I played high school football in Indiana and was also very good academically. I suffered quite a bit of heckling from teammates for being a "nerd." I also have a friend who is a grad student with me now that had a similar experience growing up in Colorado and he had a very good way of describing the typical coaching strategy:
Say you are a basketball coach with 4 players all lining up to practice their free throws. Suppose all of them usually have an accuracy of about 85%, which is pretty good. In the first 10 attempts, though, it could easily be the case that Player 1 happened to miss a lot and only made 4 shots, Players 2 and 3 happened to make 7 and 8 shots respectively, and player 10, through statistical oddity, happened to make all 10 shots.
The coach will usually do the following: because Player 1 made the fewest shots, the coach will yell or offer some kind of critical instruction. Because Player 4 made all 10, the coach will offer praise and positive comments. The other two players are more or less where they should be, so the coach won't really single them out for extra attention.
Due to regression to the mean, as the number of free throw attempts gets large, all the players will converge to their expected percentage of 85%, making between 8 and 9 shots out of every 10. What will the coach believe has happened?
Yelling or being critical of the player who randomly got off to a bad start must have caused that player to improve and pick up the slack and get back up to the usual level. Praising the player who randomly got off to a good start caused them to slack off and drop back down to the normal level. Not saying anything to the two who got off to a normal start ultimately had no effect.
So, if you're a coach, yelling makes bad players do better and praising makes good players do worse. Thus, regression to the mean will reinforce the idea that you should just yell at the people doing below average. I found this to be a particularly illuminating way to look at it. This may also be true for bosses in a typical work environment.
On a side note, this same friend has pooled some very interesting statistics about American sports. For example, if you plot the location of the pitcher's mound as a distance from home plate and you look at how that distance has changed over time, what you'll see is basically a perfect example of the bisection method for root finding, where in the case of baseball, the number that the pitching distance controls is the percentage chance of a given batter getting on base. The current pitcher's distance causes there to be about a 0.5 probability of any given batter making it on base, which is maximum entropy (maximum surprise) from a fan's perspective. Similar results hold for the specifications for field goal posts in football and the three-point line, free-throw line, and basket height in basketball. In basketball, these settings basically cause a 0.4 field goal percentage for all shots across all players in a game... again very good for high entropy and high scoring.
Basically, your athletic skill only matters to get you into the pro game. Once you're there, the statistical settings of the playing surfaces makes it essentially a random competition. This is less true in college sports where talent distributions are more skewed, but still plays a role.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
The rationalist in me wishes we would just have competitive coin flipping and get it over with.
That would be awesome. However, it would not have the results you expect at all. I can bias a coin that I flip to about 60%; some professional magicians can do 95%+.
http://blogs.scientificamerican.com/guest-blog/2011/09/22/cognitive-biases-in-sports-the-irrationality-of-coaches-commentators-and-fans/