Can Late-Season Momentum Explain Playoff Upsets?

Outcome bias is a powerful habit in forming mainstream opinion, and one of the most common NFL-related ones entails "momentum."  It's easy to look at a team that wins the Super Bowl and point to a late-season three-game winning streak as a sign that the future champs "figured things out" or "got the ball rolling."  Fill in your favorite cliche and voila, instant storyline.

But how often does so-called momentum play a role in playoff success?  This isn't a new question, and many analysts and fans have realized that success at the end of the regular season is not a prerequisite for a deep postseason run.  Last season's Baltimore Ravens won it all despite losing four of their final five regular season games.

Lambeau Madness & Twitter Outcries

With a little over five minutes remaining in the 3rd quarter, down 17-14 to the Steelers, the Packers had their field goal blocked only to have chaos unleashed at Lambeau. I won't go into the details, but essentially it was ruled that the Steelers never had full possession (when they did and should have been determined down by contact) and then due to an illegal batting out of bounds, the Packers got the ball back with a fresh set of downs, 1st-and-Goal from the 2-yard line.

All holy heck has broken loose in Green Bay.
— Rich Eisen (@richeisen) December 22, 2013

Twitter erupted. Everyone was outraged at the blasphemous call. And even more, everyone was outraged that possession was an unchallengeable call. All over the place, people were comparing it to the Seattle/Green Bay replacement ref debacle from last season.

Playoff Clarity

Sam Waters is the Managing Editor of the Harvard Sports Analysis Collective. He is a senior economics major with a minor in psychology. Sam has spent the past eight months as an analytics intern for an NFL team. He used to be a Jets fan, but everyone has their limits. 

The NFL season might only be nine weeks old, but the league’s playoff picture is already starting to gain clarity. Having a playoff picture that is too clear, too early, might make games a little less exciting, so I thought it would be interesting to see if this year’s playoff qualifiers really are more certain at this point than in past years.

We can start to attack this question using the projections at nfl-forecast.com, which use the team efficiency ratings here at Advanced NFL Stats to estimate each team’s chances of making the playoffs. According to these projections, eight teams currently have a probability of playoff qualification higher than ninety percent. While these teams (like Denver, Kansas City, and Seattle) are virtual locks, we have thirteen teams with a ten percent chance or less of qualifying, leaving us with a pretty polarized distribution of playoff odds after nine weeks of play:

The Importance of Playoff Seeding

This is the time of the year for joy and family and gifts--all that good stuff. But more importantly, it’s also the time for teams to jockey for playoff seeds. I get the sense that the conventional wisdom is that yes, seeds are somewhat important, but the notion that ‘just get in the playoffs and anything can happen’ is the dominant view. But as we'll see, seeding is critically important.

We’ve seen many wildcard teams make it to, and even win, the Super Bowl. There are four wildcard berths each year, and when we see a wildcard team make it to the Super Bowl, it’s noted, highlighted, and becomes part of the team narrative. No one remarks when the #3 seed makes it to the big game, despite it being less likely than either of a conference’s two wildcard seeds to make it.

Although it’s certainly true that ‘anything can happen’, that’s really only true from the perspective of a neutral observer. If you’re looking at the chance that any one of the four wildcard teams make it to the Super Bowl, you’ve got a pretty solid chance of seeing that happen. But if you look at it from the perspective of one particular wildcard team, your chances of going to the Super Bowl are relatively slim. It’s all a matter of perspective.

Football commentators certainly understand that seeds are important—a team would always prefer a higher seed. But I sense that they don’t fully appreciate how critical seeds are in the current NFL format. I hear talk about having home field advantage and having a week off to get healthy, but commentators seem to overlook the most important part of a playoff bye: It’s an automatic win in the first round. Maybe it’s overlooked because it’s so obvious, but those other considerations pale in comparison to the value of a free win. Right away, a bye practically doubles a team’s chance of making it to the Super Bowl. Doubles. A different way of thinking of the playoff format is that the top two seeds are the only two that actually ‘make the playoffs’, and the other four seeds must first win a play-in game.

