I’ve always thought violin plots of data with normal distributions look like footballs. So here I’ve generated some violin plots of football data, showing the passing yards per game for 14 quarterbacks. Only games in which the quarterback threw for positive yards were included.

A violin plot is a box plot (the white dot is the median, the thick black bar represents the interquartile range, and the thin black bar represents 95% confidence intervals) combined with a kernal density plot, which shows the probability density function. Basically, the thicker the “football” (or violin), the more probable it is that the quarterback would throw for that many yards in a game. This allows you to see which quarterbacks threw consistently for the same number of yards (e.g., Peyton Manning or Dan Marino), and which were more variable (e.g., Drew Brees or Johnny Unitas). In the case of Brett Favre, we see almost a bimodal distribution! One other item to note is that active quarterbacks tend to have higher medians (white dots shifted to the right) than retired quarterbacks, suggesting that teams throw the ball more now than they did in the past.

Data source: www.pro-football-reference.com

