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. [↩]

{ 24 comments… add one }

Excellent work, Chase. You mentioned that your findings concurred with some previous analysis (by ANS and FO). I just wanted to note that it also concurs with Keith Goldner’s findings here: http://www.drivebyfootball.com/2011/04/ratio-of-relative-importance.html

Goldner calculated:

Offense = 50.68%

Defense = 33.00%

Special Teams = 16.32%

Again, removing special teams, this is 60.56% Offense to 39.44% Defense.

Very cool. That’s a good article by Keith, and it does reinforce the 60/40 split.

This could be stupid and totally wrong, but I have a question about offenses having a higher distribution than defenses. It seems like the nature of points in football could explain at least some of this. A really great defense has a ceiling on how great their game can be. They can allow 0 points; they obviously can’t do any better than that. And, also obviously, the same isn’t true for offense. Great offensive games can be differentiated when one team scores 49 points and another scores 56. However, two shutouts are measured equally despite possible variations in performance. This would only really be relevant in situations with shutouts, and those are pretty uncommon. But is there a chance it explains….1-2% of it?

” A really great defense has a ceiling on how great their game can be. They can allow 0 points; they obviously can’t do any better than that”

That’s not entirely true. A defense could allow a net of -7 points by posting a shut-out and returning an interception for a touchdown. A defense could also put its offense in a better spot with better field position, either from stopping drives quickly or forcing turnovers.

An insane defense could force the offense to take a loss in yardage each play. It’s not very practical to ever expect a defense to do this, but that’s how bad the Cardinals offense was last year once Kolb went out: http://www.thebiglead.com/index.php/2012/12/13/the-arizona-cardinals-should-just-stop-playing-with-a-quarterback/

It’s also worth noting that as a technical matter, neither Aaron’s nor Brian’s system has the same “floor” with respect to defensive ratings. And they land in the same spot.

I’ll have to think this over — maybe Neil or Doug will chime in, as I know they lurk in the comments.

Note that a somewhat similar point was brought up by Doug seven years ago when he discussed some of the drawbacks to the SRS in his first post on the topic:

That’s one of the reasons we also use things like Pythagorean record, which is not biased against defensive teams because it squares points squared and points allowed. And I essentially used the same formula when I measured the variance.

I took the square of the standard deviation in points scored and divided it by the sum of the square of deviation in points scored and the square of the standard deviation in points allowed. Over the last five years, this tells us that 61% of the variation is due to points scored.

Offenses appear to have a wider distribution than defenses because offensive production is made up of 3/5 offense and 2/5 opposing defense, while defensive production is made up of 3/5 opposing offense and 2/5 defense. Since over the course of a season, that 3/5 number (for defenses) is going to get pretty close to league average, that will naturally shrink the width of the distribution. (Note that this is not an argument I’m making, just restating the conclusion.)

Does the info account for defensive scoring (int/fumble returns), special teams (kickoff/ punt returns) and then adapt offensive scoring accordingly. For example, the Patriots-Titans game you cited included a fumble recovery for a td. It hardly seems fair to credit Brady and his offence for that!

IKCL,

No, this is simply points scored and points allowed. I am not concerned that the results would change materially if we removed those things.

I totally agree with the general thrust of the article. As you say it’s fairly common knowledge that offense matters more than defense. But I’m not sure this helps us define what “more” is as much as you claim it to. I feel like ignoring the aforementioned factors greatly undermines what you’re attempting to prove.

I know you acknowledge this, but I think merging scoring with offense dilutes your point considerably.

I can probably re-run things in a future post. Neil is also working on a separate post on this, although it won’t address your point.

Thanks for your reply, enjoyed the article! Looking forward to the next one.

Just out of curiosity I ran the numbers for 2012, to see how much impact non-offensive scores had. This chart shows: Total Points scored, Defensive Points scored (% of total points), Special Teams Points (% of total) and then percentage of non-offensive points.

[Chase edit. You need to wrap the data in pre tags (<>) for it to format properly.]So Tennessee and San Diego scored nearly 20% of their points from offense and special teams! While Pittsburgh, Philadelphia, Detroit, Oakland and Jacksonville all got 7 points or less production outside their offense.

Leaguewide, nearly 8% of scoring came from Defense+Special Teams.

I agree with IKCL’s comment: if you are trying to measure the impact of offense versus defense, you would have to only include offensive scores and would have to find a way to account for defensive scores. And what about situations when the defense creates a short field with a turnover, the offense doesn’t move the ball, and they kick a field goal? That does not accurately measure the impact of the offense. Similarly, turnovers by an offense that set up a short field for the defense should not be solely chalked up against the defense “points allowed.” Your comment “I recognize that I am using offense as a synonym for scoring, which is not appropriate. Nothing bad will happen as a result” sums up the problem with this post – the fact that you conflate the two throws off the whole analysis.