To isolate just how critical seeding is, I calculated the chances each seed would make it to the Super Bowl due to seeding alone, ignoring differences in team strength.

Super Bowl Winner Stats

Last year I looked at how often teams won playoff games based on their season-long performance in various categories. I basically looked at how predictive various stats are in forecasting playoff wins. For example, how often does the team with the better passing efficiency win? I learned some interesting things such as how important run defense appears to become in the playoffs.

This time around I looked at just Super Bowls. How often does the team with the better season-long performance in each category win the big game? The sample size is very small, but the Super Bowl is a unique game in many ways, so we might learn something.

I only looked at Super Bowls since Super Bowl XV, the 1980 game between the Raiders and Eagles. In 1978, the passing rules changed and significantly altered the sport, but the league did not adjust for another couple years. Yes, this shrinks the sample to just 28 games, but I’m not going for statistical conclusions, just an initial look to see if anything stands out. No fancy regressions this time, just straightforward percentages.

The results are in the table below. You can read it as saying “the team with the better [efficiency stat] won the Super Bowl [x%] of the time.”

Stat	Win %
O Pass	50
O Run	57
O Int	61
D Pass	61
D Run	46
D Int	54

I’m a little surprised that the team with the better offensive passing efficiency only won 50% of the time. I’d think that would be a fairly solid advantage. Defensive passing looks like it might be the more important category.

Also, defensive run efficiency doesn’t appear to hold the same importance that it has in the playoffs lately. The better run-stopping team only won 46% of the time.

But again, we can’t really draw any conclusions. There are only 28 games in the sample, so a single game swings the percentage by about 3%.

In case you’re curious, the Steelers have the advantage in offensive running and all the defensive categories. The Cardinals have the better offensive passing efficiency and the lower interception rate.

Year of the Run Defense?

Before the playoffs started last year, I did a post on which facets of team strength are most decisive in the playoffs. I looked at passing offense and defense, running offense and defense, turnovers and penalties. For each game, I tabulated how often the team with the better season-long performance in each stat won the game. For example, in the playoffs, the team with the better season-long offensive interception rate won the game 58% of the time.

I also looked at playoff-caliber match-ups in the regular season. Playoff-caliber was defined as teams that would finish with 10 or more wins. I wanted to see if there was something special about "playoff football" beyond the fact that there are (usually) only good teams on the field.

The most intriguing result was the sudden importance of run defense. Teams with the better defensive run efficiency won regular season playoff-caliber games 48% of the time. But in the playoffs, teams with the better run defense won 67% of the time.

This year, the four remaining teams in the playoffs feature the #2, #4, and #5 best run defenses in the league. The team with the better defensive run efficiency has won every single playoff game but one so far this year. That's 7 for 8.

But I'm not sure this means anything. My analysis only used 5 years of data--55 playoff games. This year obviously supports the notion that run defense somehow takes on special importance in the playoffs. But 2007 showed the opposite. Only 2 of 9 games were won by the team with the superior run defense. Two more games were pushes.

Still, that's 64% overall for the 2002 through 2008 seasons. You'd expect a team stronger in any category to win more often, but 65% is the highest of all the core abilities including offensive passing, offensive running, defensive passing, and even turnovers. It's particularly remarkable because run defense seems relatively insignificant in the regular season.

I'm not sure what causes the effect. It could be just random variation and small sample size. But the effect might be real and it could be due to weather or even conservative gameplans. (We could call that the Schottenheimer Effect.)

Cold Weather Effect on Scoring

In a recent post I theorized that the sudden importance of run defense in the playoffs might be due to cold weather. This post will continue that line of analysis and look at the effect of cold weather on scoring.

