Introducing "Air Yards"

If I've proven anything over the past year of analyzing NFL stats, it's that passing is by far the most important part of the game. So let's look at the pass and passing stats in more detail than usual.

The football pass is typically judged by how many yards it produces. Quarterbacks and receivers are judged by the their yardage compiled per game or per season. But there are two distinct components of the pass.

A NEW STAT

One of the components that is often discussed is Yards After Catch (YAC). Although it is not an official NFL stat, it is kept by Stats, Inc., and has become a buzzword when talking about the west coast offense. YAC is the yardage gained by the receiver after catching the ball.

The other component of the pass, the complement of YAC, has never been mentioned to my knowledge. It has no name...until now. The distance forward of the line of scrimmage that the passer throws a complete pass through the air is hereby called Air Yards. It can be expressed in a simple equation:

Pass Yds = Air Yds + Yds after Catch

From 2002 to 2006, NFL teams accumulated an average of 3533 yds per season. Of those passing yards, 2008 yds (57%) came through the air and 1533 (43%) yds came on the ground as YAC.

THE IMPORTANCE OF AIR YARDS

Digging a little deeper, I ran a couple very simple regressions. I estimated Passing Yards per Completion using Air Yds/Completion and then using YAC/Completion. (I couldn't run a single regression using both components because multivariate regression doesn't work when the predictor variables comprise the entirety of the dependent variable).

Air Yds/Completion accounts for 56% of the variance in Yds/Attempt, while YAC/Completion accounts for 20% of the variance. As a proportion of the total variance explained by both variables, Air Yds accounts for 74%, and YAC accounts for the other 26%. Put simply, Air Yards are 3 times as important than YAC in producing total passing efficiency.

Here is one way to interpret these results. Although Air Yds yards comprise 57% of total passing yards, it is far more critical than YAC. YAC is less variable among teams. Air Yards, therefore, is much more of a "difference maker" in determining total passing yards.

In future posts, I'll examine how much QBs contribute to YAC. Air yards are a far more appropriate and accurate measure of a QB's ability than total yards or yards per attempt. We'll also see how QBs vary greatly in their ability to produce air yards. Ultimately, these results will contribute to a better QB rating formula.

NFC North 2007 Predictions

Here are the predictions for the 2007 season in the NFC North. Methodology is described here. Note the predictions do not account for personnel changes such as free-agent acquisitions, draft picks, retirements, or otherwise. It is still the best purely statistical prediction available.

NFC South 2007 Predictions

Here are the predictions for the 2007 season in the NFC South. Methodology is described here. Note the predictions do not account for personnel changes such as free-agent acquisitions, draft picks, retirements, or otherwise. It is still the best prediction available.

AFC East 2007 Predictions

Here are the predictions for the 2007 season in the AFC East. Methodology is described here. Note the predictions do not account for personnel changes such as free-agent acquisitions, draft picks, retirements, or otherwise. It is still the best prediction available.

AFC South 2007 Predictions

Here are the season predictions for the AFC South. The solid lines are the probabilities (on left of graph) that each team will finish with that particular amount of wins. The curved line is the probability each team will finish with at least that many wins (on right). Methodology of estimating these probabilities is explained here.

AFC North 2007 Predictions

Based on the assumptions described previously, here are the predictions for the AFC North division. The graphs represent season wins for each team. The solid bars represent the probability that the team will achieve exactly that number of wins in 2007. The curving black line represents the probability that win at least that many wins.

Notice how that for each team the distribution of win probability is almost perfectly normal. The "at least" win distribution is sigmoidal, i.e. an S-curve. It is a CDF--a cumulative distribution function.

Note that the model does not predict CLE will have have 4 wins. It predicts that it's win-probability-distribution is centered at 4 wins. The Browns could have up to 9 wins, or could go 0-16. Although BAL has the best chance to win the division, PIT and CIN have solid chances as well.

This does not take into account personnel changes--draft picks, free agent singings, or retirements (or suspensions in the Bengals case). It merely extrapolates last season's performance stats onto this year's schedule, then calculates the total probabilities of every possible outcome.

2007 Season Win Predictions

I've assembled a new and larger database and tested the most predictive variables for wins. Now it's time to apply the data to the upcoming 2007 NFL season.

Using data from the 2002-2007 seasons, I've run a logit regression on the efficiency stats most predictive of winning for every game played. The result is a model that correctly predicts the winner of 68.9% of games during the 5 most recent seasons.

