Today’s insane statistic comes courtesy of RJ Bell: the difference between Denver and the #2 team in points per game is larger than the difference between the #2 and #31 teams. The Broncos are averaging 39.8 points per game this season, 11.6 points more than the (surprisingly second-ranked) Bears. And Chicago is averaging just 9.9 more points per game than the Jets, the #31 ranked scoring team.

That is, well, crazy. The record for points per game in a season is 38.8, set by the 1950 Rams. The 2007 Patriots are second at 36.8, and both of those teams scored slightly more points through ten games than the 2013 Broncos. So while Denver is on pace to break the scoring record, some regression to the mean over the final six games should be expected.

If the Broncos want to set the record for most points scored relative to the second highest scoring team in the league, Peyton Manning and company have some work to do. That mark is held by the ’41 Bears, who averaged 36.0 points per game, 12.5 more than the Packers that year. Second and third on that list are the ’07 Patriots (8.4) and ’50 Rams (8.3), so Denver has a realistic shot of setting the modern record.

I’ll be honest: as dominant as the Broncos offense has been, I’m a little surprised to see them so far ahead of the competition in points scored. After all, consider:

• The Eagles have just 19 fewer yards than the Broncos, and Nick Foles actually leads Manning in both passer rating and Adjusted Net Yards per Attempt;
• In PFR’s Expected Points Added, the Broncos offense is at 14.7 EPA-added per game, while the Saints offense is at 11.3. That’s a relatively small difference considering the fact that Denver has scored 12.1 more points per game than New Orleans.
• The Chargers have a higher completion percentage than the Broncos and six fewer turnovers, but have averaged 17 fewer points per game.
• The Packers are actually a hair ahead of Denver in yards per play (6.3531 to 6.3529), but have scored two fewer touchdowns per game.

So what’s going on? I’m perfectly fine with Denver being general run-of-the-mill dominant, but the team’s points scored numbers makes it seem like the Broncos might be the greatest offensive machine ever. I think I’ve identified the two reasons to explain the gap:

Red Zone success

Philadelphia has scored a touchdown just 46% of the time the Eagles made it into the red zone, which ranks 28th in the league. San Diego isn’t much better at 50% (22nd). The Saints are at 52.5% (20th), and the Packers are down at 30th at 43%. So some excellent offenses are really struggling in the red zone, which gives them disproportionately low points per game averages. Oh, and Denver? They’re at 79.1%, by far the highest rate in the league. It’s not unusual for a great offense to dominate in the red zone — the ’07 Pats were at 70% — but what is unusual is seeing the other top offenses struggle there.

I have red zone data going back to 1997, and the highest ever performance was set by Kansas City in 2003. The Trent Green–Priest Holmes–Tony Gonzalez Chiefs scored a touchdown on 77.8% of all red zone opportunities (42 out of 54), so the Broncos (34 out of 43) could break that record this year. More likely, though, is that the Broncos go from otherworldly in the red zone to just great, which would drop the team’s points per game average.

Number of Drives

The Broncos are averaging 2.85 points per drive, while the Saints are #2 at 2.46. That’s not a huge difference — the gap between #2 and #7 is slightly bigger. The difference, as you can deduce, is that the Broncos are averaging 13 drives per game while the Saints are at just 11.3 drives per game. Why is that? New Orleans’ average drive takes 2:56 minutes, the third-longest in the league (and San Diego is #1 at 3:13), while the Broncos are in the bottom five at 2:17 (the Eagles are last at 2:02). That Chip Kelly edge is erased, though, because Philadelphia’s opponents average 2:48 per drive, the third highest rate in the league. Denver’s opponents take just 2:18 per drive, the third lowest (just a second ahead of Detroit and eight seconds longer than Kansas City).