The past weekend's conference championship games were played in frigid weather. It seemed that expert after expert remarked that cold weather would keep the scoring down. Certainly it makes sense to anyone who's played sports in extremely cold weather. It definitely makes it harder to throw, catch, and even kick. But it's just as cold for defenses as for offenses. So does cold weather really keep NFL scores lower?

Here are the average home and visitor scores for various circumstances. The first column is for all regular season games in the 2002-2006 seasons (n=1280), and the second column is for those games played in cold climates (n=114), as defined here. Since many playoff games are played in cold weather, the third column is for all playoff games (n=50+5). (Super Bowl scores are not included because there is no home advantage.)

	Reg. Season	Cold	Playoff
Home	22.3	22.5	25.0
Visitor	19.8	18.6	19.9

The second table looks at scores from the same sets of games differently. The average scores of the winning and losing teams are listed. (Super Bowl scores are included as playoff games here.)

	Reg. Season	Cold	Playoff
Winner	26.8	27.0	28.9
Loser	15.3	14.1	16.5

Cold weather doesn't appear to have a large effect on scoring. It seems to slightly enhance the spread between winner and loser by depressing the score of the loser. This is likely due to the "dome at cold" effect discussed in previous posts.

Playoff scores are generally higher, both in terms of winner and loser, and for the home and visiting teams.

It doesn't appear that cold weather reduces scoring.

I can understand where the perception might come from. Because dome teams are at a disadvantage playing outdoors in cold weather, it follows that they would score less. Many competitive dome teams in recent years have been ones with fast-scoring offenses. The Vikings, Rams, and Colts of recent memories all featured very strong offenses. When these teams were competitive late in the season (and when people were paying attention to them), they would be expected to score less when playing outdoors. But this effect on dome teams would be limited to these specific circumstances and not affect teams in general.

When the Giants played in Green Bay or the Chargers played in Foxboro yesterday, we should not have expected low scores due to the cold temps. Although the frigid sub-zero temperatures yesterday were extreme, even for Green Bay standards, the point is that the weather affects both offense and defense.

Run Defense Dominates in the Playoffs

In the last post I indirectly analyzed playoff games by looking at regular season games that only featured opponents who both went on to win at least 10 games. We saw that teams with the better running games actually won less than 50% of the time.

In this post, I'll look at actual playoff games directly. Compared with the 114 "good vs. good" regular season games I looked at yesterday, there were 50 playoff games, plus 5 Super Bowls, in the 2002 through 2006 seasons.

The table below lists the winning percentage of the team with the superior season-long performance in each stat. In other words, the team with the better [stat] won [x] percent of the time. The regular season good vs. good match-ups are also listed for comparison. (The home win percentage excludes the five Super Bowls during the period.)

Stat	Good vs Good	Playoffs
Home	59.6	64.0
O Run	45.6	45.5
D Run**	48.2	67.3
O Pass*	52.6	63.6
D Pass	51.8	56.3
O Int Rate	50.9	58.1
D Int Rate	55.3	58.1
O Fum Rate**	55.3	40.0
D FFum Rate	54.4	54.5
Pen Rate	47.3	52.7

** = good vs. good / playoff difference is significant at the p=0.05 level
* = good vs. good / playoff difference is significant at the p=0.10 level

The home team won more often in the playoffs than in good vs good regular season match-ups, which is expected because higher seeded teams host the playoff games.

The team with the better run efficiency won only 45.5% of the 55 playoff games during the '02-'06 period. Keep in mind the small sample size could make these results misleading. 45.5% is only 2.5 games below 50%. But the result echoes the same result for the regular season good vs. good match-ups.

Defensive run efficiency is a different story. Although the team with superior run stopping ability won only 48.7% of the regular season good vs. good match-ups, it won 67.3% of playoff games. This is a striking difference to say the least, especially considering how unimportant run defense is based on regression models of regular season games.

The passing game stands out as well. Both offensive and defensive passing stats appear to be more important in the playoffs. Interception rates also appear very important.

