Regression to the mean – What statistics can teach you about your coaching feedback.

Have you ever wondered why when someone performs a rep of something it never really quite looks the same even when they are highly skilled at the exercise.  If you watch a world class level weightlifter performing a snatch or clean attempt there will almost always be slight differences in it’s execution even in made attempts at the exact same weight.  Even on a relatively simple exercise like squat form will change with in the same set and it will also change as more weight goes on the bar.

Below is a video taken from the 2012 USA weightlifting nationals in the front of the shot is an experienced lifter (Jared Enderton) performing the back squat and in the back of the same platform is a girl performing snatch.  Pay close attention to both for any deviation in the way they move in the same sets and different sets.

Notice how on Jared’s squats with the bar and 70kg his form stays almost identical however as the weight increases (220kg – 240kg) his velocity and hip placement varies much more from rep to rep even on a simple exercise like squats.  The girl in the background has variance almost every time she does a rep of something if it be pulls or snatches she puts the bars in a different position, catches in a different manner etc.

This shows that even a relative expert doing a relativity simple exercise like back squat still exhibits variance that represents a distribution.  In science the bell curve is used to describe a “normal” distribution around a mean.

For instance if you where to order the same 500g baugeutte from a bakery every day for a year and measured it’s weight you will find that it doesn’t always weight exactly 500g.  It may weight 450g one day or you might be lucky and catch the baker on a particularly ostentatious day and get a 550g loaf.

However if you where to plot a scatter graph you should see that the majority of the points congregate beside the 500g mark.  This represents a bell curve.

Another concept worth noting is regression to the mean.  When learning a skill there will be a massive amount of variance in the execution of your skill with the mean of your effort being a poor performance, whilst an advanced lifter will have less variance and the mean of their efforts might be good performance.  Below you can see a graph illustrating this point for three lifters of different skill levels.     
The peak represents the category where most of their lifts are rated the further right you can shift your average then the more skilled of a lifter you will become.  Regression to the mean states that even though you might get a luckily good result here or a really bad result there with enough attempts you will tend to revert back to your average performance.  
This is pertinent for coaching feedback and is very well explained in this anecdote 
The psychologist Daniel Kahneman, winner of the 2002 Nobel prize in economics, pointed out that regression to the mean might explain why rebukes can seem to improve performance, while praise seems to backfire.[8]
I had the most satisfying Eureka experience of my career while attempting to teach flight instructors that praise is more effective than punishment for promoting skill-learning. When I had finished my enthusiastic speech, one of the most seasoned instructors in the audience raised his hand and made his own short speech, which began by conceding that positive reinforcement might be good for the birds, but went on to deny that it was optimal for flight cadets. He said, “On many occasions I have praised flight cadets for clean execution of some aerobatic maneuver, and in general when they try it again, they do worse. On the other hand, I have often screamed at cadets for bad execution, and in general they do better the next time. So please don’t tell us that reinforcement works and punishment does not, because the opposite is the case.” This was a joyous moment, in which I understood an important truth about the world: because we tend to reward others when they do well and punish them when they do badly, and because there is regression to the mean, it is part of the human condition that we are statistically punished for rewarding others and rewarded for punishing them. I immediately arranged a demonstration in which each participant tossed two coins at a target behind his back, without any feedback. We measured the distances from the target and could see that those who had done best the first time had mostly deteriorated on their second try, and vice versa. But I knew that this demonstration would not undo the effects of lifelong exposure to a perverse contingency. Wikipedia 2012
You almost always get good results from criticising a person for doing an unusually bad rep because they will regress to their mean skill level which will be better than which you have seen and vice-versa you will usually get bad results for praising an abnormally good rep since they will revert back to their normal skill level which will be worse.  
It is through practice that you shift your hypothetical average to the right (thus making it better) and if psychology is to believed then you require 10,000 hours of practice to achieve skill mastery and anyone who has lifted weights will understand just how much of a task this is with in the context of weightlifting. 
Things to remember when self coaching or coaching someone in the unique skill of lifting weights
  1. Beginners will have massive variance at a skill and thus require much more practice, use feedback sparingly where possible and try and allow the lifter to find their own way through experience, trial and error.
  2. Skill learning is a LONG PROCESS getting good at exercises takes a long time with the more complex the movements the longer it will take to get from beginner levels to advanced.  For movements such as squatting this can take 1-2 years for and for movements like snatching or cleaning this can take 5+ years of continual and consistent practice
  3. As lifters increase in skill level and variance creeps out of their lifting then feedback becomes much more powerful.  Try and target your feedback on one thing that at a time something they can act upon and improve their lifting and allow them sufficient time.  
  4. Feedback you give shouldn’t solely be in the form of negative or positive since this is an inherently flawed and random way of teaching and not much better than just doing it on your own.  Your feedback should be actionable, lifters should feel the benefit of it in short order (i.e. if the lift feels easier for the lifter after acting on your cues it was probably good feedback). 
  5. Increasing force demands increase the variance of the skill for instance lifting 20kg in a squat lift introduces much less motor pattern “noise” than squatting 350kg.  The larger the force demand, the larger the number of motor unit’s involved and the more difficult it is to get reps to look the same.  When you include the physical exhausting nature of these efforts it shows how difficult it is to achieve “skill mastery” when lifting very heavy.
  6. Being mindful of point 5 – a lifters ability to respond to the feedback you provide is almost inversely proportional to the amount of weight on the bar.  The heavier you go the more useless feedback becomes.  In essence as the weight gets heavy shut your goddamned pie hole and let them lift.  
  7. When programming for beginners, intermediates and advanced lifters try to be mindful of weightlifting as a skill learning process.  It might be a better idea to give rank beginners a block of 20 minutes say to practice snatch/drills rather than blindly prescribing sets x reps since they are gonna need a lot of practice.  Conversely someone who is good at the skill is going to need an overload stimulus to get stronger and sets x reps might be more appropriate in that case since they have only so much energy and you would be better in providing guidance on how they can optimally expend their reserves to increase their fitness.
That concludes our little foray into stats and coaching.