The Broncos defense is not great, but it does rank 6th in completion percentage allowed. Combine that with the fact that Denver ranks 4th in percentage of opponent plays that are passes, and incomplete passes occur on 25% of all plays run by Broncos opponents, the second-highest rate in the league behind Kansas City. That’s not surprising for a team with such a high Game Script, but it does stop the clock from running for long stretches, which gives Denver’s offense more possessions The Chargers are 28th in this statistic (18%), which is one reason why San Diego is dead last in offensive drives (10.2 per game).

But there’s another reason why Broncos’ opponents tend to have short drives: Denver leads the league in 20+ yard plays allowed at 54. As a result, teams don’t end up with many clock-chewing drives against Denver: opponents tend to gain big yards quickly or throw incomplete passes. That increases the number of drives for the Broncos, which (one could argue) inflates the success of the team’s offense. It’s all relative, of course — Denver is still #1 in points per drive by a wide margin — but it’s worth recognizing that Denver has scored 75% more points per game than an average of the other 31 teams, but “just” 62% more on a per-drive basis. That accounts for about 3 points per game. Add in the insane success in the red zone, and the lack of success there by the other top teams, and you have the reasons for the crazy stat at the top of today’s post.

Manning Record Watch Update

After six games, I analyzed how likely Manning was to break the single-season touchdown record. At the time, he had 22 touchdowns, and the formula projected him to throw 2.99 TDs/G the rest of the way to finish with 52 touchdowns, narrowly breaking Tom Brady’s record.

Now? Manning has 34 touchdowns, as his pace has only slightly declined. What does that mean? To calculate Manning’s odds using Bayes Theorem we need to know four things:

1) His Bayesian prior mean (i.e., his historical average): 2.38, as this number wouldn’t change from the original post.

2) His Bayesian prior variance (the variance surrounding his historical average): Again, no change here, so we use 0.0986.

3) His observed mean: Instead of 3.667, we will use 3.4.

4) His observed variance: This one involves just a little bit of work. What I suggested we do last time is calculate the number of passing touchdowns per game Manning averaged in the first six (now ten) games of each season since 2000, along with his average over the rest of the season (then, 8-10 games, now, 4-6 games). Then we take the difference of the variances of each column, as we did in step two.

Manning’s variance over the rest of the season is 0.3052 TDs/G, while his variance through ten games is 0.2214; the differential there is 0.0838, which is the variance of our current mean.

Once you have your number for these four variables, then you substitute those numbers into this equation:

Result_mean = [(prior_mean/prior_variance)+(observed_mean/observed_variance)]/[(1/prior_variance)+(1/observed_variance)]

Or, using our numbers:

[(2.38 /0.0986) + (3.4 / 0.0838)] / [(1/0.0986) + (1/0.0838)]

which becomes

[24.14 + 40.57] / (22.08) = 2.93

After averaging 3.667 TDs/G over 6 games, we projected Manning to average 2.99 TDs/G the rest of the year. Since he averaged “only” 3 touchdowns per game over his next four games, we downgrade him from 2.99 to 2.93. Of course, we already had a significant regression factored into his future projection — we dropped him by 0.67 TDs/game from his average, which is the point of using Bayes Theorem. So while he’s at “only” 3.4 TDs/G on the season after 10 games, since he’s played at that level for longer, he only loses about half a touchdown per game over his projection the rest of the way.

That gives Manning 17-18 touchdowns, which puts him at a season-ending projection of 51-52 touchdowns. He’s still more likely than not to break the record, although obviously this analysis ignores lots of elements like strength of schedule. And with a visit to Kansas City and a game against the Titans (who have allowed a league-low 7 touchdowns through the air), perhaps he’s actually an underdog to even tie Brady at 50.