Another striking result is that of offensive fumble rates. The team with the lower fumble rate wins only 40% of playoff games. As one of the more random stats, it's not too surprising to see a spurious result for fumble rate, but 40% is fairly low, even for such a small sample size.

I suspect that coaches may become too conservative in the playoffs, relying on the run. This might explain why having a good running game doesn't help teams win and why the ability to stop the run suddenly becomes very important in the playoffs.

My own gut feeling is that coaches don't coach to win. They coach to avoid a loss. It sounds inane, but there is a difference. Maybe the play-calling in the playoffs becomes even more timid. But then again, perhaps the January weather has something to do with it. Previous research has established the importance of climate, especially when dome teams play outdoors. Weather may explain the 67% win percentage of teams with the better run defense. Defense may win championships after all, particularly run defense.

Maybe Defense Does Win Championships...

...but the running game probably doesn't help at all.

I previously thought that the "defense wins championships" theory was conventional wisdom bunk. But after doing a new analysis, I think it might be true. It's the importance of the running game, however, that really surprised me.

In a recent post, I illustrated the distribution of offenses and defenses in terms of total efficiency (yards per play). The distribution for offensive efficiency was wider than for defensive efficiency. This indicated that "good" offenses were better than the equivalent "good" defense. In other words, the best offenses in the league tend to get more yards per play above average than the best defenses in the league give up below average.

"Having a good running game is not only unimportant, it actually seems counter- productive."

However, that analysis was for regular season games. Post season games comprise a smaller sample size, usually too small for very meaningful analysis. They're also biased in certain ways. For example, the home team is usually the better team, and it would therefore be hard to separate the advantage in team strength from home field advantage. But the biggest difference between the regular and post seasons is the level of competition.

As an indirect way to infer tendencies about post-season competition, I analyzed regular season games that featured only opponents that would go on to win at least 10 games. I think this criteria best reflects the level of competition usually found in the playoffs. Although 9-win or even 8-win teams occasionally make the playoffs, many do not. Plus, 9 wins is only 1 win above a .500 win percentage, and a 9-win team has never won a championship.

First, I looked at how important various team stats were in determining the winner of match ups between 10+ win teams. I looked at offensive running and passing efficiencies, turnover efficiencies, penalty rates, and home field advantage. The data is from the 2002-2006 seasons, and there were 114 such games between "good" teams. (The stats used here are year-long stats, not stats only within that particular game.)

Instead of an advanced regression analysis, I started by looking at how often a team with an advantage in each particular stat won. The table below lists various team efficiency stats along with the win percentage of the team superior in that stat. For example, the team with home field advantage won 59.6% of the match-ups between 10+ win teams. And the team with the better offensive pass efficiency won 52.6% of the match-ups. The winning percentage for all regular season games is included for comparison. Significant differences in winning percentages between good vs. good games and all games are noted.

Stat	Good vs. Good	All Reg Season
Home	59.6	57.4
O Run**	45.6	55.0
D Run	48.2	50.0
O Pass**	52.6	63.8
D Pass**	51.8	59.8
O Int Rate**	50.9	59.5
D Int Rate	55.3	59.4
O Fum Rate	55.3	60.8
D FFum Rate	54.4	58.0
Pen Rate*	47.3	54.1

** = difference is significant at the p=0.05 level
* = difference is significant at the p=0.10 level

What immediately strikes me is that being good in the running game, both on offense and defense, appears to be no help in beating other good teams. Teams with the better offensive running efficiency won only 45.6% of the games, and teams with the better defensive running efficiency won only 48.2% of the games.

Teams with superior passing, fumbles, defensive interception rate, and penalties win slightly more than 50%-55% of the games. I'm surprised passing efficiencies don't appear to be more important. The stats that tend to be more random, such as fumbles and interceptions, appear to make the biggest difference. This result may be due to the fact that when good teams play each other stats like passing efficiency and offensive interception rates are very good for both teams, and the difference is in the more random stats.

