On Playing Trombone

 

Regression to the Mean

 

Teachers and students regularly observe a curious and frustrating phenomenon. In a lesson the teacher will help the student reach for (and sometimes achieve!) a new understanding or level of performance. Student and teacher generally like seeing this happen and at the end of the lesson everyone involved is filled with satisfaction and hope. In subsequent days, that sense of hope and satisfaction is destroyed by the slowing and reversal of upward progress. By even the second day after the lesson the student is usually seeing degradation of the wonderful achievements of their lesson. No matter what they do they cannot seem to recapture the sound or clarity of expression that they rose to during their last lesson. It does not seem to matter what the subject matter of the lesson was – it is rare that it is recaptured after one or two days after the lesson.. In fact, a general tendency is for the ability of the player to diminish rather constantly right up to the next lesson. What could be more frustrating? Finally, the student has their next lesson with the usual return to new highs. Progress is never a smooth steady road – in fact it actually looks like this:

 

Quality of progress from day to day

 

The highs and lows experienced each week varies quite a bit. The peaks are often high and the lows (just before the next lesson) are quite low. But we need to take notice of something very important, the slope of the average of all points is slightly positive. This represents a gradual increase in quality over time. Often any sense of progress gets lost in this highly variable data “storm”. After all, we experience each data point serially and only rarely get a sense of the larger “sweep” of our movement toward excellence. What we are experiencing is called “Progression to the Mean” and it is important to understand what this means. No matter what happens on any day, in any week and on any test, we tend to return to the “mean” level, the average, of our playing. Basically, our best playing moments and realizations don’t stick very well, neither do our worst – thank goodness.

The student’s GPA is an excellent example of a mean. A single grade of “A” or “F” has little effect on a student’s GPA as averaged over four years of high school or college. Yet, the GPA does indicate the success of a student at meeting the expectations of their teachers in a variety of disciplines over a period of time. Another excellent example of regression to the mean is the phenomenon of the fantastic rookie hitter. Sometimes a rookie hits 400 their first year in the Major leagues. We should never be surprised that their average declines in subsequent years. Still, everyone is disappointed when the averages of these players drop in the second and third season. In fact, this drop is often characterized as a “slump”. But for just a moment let’s take a look at all league batting averages. The mean of the batting averages of all major league players is about .260. The wisdom to be taken from this is that anyone hitting well above this mean will probably move down over time and those below it will – over time – tend to move up. This tendency is amplified on the low side since players with consistently low batting averages will find themselves working at other occupations.

None of us ever play at our very best all of the time. We all have our own mean level of excellence and although this does change over time – it tends to do so slowly. Radical changes are generally short lived and, if persistently negative, are usually linked to physiological or psychological trauma. The lesson here for all of us is to stay calm. Don’t get too thrilled when you have a great day. Enjoy it – yes! By all means! Revel in it! But don’t expect it to be sustained day after day. It is more likely that you will return to your own mean quite rapidly. Likewise, a bad day, a bad performance, lesson or even an unproductive week of practice is not a cause for any deep concern. It is also temporary. 

We all return to the mean. The true challenge is to remain committed to maintaining the slow, positive upward slope of our progress. It is again the case of the tortoise and the hare. Eventual, long-term success belongs most often to the plodders. Committed, sustained work toward improvement is the surest way to gain any difficult skill or achieve any complex goal. Slow practice, detailed mental work, good basic habits and purity of concentration count a great deal more than sudden jags of practice and achievement followed by deep depressions and periods of personal abuse and long layoffs.

The principle of regression to the mean is an extremely useful intellectual tool to help us understand and not overreact in our emotional response to either success or failure. It helps us understand that the goal is equilibrium of attitude; the goal of learning to live in the center of this idea so that we do not react so strongly to our deviations – be they positive or negative.