Peyton Manning is not a 51 touchdown per-season quarterback, but that doesn’t mean he won’t average the necessary 2.9 touchdowns per game over his final ten games this season to break Tom Brady’s touchdown record. Before the season, Footballguys.com projected Manning as a 2.38 passing touchdown per game player.  And while he has looked unstoppable thus far, with 22 touchdown throws in six games, Manning has been known to have great spurts before, too.  All quarterbacks have hot and cold streaks, Manning included.  From 2003 to 2012, after removing games where he sat late in the season, Manning averaged 2.17 passing touchdowns per game with a standard deviation of 1.31 touchdowns. ^[1]That was after removing week 17 of the ’04, ’05, ’07, ’08, and ’09 seasons, and week 16 of the ’05 and ’09 seasons, when Manning left early. Why did I pick the last ten years? I don’t … Continue reading  In the ’04 season, Manning threw at least 20 touchdowns in each of his trailing six game stretches from week 7 all the way through week 15, with a peak of 27 touchdowns in his prior six games in weeks 11 and 12.  Manning also threw 19 touchdowns in his last two full regular season games of 2010 and his first four games of 2011.  White-hot streaks happen, even to the best players, so we shouldn’t just assume that he’s now a 3.67 touchdown per game player.

On the other hand, it would be naive to assume that we should ignore the first six weeks of the season and continue to project Manning as a 2.38 touchdown per game player for the rest of the year.  The question becomes, how much do we base projection over the final 10 games on his preseason projection and how much do we base it on his 2013 results? In Part I, after four games, a regression model produced a projection of 2.56 touchdowns per game the rest of the year. But the problem with a regression analysis is that Manning is an extreme outlier among NFL quarterbacks; to project Manning, it would be best if we could limit ourselves to just quarterbacks named Manning Peyton Manning.

Before continuing, I want to give a special thanks to Danny Tuccitto, without whom this article wouldn’t be possible. Danny provided this great link and also spent a lot of time walking me through the process. To the extent I’ve mucked it up here, you should blame the student, not the teacher. But after walking through some models online, I realized that the best explanation about how to use Bayes Theorem for these purposes was on a sweet site called FootballPerspective.com. And the smartest person on that website had already laid out the blueprint.

In the comments to one of his great posts, Neil explained that we can calculate Manning’s odds using Bayes Theorem if we know four things:

His Bayesian prior mean (i.e., his historical average):

His Bayesian prior variance (the variance surrounding his historical average):

His observed mean:

His observed variance:

Let’s go through each of these:

1) Manning’s Bayesian prior mean: this is simply what we expected out of Manning before the season. I will use 2.38, since Footballguys is the gold standard of football projections in my admittedly biased opinion. But you can use any number you like, as I’ll provide the full formula at the end.
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The New York Giants are now 0-6. There are many reasons for the team’s struggles: questionable drafting, injuries, Eli Manning interceptions, injuries, coaching mistakes by Tom Coughlin, and injuries. But let’s say you have a buddy who is convinced that the Giants are not that bad: in fact, he thinks New York is just a .500 team that has been really unlucky.

Your first inclination might be to stop being friends with this person, but after that, you might wonder: “Hey, how likely is it for a .500 team to start off 0-6?” This is the same (ignoring strength of schedule, the fact that games are not independent, and several other variables) as asking the question “how likely is a coin to land on heads six times in a row?” The answer to both questions is pretty simple: 0.500^6, or 1.56%. Using the binomial distribution (in Excel, this would involve typing =BINOM.DIST(0,6,0.5,TRUE) into a cell) — which assumes that the talent level of NFL teams is normally distributed, an assumption I will make throughout this post — would give you the same result of 1.56%.

That answer is simple, but it actually answers a different question. What you want to know is the likelihood that the Giants are actually a .500 or better team. It’s a minor but crucial distinction: what we just determined was the likelihood that, given the assumption that the Giants are a .500 team, that they would start 0-6. To address the question of how likely the 2013 Giants are actually a .500 (or better) team despite the 0-6 start, we need to use Bayes Theorem.

Much of the math involved in this process is frankly over my head, but fortunately, Kincaid over at 3-D baseball already did much of the work (and thanks to Neil for giving me that link). I will be blatantly copying his article (with the only changes being stylistic and making this for, you know, football), so make sure to give him all the credit he deserves. It’s a fantastic piece that has many useful applications.
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