Top Offenses > Top Defenses

Here are three graphs I posted recently that plot each team's defensive performance against its offensive performance. Each graph uses a different metric:  Success Rate (SR), Expected Points Added (EPA), and Win Probability Added (WPA). Instead of looking at the connection between offensive and defensive performance, look at the shape of the pattern formed by the data. Notice that the width of each plot is bigger than the height. In other words, offenses have wider distributions than defenses in SR, EPA, and WPA. The data set is comprises all 2000 through 2009 regular season teams.


In terms of SR and EPA, the best offenses are "better" than the best defenses in terms of performance. And in terms of WPA, the best offenses have bigger impacts on game outcomes than the best defenses do. This is something I wrote about three years ago, when I noticed that the distribution of yards-per-play efficiency was wider for offenses than for defenses. Now, in terms of more advanced statistical measures in a broader set of data, the same trend holds.

A variable's standard deviation (SD) is a measure of the width of its distribution. The ratio of the SD of offensive SR to the SD of defensive SR is 1.25. The ratio for EPA is 1.27. And the ratio for WPA is 1.26. Offenses are spread out 25% wider than defenses in terms of performance and impact on outcomes.

The reason, I suspect, is that most of the offense flows throw the QB or RB. The QB in particular is singularly critical to offensive success. The QB is responsible for much more than just throwing passes. He calls audibles, reads the defense, calls blocking assignments, and is responsible for organizing and managing the offense. Nearly every play an offense makes is heavily dependent on the skill of a single player.

On defense, success depends on a more equal division of responsibility. The wider the division of responsibility, the more "average" the success of the squad. In individual-player sports such as tennis or golf, individuals can dominate the field for many years. Federer or Woods did not have their talent level diluted by less dominant teammates. A five-man bball team can be "star-based" because there are only four other players to dilute the skill of the star.

But football teams average their talent level over at least 22 starters. The QB, and perhaps to some degree the RB, are the exceptions. Because offensive players do not make equal impacts on the outcomes of plays, the effective talent level is less diluted. The result is that the distribution of offensive success is wider than that of defensive success. The best offenses therefore tend to be better statistically than the best defenses.

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20 Responses to “Top Offenses > Top Defenses”

  1. Adam Davis says:

    I would love to see this taken one step further, showing the *aggregate* Defensive + Offensive stats versus actual wins. My theory is that, while offensive proficiency may generally be more valuable than defensive proficiency, the most successful teams tend to be those that have the best combined proficiency. In other words, sure, offensive is very important to success, but if your defense is absolutely atrocious, you're still going to have a very hard time climbing the mountain.

  2. Adam D says:

    Another bit of evidence for your theory is that points scored is generally closer to the offense's average than the opposing defense's average. Obviously there's more luck/error/stdev involved there because points are more unpredictable than efficiency stats, but points are much less work :)

    BTW my name's Adam Davis too! What are the odds...

  3. SportsGuy says:

    There are other sports where the offensive variability exceeds the defensive side. Its true in the NBA too, or it least it was when I looked at it back in the early 90s.

  4. David Hess says:

    I imagine it's partly due to the offense being the team in control of the ball. They get to pick the method of attack (pass/run/option), and the defense has to react. So defenses are by necessity generalists, while offenses are specialists.

    The defense may be really good at a couple things, but the offense can plan around that, and the defense only gets a couple plays a game that are right in their wheelhouse. Meanwhile, the offense goes to their strength as many times as they choose. So even an equal distribution of strengths/weaknesses leads to more variation in the offensive numbers (if I'm thinking about this correctly).

    That would explain why, as SportsGuy pointed out, you see this in other sports as well. For example, right now in college basketball, Pomeroy's adjusted offensive efficiencies have a larger standard deviation than the defensive efficiencies, with a similar ratio as that in the NFL: 1.20.

  5. Jim Glass says:

    the best offenses are "better" than the best defenses ... The reason, I suspect, is that most of the offense flows throw the QB or RB. The QB in particular is singularly critical to offensive success

    I'll take this as a good part of it, and David Hess beat me to the other part. The offense specializes in what it wants to do, the defense has to prepare for everything -- which limits specializaion in schemes, practice and personnel.

    Take the Navy football. It's offense can focus on the Navy version of the option exclusively. The defense has to be able to play against everything from the wishbone to the west coast, spread, whatever, usually on a week's notice. Specialists hit higher levels of performance.

  6. JMM says:

    Should there be a "zero-sum game" type thing going on here?

    I would have expected a play to result in a success for either the "O" or the "D".

    What am I missing?

  7. Anonymous says:

    JMM, the total SR for offense and defense are opposites. The difference is in the spread between the worst and best.

    Take an example of something the defense shouldn't affect, say FG%. Say the league average is 75% (for illustration purposes only). Each KICKING team has their own kicker. So the best team has a 90% kicker and the worst has a 60% kicker. The spread is from 60 to 90 for the kicking team. However, from the defensive perspective, you face all kickers, so every team's OPPONENT FG% should be right around 75%, say 70% to 80% with random variation factored in.

  8. Brett says:

    Look at the way teams are built. Usually the defensive scheme is installed, then the team tries to acquire players who fit the scheme, and these are not necessarily the best available players. For example, Dwight Freeney would not be a successful DE in a 3-4 scheme, and he is probably not good enough in coverage to play OLB. I think this causes the good defensive players to be distributed more evenly among different teams. On offense however, most players play equally well in any scheme, as offensive schemes in the NFL are not as diverse as defensive schemes, so teams simply try to acquire the best available players at the positions of need.

