2017 Adjusted Pythagorean Wins

2017 Adjusted Pythagorean Wins
2017 Adjusted Pythagorean Wins
Photo: USA Today Sports Images

Guest column by Brett Lieblich

Prior to the 2017 season, I presented an incremental improvement to the common "Pythagorean Wins" statistic in the NFL by removing the garbage time scores. I dubbed the statistic the boring and utilitarian name "Adjusted Pythagorean Theorem (ADJ PYTH)". Let's dive into the results of the S.S. Adjusted Pythagorean, and an assessment of its predictions for the now-completed 2017 regular season.

2017 was a year marked and defined by injured NFL superstars. When we look back on the year, it's hard to see past these injuries, the replacement players who stepped in, and the incredible unexpected stories which comprise the narrative of every NFL season. Before the season started, however, we all had a vastly different set of expectations and predictions -- ones that were informed by the results of the 2016 season.

As a reminder, "garbage time" was limited to the following two scenarios:

  • Points scored by the winning team while leading by 17 or more with fewer than nine minutes left in regulation.
  • Points scored by the winning team while leading by nine points or more with fewer than four minutes left in regulation.

I also examined the effect of removing points scored by the losing team while in comeback mode -- i.e., down 24 points or more in the fourth quarter. However, these points actually proved to be a good indicator of future results.

Garbage-time points were adjusted for both the offense and defense when the winning team scored. Further details on the selection process for garbage time criteria can be found in last year's article.

2017 Wins vs 2016 Adjusted Pythagorean Wins

The following table shows the expected change in wins from 2016 to 2017 as predicted by Adjusted Pythagorean, as well as the actual change in wins from 2016 to 2017. Teams are ranked by descending magnitude of Pythagorean Difference, so that the teams which were predicted to improve or decline the most are at the top. The Raiders, Jaguars, and Chargers were the Adjusted Pythagorean poster children for teams most likely to change their win totals, but not everything went exactly to plan. The bolded teams are those which Adjusted Pythagorean predicted an opposite result from the actual change in wins (for example, the 2017 Cleveland Browns declined by one win despite outperforming their 2016 win total by 2.55 Adjusted Pythagorean Wins).

Expected Changes in Wins vs. Actual Changes in Wins, 2016 to 2017
Team 2016 Wins PYTH ADJ PYTH Pythagorean Difference
(ADJ PYTH - 2016 Wins)
Abs Pyth
2017 Wins Change in Wins
OAK 12 8.79 8.61 -3.39 3.39 6 -6
JAX 3 5.79 6.03 3.03 3.03 10 7
SD 5 7.68 7.60 2.60 2.60 9 4
CLE 1 3.34 3.55 2.55 2.55 0 -1
ARI 7 9.44 9.46 2.46 2.46 8 1
HOU 9 6.49 6.57 -2.43 2.43 4 -5
MIA 10 7.54 7.73 -2.27 2.27 6 -4
CIN 6 8.30 8.21 2.21 2.21 7 1
NYG 11 8.82 8.92 -2.08 2.08 3 -8
DAL 13 11.02 10.95 -2.05 2.05 9 -4
CHI 3 4.71 5.02 2.02 2.02 5 2
PHI 7 9.01 9.00 2.00 2.00 13 6
SF 2 3.94 3.99 1.99 1.99 6 4
KC 12 10.15 10.11 -1.89 1.89 10 -2
PIT 11 9.94 9.26 -1.74 1.74 13 2
BUF 7 8.55 8.53 1.53 1.53 9 2
Team 2016 Wins PYTH ADJ PYTH Pythagorean Difference
(ADJ PYTH - 2016 Wins)
Abs Pyth
2017 Wins Change in Wins
TB 9 7.59 7.47 -1.53 1.53 5 -4
NE 14 12.82 12.56 -1.44 1.44 13 -1
NO 7 8.34 8.34 1.34 1.34 11 4
DET 9 7.66 7.66 -1.34 1.34 9 0
CAR 6 7.14 7.02 1.02 1.02 11 5
TEN 9 8.08 8.08 -0.92 0.92 9 0
GB 10 9.10 9.19 -0.81 0.81 7 -3
BAL 8 8.64 8.65 0.65 0.65 9 1
LAR 4 3.31 3.43 -0.57 0.57 11 7
IND 8 8.48 8.56 0.56 0.56 4 -4
MIN 8 8.60 8.52 0.52 0.52 13 5
ATL 11 10.89 10.60 -0.40 0.40 10 -1
NYJ 5 4.39 4.60 -0.40 0.40 5 0
SEA 10 9.82 10.35 0.35 0.35 9 -1
DEN 9 9.09 9.22 0.22 0.22 5 -4
WAS 8 8.34 8.16 0.16 0.16 7 -1
Teams in bold improved when they were expected to decline, or vice versa.

