# Accepting/Declining Penalties and First Down Likelihood

By Max Mulitz

Using data from PHD Football‘s Github Page we can look at the likelihood of an offense obtaining a First down from various down and distances.The probability the drive results in a  1st down based on the current state of the drive from PHD Football’s study of the 2000-2011 season. At some point I will be replicating his study with current data.

 Drive First Down Conversion Rate By Down and Distance 1st Down 2nd Down 3rd Down Distance 1 89.47 73.74 2 85.03 60.82 3 79.01 54.92 4 74.35 52.89 5 84.3 70.84 48.48 6 66.21 45.13 7 63.02 42.25 8 58.06 37.77 9 56.22 36.48 10 67.08 53.32 34.88 11 49.84 30.2 12 46.69 28.44 13 42.61 24.29 14 44.36 23.96 15 55.16 37.81 20.3 16 37.22 20.74 17 37.64 16.24 18 33.28 18.34 19 27 14.81 20 42.89 30.62 12.88

We can use the table to inform our Penalty Accept/Decline decisions in normal situations outside of FG range. For instance, 1st down Probability tells us 1st & 15 converts for a 1st down 55.16% of the time, slightly more than 2nd and 10, so a team should at least consider declining a 5 yard 1st Down penalty where the opponent does not gain any yards and should certainly decline if the opponent loses yards on their 1st down play. 1st and 20 converts right about as often as 2nd & 13 or 14, but a 2nd & 15+ is preferable to a 1st and 20 from the defensives perspective. Offensively, a 1st and 5 is preferred to everything but a 2nd & 1 or 2.

One thing that struck me was how closely this tracks with Football Outsiders’ Success Rate Formula, which says an offense is efficient if they gain 40% of the Yards needed on 1st down or 60% of the Yards to go on 2nd down, that pretty reliably tracks with the table above. 1st & 10 and 2nd & 6 are within 1 percentage point of 1st down conversion probability, as are 2nd & 10 and 3rd & 4.