"When teams very close in ability meet, the more important other factors such as randomness and home field advantage become."

Home field advantage also appears more important than is typical in the NFL. Home teams usually won 57.4% of all regular season games in the period studied. In the good team vs. good team match-ups, home field advantage appears slightly stronger. Again, the closer the teams are in ability, the more important other factors become.

But having a good running game is not only unimportant, it actually seems counter-productive. How can this be? (First, I should note this is not a regression tested for significance, but with 114 observations, and the fact that both offensive and defensive running abilities appear unhelpful, the results are likely somewhat meaningful.) If true, my theory is that winning teams that count on the running game to win might overuse the run against better opponents. Leaning on the running game wouldn't help, and may actually hurt.

Running too frequently would do harm because the pass does have a higher expected return per attempt (link requires registration), even accounting for the possibility of an interception. Every run attempt precludes a pass attempt, reducing ultimate effectiveness.

To get a better context of the results in the table above, I also calculated the winning percentage of teams with superior stats for other types of match-ups. I analyzed "bad vs. bad" match-ups which featured both opponents that ultimately earned 9 or less regular season wins. Also analyzed were "good vs. bad" match-ups which featured a 10+ win team against a 9- win team. (I realize 9 wins is not "bad," but it's a lot shorter than "other than good.")

The winning percentage of teams with the better stat are listed for each type of match-up in the table below.

Stat	Good vs Good	Bad vs Bad	Good vs Bad
Home	59.6	57.0	56.0
O Run	45.6	53.7	55.8
D Run	48.2	51.4	67.9
O Pass	52.6	63.6	65.4
D Pass	51.8	59.8	63.7
O Int Rate	50.9	59.5	53.8
D Int Rate	55.3	59.4	57.3
O Fum Rate	55.3	60.5	63.7
D FFum Rate	54.4	58.0	62.3
Pen Rate	47.3	53.8	71.9

The results for the other types of match-ups seem to make sense. Being superior in any of the stats does not appear to be unhelpful (as with running in the good vs. good match-up). The bigger the difference in team record, the larger we would expect the difference in each team stat. Accordingly, the winning percentages are higher for the bad vs. bad and good vs bad match-up types than the good vs. good match-up type.

I could go on and on with observations. Penalty rates appear critical in good vs bad match-ups, offensive passing efficiency appears most important in the bad vs. bad match-ups, etc. I'll leave it to others to draw their own inferences.

Ultimately, when teams very close in ability meet, the more important other factors such as randomness and home field advantage become. Playoff teams are by definition relatively similar in ability, so home field and randomness become critically important. Turnovers are the most random of the stats, especially defensive turnover efficiency. Perhaps then it is randomness that wins championships. And because defensive performance trends are more random than offensive trends, perhaps that's why we see defense as more important come January.

Road Winners in the Playoffs

One notable difference between the regular season and the playoffs is that the higher seeded playoff team hosts the game. If the seedings reflect the actual strength of the teams, we should expect to see a larger winning percentage for home teams than in the regular season. Teams that win on the road through the playoffs would be truly remarkable teams.

In this post I'll look at road winners in each round of the playoffs from 1994, the year the salary cap began, through 2006, the most recent year. I'll also look at differences in road winners from two different playoff periods. The first period is from 1994-2001, when the playoffs featured 3 division winners and 1 wildcard team from each conference. The second period is from 2002-2006 when the playoffs featured a 4th division winner and two wildcard teams. The sample sizes aren't terribly large, but large enough to begin to see some possible trends.

The first table lists each round of the playoffs for the entire post-salary cap period, and the number and percentage of road winners. Overall road teams won 33% of games in the playoffs. This is in contrast to the normal 42-43% rate in the regular season.

