## Archive for November 25, 2020

### Guess the Graph

The bar graph below was created because of a recent discussion with my wife. The title and axis labels have been removed. **Can you identify the data set used to create the graph?** I’ll give you some hints:

- The data set contains 32 elements.
- It’s based on a real-world phenomenon from this year.
- The middle five categories account for 81% of the data.
- The special points marked by A, B, and C won’t help you identify the data set, but they will be discussed below.

Got a guess?

No clue? Okay, one more hint:

- The vertical axis represents “Teams.”

Still not sure? Final hints:

- Point A represents the lowly J-E-T-S, who are currently winless.
- The region outlined by B shows that 26 teams have from 3 to 7 wins.
- Point C on the graph represents my Pittsburgh Steelers, whose record is a perfect 10‑0. (It’s my hope that I’ll still be able to gloat on Friday morning, after the Steelers host the Ravens on Thanksgiving night.)

This graph was generated while discussing the current standings in the NFL with my wife, who speculated that there seemed to be a lot of really good teams and a lot of really bad teams this year. The horizontal axis represents the number of wins. As it turns out, the distribution above is somewhat typical at this point in the season. At the end of most seasons, about 2/3 of the teams finish a 16-game season with 5 to 10 wins. It may be a little unusual that there are 8 teams with 7 wins, but it’s not statistically cray-cray.

If you’ve read this far, then you may enjoy these other math-related football trivia questions:

- Describe two ways in which an NFL game can end with a score of 2‑0.
- What’s the greatest score that cannot be attained by scoring only touchdowns (7 points) and field goals (3 points)?
- Express the ratio of width:length of a football field. For length, include the end zones.
- What are the only positions allowed to wear single-digit uniform numbers?
- During a typical broadcast of an NFL game, approximately what percent of the time is spent actually playing football (as opposed to commercials, half time, or just milling around between snaps)?

Happy Drinksgiving! And, go Stillers!

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Answers

- A game can end 2‑0 if one team scores a safety and the other team doesn’t score at all. It can also end 2‑0 if one team forfeits before either team has scored, by league rule. (In high school and college, a forfeit is officially recorded as a 1‑0 loss.)
- 11 points. Any point total above that is (theoretically) possible. Below that, it’s not possible to score 1, 2, 4, 5, or 8 points.
- A field is 53 1/3 yards wide and 120 yards long. In feet, that’s 160:360, which can be reduced to 4:9.
- Quarterbacks and kickers.
- According to several analyses, 11 minutes of a three-hour broadcast is spent actually playing. That’s about 3%. Sheesh.