  9. Anonymous says:

    Not to be nitpicky, but where is the evidence to back up a statement like "Dwight Freeney would not be a successful DE in a 3-4 scheme."?

    This is less an attack against an unqualified statement and more a statement of an unqualified critic. Basically, I'm curious as to what the reasoning is.

  10. Jim Glass says:

    It may be worth mentioning the explicit value of having the initiative. In tennis players with the serve win more points than players returning it. In chess the players have perfectly symmetrical resources (with no complications from chance factors such as pawns that miss blocks, rooks that fumble, or the wind blowing a knight to the wrong square). In matches between strong players who alternate taking white and black, white scores significantly higher. The sole factor causing this is that white has the first move -- which gives white more influence in choosing the style of play and the "field of battle", so to speak, for the contest. In football the offense has this advantage of the initiative against the defense.

  11. James says:

    I disagree with the first initiative explanation as that does not explain why there are more bad offenses then bad defenses. If getting to choose the play was such a big advantage you would expect the opposite pattern i.e. more bad defenses as even a bad offense can target a defense's weaknesses. And so a bad defenses would be really bad.


    I think the star player effect is a more likely explanation.

    What is the variaiton in any of these metrics if two even teams played each other 100s of times. That would allow you to determine the relative differences in skill between offenses and between defenses using the approach Tom Tango used in THE BOOK i.e. total variance = skill varinace + random variance.

  12. Brett says:

    Anonymous, obviously there is no hard evidence that Dwight Freeney would be less successful in a 3-4 scheme since he has never actually played in one. He was just the first player I could think of with a very specific skill set which allows him to be successful in a 4-3. What he does best, racing past the left tackle in passing situations, is simply not what DEs are asked to do in a 3-4. A great athlete like Freeney could probably adapt his skill-set and become a serviceable 3-4 end, but we're talking about one of the greatest pass rushers of the last decade. "Serviceable" would be a huge downgrade.

  13. Jim Glass says:

    I disagree with the first initiative explanation ... If getting to choose the play was such a big advantage you would expect the opposite pattern i.e. more bad defenses as even a bad offense can target a defense's weaknesses.

    I don't see how that necessarily follows. Statistically, if I have an offense that's great at forcing mismatches to rip Ds apart, that boosts my O's stats 16 of 16 games but hurts opposing Ds' stats only 1 or 2/16ths each, so my O's numbers shoot up out of the pack but the opposing Ds' numbers remain clumped together as we see. Same in reverse if my O is so bad it can't use the initiative at all -- force mismatches or control the clock when ahead if it ever gets there. Then it is definitionally bad (not average so it can beat up on defenses anyhow) with the same statistical effect.

    In my undeducated opinion the three ideas mentioned in these comments - "star player", "specialist-generalist", "initiative" - seem entirely consistent with each other and probably all are true and interact. E.g., if Peyton Manning rips apart a top D by ignoring the CB who is Revis and incinerating the one who isn't (as in last year's AFC title game) that's a star player exploiting the initiative. If the opposing QB is a Kellen Clemens trying the same thing, there's going to be pretty big gap in results.

  14. Jim Glass says:

    Or in simplest terms: offenses will vary in their ability to utilize the initiative against Ds. With no corresponding variation in the performance of Ds, the existence of the initiative will cause O performances to vary more widely than D performances, other things equal ... And while Freeney might be OK in the right 3-4, nobody would want to use him as the typical two-gap 3-4 DE whose job is to stand-up the OL players and effectively block for the linebackers.

  15. Anonymous says:

    I don't know a lot about advanced statistics, but seems like the information given suggests that the greater importance is placed on QB's, as opposed to offenses in general. It is the QB that has the greatest effect on the offense, and the QB faces the defense taken as a whole. So would it best fair to ask whether or not it's rather the best QB's are more valuable than the best defenses? This would seem to hold with conventional "wisdom".

  16. Anonymous says:

    I'm not able to challenge the math, but since preventing a touchdown has as much value as scoring a touchdown, I can't see how an offense can have more impact on winning than a defense

  17. Anonymous says:

    Couldn't it be as simple as saying that football in general plays more into the defense's favor. It is statistically more difficult to get a first down, score a touchdown, etc. than it is to stop these from happening, therefore offenses that can do these things at a higher rate than other teams create much more value toward winning?

  18. Anonymous says:

    I think this has something to do with the average score in Football being a relatively low number. The best performance a defense can have is to limit an opponent to 0 points, while an offense has no limit. With a low average score, there are occasions where an excellent defense hits the lower boundary for opponent points - thus limiting the outliers and standard deviation of the distribution. That natural limit would seem to force the best defenses to be closer to average than the best offenses.

  19. Anonymous says:

    So do you still think this applies? The Seahawks have dominated the top offense in the league on several occasions. The Broncos were lucky to score at all, and the Seahawks did the same thing to other top offenses in the past 2 years.

  20. Anonymous says:

    Anonymous says:
    Saturday, March 01, 2014
    So do you still think this applies? The Seahawks have dominated the top offense in the league on several occasions. The Broncos were lucky to score at all, and the Seahawks did the same thing to other top offenses in the past 2 years.

    It's based on averages. A few specific cases don't trump the general. I was arguing with someone about this a few weeks ago, and he just kept bringing up special cases and ignoring the big picture.

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