MJP,

I might be inclined to re-run the numbers after crediting defenses with defensive touchdowns and removing non-offensive touchdowns from what is credited to offenses. But as you imply, that doesn’t get us all the way, either.

The reason I said ‘nothing bad will happen as a result’ is that both Football Outsiders and Advanced NFL Stats measured purely offense and defense, and came to the same general answer. I also don’t think the “errors” in the data would be likely to prejudice things very much if at all.

Another advantage of offense is that it is more consistent from season to season, meaning not only is a great offense more likely to produce wins in year N than a great defense, it’s also more likely to remain great (and therefore continue producing wins) in years N+1 and N+2. You see this a lot in the most consistent teams in history. Indy won a dozen games in a record 7 straight years on the back of an elite offense and a middling defense. New England has won double digit games every year for a decade with an offense that on average ranks 5.3rd in points scored and 6.2nd in yards gained, and a defense that ranks 7.1st in points allowed and 15.4th in yards allowed (and this is with 2003 tanking the averages- since then, New England’s offense has been top 10 in every season and their defense has been… not). Pre free-agency, teams like San Francisco were able to build much longer sustained runs of dominance, but even then you’ll notice that their offenses were far more consistently great than their defenses. The Steelers since 2000, on the other hand, are a fantastic example of what a team built on a dominant defense looks like- much less consistent from season to season, more likely to perform poorly and miss the postseason, and much less consistent dominance from its primary unit.

If I were to posit the reason why offense was more consistent from year-to-year, I’d start with the fact that no one player is more responsible for the success of his unit than the QB is for the offense, and giving disproportionate weight to that one variable would be expected to reduce random fluctuations. Either way, if I were building a team from scratch, I would focus on building an elite offense and worry about improving my defense later. If you go the other way around, by the time you get around to improving your offense, your defense has already started to regress.

Agreed.

Ok, sorry I did not realize that the formulas measured defense in a more complicated way. Sounds like it may be understating defense, but not because of anything relating to shutouts specifically.

After reading some of the comments, I thought of a specific example where team’s offensive output is probably fairly overrated. Take the Bears from say, 2006-2013. You’d have to find a specific year in there where Devin Hester and the defense were both at the height of their powers (something, that sadly, rarely overlapped). Off the top of my head, either 2006 or 2011 might be the closest thing. Regardless, this is clearly an offense that is getting gobs of help from defense and special teams. The defense is creating loads of turnovers to either score points or give the offense great field position. And on top of that, the field position is even better because kickers are literally just squibbing the ball instead of actually kicking it away, and punters are kicking it 20 yards sideways and out of bounds.

This case is probably somewhat anomalous, as the convergence of a guy like Hester and a defense that voraciously creates turnovers like Lovie Smith’s Bears is pretty hard to replicate. But it’s a long winded way of saying, I wonder if field position could be factored in to paint a more accurate picture.

Scott,

Yes, Burke and Schatz both created metrics that are neither points nor yards; they are simply measures of offensive and defensive effectiveness (Football Outsiders also measures special teams). Both of their methods factor in field position and things like that.

PFR also has their own version of EPA (slightly different than Burke’s model). I could probably run the numbers using that as the input. The question then becomes, should EPA or points scored be the output?

Ok thanks, that’s clearer now.

Seems like EPA is a more accurate picture; what would the argument be to use points instead?

Just checking – do you have any photos that aren’t Brady & Manning?

Hey, at least this is a

differentManning/Brady photoIf the Patriots averaged 35.4 points per game, they should be expected to score 35.4 points per game against the average defense; they should be expected to score more than 35.4 points per game against a below-average defense like the Titans. Certainly more than 33 points.

Suppose the average offense scores N points per game, the Patriots are averging X points per game, and the Titans are giving up Y points per game. A very rough estimate of what the Patriots should score against the Titans is not (X + Y)/2. Rather, it is N + (X + Y – 2N)/2.

That’s a good point.

I re-ran numbers using:

— PPG for Team A above average in other 14 games as my 1st input

— PPG allowed for Team A_opp below average in other 14 games as my 2nd input

— Points above average scored by Team A against Team A_opp as my output

I forced the constant to be zero; the best-fit formula was 0.622*Team A + 0.469*Team A_Opp

Based on your very rough estimate, you would expect the coefficients to equal close to 2 (i.e., we just say the Patriots are 12.6 PPG above average, the Titans are 7.0 points below average, therefore NE should score 19.6 points more than average when playing TEN.) As it turns out, the coefficients only add up to 1.1. Interesting.

The more on-point issue for this post would be that the ratio of Team A to Team A_Opp is 57%, in line with our other numbers. You should also check out Neil’s post today: http://www.footballperspective.com/another-note-on-the-relative-impact-of-offense-vs-defense-on-scoring/

Sorry, that last formula should have been X + Y – N. (I should not have divided by 2.) That’s what happens when I post past my bedtime.