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Deflate-gate statistics

Naomi Neff sent a link to the following, noting that a "stat-spat" sounded interesting.

Deflate-gate triggers stat spat as analysts attempt to solve why Patriots don't fumble
by Eric Adelson, Yahoo! Sports, 28 January 2015

For anyone who hasn't heard the details, the controversy over whether the New England Patriots broke the rules by deliberately underinflating footballs now has its own Wikipedia page. Indeed, there have been seemingly daily updates in major papers and evening television news. While some observers have lamented the disproportionate attention this story has received, it has at least been refreshing to see an exposition of the ideal gas law in the popular media! (See, for example, Deflation experiments show Patriots may have a point after all New York Times, 29 January 2015.)

The "stat spat" refers to an analysis claiming that New England has had an exceptionally low fumble rate in recent years, with the implication that the team has been cheating all along, deflating footballs so that they are easier to hold on to:

Stats show the New England Patriots became nearly fumble-proof after 2006 rule change proposed by Tom Brady
by Warren Sharp, Sharp Football Analysis, 26 January 2015

Sharp's analysis

The data analysis community taken a closer look at these claims, and found that they fail to hold up. The post

Your guide To Deflate-gate/Ballghazi-related statistical analyses
by Neil Payne, FiveThirtyEight.com, 28 January 2015

reviews a number of such responses.

To be continued...

Submitted by Bill Peterson

More on Gini

The analysis received news coverage elsewhere, for example:

How airline seating reflects income inequality
by Michael Hiltzik, Los Angeles Times, 2 December 2014

Some math doodles

<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>


Accidental insights

My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end. I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics. But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.

While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.

BrokenTile.jpg

As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.” Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.

Piece Sq. Inches % of Total
1 43.25 31.9%
2 35.25 26.0%
3 23.25 17.2%
4 14.10 10.4%
5 7.10 5.2%
6 4.70 3.5%
7 3.60 2.7%
8 3.03 2.2%
9 0.66 0.5%
10 0.61 0.5%
Montante plot1.png

The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line. I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head: “On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”

Montante plot2.png

My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from Nature News on research by Hans Herrmann, et. al. Shattered eggs reveal secrets of explosions. As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. Bill also provided a link to a vignette from CRAN describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.

Submitted by William Montante