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, and most dancers aspire to be in the group that is so recognized.

2. 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 that form the basis of a large number of calls and concepts - examples are Circulate, Rotate, Trade, Hinge, Roll, etc.
   3. Ability to help: - better dancers can assist others.
   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: - better dancers can 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 and therefore a mistake has been made.
   8. Ability to Recover: - better dancers tend to recover their own mistakes without assistance.
   9. Confidence: - better dancers display confidence that they know what they are about.

3. 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 or 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.

4. 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 conclude that attending a higher level dance makes someone a better dancer.

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

6. The equation between dance-level and prestige has resulted in an unfortunate decline in the average dancing skills 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 consists of a single point, with a number of supporting elements. I think that better dancers make fewer mistakes because they have a good grasp of the fundamentals, are adaptable, can deal with distorted setups, are precise, recognize errors, and know how to recover. Moreover, dancers who make fewer mistakes tend to be confident and are more liable 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 it is far and away the most important. 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, I need to define "mistake". I'm referring to those killer mistakes that cause squares to crumble - the fatal errors. I define a fatal error as an incorrect action (or inaction) which:

1. if left uncorrected, would result 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?".

Underlaying our concern with errors, is the fact that mistakes contribute directly to broken squares which, in turn, cause dancers to be transferred into spectators who stand and watch while 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 questions 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 Questions.

First we need to quantify our terms in a way that makes analysis possible.

I think the most useful way to quantify mistakes is to express them, at a 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 dances 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 want to know 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:

LESS THAN HALF of the sequences!!!

or in other words, they would be standing idle 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. How well do the individual dancers have to perform in order for the square as a whole to make 90% of the sequences. We need a number N such that:

If you work it out, it turns out that N = 0.987 or 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 2½ hour dance comprises 7 or 8 tips, each containing 10 or 12 sequences, then 98.7% represents at most ONE mistake a night. Perhaps attempting to achieve a 90% level of success for the square is shooting too high.

Table 1 shows the dancer performance levels that are necessary to achieve several different success ratings for the square. How much spectating time are you willing to accept?

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, dancers who were performing at well below 50%, 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 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, a dancer performing at 120% theoretically could compensate for another dancer at 80% (i.e., 100% of their own part plus the 20% that the 80% dancer is missing). Therefore, the square could average out to 100% success, even though not all dancers are contributing to that success in equal measure.

This phenomenon is an integral part of the dancing process. More often than not, when one dancer make 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. We all make mistakes and require steering upon occasion. In a balanced square, the individual dancers participate both as providers and receivers of help. The dancer who fixes somebody else's mistake during one sequence receives help for their own mistake during a later sequence - perhaps from the same dancer they had previously aided. The process becomes pathological, however, when the help always flows in a single direction; when one person always helps and another always receives help.

If we apply this view of square dynamics to the more general square dancing scene, some interesting features emerge. 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 are not fully competent at the level. They would make few sequences were it not for the presence of other dancers who correct errors.

2. Dancers who can dance their own level competently. They can dance their own part without assistance, provided other dancers in the square do likewise. A square of such dancers consistently should be able to attain success levels in excess of 90%.

3. Dancers who are not only capable of dancing their own parts at the 100% level but also are capable of helping others. These are the people who make it possible for the dancers in the first category to survive on the floor.

At this point, it is important to understand that this mix of competence levels is not only unavoidable, it is 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 three phases of growth that a dancer goes through as he or she gradually masters a dance level.

Therefore, in an ideal world, "Phase 1" people would be the novices at the level. They might know all the calls and concepts on the list, but we cannot reasonably expect a novice to flawlessly execute all possible contortions of the material. 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 a corresponding number of "Phase 3" dancers. Back in our ideal world, any given level would always be populated with dancers from all three levels in balanced proportions - for instance, 20% in Phase 1, 60% in Phase 2, and 20% in Phase 3.

But the world is not ideal 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 they revert to Phase 1).

As this phenomenon becomes more common, the proportion of Phase 3 dancers at all levels erodes, thereby diminishing the help that is available to new dancers. With less help available, Phase 1 dancers mature 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 read through 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 must acknowledge the fact that when we join other dancers in a square, we incur an obligation. 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 dances, one which we impose upon them unilaterally by arriving in their square. What is our fair share? I believe that it varies according to our experience at the level:

1. Phase 1 - When we first attempt a level, our fair share will be relatively low, perhaps 75% to 80%. Our mistakes, however, should not be due to ignorance of the documented list material. They should result only from a lack of experience in executing the material at dance speed - experience which can be gained only on the dance floor.

2. Phase 2 - With experience, our fair share increases to 100%. Other dancers have a right to expect us to dance our own part virtually error-free.

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

It is important to recognize that while we are in the first phase we are imposing on the strength of others. The justification for doing so lies in the premise that in time we will progress from Phase 1 to Phase 3 and, in effect, pay back what we were given.

If we move on without repaying the help we were accorded, we are short- changing the people who follow us into the level. If we move on before we are competent at the level we are currently inhabit, then we are short-changing both the level we leave and the level to which we move.

But most important of all, when we move prematurely we short-change ourselves. There is no feeling quite like the rush of exhilaration that comes with the dawning realization "Hey - I can actually dance this stuff!".