1994-2006	Games	Road Wins	Road Win%
Conference	26	11	42
Division	52	13	25
Wildcard	52	15	29
All Rounds	130	39	32

The next two tables break up the data into the two playoff periods. The first table lists the road winners from '94-'01. The second table lists them from '02-'06, featuring the NFL's current playoff structure.

1994-2001	Games	Road Wins	Road Win%
Conference	16	6	38
Division	32	7	22
Wildcard	32	7	22
All Rounds	75	20	29

2002-2006	Games	Road Wins	Road Win%
Conference	10	5	50
Division	20	6	30
Wildcard	20	8	40
All Rounds	50	19	40

Again, the sample sizes aren't large, but we can make some observations. First, the playoff seedings do appear to reflect a stronger home team winning percentage. The better team is probably seeded higher and hosts the game. But this effect could also be due to the "dome at cold" effect. With bitter cold weather in most cities in January, dome teams would be at a severe disadvantage when playing on the road outdoors. In fact, of the 14 "dome at cold" match-ups, dome teams have won only 2 (14%), which is same the rate as in December in the regular season.

The conference championship games reflect a relatively high number of road winners (40%). This makes sense for a couple reasons. Low-seeded dome teams have already been eliminated. Also, the games feature the closest match-up between relative team strength. They ostensibly would feature the two best teams at the time (the true 1 and 2 seeds), regardless of their official seeding.

Third, there is a noticeable difference between the '94-'01 wildcard rounds and those of '02-'06. Road teams have been winning more frequently lately in the wildcard round (40%, vs 29%). There isn't enough data yet to make any firm conclusions, but it makes sense intuitively.

I think we're seeing more road winners or "seed"-upsets due to the new division structure. With four division winners in each conference, it's more likely an average team can luck into the division championship, especially with a weak division. With only four teams in each (compared to five or six previously), it's more likely to have a thoroughly weak division. The wildcard teams, which are road teams by rule, are probably from the stronger divisions and possibly stronger teams than their seeding indicates. Similar to the conference championship games, the modern wildcard round feature games between closely seeded teams (5 vs. 4) and (3 vs. 6).

This year, the two 5 vs. 4 seed games are expected to be toss-ups. JAX is slightly favored over division-winner PIT by 2.5 points, and TB is favored over NYG by 2.5 points. SEA, the division winner of the clearly weakest division, is only favored over WAS by 3.5 points.

Does Defense Win Championships?

Well, of course. And so does offense. But the conventional wisdom that "defense wins championships" implies that defense is particularly more important than offense in the playoffs and the Super Bowl. This post will begin to look at whether defense really does matter more than offense in the NFL by comparing the right tails of the performance distributions of offenses and defenses--where playoff teams come from.

This time of year we are helped to the standard slew of articles declaring that defense is more important. Here is the latest example from ESPN.com. It's a good example because it suffers from some fatal flaws (itemized by Phil Birnbaum here). Typically, these articles look at past examples of NFL champions and comparing the offensive and defensive rankings of each team. I don't think this kind of analysis is necessarily very valid--

• They are anecdotal
• The sample size is usually very small, and results are probably not statistically significant--just due to chance
  
• If the sample size is large, it covers very distinct periods of NFL passing and blocking rules, confounding any results
  
• If the sample size is limited to one period of NFL rules, it can be dominated by one or two particular teams would skew the results (PIT in the 70s or NE currently, for example)
• Often, the analysis shows that defense is indeed important, but not more important than offense
• The rankings of each squad is almost always based on points scored or total yards, which are more often than not deceiving about the true performance of a squad

The biggest flaw may be using total points or total yards to compare squads. Offensive points scored is dependent on defense ability and special teams. Defenses that provide good field position allow an offense an easier time scoring. Teams with poor defenses provide poor field position, which allows their offense to gain more yards but probably fewer points scored. Additionally, teams that are winning will usually sacrifice total yards for chewing up time on the clock.

