Strength of Schedule Adjusted TAY/P

Last week, I posted the final team strength stats for the 2015 season. I concluded the article with my homegrown TAY/P stat, but having already included four other tables with commentary, I didn’t think taking the time to adjust for opponents was a wise move. I want to take a little more space to explain where the numbers come from, so I am giving strength of schedule adjusted TAY/P its own post.

First, I’ll explain what TAY/P is, for the uninitiated. It stands for Total Adjusted Yards per Play, and it is probably most well known for being the metric I use to rate quarterbacks. However, I also use teamwide TAY/P to account for the performance of both offense and defense. The formula is:

TAY/P = (Yards + 20*Touchdowns + 9*Non-TD First Downs – 45*Interceptions – 25*Fumbles)/Plays1

After finding a team’s TAY/P, we have to find total TAY/P for the team’s opponents. We also have to find the average TAY/P of the rest of the league.2 Once we do this, we can adjust each team’s offensive and defensive TAY/P for the schedule they have faced (so we adjust each offense based on defenses faced, and we adjust each defense based on offenses faced). After finding the adjusted TAY/P ratings, we then find the average of each team’s newly adjusted opponents.3

The method I use to adjust for opponent is a bit convoluted, but the results have been generally agreeable. To adjust for opponent, I first convert each team’s marginal TAY/P into an expected winning percentage. The formula to do this is based off a regression analysis I did on every team’s marginal TAY/P and win rate from 2002-2014. The math is simple:

Adjusted marginal TAY/POffense = 0.502063 + 0.124932*marginal TAY/POffense

Adjusted marginal TAY/PDefense = 0.499185 – 0.11984*marginal TAY/PDefense

I’ll use the Arizona Cardinals as an example. Their marginal TAY/P was 1.01 on offense and -0.66 on defense. Plugging those into the regression equations gives us converted rates of 0.238 and 0.578. After finding those numbers for every team, we plug them into the schedule. Arizona’s offense faced an average defensive slate of 0.492, just below average. Their defense faced an offensive schedule of 0.498, also just worse than average.

Once I find those numbers, I treat the model similar to the way I treat SOS-adjusted Pythagenpat. I convert offensive and defensive scores to Win Ratios. For Arizona:

Win RatioOffense = 0.628/(1 – 0.628) = 1.68

Win RatioDefense = 0.578/(1 – 0.578) = 1.37

Now, I can adjust each team’s scores by adjusting for strength of schedule. The formula is simple:

Adjusted Offense = 1/(1+((1/Average Opponent Defense)/(1 – Average Opponent Defense)*Win RatioOffense))4

Step by step, we see that the Win Ratio for the Cardinals’ average opponent is (1/0.492)/(1 – 0.492), or 0.969. We then multiply that by Arizona’s offensive Win Ratio to get (0.969 * 1.68) 1.64. Then 1/1.64 is 0.611. Add 1 to get 1.611. Finally, 1/1.611 is 0.620, Arizona’s adjusted offensive score. Do this for every team, then put them back into the schedule to find Arizona’s adjusted strength of schedule. For the Cardinals, adjustments raise their offensive SOS to 0.499 and their defensive SOS to 0.503.

Now all we have to do is convert these win percentage scores back into marginal TAY/P. To do that, we just work backwards from our regression equations. Arizona’s 0.620 offense adjusts to (0.620 – 0.502063)/0.124932 = 0.95 marginal TAY/P. Their 0.576 defense adjusts to (0.576 – 0.499185)/-0.11984 = -0.64 marginal TAY/P. After doing this for every team, we add the marginal scores back to the new league averages to find the new adjusted TAY/P. The new league average is between 7.27 and 7.28, so the Cardinals 0.95 marginal TAY/P on offense gives them an adjusted TAY/P of 8.22. In other words, after adjusting for strength of schedule, the Cardinals don’t look as good on offense or defense.5

Of course, we don’t just want to know how a team stacks up relative to a league average baseline. We also want to know how a team fares relative to expectation, based on their opponents. Continuing with the Cardinals, we know their offense was 0.95 TAY/P better than the rest of the league. However, we also want to know how well Arizona played based solely on output versus opponents. To figure this out, we simply take their actual output (8.25 TAY/P) and subtract their SOS (7.37 TAY/P allowed) to come up with 0.88 TAY/P above expectation.

Strength of Schedule Adjusted TAY/P: Offense

The following table is sorted by TAY/P+. Read it thus: The New Orleans Saints gained 9129 total adjusted yards at 8.33 per play, which was 1.09 better than the rest of the league. The average defense they faced allowed a TAY/P of 7.38. After adjusting for the weaker than average schedule, the Saints’ new marginal TAY/P is 1.06, and their new TAY/P is 8.34.6 Given the schedule the Saints faced, they outperformed their expected TAY/P by 0.94, best in the NFL.


Led by MVP Cam Newton, stiff-arm specialist Jonathan Stewart, and sure-handed Greg Olsen, the Panthers brought the league’s most prolific offense into the Super Bowl. On the surface, the Panthers have far and away the most total adjusted yards of any team. Of course, they were one of just two teams to play in 19 games this year, so those numbers are a bit skewed. On a per game basis, the Saints (571) and Patriots (540) had greater output than did the Panthers (537).

