So exactly *what percentage* of the points scored by a team in any given game is a function of the team, and what percentage is a function of the opponent? There are several ways to look at this, but here’s what I did.

1) I looked at the number of points scored and allowed by each team in each game in the NFL from 1978 to 2012.^{1} Since teams often rest players in week 17, I removed the 16th game for each team from the data set.

2) I then calculated the number of points scored by each team in its other 14 games. This number, which is different for each team in each game, I labeled the “Expected Points Scored” for each team in each game. I also calculated the expected number of points allowed by that team’s opponent, based upon the opponent’s average points allowed total in *their* other 14 games. That number can be called the Expected Points Allowed by the Opponent.

3) I performed a regression analysis on over 10,000 games using Expected Points Scored and Expected Points Allowed by the Opponent as my inputs.^{2} My output was the actual number of points scored in that game.

**The Result**: The best measure to predict the number of points a team will score in a game is to use 58% of the team’s Expected Points Scored and 42% of Expected Points Allowed by the Opponent of the team.

Week 1 last year saw this game between the Patriots and Titans; we didn’t know it at the time, of course, but New England in that game would be expected to score more points than any other game in my data set. This isn’t surprising: in 2012, the Patriots finished 1st in points scored while the Titans 32nd in points allowed. New England averaged 35.4 points in games 2 through 15 last year, while the Titans allowed 29.8 points over that same stretch. Using the 58/42 formula, we would project the Patriots to score 33.0 points. In reality, they scored 34.^{3}

So if the answer is 58%, why does today’s post say 60%? If we do the exact same study but only use data beginning in 2002, a team’s Expected Points Scored becomes responsible for 5/8ths (62.5%) of the projection for that team in any one game. That number holds if you look at the last five years or the last three years, too (although the number dipped to 61.1% last year). Here we have the traditional tradeoff between larger data (going back to 1978) or more relevant data (going back to 2002); I’ll split the baby and say Team A is responsible for 60% of the points scored by Team A in any given game, while Team B is responsible for 40% of the point scored by Team A.

Note that this result jives with an old Advanced NFL Stats article. There, Brian Burke noted that the best offenses are “better” than the best defenses in that their distributions are wider. He found that whether you examine success rate, expected points added, or win probability added, offenses are spread out roughly 25% wider than defenses in terms of performance and impact. Note a ratio of 1.25:1 is akin to saying offenses are responsible for 56% of the deviation.

I went ahead and did some standard deviation calculations of my own. The standard deviation of points scored per game by teams across the league, from ’78 to ’12, was 4.3 points per team; conversely, the points allowed per game by teams was just 3.7.^{4} If you square those standard deviations, you get the variance, and if you divide the variance in points scored (18.2) by the sum of the variance in points scored and points allowed (18.2 + 13.7), you get 57%. This would tell us that 57% of the variance in scoring in the NFL comes from the scoring team, which is another source of confirmation that offenses^{5} in general are responsible for 4/7th to 5/8th of the game. If we go back to only 2002 and measure the variances, Team A becomes responsible for 61% of the scoring deviation in the NFL (which remains true if you measure the data over only the last five or last three years, too).

None of this should be shocking, but there’s utility in precision. We know that Peyton Manning makes an offense great, and I think most fans know that offense “matters more” than defense. This just helps us try to define what “more” means.

I e-mailed Aaron Schatz, founder of Football Outsiders (you can read my interview with him in November here) to see his thoughts. Aaron noted that the classic Football Outsiders statement has always been that winning football games is 3 parts offense, 3 parts defense, and 1 part special teams (although Aaron mentioned that recent research indicates that a 4/3/1 model is probably more appropriate); however, the strongest offenses are better than the strongest defenses, and the weakest offenses are worse than the weakest defenses (this matches Burke’s point). Aaron continued:

If there’s a larger range in performance on offense, it suggests that it is more important to build a good offense than a good defense, because an offense that is in the 90th percentile will be better than a defense that’s in the 90th percentile. So if you look at the range of DVOA the last few years, taking out outliers, you end up with these ranges:

offense -35% to 35%

defense -30% to 25%

special teams -8% to 10%That gives you the a split of (49/38/13) instead of (43/43/14). And if you take out special teams, that comes out close to your 60/40.

Pretty neat.

- I removed the 1982 and 1987 seasons due to the player strike, and I also removed the 1999, 2000, and 2001 seasons. In those three years, the NFL had an odd number of teams, and therefore removing the last week of the season was going to make things messy, so I just opted to delete them. [↩]
- For technical geeks, I also chose to make the constant zero. We don’t care what the constant is in this regression, we just want to understand the ratio between the two variables. [↩]
- Because I know someone out there wants to know what were the craziest outliers… you can look towards this 1980 Bears/Packers game. Chicago scored 16.4 points in its other 14 games while the Packers allowed 20.4 points; in that game, the Bears scored 61 points. The the 58-0 Seattle/Arizona game in 2012 was the biggest positive outlier last year. The biggest negative outlier came last season, when a good Bucs offense faced a horrendous Saints defense and came away empty-handed. [↩]
- To be clear, this means taking the standard deviation of the points per game average for each team in the data set. [↩]
- I recognize that I am using offense as a synonym for scoring, which is not appropriate. Nothing bad will happen as a result. [↩]

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