Guess the Graph

November 25, 2020 at 5:46 am 4 comments

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:

  1. Describe two ways in which an NFL game can end with a score of 2‑0.
  2. What’s the greatest score that cannot be attained by scoring only touchdowns (7 points) and field goals (3 points)?
  3. Express the ratio of width:length of a football field. For length, include the end zones.
  4. What are the only positions allowed to wear single-digit uniform numbers?
  5. 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!


  1. 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.)
  2. 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.
  3. 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.
  4. Quarterbacks and kickers.
  5. According to several analyses, 11 minutes of a three-hour broadcast is spent actually playing. That’s about 3%. Sheesh.

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Mathy Portmanteaux KenKen 12 Puzzle for 12/12

4 Comments Add your own

  • 1. Roger  |  November 25, 2020 at 7:38 am

    Re #3: in feet, it’s 160:360 (or 4:9), not 120:360. am i missing something? but, from this fan of the northern ohio team that sits atop the tallest bar on your graph, looking down on #10, thanks for the football topic. 😉 happy t-day!

  • 2. Ihor Charischak  |  November 25, 2020 at 7:46 am

    5. 11 minutes of actual playing time is not reasonable. A TV broadcast shows all the plays. There are 60 minutes of playing time. Since most games last about 3 hours. That means that 60/180 or 33.3% of the time you see the game. What am I getting wrong? BTW – go Steelers!

    • 3. Roger  |  November 25, 2020 at 2:53 pm

      Hello Ihor, Well there are 60 minutes of ‘clock running’ time, but as much as 45 seconds can elapse between each play, which will then typically take only 5 seconds or so. Granted that the clock does stop between some plays, but still much of that ‘clock running’ time is spent in huddles, waiting for the snap, and then unpiling after the whistle. An NFL team averages about 65 plays per game, for a total of 130 by both teams. 130*5 = 650 seconds, or about 11 minutes. Cheers!

      • 4. venneblock  |  November 25, 2020 at 4:45 pm

        To Roger’s point, football is often described as a “4-and-40” format, meaning 4 seconds of activity separated by 40 seconds of not doing much (huddling, returning to the line of scrimmage, etc.). That gives the already low ratio of 1:10, and that doesn’t count half time or commercials. Admittedly, there is entertainment value in watching players celebrate, point fingers, holler at each other on the sidelines, etc., but it’s not actual playing time.

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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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