There is also an assumption that playoff football is somehow systematically different than regular season football. I'm not comfortable with that assumption--the rules are the same, the refs are the same, the field is still 100 yds long, and a touchdown is still 7 points. There are some unique things about the playoffs, but for now I'm going to set them aside and begin to look at how offenses and defenses compare in general by using regular season stats. (Using post-season stats is possible, but very problematic. About half of all playoff teams only play a single game before being eliminated, yielding very erratic and extreme team averages).

To best compare offensive and defensive performance and ability, squad efficiency--yards per play--should be used. Offensive and defensive efficiency are independent of each other. They aren't dependent on special teams or field position considerations. And perhaps most importantly, they aren't confused by the direction of causation. For example, total rushing yards correlates strongly with winning, but it's actually the winning that allows teams to inflate their rushing yards by eating the clock at the end of a winning game.

Efficiency stats are usually divided into passing and running efficiencies here at NFL Stats. But in this article we're interested in offenses and defenses as a package and not pass/run balance, so we'll use offensive efficiency (yards gained per offensive play) and defensive efficiency (yards allowed per offensive play). Data is from the 2002-2006 NFL seasons (N=160).

The graph below illustrates the actual distribution of team offensive and defensive efficiencies. The vertical axis represents the number of squads with the noted efficiency level (horizontal axis).

Team efficiencies are expected to be distributed approximately normally. That is, there are a few really great offenses, an equally few really poor ones, and a bunch of average ones. League offensive and defensive efficiency must be balanced--there has to be equally as many yards gained as allowed. Accordingly, the average offensive efficiency and the average defensive efficiency are both 5.3 yards per play. The standard deviations are different, however. Offensive efficiency is 0.49 yds and defensive efficiency is about 20% smaller at 0.38 yds.

With enough observations, we would expect the distributions to smooth out, resembling more of a typical bell-shaped normal distribution. With the given averages and standard deviations, the theoretical efficiencies are approximated in the figure below.

The actual and theoretical distributions show the same tendency--offensive efficiencies are spread wider than defensive efficiencies. Notice the right tails of the distributions (below). This is where playoff and championship teams come from. (Actually, we should be comparing the right tail of the offense and the left tail of the defense. But the normal distribution is symmetrical, so rotating the defense about the league average yields the same comparison.)

This means that great offenses tend to be "better" than great defenses, and terrible offenses tend to be "worse" than terrible defenses. If my offense is 2 standard deviations (SD) above the mean and your defense is 2 SD above the mean, my offense would tend to prevail because a great offense tends to gain more yards above the NFL average than an equally great defense allows below the NFL average.

So if a great offense usually trumps a great defense, where does the perception that "defense wins championships" come from? Truly dominant defenses such as the 2000 Ravens, 2002 Buccaneers, or 1985 Bears are relatively rare, and are therefore more memorable. Also, defense has traditionally been overlooked, at least by the mainstream hype-laden media. Even football insiders seem to focus on offense, demonstrated by who is inducted in the Hall of Fame, or who the MVPs tend to be. So the phrase "defense wins championships" may really mean "defense helps win championships more than most people think they do."

One thing that this analysis does not do is focus on the specific case of great offensive vs. great defense. It considers team efficiencies as a whole. While this analysis indicates the likely outcomes of strong offenses vs. strong defenses, it is an indirect inference. A case by case study could look at playoff-type match-ups of good teams only, and tell us more.

Admittedly, there are some special qualities about the playoffs. The outdoor weather in northern cities can be extreme, and the home team is more often the better team. Weather may indeed affect the balance of offense and defense, but it likely affects the balance between running and passing games more. And weather affects both opponents in a game, so it's not clear if it really matters. Playoff weather could also be analyzed in further research.

So when looking at the NFL as a whole, offense and defense balances symmetrically. But when focusing on the right tails of performance, where playoff teams come from, we see that great offenses out-pace equally great defenses.