of six dancers dancing 100% and a seventh dancing 80%. If the eighth dancer merely dances 100%, then the square gets 80% of the sequences. But if the eighth dancer can dance all of his or her own part, plus fix half of the seventh dancer's mistakes, the square could attain 90% success. Thus, it can be argued that the eighth dancer is performing at 110%; 100% on his or her own behalf, plus 10% of the seventh dancer's responsibilities. If one of the other dancers could also manage this feat, then the square could theoretically attain a 100% success ratio despite the presence of an 80% dancer.

This phenomenon is an integral part of the dancing process. More often than not, when one dancer makes a mistake, another dancer is able to correct it and avoid damage to the square. This process is essential to a healthy square and is a normal part of good dancing. Where it becomes pathological, however, is when the help always flows in a single direction. Instead of a bi-directional interplay, we have one person who always helps and another always on the receiving end. I believe that this last point goes straight to the heart of the quality-of-dance issue. If we were to survey the dancer population at any given level, the skills of the dancers could be grouped into three categories:

  1. Dancers who, on average, are not fully competent at the level. They would make very few sequences were it not for the presence of other dancers who correct their errors.

  2. Dancers who, on average, dance the level competently. They can dance their own part without assistance. Their level of performance is very close to 100%. A square of such dancers should be able to attain success levels of at least 90%.

  3. Dancers who, on average, are capable of dancing their own parts at the 100% level and, in addition, can help others. These are the people who make it possible for the dancers in the first category to be on the floor.

At this point it is important to understand that all three of of these categories are necessary. Some might think that if we dispense with the dancers in the first category, our problems are solved. Not so! You can quickly see why if you look back at the three categories and view them as the three phases that a dancer moves through as he or she comes to master any given level. Therefore, in an ideal world, the people at phase 1 would be the novices at the level. Since there is a great deal of material at the advanced and challenge level that can only be mastered through experience, it is to be expected that people who are new to a level will exhibit higher error rates. Even after you intellectually understand Magic Diamonds, how many times do you have to work in them before you can dance such material with any panache?

So we cannot just dump these phase 1. dancers - they are the future. Since they require help, however, they must be balanced by an appropriate number of phase 3 dancers. In a perfect world, any given level would always be populated with dancers from all three phases in balanced proportions - for instance 20% in phase 1, 60% in phase 2, and 20% in phase 3. But the world isn't perfect and therein lies the crux of our problem. Because of the pressure to advance from level to level, many people are short-cutting the three phases. They progress from phase 1 to phase 2 and then move up to the next level (where, of course they are phase 1 again). As this becomes more prevalent the proportion of phase 3 dancers at all levels starts to erode which diminishes the help that is available to the new dancers. With less help available, phase 1 dancers progress to phase 2 less rapidly - or not at all.

Now comes the most insidious part of the process. New dancers arriving at a level find that there are no phase 3 dancers available to help them become competent. Nobody at this level seems to know what they're doing. But, of course, we all know that the better dancers all dance at some level higher than we do, therefore the answer is to memorize the calls on the list for the next level and move on up. This process results in dancers who have yet to master C1 showing up on C3 floors.

As Bill Heimann said towards the end of his article, it is time to clean up our act. We need to acknowledge that when we present ourselves on a dance floor at any given level, we have an obligation to the other dancers. That obligation is to dance our fair share of the material. To the extent that we cannot dance our fair share, we represent a burden on the other dancers, one which we imposed upon them unilaterally by arriving in their square. What is our fair share? I believe that it varies with experience at the level:

  1. Phase 1 - When you first attempt a level, your fair share will be relatively low, perhaps 75% to 80%. Other dancers have a right to expect you to know all the calls and concepts on the list, but it is not reasonable to expect a novice at the level to be able to flawlessly execute all possible contortions of the material.

  2. Phase 2 - After gaining some experience at the level, your fair share increases to 100%. That is, other dancers have a right to expect you to dance your own part without error. True, everybody makes mistakes from time to time. But they should be in the nature of transient abberations caused by momentary inattention, mis-hearing a call, or because your shoe is untied. They should happen very seldom.

  3. Phase 3 - After gaining a great deal of experience at the level, your fair share again increases to something beyond 100%. It is now your responsibility to help those who are novices at the level and compensate for their errors.

It is important to recognize that while you are in the first stage you are imposing on the strength of others. The justification for doing this lies in the premise that, in time, you will progress from the first stage to the third stage and, in effect, pay back the help you were given.

If you move on without repaying the help you were accorded, you are short-changing the people who follow you into the level. If you move on before you are competent at the level you are currently in, then you are short-changing both the level you leave and the level you move to. But most important of all, you short-change yourself.

Barry Clasper