Nate's Notes: Regression to the mean


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"I'm going to read off fifteen words," my statistics professor Daniel Ho said, "and then give you a chance to write down as many words as you can remember."

Professor Ho read the words, waited fifteen seconds, and then told us to start writing. Once we had all finished, we repeated the exercise with a second set of fifteen words.

Once the second exercise had concluded, Professor Ho said, "Raise your hand if you remembered seven or more words from the first list." About half the hands went up.

"If you remembered eight or more keep your hands up." Several hands dropped.

"Nine?" Most of the hands dropped. Only five remained.

"Ten?" All of the hands dropped.

Professor Ho continued, "Those five of you who remembered nine words, how many of you remembered nine or more words the second time?

Four of the five hands dropped.

The professor then switched gears, and identified the four people who had memorized the fewest number of words—-four people had only remembered four words from the first list (give them credit for ‘fessing up). Professor Ho asked those four, "How many of you remembered more than four the second time." All four hands went up.

"What explains this?" asked Professor Ho. "Those who did the best on the first list did worse on the second list, and those who did the worst on the first list did better on the second list?"

An astute classmate from the back of the room, who had presumably done the reading for the class (or maybe just intuited the answer), raised his hand and said just four words: "Regression to the mean."

*******

The most common question I receive during the offseason is naturally, "How's the team going to be this year?"

I typically answer this question by saying, "Pretty good," and not much more. Ever since my junior season at BYU, in 2005, when I was certain we would have a tremendous season (we finished 6-6), I've learned to temper my expectations.

When asked about the offense and defense this year I've had a little more to say.

The offense? Better, probably. The defense? Worse, probably.

I don't make these predictions on gut feel nor do I make these predictions because I doubt the abilities of Kyle Van Noy and company. I make these predictions based on regression to the mean.

"Regression to the mean," states Wikipedia, "is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and, paradoxically, if it is extreme on its second measurement, it will tend to be closer to the average on its first."

Or in other words, if you have a wildly successful season that lands you on the cover of Madden's NFL video game, you will probably have a difficult time replicating the outlier success the following year. Some people call it the Madden curse. Statisticians call it regression to the mean.

And if you are in a statistics class and you remember nine words from the first list—-more words than anyone else in the class—-chances are you will remember fewer words from the second list.

*******

During Robert Anae's six years as offensive coordinator, the offense averaged a national ranking of 30th in scoring offense. The 2006 season was Anae's best—-5th in the nation. The 2010 season, Anae's last, was his worst—-70th.

For comparison, the offense averaged a national ranking of 53rd under Doman. Last season the offense ranked 64th nationally. Thus, regression to the mean suggests that the 2013 offense will be better than the 2012 offense.

BYU Scoring Offense, 2005 through 2012

SeasonPoints Per GameFBS Rank
200533.024
200636.85
200730.147
200834.220
200935.511
201026.270
201130.142
201228.764
Average under Anae32.630
Average under Doman29.453

During Bronco Mendenhall's five years as defensive coordinator, the defense averaged a national ranking of 25th in scoring defense.

The 2012 season was Mendenhall's best—-3rd in the nation. Mendenhall's first year, 2005, was his worst-—83rd. Under Jaime Hill, the defense averaged a national ranking of 34th. Regression to the mean suggests that the 2013 defense will be worse than the 2012 defense. (I have excluded the 2010 season from the analysis, the year Jaime Hill was fired as defensive coordinator part way through the season).

BYU Scoring Defense, 2005 through 2012

SeasonPoints Per Game AllowedFBS Rank
200529.283
200614.710
200718.59
200821.939
200921.529
201021.632
201120.422
201214.03
Average under Mendenhall19.425
Average under Hill21.734

In the words of Coach Mendenhall: "In order for our defense to be as good as it was last year, we actually have to be better than last year, because of our tougher schedule."

What may be even more important than the individual rankings of the offense and the defense is the disparity between the offense and defense. The 2012 team had the largest disparity between offense and defense of any of the Mendenhall teams.

Ranking Disparity, Offense v. Defense, 2005 through 2012

SeasonOffensive RankDefensive RankRanking DisparityWinsLosses
20052483-5966
2006510-5112
200747938112
20082039-19103
20091129-18112
201070323876
2011422220103
20126436185
Average3528794

Of course, disparity means little if neither the offense nor defense is highly ranked.

If the 2013 defense can replicate the success of the 2012 defense, and the offense can close the disparity gap, the 2013 team could actually have an outlier-type season. Regression to the mean says both things probably won't happen.

But as a player, I couldn't have cared less about regression to the mean. As a fan, I never hope for average, regardless of circumstances. As a media member, I find it interesting.

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Nate Meikle

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