At the other end of the spectrum, we have the Rams. They had the lowest output overall and on a per game basis (373). Interestingly, the Broncos don’t rank last among playoff teams. With 431 TAY/G, they rated slightly ahead of the Minnesota Vikings (426). This doesn’t mean Denver had a super offense (they didn’t); it just means that Denver had higher output each game.

Sinking ship captain.
Sinking ship captain.

When we sort by TAY/P, the Saints show up as the top team in the league. Drew Brees received more than is share of negative media attention for the poor performance of his team. However, Brees and the rest of his offense played better than any other squad over the course of the season. In fact, they played so well that New Orleans went 7-9, despite fielding arguably the worst defense in modern NFL history (more on that later).7

It’s worth noting that the Cardinals would own the top spot if this only accounted for the regular season. However, Carson Palmer injured his finger (and we all know the finger bone’s connected to the decision making bone) and led Arizona to one mediocre and one horrendous postseason game. Given Bruce Arians’s high variance style of offense, I waited every week for them to flip tails. It only happened a few times, but I am compelled to believe they’ll see heads a lot less next year.

Notice that looking at efficiency per play moves the Vikings ahead of the Broncos. It also moves the Texans below the Broncos and into the last place spot among playoff offenses.

When we look at value over average, the Saints have the most extreme offense in the league (their +1.09 has a greater absolute value than the Colts’ -1.02). We also see that there was little range this year, with no historically spectacular or terrible offenses.

The Jets, Panthers, and Washington all faced a fairly easy slate of defenses, so look for them to turn back into pumpkins next year. Also, take note that teams fielding Jameis Winston, Blake Bortles, and Marcus Mariota faced subpar defenses. That doesn’t mean they will play poorly next year, but I definitely expect Bortles to come back down to earth.

On the other hand, the Steelers put an incredible offense on the field and had an output to match, despite facing the toughest slate of defenses in the league outside of Cleveland. Look for Ben Roethlisberger to keep adding fancy stats to his Hall of Fame resume with Antonio Brown defending his title for top receiver in the league.

Once we adjust for SOS, Tom Brady and his band of Patriots take the top spot for offensive efficiency. This shouldn’t come as much of a surprise, given the success of New England’s offense with Brady at the helm. Over the last decade, they have fielded one of the most consistently excellent offenses in history.

When e compare performance solely against expectation, the Saints jump back into first place. The most interesting team to me, however, is the NFC champion Panthers. Their schedule was fairly ho hum, but they didn’t play down to their competition. They did what good teams are supposed to do and wiped the floor with the poor defenses they faced.

Strength of Schedule Adjusted TAY/P: Defense

This table is sorted by defensive TAY/P+. Read it thus: The Carolina Panthers allowed 7267 total adjusted yards at 5.87 per play, which was 1.59 better than average. The average offense they faced gain 7.28 TAY/P. After adjusting for that, Carolina’s new marginal TAY/P becomes -1.66, and their new TAY/P allowed becomes 5.73. Given the offenses they faced, their TAY/P allowed was 1.42 better than expectation, tops in the league.


If you look at the rest of the top teams in this metric, you may notice that there is much overlap between the best offensive teams and best defensive teams. It’s no surprise, then, that those teams posted the NFL’s best records and made the playoffs.8

If we just look at total adjusted yards, the Jets appear to have had the stingiest defense in the league last year. With 6405 TAY allowed in 16 games, they were, indeed, stingy. However, on a per game basis they come out in fourth place (400). The Broncos (372), Seahawks (375), and Panthers (382) all rate well ahead of the Jets.

The bottom four teams in TAY are interesting because, despite playing no extra games, they all gave up more on defense than any playoff team. New Orleans was especially egregious, ceding 578 TAY/G. The Saints were also the worst defense per play, giving up an average of 9.27 TAY every time an opponent snapped the ball. As good as they were on offense, they were orders of magnitude worse on their singularly inept defense. For every bucket of water Brees and co. dumped off the sinking ship, the defense opened a giant hole to the ocean below. The wanton waves of the NFL schedule eventually submerged the vessel.

Head Coach Sean Payton has a great deal of respect, as far as NFL coaches go. He helped revitalize Brees’s career and helped bring a ring to the forlorn fans in the Big Easy. However, a head coach’s responsibility is to put the right people in place to be successful. No one disputes Payton’s ability to coach an offense, but he must bear his share of the blame for failing to complement his stellar offenses with even average defenses.9

Sorting by the top TAY/P (lower is better), we see that nine of the top ten – and 11 or the top 13 – defenses made the playoffs (plus the bad luck Jets and a Rams team quarterbacked by Nick Foles and coached by Jeff Fisher). Washington was the only team with a legitimately bad defense to make it to the second season, and it’s fair to say they wouldn’t have made the tournament in most other divisions.

Looking at SOS, the Patriots actually faced the toughest schedule of opposing offenses (as measured by TAY/P, that is). That’s probably not going to happen again. A likely easier slate of offenses, coupled with a consistently effective offense of their own, should keep New England on top of the AFC East as long as Brady and Belichick are around. The Jets also had a hard schedule of offenses, but I look for this to basically be a wash when combined with the easy-ish slate of defenses they faced.

