## Sunday, May 8, 2016

### Awesomeness, Regressing to the Mean, and the Sports Illustrated Effect

I spent a lot of this past week volunteering for my choir. I've received many thanks and compliments for this, to which I replied, "We'll see how long it takes before I return to my baseline level of awesome." In statistics, this is known as regressing to the mean.

In order to understand this concept, we have to start with our good friend, the normal distribution.

Let's talk first about how to read this guy. This is what's known as a frequency distribution. Along the X-axis are scores. The Y-axis is frequency, how often those scores occur. Because this is a symmetrical distribution, the very middle is the mean or average. But the normal distribution also has two additional features. The middle is also the median, the place that divides the distribution into 50% on each side. And it's also the mode, the most frequent score.

As you can see the scores in the middle are very common. The scores on the far ends are rare. If we think in terms of probability - and the normal distribution is actually a probability distribution, giving the likelihood of various scores - middle scores are likely and extreme scores are unlikely. As a result, if I give a group of people a test once, I'll see many middle scores and few extreme scores. If I gave that same test again, the extreme scores would probably move (regress) toward the middle (mean).

So let's say the test is of ability. There are many variables that affect those scores besides knowledge: level of fatigue, environmental conditions (like lighting and temperature), and even mood, to name a few. Those variables would impact some of those scores, and we would see some extreme scores. We would expect those additional variables to, well, vary, so giving you an ability test again, we would expect those variables to be different, and the extreme scores less extreme. Any time you specifically select people because their scores are extremely high or extremely low, you're going to see those scores become less extreme on average even if you do nothing to the group. True, some people have genuine extreme scores, but for many, you may just be capitalizing on chance.

To use a real-life example, let's think about a different kind of ability: athletics. Basketball players may suddenly be "on fire" during a key game. Baseball players may suddenly start hitting home run after home run. A golfer may suddenly hit a hole in one. They may be signs of high ability, but they may also be, at least in part, luck.

 And for my friends who don't like sports, how about a Star Wars reference? Because we all know what happened to Obi-Wan shortly after he said this...

Those extreme examples get a lot of attention, and may lead that player to be put on the cover of Sports Illustrated. Many have noticed that after being on the cover, the player suddenly doesn't perform as well, known as the Sports Illustrated effect, or even the Sports Illustrated curse.

What we're probably seeing isn't a curse resulting from being on the cover of Sports Illustrated. More likely, it's simply regressing to the mean. This is especially like if a player was good but not fantastic before, and suddenly started performing really well. Or, you know, maybe steroids. But I digress. The point is, extreme scores tend to become less extreme over time.

So my current levels of awesome are likely to dissipate. But that's okay!

And by the way, if you'd still like to check out Apollo Chorus of Chicago's Broadway concert, you have one last chance today!

1. There's something similar to the "Sports Illustrated effect" observed with medieval battles. "It always rains the day after a battle" is an old aphorism in Europe. This could be because (a) it typically rains about every 4-5 days in Europe in summer, when battles are taking place; and (b) it takes 2-3 days for the battlefield to be dry enough to support all those horses and men.

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