Adjusted Pythagorean identified a relatively large Pythagorean Difference (greater than one win over/under performance in 2016) for 21 of the 32 NFL teams. Historically, only 45 percent of teams over the past 10 years had a Pythagorean Difference of more than one win, so 2017 projected to be a year of great change.


Of those 21 teams in 2017, only the Browns and Steelers went against the prediction of Adjusted Pythagorean. In all, only five of 32 teams went against their Pythagorean Difference prediction, and the correlation of "Pythagorean Difference" to "2017 change in wins" was 0.45 -- amazingly strong for any single NFL metric. In some cases, the reasons that specific teams bucked the trend were easily explained by the myriad of factors outside the realm of Adjusted Pythagorean: the Colts and their injury debacle with Andrew Luck, or the forcible removal of the Jeff Fisher restrictor plate by Sean McVay with the Rams. The Pittsburgh Steelers were also a strong regression candidate based on Adjusted Pythagorean, but the statistic has historically struggled to predict repeat high win performances by teams with high-level quarterbacks. Pittsburgh's two-win improvement can also be explained by their relatively easy 23rd ranked schedule by DVOA in 2017.

While Adjusted Pythagorean was successful in predicting the direction of a team's improvement or decline, it was also a successful predictor of the magnitude of said change. Of the 16 teams to improve or decline by four or more wins in 2017, 12 of them had a corresponding large (greater than one win) Pythagorean Difference in 2016 which predicted that drastic change.

Teams With Most Drastic Changes in Wins From 2016 to 2017
Team 2016 Wins
PYTH Difference
(ADJ PYTH - 2016 Wins)
2017 Wins Change in Wins
NYG 11 -2.08 3 -8
JAX 3 3.03 10 7
LAR 4 -0.57 11 7
PHI 7 2.00 13 6
OAK 12 -3.39 6 -6
CAR 6 1.02 11 5
MIN 8 0.52 13 5
HOU 9 -2.43 4 -5
SD 5 2.60 9 4
SF 2 1.99 6 4
NO 7 1.34 11 4
MIA 10 -2.27 6 -4
DAL 13 -2.05 9 -4
TB 9 -1.53 5 -4
IND 8 0.56 4 -4
DEN 9 0.22 5 -4
Teams in bold improved when they were expected to decline, or vice versa.

In short, save for the aforementioned Los Angeles Rams, almost all of 2017's surprise upstarts -- such as the Jaguars, Eagles, Panthers, Chargers, and Saints -- made good on an Adjusted Pythagorean promise that they made in 2016. Historically, teams that underperform by one or more wins improve by at least 1.8 wins the following season, while those that underperform by two or more wins improve by an average of 3.2 wins. 2017 strongly continued that trend.

2017's major disappointments -- former playoff teams such as the Raiders, Giants, Texans, Dolphins, and Cowboys -- regressed to the norm after over-performing in 2016. Certainly, each of these teams can point to a number of factors which exacerbated their decline: injuries to Odell Beckham or J.J. Watt, a suspension to Ezekiel Elliott, swapping Ryan Tannehill for a hot-off-the-press-box Jay Cutler. Realistically though, these were flawed teams in 2016 that only showed their pre-existing warts in 2017.

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Despite the success of the metric in correctly predicting the magnitude of change for team results from 2016 to 2017, there remains a huge amount of variance from season to season in the NFL. Adjusted Pythagorean did not have a strong opinion on the Broncos or Rams or Vikings, and yet these teams changed dramatically in terms of results.

These teams represent important reminders to evaluate the full profile of changes from year to year. The Broncos and Rams both had new head coaches, and all three teams had evolving and new quarterback situations in 2017. Together with player movement and injury luck, these factors more than outweighed the Adjusted Pythagorean impact. It's also plausible that the Vikings and Rams were over-performers in 2017 and prime candidates to regress next year (hint: true for Minnesota, not for L.A.).

