# 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.

# How Much More Important Is Passing Efficiency Than Rushing?

By Max Mulitz

One observation from our model of Team wins is that Passing Yards/Attempt seems to be far more important than Rushing Yards/Attempt. A team who’s defense that allows 1 fewer yard per pass attempt can expect to win 1.87 more games, but if the same team allows 1 fewer yard per carry, they can only expect to win .95 more games. Suggesting passing is about twice as important as rushing. Similarly, if a team increases it’s Passing Yards/Attempt by 1, holding all other variables constant, it can expect to win 1.66 more games, but if it increases its rushing yards per attempt by 1 holding all other variables constant it can only expect to win .72 addition games, suggesting passing is 2.3 times as important as rushing.

One reason for this might be that teams pass about 1.5 times as often as they run, so we would expect passing to be 1.5 times as important for that reason alone. It also makes intuitive sense to me that passing plays as a group have more leverage than rushing plays. For example, we know a teams 3rd down percentage is highly correlated with it’s passing efficiency, so passing being about twice as valuable as rushing strikes me as a reasonable result.

This analysis from Brian Burke using an unrelated method suggests passing efficiency is 2.24 times as important as rushing efficiency.

# Estimating The Monetary Value of a Star NFL Kicker

By Max Mulitz

Now that the NFL has completely disincentivized kicking touchbacks, the value of a Place Kicker falls almost entirely into his Field Goal kicking ability. Using this awesome paper from the Sloan Sports Analytics Conference, we can estimate the seasonal value of an elite kicker.

In each of the past three seasons, teams have averaged 1.9 FG attempts per game.  A top-10 kicker over the sample of the paper was worth about 0.1 points per field goal attempt above average. If we set a replacement level at bottom 3rd of the 55 player sample, then replacement level is about -0.06 points added per kick, so a top-10 kicker is worth about .2 points a game above average and maybe .3 points a game above replacement level. The best kicker in the sample was Rob Bironas, who was worth .262 points per kick above average. For the sake of a thought experiment, we can imagine an uber kicker who is the greatest kicker ever and is worth .3 points per kick above average, with kickers improving throughout the league, it may be unlikely we ever see this player, but this acts as a good fill in for the possible ceiling for a kickers’ value. This uber kicker would be worth just under .6 points per game above replacement. The following table shows these estimates extrapolated to a 16-game season, assuming 2 attempts per game.

Per the HSAC’s Pythagorean won loss formula, about 36 points equals a win, so the hypothetical best kicker possible is worth a quarter of a win per season and 0.3 wins per season over replacement and a top 10 kicker is worth about 0.08 wins per year.

In terms of betting lines, a team that is a 9.5 point favorite in a given game is 81.1% likely to win the game, so if we imagined all the value of our Uber kicker compressed into one game he would be worth ~.3 wins, very similar to our estimate. 3 Point favorites win 59.4% of the time, so if we imagined all of the value of a top 10 kicker in a season concentrated into one game he would be worth .09 wins per year, again mirroring our earlier estimate.

Using our Season Win Probability Model, we can find some equivalent values for .3 and .1 wins per season.

 .3 Wins is Equal to… .1 Win is equal to… Improving Offensive or Defensive Yards/Carry by   .3 Improving Offensive or Defensive Yards/Carry by .1 Improving Offensive or Defensive sack rate by 1.2 sacks/100 Improving Offensive or Defensive sack rate by .4 sacks/100 Improving Offensive or Defensive Yards/Attempt by .2 Improving Offensive or Defensive Passing Yards/Attempt by .06

Basically, any player that provides even a marginal improvement in the running or passing game is as valuable as a very good kicker. Further, the ability of a kicker to provide surplus value is limited by the low ceiling for even the best kicker imaginable.

# Modeling NFL Team Wins using Multiple Linear Regression to Determine What Makes Teams Win

By Max Mulitz

Brian Burke was the first to use multiple linear regression to do exploratory analysis on what makes teams win, however he hasn’t revisited model recently and the game has changed a little bit in the past 5 or 6 years, so I thought I would take a crack at it.

I looked at team data from the 2011 through 2015 regular seasons. I got my data from Pro Football Reference, except defensive forced fumble data, which is from ESPN though I did have to convert some gross stats to rate stats (fumbles divided by total plays to get fumble rate, for instance). Below are my variables and their significance:

Coefficients: Estimate Std. Error t-value Pr(>|t|)
(Intercept) 12.1054 3.105 0.000147 ***
D Rushing Yards/Attempt
 -1.87068
0.34397 0.006679 **
D Passing Yards/Attempt -1.87068 0.23377 3.37E-13 ***
D Sack Rate 0.23648 0.11047 0.033947 *
D Interception Rate 0.85697 0.16471 6.48E-07 ***
O Rushing Yards/Attempt 0.71702 0.30678 0.020777 *
O Sack Rate -0.28892 0.0792 0.000366 ***
O Passing Yards/Attempt 1.65931 0.21368 1.28E-12 ***
O Interception Rate -0.82088 0.16853 2.84E-06 ***
O Fumble Rate -1.14288 0.26673 3.29E-05 ***
Team Penalty Rate -0.25935 0.07812 0.001136 **
Opponent Penalty Rate 0.3174 0.10658 0.003394 **
D Forced Fumble Rate 0.2584 0.28161 0.360335

My adjusted R squared was .745, almost identical to what Burke found almost 10 years ago. All “Rate” stats are based on per 100 plays, so Team Penalty Rate is the number of penalties the team took per 100 plays. Don’t worry about the intercept term. The way to read the estimates is that, holding everything else fixed, a team that increased its rushing yards/attempt by 1 would expect to win 0.71702 more games. If a team’s defense increased it’s sack rate from 6/100 plays to 8/100 plays, holding all other stats constant, it could expect to win 2 * 0.23648 = ~.47 more games. Every variable was statistically significant at P=.05 except Defensive Forced Fumble Rate.