On Monday, I looked at the greatest defenses — measured simply by points allowed and adjusted for strength of schedule — in NFL history. Today, I want to look at which offenses were the greatest in regular season history, and see where the 2013 Broncos stack up.

As noted in the post on defenses, during Super Bowl week, Bill Barnwell’s article ranked Denver’s 2013 offense as the greatest scoring machine ever. He used the statistical measurement known as the Z-Score to show that Denver’s offense was 3.3 standard deviations above average, and no offense had ever been 3.3 standard deviations above average before.

Where does that 3.3 number come from? Denver averaged 37.9 points per game during the regular season. The league average was 23.4 points, which means that Denver’s offense was 14.5 PPG better than average. The standard deviation of points per game among the 32 NFL offenses in 2013 was 4.36 points; therefore, Denver gets a Z-score of 3.32, because the Broncos scored points at a rate that was 3.32 standard deviations better than the mean.

But since Denver faced an easy slate of defenses, ^[1]That’s not true! isn’t that 3.32 number a little misleading? After all, Football Outsiders graded the Broncos offense as having faced the 3rd easiest schedule this year. So like we did on Monday, I derived offensive and defensive SRS grades, which adjust for strength of schedule. And again, I am going to conflate the labels of best scoring team and best offense.

If you did not read Monday’s post, the SRS is simply margin of victory (or, in the case of offenses and defenses, margin of production above league average) adjusted for strength of schedule. The key is using an iterative process, where, in Excel, we adjust the ratings hundreds of times; after all, to adjust for SOS, you have to adjust for the SOS of each opponent, and the SOS of each opponent’s opponent, and so on.

As it turns out, the Broncos schedule wasn’t particularly easy, at least as far as points allowed. Now, points allowed is far from a perfect measure — for example, San Diego had a terrible defense (and ranked last in DVOA) but ranked 12th in points allowed because of the offense’s slow pace. But the Broncos’ offense, after adjusting for strength of schedule, faced the 17th toughest schedule in the NFL this season, making it nearly league average in terms of points allowed.

The table below shows the top 200 scoring teams since 1932. Here’s how to read the 2013 Broncos line. In 2013, Denver averaged 14.5 more points per game than league average. The average defense the Broncos faced — using the iterative method to derive SOS grades — was 0.4 points below average. Therefore, Denver is credited with an adjusted rating of 14.1 PPG above average. The standard deviation of offensive ratings in the NFL in 2013 was 4.17, giving Denver a Z-score of 3.38, the highest ever.

Interestingly enough, since the SOS adjustment compressed team ratings in 2013, Denver’s Z-score is higher in this article than in Barnwell’s despite the slightly negative SOS adjustment. Eight other Peyton Manning teams appear in the top 200, including the ’04 team that ranks 14th. The 2007 Patriots rank 4th in this analysis, and are actually slightly behind the ’10 team. More on that in a minute, but if you sort the table by the Adj PPG column, the Tom Brady–Randy Moss–Wes Welker 18-1 Patriots have the best rating since World War II.

Some other notes on the top teams:

• The GSOT Rams, with potential or actual Hall of Famers Kurt Warner, Marshall Faulk, Orlando Pace, Isaac Bruce, and Torry Holt, had two of the top ten offenses… and that doesn’t even include the 1999 team! But it’s the Norm Van Brocklin/Bob Waterfield/Tom Fears/Elroy Hirsch/Glenn Davis Rams of 1950 that holds the franchise record for points above average.
• Steve Young’s 49ers dominate the list, with two top-ten teams and a few others in the top 100. Having Jerry Rice sure does make life easier, as Joe Montana’s 1987 49ers are also in the top 20. Of course, Montana’s ’84 49ers — in the pre-Rice era — also cracked the top 75. Those three guys were pretty good.
• The rest of the top ten is littered with great offensive teams behind a Hall of Fame quarterback – Johnny Unitas on the ’59 Colts, Brett Favre on the ’96 Packers, and Dan Fouts on the ’81 Chargers, while John Elway’s ’97 Broncos are 11th. Only two of the top 15 offenses were led by a quarterback who won’t wind up in Canton — Washington in 1983 (Joe Theismann) and Minnesota in 1998 (Randall Cunningham). Of course, those offenses had outstanding supporting casts, too, and both set the single-season record for points scored in a season.

What about the worst offenses?

Why yes, Randy Moss played for one of the worst scoring machines one year before playing for one of the best. Some famously bad offenses top the list — none of the five teams at the top of the list won more than two games. I’ll leave it to you guys in the comments to pick out your favorite, although let Shattenjager write the summary on how many times Marion Campbell’s teams appear on the list.

Instead, I’ll reserve the remainder of this post for a Brady/Manning discussion. And in an unusual twist, I’m taking the side of Brady. The question here is whether the Z-Score is an appropriate way to vault the ’13 Broncos over the ’07 Patriots. Putting aside the Sid Luckman Bears, the top two scoring machines in NFL history — measured by Adjusted PPG over average — were the ’13 Broncos and ’07 Patriots. Despite the lower Z-Score, New England averaged more points per game relative to league average and also faced a harder strength of schedule. The only reason the Broncos have a higher Z score is because the standard deviation of offensive grades in 2007 was much wider than it was in 2013. The threshold question is whether that difference is due to randomness, in which case, we would want to keep the ’07 Patriots ahead of the ’13 Broncos. The graph below shows the standard deviation of offensive SRS grades in each season since 1978:
[visualizer id=”17773″]

In general, the trend appears to be towards greater variance among NFL offenses, and 2013 was just a “down” year. Since 2007, the trend looks like a row of shark teeth: that leaves me inclined to believe there was no material difference between the 2007 and 2013 variances. Instead, the observed difference in variances is simply the result of a relatively small sample size.

But that’s just my gut; fortunately, there’s a way to test this theory, so we don’t have to rely on statements like “I’m inclined to think.” It’s called an F-Test. The standard deviation of offensive ratings was 5.21 in 2007 and 4.17 in 2013. To perform an F-Test, we need to determine the ratio of the two variances. So we square both numbers, giving us 27.1 and 17.4, and then divide the bigger number by the smaller one, resulting in an F of 1.555. Next, we need to know the degrees of freedom in both samples, which is simply N-1, or 31, for both sets of data. If you type =FDIST(1.555,31,31) into Excel, you will get a result of 0.11. That indicates an 11% chance the differences between the two data sets was really due to random error.

That doesn’t necessarily answer the question, of course. But typically, we like a p-value to be significant at the 90% or 95% level to reject the null hypothesis. That’s because we often see random splits that look meaningful but really aren’t. This one is on the border, but I’m inclined to reject the hypothesis that the difference between the two standard deviations was meaningful.

There are better ways to judge an offense than just points scored, of course. Using points scored per game relative to league average is a necessary tweak, and adjusting for strength of schedule makes sense, too. But there are many other factors to consider. And since it’s now officially the offseason, we will probably do that here at Football Perspective sometime this summer. Perhaps the most important adjustment we can make is for the number of drives a team had, and that tilts the scales strongly in New England’s favor. The Patriots had just 158 offensive drives in 2007, compared to 192 for the 2013 Broncos.

Regardless, if we are limiting ourselves to just the metrics in this post, I’d still be inclined to pick the ’07 Patriots regular season over the ’13 Broncos. The difference between the two teams’ PPG ratings matters carries the day for me, as I believe the Z-score is biased due to the (randomly) narrow distribution of offenses in 2013. Of course, both the ’07 Patriots and ’13 Broncos have something else in common: struggling mightily on the game’s biggest stage.