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Random (possibly meaningless) statistical fact

Posted by Doug on August 3, 2007

I was quickly browsing the 2006 NFL team stats, and I noticed that the league's top scoring team, San Diego, scored many more points (492) than the league's worst defensive team allowed (San Fran, 412). Five teams, in fact, scored more points than the 49ers allowed. On the other end, the league's worst offensive team, the Raiders, scored far fewer points than the league's best defensive team, the Ravens, allowed (168 vs. 201).

A bit more calculation shows that the standard deviation of points scored in last year's NFL was 67.3, while the standard deviation of points allowed was 47.1. In plain English, this means that the defenses were much more tightly bunched around average than the offenses were.

Last season, while a bit more extreme than usual, was not an anomaly. It was the fifth straight year that offenses were more spread out than defenses. If we go back to the beginning of the 16-game schedule in 1978, we find that offenses have been more spread out than defenses in 21 of 29 seasons. Here's the data.

 Yr     PF STD   PA STD
=======================
1978      47.1    50.8
1979      54.7    51.4
1980      59.6    58.7
1981      55.8    62.1
1982      43.4    32.2
1983      71.4    51.4
1984      69.2    63.1
1985      61.6    62.8
1986      59.1    60.6
1987      55.3    47.4
1988      60.1    48.7
1989      57.8    57.6
1990      55.8    64.8
1991      72.7    53.1
1992      63.5    53.8
1993      60.8    47.4
1994      57.8    50.2
1995      57.1    39.2
1996      52.2    63.3
1997      51.1    51.4
1998      81.2    47.9
1999      66.4    61.0
2000      82.3    73.5
2001      57.1    65.5
2002      60.7    54.9
2003      70.3    51.2
2004      68.7    58.7
2005      65.7    58.2
2006      67.3    47.1
=======================
AVG       61.6    54.8

Questions:

  1. Why?
  2. Do we care?
  3. Does this same tendency exist in other sports?

My initial reaction to the first question is that this happens because offense is much more dependent a single person than defense is.

On the second question, I think probably not, but I'd be interested in hearing other opinions.

This entry was posted on Friday, August 3rd, 2007 at 4:41 am and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.