As we look towards 2018, Adjusted Pythagorean observed a more than one-win Pythagorean Difference for more than half of NFL teams based on the 2017 numbers. Most of the candidates to improve are teams that had low-win seasons for various reasons such as injuries, coaching, or inconsistent young quarterback play (or all of the above as with the Browns.) Teams such as the Browns, Giants, Bucs, and Bears fall into this category. However, Pythagorean also predicts continued improvement from the Jaguars and Ravens, the first- and third-ranked defenses by DVOA, a prediction which was punctuated by Jacksonville's strong playoff performance.

2017 Adjusted Pythagorean Projections
CLE 0 3.29 2.92 2.92
BUF 9 6.35 6.68 -2.32
PIT 13 10.63 10.83 -2.17
JAX 10 11.95 12.02 2.02
CAR 11 9.02 9.11 -1.89
ARI 8 6.08 6.25 -1.75
HOU 4 5.51 5.71 1.71
BAL 9 10.52 10.64 1.64
TEN 9 7.38 7.42 -1.58
TB 5 6.71 6.51 1.51
NYG 3 4.02 4.35 1.35
PHI 13 12.00 11.71 -1.29
ATL 10 9.10 8.71 -1.29
MIN 13 11.69 11.73 -1.27
NE 13 11.99 11.76 -1.24
CHI 5 6.23 6.23 1.23
MIA 6 4.90 4.94 -1.06
LAC 9 10.46 9.77 0.77
CIN 7 6.25 6.25 -0.75
NYJ 5 5.65 5.63 0.63
LAR 11 11.55 11.62 0.62
DEN 5 5.38 5.47 0.47
GB 7 6.23 6.60 -0.40
DAL 9 8.63 8.71 -0.29
KC 10 9.99 9.82 -0.18
SF 6 6.57 6.16 0.16
IND 4 4.17 4.15 0.15
NO 11 11.05 11.14 0.14
DET 9 8.87 8.87 -0.13
WAS 7 6.75 6.93 -0.07
SEA 9 8.95 8.95 -0.05
OAK 6 5.96 5.99 -0.01

Houston also figures to be a major improvement candidate as they are getting high-profile players like Deshaun Watson, J.J. Watt, and others back from injury, and also feature the third highest Pythagorean Difference. These two factors together figure to push them back into the AFC South race.

Teams that project to decline include your typical 13-plus-win teams like the Eagles, Patriots, Steelers, and Vikings. The only 11-win or better teams that project to improve or hold their stature are the Saints and Rams, and that is despite a downward adjustment due to garbage-time points scored (26 for L.A., 13 for New Orleans.) The reality is that it's incredibly hard to win so many games in the NFL, and when it occurs it's usually a sign that the team won a few extra close games.

The predictable decline candidates for 2018 are the Titans and Bills, two over-performing teams identified by traditional metrics and analysis as pretenders come playoff time. According to Adjusted Pythagorean, don't be surprised to see both of these teams outside the playoffs next season. The Titans' decisions to hire new head coach Mike Vrabel certainly muddies the waters there.

While the NFC South seemed like the strongest division in 2017, the Panthers and Falcons project to decline in 2018, although both should remain in the top half of the NFL. Miami interestingly projects to decline for the second consecutive year (after dropping four wins from 2015 to 2016) but a successful return from Ryan Tannehill could prevent another slip.

Ultimately, 2017 proved to be a very strong supporting year for the predictive quality of Adjusted Pythagorean. While Pythagorean will never be an all-encompassing crystal ball for the NFL given the inherent unpredictability and variance of a sport with only 16 games and incredible year-to-year roster turnover, that's perfectly acceptable. By improving our frame of reference via Adjusted Pythagorean, we have a more educated point from which to base future assumptions and predictions about players, coaches, schedule, and other complicating factors. When it comes to predicting how an NFL team's results will change going into the next season, Adjusted Pythagorean is a logical starting point.

Brett Lieblich is a Green Bay Packers fan living in Philadelphia and co-founder of Dash Solutions (dashsdk.com). He is a sports analytics advocate who once charted all the passes in a Tufts University Ultimate Frisbee game. You can contact him on Twitter @reptilestuff.


