Penalties Don't Matter Much

Penalties can be a big deal in certain circumstances. We all know this. A punt return touchdown is called back. A third down stop is negated by a personal foul. A kicker misses a field goal but someone runs into him, giving the guy another chance. Pass interference is called on fourth down in overtime of the national title game. Again: big deals.

On the whole, however, penalties don't matter much. It's something that I like to highlight once an off season because so many folks either don't know or immediately forget when their team loses a game in which it racks up 11 flags.

In general though, penalties are a mere annoyance to the best teams because they can be overcome relatively easily. To lower quality teams, they seem like killers even though the team wouldn't have succeeded anyway in a lot of the same situations. Let's go to the numbers to back this up.

In 2009, the strongest correlation between any penalty stat and winning percentage was penalties per game with -0.128. For a point of comparison, over the last decade a team's previous year's record has a correlation of 0.584 with its current year's winning percentage. In other words, penalties have a weak relationship with winning. Penalty yards per game had a -0.112 correlation with winning percentage in '09, and yards per penalty had an incredibly weak 0.025 correlation.

Of course, correlation deals with linear relationships only. Perhaps a scatter plot might reveal some kind of non-linear relationship?

That would be a no. The scatter plot for penalty yards per game looks similarly messy, and the scatter plot for yards per penalty looks almost like a vertical line. That's because the distribution for yards per penalty is very narrow, with a minimum of 7.25 and a maximum of 10.38. There just isn't much variation there at all.

Now fortunately for all of us, the NCAA began adding stats on first downs at some point this year. As I said at the beginning, defensive penalties that cause the other team to get a first down is one of those situations where the penalty is unequivocally a bad thing. How does that compare?

The correlation between the raw number of penalty-caused first downs a team gives up and its winning percentage is 0.197. I calculated the percentage of all first downs allowed that are caused by penalties for everyone, and the correlation between that and winning was stronger at  0.295. Just for fun I ran a linear regression on those two, and the R-squared was 0.087. So, roughly 8.7% of variation in winning percentage can be traced to the factors involved in percentage of penalty-caused first downs allowed.

That's not a whole lot, despite being the strongest influence on winning that I could find in any penalty-related stats. Again: situationally, penalties can be very bad. Overall, they don't matter much when it comes to winning.