For every game, the model produces a probability that each team would win. We can apply this model to future games as well, assuming we can estimate the values of each team's efficiency statistics. As any shrink will tell you, the best predictor of future behavior is past behavior. We'll use 2006 stats as our baseline for 2007. I realize this is highly imperfect, but it is the best predictor available. Although this method does not account for personnel changes, efficiency stats are relatively very steady from year to year--much steadier than actual win totals. Previous year 'expected win' totals are singificantly better predictors of the following year's record than are previous year actual wins. Plus, this is all just for fun.

I now have win probabilities for all 256 upcoming regular season games and I've sorted them by team. The probabilily of every possible sequence of game outcomes for a team (there are 2^16 of them--65,536) was computed. Then each sequence of outcomes that result in a certain number of total wins is summed. (There is 1 possible sequence for 16 wins, 16 sequences for 15 wins, 256 sequences for 14 wins,...) Now I have estimated probabilities for every win total for each team.

For example, the Ravens have a breakdown of win probabilities that centers on 11 wins. Although they had 13 wins last year, they appeared to squeak by on a couple wins on luck, and they had a relatively easy schedule. This year, they'll play a much tougher schedule. The table below lists the probabilities for each game on their '07 schedule based on last year's efficiency stats.

Vis Home VPROB HPROB
---------------------------
BAL CIN  0.54  0.46
NYJ BAL  0.26  0.74
ARI BAL  0.17  0.83
BAL CLE  0.82  0.18
BAL SF   0.69  0.31
STL BAL  0.32  0.68
BAL BUF  0.67  0.33
BAL PIT  0.47  0.53
CIN BAL  0.28  0.72
CLE BAL  0.09  0.91
BAL SD   0.32  0.68
NE  BAL  0.34  0.66
IND BAL  0.49  0.51
BAL MIA  0.57  0.43
BAL SS   0.69  0.31
PIT BAL  0.34  0.66

The next table lists the probability of winning each possible number of games. The 'cumulative' column lists the probability of the Ravens winning at least that number of games.

WINS PROB CUMULATIVE
---------------------------
16   0.00     0.00
15   0.01     0.01
14   0.03     0.04
13   0.09     0.14
12   0.17     0.30
11   0.21     0.52
10   0.20     0.72
9    0.15     0.87
8    0.08     0.95
7    0.03     0.99
6    0.01     1.00
5    0.00     1.00
4    0.00     1.00
3    0.00     1.00
2    0.00     1.00
1    0.00     1.00
0    0.00     1.00 

The stats say 11 wins is the most probable of all win totals for Baltimore (21% probability). Keep in mind however, they're far more likely to finish with some other total (79%). The cumulative probabilities indicate they have a 50/50 chance to finish with at least 11 wins (52%).

Year-to-Year Team Wins

My recent analysis of draft picks and their relative value was complicated by the problem of every team’s tendency to regress to mean. Good teams appear to get worse, and bad ones appear to improve. Because draft picks are allotted according to team record, it is very difficult to tell whether the change team in record was due to the draft picks.

One factor dominates the equation when trying to predict the following year’s record with draft values—the previous year’s record. Teams with high numbers of wins tend to have fewer wins the following year, and teams with low win totals tend to have more wins in the next season. This tendency is strong.

In fact, if you look at a graph of every team’s change in wins from year to year (DELTAWINS) vs. the team’s win total from last year (LASTWINS), you see a very strong trend towards mediocrity, i.e. regression to the mean. The graph includes all teams from 2002-2006.


In fact, between ‘02-’06 no team that had 13 or more wins improved their record the next season, and no team with 3 or fewer wins got worse. Only 1 team with 4 wins earned fewer wins, and only 2 teams with 5 wins got worse.

The reasons for teams to tendency to regress to the mean are likely the obvious ones. First, there is the scheduling system. Each team is given 2 strength of schedule games in which they play the teams that finished in the same order in their respective divisions. First-place teams play the other first place teams, second place teams play each other, and so on. Additionally, there is the draft which allocates draft position in reverse order of win-loss records. Lastly, there may be effects of salary cap boom/bust cycles in which individual teams load up on talented and costly players by amortizing signing bonuses into out-years. This causes teams to 'purge' their rosters of those players, and others, to allow cap room for the dead weight of past signing bonuses.