As a former college offensive linemen, I’m well aware of the reputation that holding penalties have – ‘you could call one on every play’ goes the old adage.
Kevin and I wrote a paper, recently appearing in JQAS, in which we looked at the rates of NFL penalties. Specifically, we wanted to address how rates fluctuate over the course of the game.
Quick summary: the rates of discretionary penalties in NFL games are hugely correlated with time.
Here’s my favorite plot, where, letting OHR be the holding rate on run plays, OHP the holding rate on pass plays, and DPI the defensive pass interference rate, we compare versus game minute (1 through 60). These rates are adjusted for play and game characteristics, and given per 1000 plays along with 95% confidence limits.
The association between game minute and penalty likelihood is strongest for holding on running plays – with rates 4-5 times higher during parts of the second and third quarters, when compared to the beginning and ends of a contest. Holding penalties, and to a lesser extent the other judgemental calls that we looked at, are exceedingly rare in the game’s first and last minutes.
If you are interested in the paper, feel free to drop me an email and I can send you a copy.
Cheers.
StatsbyLopez 
Reblogged this on Stats in the Wild and commented:
Holding penalties in the nfl
Would like to read your paper on penalties in during different points in time during NFL games. Also I recently read a book called score casting where the authors demonstrated home field advantage is largely due to referees/umpire bias. I have been wanting to try and do some of my own research on this topic in regards to college football and was wondering if you knew where I could find the data to do my research. So really just want to read your paper and the second part is just a shot in the dark
Thanks”
Robert
Hi Robert,
Send me an email (mlopez1 at skidmore dot edu) and I can send you the paper. Not sure I can help with NCAA football data, though, as I am unaware of any massive archive for public use.
-Mike