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Regression to the Mean

By: Paul Arrington, M.D.

So why, if positive reinforcement is so great, does punishment seem to be more effective? To answer this we need to understand the statistical phenomenon called, “Regression to the Mean.” In any sequence of events in which there is some degree of randomness, any extraordinary event (good or bad) is most likely to be followed by a rather more ordinary event. This is seen graphically below:

Random number sequence demonstrating regression to the mean

Since there’s almost nothing in life that isn’t at least partly a matter of chance,
regression shows up in a wide variety of unlikely places. As applied to sport, despite the fact that coaches want to see continual improvement, when there is any behavior well above or well below the average behaviors, the next attempt will be back closer to the average. During practice, the only time coaches praise is when the attempt is much better than average. The subsequent attempt will be worse (back toward average). However, when coaches chastise or otherwise punish, it is because the attempt was well below average. After the punishment, the next attempt will be better (back closer to the average). Regression to the Mean!! The feedback was inconsequential. However, most coaches assume the improved attempt resulted from the punishment, hence, the misconception that punishment is more effective than positive reinforcement.

The continuation of poor coaching behaviors can be understood by the “Regression to the Mean” scenario discussed above. Let’s assume that the goal is to have continual improvement in performance. In this scenario, when the coach praises an attempt he is rewarded with a performance than is poorer than the one he just praised. His good coaching behavior results in not only the apparent consequences of extinction (he is not getting what he wants, i.e. continuous improvement of performance), but also in punishment (he is getting what he doesn’t want, i.e. worsening performance). However, when he criticizes the athlete’s poor performance he is rewarded with improved performance (positive immediate certain reinforcement). Is it any wonder we are inclined to yell and be critical of our athletes?

Because of this tendency for our good behaviors to receive the consequences of punishment and extinction, and our bad behaviors to receive positive immediate certain reinforcement, we must be continually vigilant to avoid this trap. We must be content with future uncertain consequences and not give in to the extinctive consequences and punishments. This is no easy task, however, if we have our own process goals with time lines for each, it is easier to avoid the trap.

The results of failing to recognize regression to the mean is amply demonstrated in the following newspaper report during the 2007-2008 college basketball season:

LUBBOCK, Texas (AP) — Pat Knight ratcheted up practice his own way after Texas Tech lost by 44 points earlier this week.

It seemed to make a difference in his players’ efforts as the Red Raiders beat No. 5 Texas 83-80 on Saturday.

Bob Knight, said his son, did “regular old drills” that in some way involved basketball. On Thursday, the younger Knight left the court behind and made his players run sprints while carrying weights. Then they shot lots of free throws. After that Pat Knight made them carry tractor tires and then flip them over — in relay races.

“I honestly believe they might have wished my dad didn’t retire after Thursday,” Pat Knight said. “I wanted to take it up a notch. I wanted to leave my stamp on it, so I think everything was pretty original that we did.”

One can only wonder about Pat Knight’s thoughts after Texas Tech’s record setting loss of 52 points in their very next game after the big win over Texas. It is obvious that he fails to understand the real reason for their perceived improvement after punishment.


  1. good performance praise, bad punish. got it.

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