Hot Topics

# An explanation of our box-and-whiskers plots for football

Our football stats are new and improved this year, but you might need a math teacher to explain how they work and what they show. (I hope so.)

We were going to wait until the week of Aug. 13 to show our new statistical graphics on the Illinois high school varsity football pages, but by that time, teams will be practicing and won’t be able to read up on the stats.

Of course, at this point, the only actual data that’s available is from last season (the fall 2011 season). That’s OK, because once the season gets going, a great deal of attention will be paid to showing side-by-side (or top-to-bottom) parallel comparisons with the team last season. The point is to show improvement (or the lack of it).

You would be hard-pressed to find this level of coverage anywhere else—on the Web or in newspapers. A few key statistics for every team in Illinois will be presented every week. The usual format will be a box-and-whiskers plot, with the location of the statistic for the team whose page you’re looking at shown with a red arrow. Let’s look at the example above.

Above each plot are the title for the statistic and a number line with enough evenly spaced tick marks to give you an orientation. The left endpoint on the box-and-whiskers plot is the minimum value for that statistic. In 2011, there were actually two teams that posted point totals of 0. The right “whisker” on the plot extends to the maximum value. It’s important to note that these graphs include every team for which a given statistic is available. In most cases, that will be about 577 teams for 2011 statistics and about 580 teams for 2012 statistics. However, not all statistics are available for all teams.

Don’t be fooled by how long the whisker is. For example, there were only 17 teams last year that scored 500 or more points, and only four that scored 600 or more points. The length of the line has to do with the range of the data, not how many teams are represented in each position. The only thing you know about numbers from a plot like this is the high and low values for each quartile of the distribution.

Going on, as is typical for box-and-whiskers plots, the line in the middle of the box is placed at the median value of the statistic among all Illinois teams. In other words, half the teams in the state had a higher value than this, and half the teams had a lower value than this, not counting ties. The median for both the “Total Points Scored in 2011” and “Total Points Given Up in 2011” was about 226, as shown on the graphs.

The left end of the box is placed at the first quartile, and the right end of the box is placed at the third quartile. In other words, 25 percent of the teams had values below the first quartile value, and 25 percent of the teams had values higher than the third quartile value.

The values shown above, 241 and 169, are in between the median and the third quartile, and below the first quartile, respectively. This is generally good, since it says this team held its opponents in 2011 to fewer points than more than three-fourths of the teams in Illinois, and it scored more points than more than about half of the teams in the state.

You would expect very strong teams to have “Total Points Scored” in the portion of the graph to the right of the box and “Total Points Given Up” in the portion of the graph to the left of the box, each on the whiskers.

#### About the Author

##### Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.