Arrests in the NFL versus the general population

I saw, on FB, this article on how a single NFL team has had no players arrested in the last 3 years, and since I'm a statistician, my first thought was, "how does that compare to the general population?"

Very back-of-the-envelope speaking, there were about 3.2 million arrests of males between the age of 21-34 (inclusive) in the U.S. in 2012**.  There were about 32 million males in that age range in the U.S..  So, very roughly speaking, about 0.1 arrests per year per male aged 21-34, which is roughly the demographic for NFL players.

Assuming that arrests occur like a Poisson process and using 0.3 arrests per 3-year interval as the parameter of a Poisson distribution, there is approximately a 74% probability of a randomly selected male aged 21-34 not being arrested in a three-year period.  The probability of 50*** randomly selected men all not being arrested is 0.74^50, or 0.00003%, so the probability that at least one person on that team was arrested is 99.99997%.

Thus, the very back-of-the-envelope estimate of the probability of all 32 NFL teams having at least one player arrested during a three-year period, if they were equivalent to members of the general public, is 0.9999997^32 = 99.999%.  So it seems to me that it's extremely unusual for *any* of the NFL teams to be arrest-free over a three year period.


** Click National Estimates, Annual Tables, 2012, Offense by Age for Males

*** 50 being approximately the size of an NFL roster

Is Duolingo trying to tell me something?

After a quick pre-test, Duolingo generously, extremely generously, marked me as 52% fluent in Spanish.  Over the last 5 days of casual use, it has corrected the estimate to 49% (still generous), and then today gave me the following in the "Medical" section.

I guess I hope this is a phrase that appears in every language track, and not something they thought would be especially useful in Spanish?  or especially useful for me personally?

Gingerbread house stained glass windows

This was insanely easy to do, I can't believe we didn't know about this before, and all future gingerbread houses will have stained glass windows.  Next year, we'll swirl them a bit to make more interesting patterns.

Important Note: strongly recommend parchment paper for this.

Just add a few Jolly Ranchers on the sheet...

...and they bake right into the frame!

Dragons or Lorelais

Tough choice.  We were all set to start A Year in the Life tonight when Game of Thrones, Season 6, disk 1 arrived in the mail (we netflix everything late).  So it's either the multigenerational conflict that promises death, drama, and fights to uphold a family's honor, or Peter Dinklage and CGI dragons.

(ed. note: this was originally posted to friends on FB in 2016, so I am backdating to that date.  It was added to this blog in 2025)

I am not throwing away my squash