When I went on the Advanced NFL Stats Podcast in late December, I discussed my use of Z-scores to measure the Seattle pass defense. Host Dave Collins asked me if I was planning on using Z-scores to measure other things, like say, Adrian Peterson’s 2012 season. I told him that would be an interesting idea to look at in the off-season.
Well, it’s the off-season. So here’s what I did.
1) For every season since 1932, I recorded the number of rushing yards for the leading rusher for each team in each league. So for the Minnesota Vikings in 2012, this was 2,097.
2) Next, I calculated the average number of rushing yards of the top rusher of each other team in the NFL. In 2012, the leading rusher on the other 31 teams averaged 974 yards.
3) Then, I calculated the standard deviation of the leading rushers for all teams in the NFL. In 2012, that was 386 yards.
4) Finally, I calculated the Z-score. This is simply the difference between the player’s average and the league average (for Peterson, that’s 1,123), divided by the standard deviation. Peterson’s Z-score was 2.91, good enough for 15th best since 1932. The table below shows the top 250 seasons using this method from 1932 to 2013; it’s fully searchable and sortable, and you can change the number of entries shown by using the dropdown box on the left.
The Z-score is a good substitute for something like “how crazy was that season?!” And it’s hard to argue with O.J. Simpson’s 1973 season as the craziest. John Brockington was second in the NFL in rushing…. with 1,144 yards. For perspective, consider that in 2012, Alfred Morris, Marshawn Lynch, and Jamaal Charles all topped 1500 rushing yards, so Peterson’s stellar season isn’t quite the outlier.
The Z-score is a nice way to compare across eras and give some love to some forgotten seasons. Joe Perry led the NFL with 1,049 rushing yards in the 12-game 1954 season; his San Francisco teammate John Henry Johnson was second in the league with 681 yards! One might find this sort of analysis useful in Hall of Fame debates. For example, Terrell Davis had three very good years, coming in at 1.9+ standard deviations from the mean in 1996, 1997, and 1998. Jerome Bettis rushed for more yards than Davis, but he has just one top-100 season by this method, and only two top-250 years.
Walter Payton leads the way with 9 top-250 seasons, while Jim Brown is the leader with 8 top-75 seasons (Eric Dickerson, Steve Van Buren, and Emmitt Smith are all tied for second with four). Barry Sanders, Payton, and Brown are the only players with seven top-150 seasons.
Among 2,000 yard seasons, Jamal Lewis receives the lowest Z-score. That’s because the spread among top running backs was very wide that year, which occurred in the heart of the stud running back era. Ahman Green rushed for 1,883 yards, and LaDainian Tomlinson and Deuce McAllister each rushed for over 1,600 yards, while the leading rusher on every other team but Baltimore still averaged nearly 1,100 yards.