13 comments, Last at 06 Jul 2018, 10:47am

4 Re: 2017 Adjusted Pythagorean Wins

Brett: what did you learn from charting that college Ultimate game?

I love playing, but I still have a rudimentary understanding of team strategy.

5 Re: 2017 Adjusted Pythagorean Wins

Can you explain how to read that first table?

Also, I'm not sure MIN is as great a candidate as you think. MIN's 2016 season was seriously depressed by historically bad injury levels along the OLine. Hell, they even lost their HC to injury! 2017 was what 2016 was starting to look like, and they still did it with their 3rd-string QB. I think that's a really good team with shaky health issues. Basically, if they regress, it's because of a bad Luck season.

6 Re: 2017 Adjusted Pythagorean Wins

As the article touches on, every team that won 13 games last year outperformed its ADJ PYTH projection by at least a full win. Based on the numbers that have been shown so far between last year's article and this year's, only 2016 NE had an ADJ PYTH projection of more than 12 wins, and no other team in 2016 reached 11.

Unless you're the Patriots, it's pretty hard to win 12 games in consecutive seasons. If you go back to 2010, besides NE (every damn year), only Denver (2012-15), Seattle (2013-14), Pittsburgh (2010-11) and Baltimore (2010-11) have managed to string together back-to-back seasons of 12+ wins. Note that Seattle didn't manage 12 wins in two of the seasons during its DVOA dynasty, and that two 15 win teams over this span (GB & CAR) weren't able to win 12 in the seasons before or after.

10 Re: 2017 Adjusted Pythagorean Wins

The key takeaways for the first table are the 2016 win totals, Pythagorean Difference, and the resulting change in wins.

Using Oakland as an example:
they had 12 wins,
they had a pythagorean difference which was large and negative, which suggested they would decline sharply,
they ended up with only 6 wins in 2017, which was a change of -6 wins.

The other columns, like abs pyth difference (which is the absolute value of Pythagorean Difference) are there for context and comparison purposes.

As far as Minnesota, the numbers say they are a minor regression candidate, which is normal for a 13 win team. They could "regress" to 12 wins and still easily win the NFC North and earn the #1 seed.

7 Re: 2017 Adjusted Pythagorean Wins

Like most NFL win/loss projections, the results are too heavily located in the body of the distribution. The fewest wins projected is 3.3 and the most is 12. I think the projections would be more realistic if you looked at the variance from the mean for the projected and used that to select from the actual distribution of wins and losses. So if the worst projection is 3 standard deviations from the average, then select the number of wins 3 std devs below 8 on the actual distribution.

8 Re: 2017 Adjusted Pythagorean Wins


I suspect that "I also examined the effect of removing points scored by the losing team while in comeback mode -- i.e., down 24 points or more in the fourth quarter. However, these points actually proved to be a good indicator of future results."

Is because that data merely moved the teams towards the center of the distribution.

9 Re: 2017 Adjusted Pythagorean Wins

Yes this is definitely true and Pythagorean wins =/= projected wins. It's merely the expected wins from that season if you replayed the season a bunch of times with the same points totals...

The metric only has two inputs: points for and points against. A metric like that will never project very low or very high win totals because high and low win teams have always needed to win/lose close games and the actual outcome is binary: 0 wins or 1 win.

Pythagorean, on the other hand, will always award a team a significant partial win for close games - whether there was a win or loss by either team.

13 Re: 2017 Adjusted Pythagorean Wins

So, um, let me get this straight...
"2017's major disappointments - former playoff teams such as the Raiders, Giants, Texans, Dolphins, and Cowboys - regressed to the norm after over-performing in 2016...Realistically though, these were flawed teams in 2016 that only showed their pre-existing warts in 2017."

I understand that the point holds for 4 of the 5 listed teams above, but Dallas is enough of an outlier that it should have garnered its own noted exception. Any team, even the Patriots, will have a tendency to "regress" after it posts an exceptional win total, but Dallas was still #2 in the league in ADJ PYTH. "Flawed team"? Only so much as any top team is flawed, it would seem.

I still think it's rather silly to apply a baseball concept (Pythag W-L record) to football - the value of the measure in baseball stems from the reliability of the sport's large sample size, whereas the results from football are inherently unreliable. But to each his or her own, I suppose.