Which defense faced the easiest set of offenses? Well, that would be the Super Bowl champion Denver Broncos. Given how incredible Von Miller, DeMarcus Ware, et al. were this year, most of us probably expect some regression. Given their somewhat soft strength of schedule in 2015, the numbers could look much worse than the defense actually plays in 2016. Just remember that when Wade Phillips makes the wrong call, or when Chris Harris Jr. makes a rare coverage mistake, the sky is not falling.

21st Century Alan Page.
21st Century Alan Page.

When we use SOS to adjust marginal ratings, the Super Bowl combatants take the top spots. When you look only at performance versus expected performance against their schedules, the Panthers actually vault the Broncos for the most efficient defense in the NFL (and by most efficient defense, I of course mean defense that makes offenses the least efficient).

My condolences to the Rams and Texans, who are a quarterback away from not wasting the prime years of Aaron Donald and J.J. Watt. You can do it, guys.

Strength of Schedule Adjusted TAY/P: Differential

The last table is sorted by adjusted marginal TAY/P differential (in other words, after adjusting for strength of schedule and comparing offense and defense to the rest of the league, how much better than average was the team’s combined offense and defense). Read it thus: The Carolina Panthers had a TAY/P differential of 2.20 (8.06 for – 5.87 against, numbers appear off due to rounding). When comparing to the rest of the league’s offenses and defenses, the Panthers’ TAY/P differential is even better, coming in at 2.40. After adjusting for opponent strength, their TAY/P differential raises to 2.21, while their marginal TAY/P differential falls to 2.33 (still best in the land).

TmTAY/P∂Mrg∂Adj TAY/P∂Adj Mrg∂

There isn’t much difference in the rankings between any of these columns, so I’ll focus on the last one, marked “ADJ MRG∂.” All this means is that I adjusted offensive and defensive TAY/P for SOS (as seen in the opening statement), find how those scores rate relative to the rest of the league, and rate teams by the differential (offense – defense = differential).

Look at the top rated Panthers, for example. Their marginal offensive TAY/P (0.67) minus their marginal defensive TAY/P (-1.66) is 2.33. Using this methodology, there are only twelve above average teams from 2015. We see a top tier of Carolina and Seattle; a second tier of Arizona, New England, and Kansas City; a third tier of Cincinnati, Denver, and Pittsburgh; and a sporadic foursome comprising the Jets, Bills, Buccaneers, and Packers rounding out the group.

There is a pretty strong correlation between TAY/P differential and team record. When you see a team like Seattle score so highly here but post a merely good record, it tells you that they were a better team than the standing indicate. Teams with higher scores win the game far more often than not. Like I say, though: titles aren’t won in spreadsheets. Neither the top ranked Panthers nor the highly ranked Patriots  could handle the Mile High front seven with the season on the line.

Hue Jackson, Chip Kelly, and Mike Mularkey have something in common: each is taking over one of the three worst teams in football and will likely get more credit than deserved if the Browns, 49ers, and Titans put a better product on the field in 2016. For new head coaches, regression is your friend.

  1.  When calculating for quarterbacks, I remove spikes and kneels from plays, which results is some negligible increases for nearly every team. However, I am not doing that today. You can find the rationale for using multipliers of 20 for touchdowns, 9 for first downs, -45 for interceptions, and -25 for fumbles in various locations across the interwebs. I have included a few links.
  2. You will notice some small differences in marginal TAY/P between the tables here and the tables I used in the Final Team Strength Stats post. In the original post, I included every team in the league when finding marginal TAY/P. For this post, I am taking each team out of the pool and calculating the average of the rest of the league, then determining how far ahead of the other teams any given squad was. For example, the Saints offense was 1.06 TAY/P better than average when you include them in the average but 1.09 better than average when you remove them first.
  3. We could do this hundred of times, in an iterative manner, like SRS scores, but doing it just twice is much easier and doesn’t produce results that are materially different or more predictive.
  4. Adjusted Defense scores are done the same way, but with offensive inputs and defensive inputs switched. I won’t clog up the screen with more examples.
  5. Yes, their defense faced a better than average slate of offenses, but adjusting every team’s scores means that there is a new baseline, and the Cardinals aren’t as relatively strong.
  6. It may seem weird that their marginal rate decreased while their overall rate increased after adjusting for strength of schedule. Some of it can be chalked up to rounding, but the primary reason for this is that, after adjusting every team in the league, the league average changes slightly, and teams are now judged off new baselines. I’ll note that the two most important columns are the “ADJ MRG” and “TAY/P+” columns, which compare performance to the rest of the league and to expectation based on opponent.
  7. Of those 9 losses, 5 came in one-score games. Brees still has it, baby.
  8. Except Washington, who won a terrible division, and the Jets, who had the bad fortune of being a good team in a strong division and conference.
  9. Keep in mind that Payton and Brees have made magic happen, consistently, on offense. When they have had average-to-good defenses, they have made noise in the postseason.