In our eyes, 2015 was a step back for TABMathletics. Of course, this assessment is relative to the rousing success of the 2013 NFL Preview and 2014 NFL Preview. The 2015 NFL Preview was still an overall successful endeavor, but it still left more to be desired when compared from the first two voyages. Part of this had to do with unexpected defiance of Expected Win Differential by two teams last year. The tempered expectations of the Arizona Cardinals and Cincinnati Bengals were overcome by two great regular season campaigns. For that, 2015 marked the first step back in the three-year run of Expected Win Differential. The results from last year were as followed:

**Arizona Cardinals (-3.34 EWD):****Improved from 11-5 to 13-3****Tampa Bay Buccaneers (+3.18 EWD):**Improved from 2-14 to 6-10**Detroit Lions (-2.37 EWD):**Declined from 11-5 to 7-9**Tennessee Titans (+2.27 EWD):**Improved from 2-14 to 3-13**Green Bay Packers (-2.15 EWD):**Declined from 12-4 to 10-6**Cincinnati Bengals (-1.93 EWD):****Improved from 10-5-1 to 12-4****Dallas Cowboys (-1.91 EWD):**Declined from 12-4 to 4-12**New York Jets (+1.79 EWD):**Improved from 4-12 to 10-6**New York Giants (+1.68 EWD):**Owned 6-10 record both seasons**Washington Redskins (+1.65 EWD):**Improved from 4-12 to 7-9**San Francisco 49ers (-1.61 EWD):**Declined from 8-8 to 5-11**Denver Broncos (-1.60 EWD):**Owned 12-4 record both seasons**New Orleans Saints (+1.59 EWD):**Owned 7-9 record both seasons**Oakland Raiders (+1.47 EWD):**Improved from 3-13 to 7-9

As you can see, EWD experiences its first two failures in its three-year history. While nine teams regressed as expected, two teams defied expectations. Both the Cardinals and Bengals improved despite their notably poor EWD totals. Arizona’s improvement can in large part be explained by the healthy return of quarterback Carson Palmer, who built off of his strong showings from late 2013 and early 2014 (re: he owned a 94.09 passer rating over his previous 16 starts before last season). One should be able to see logic in the quarterback stability leading to unrecognized regression. However, Cincinnati’s improvement is less accounted by conventional wisdom. The team improved virtually all around, and it did so without any major factor explaining away this dynamic. It’s simply best left unexplained.

To add some more frustrations, the correlation between each team’s 2014 true wins and 2015 true wins was 0.3783, while the correlation between each team’s 2014 EWD-adjusted wins and 2015 true wins was 0.3148. This marks the first time EWD-adjusted wins had a weaker correlation than true wins. With those failures in mind, EWD is still proving to be a find. So far, through 36 teams over a three-year span, 24 regressed and 10 maintained their record. Normality seems to state that teams at worst (or best) maintain their record when facing prospect of record-based regression. However, the odds normally favor for that regression to happen.

With all that said, we’re still looking to improve this formula to paint a better picture of turnover regression. Therefore, a new formula for **Turnover Win Impact regression (TWIr)** is under consideration. The new formula compensates for three things not considered in the previous TWIr formula: (1) the takeaways v. giveaways dynamic, which regresses at different rates, (2) usage of per-drive turnover rates, which accounts for pace’s impact on outlier turnover margins, and (3) the use of linear regression, which more accurately predicts future turnover rates than a “regression correlation coefficient.” The formula was developed after assessing offensive and defensive turnover rates from 1998-2014, giving us a 17-year span of data (special teams excluded) to consider for future regression projections.

This new formula is much more complicated to calculate than before, but it should make much more sense. Basically, we looked over every team from every season (from 1998 to 2014) and found correlation data based on their offensive and defensive drive-based turnover rates form one year to the next. For example, if team X turned the ball on 15 percent of drives in 2013 and 20 percent of drives in 2014, the team was assigned values of x=15 and y=5. This allowed us to create linear regression lines for the takeaway rate and giveaway rate of non-special teams play. As for special teams, we will give 100 percent regression for the turnover margin, as we simply don’t have enough information to create an accurate linear regression line for the unit.

Using this for 2014, we adjusted the linear regression lines to account the league’s mean turnover rates on offense and defense. Last year’s average drive-based turnover rate was 12.1 percent, thus we adjust the line so y=0 when x=12.1. As a result, the offensive linear regression line for 2014 is **Y _{O} = 9.524 – 0.7871x** and the defensive linear regression line for 2014 is

**Y**.

_{D}= 10.820 – 0.8942xIn order to see how these changes affect TWIr results, check out Table 1. The table shows the TWIr differential for each team in 2014.

**Table 1: Adjustments to Turnover Win Impact Regression, 2014 season**

Team | TWIr-1 | TWIr-2 | Differential | Team | TWIr-1 | TWIr-2 | Differential | |
---|---|---|---|---|---|---|---|---|

BAL |
-0.17 | -0.16 | +0.01 wins | CHI |
+0.43 | +0.34 | -0.09 wins | |

CIN |
0 | -0.10 | -0.10 wins | DET |
-0.60 | -0.55 | +0.05 wins | |

CLE |
-0.52 | -0.47 | +0.05 wins | GB |
-1.20 | -1.16 | -0.04 wins | |

PIT |
0 | +0.01 | +0.01 wins | MIN |
+0.09 | +0.15 | +0.06 wins | |

BUF |
-0.60 | -0.63 | -0.03 wins | DAL |
-0.52 | -0.58 | -0.06 wins | |

MIA |
-0.17 | -0.13 | +0.04 wins | NYG |
+0.17 | +0.24 | +0.07 wins | |

NE |
-1.03 | -1.03 | +0.00 wins | PHL |
+0.69 | +0.74 | +0.05 wins | |

NYJ |
+0.95 | +0.99 | +0.04 wins | WSH |
+1.03 | +0.91 | -0.12 wins | |

HOU |
-1.03 | -1.09 | -0.06 wins | ATL |
-0.43 | -0.61 | -0.18 wins | |

IND |
+0.43 | +0.33 | -0.10 wins | CAR |
-0.26 | -0.17 | +0.09 wins | |

JAX |
+0.52 | +0.53 | +0.01 wins | NO |
+1.12 | +1.12 | +0.00 wins | |

TEN |
+0.86 | +0.95 | +0.09 wins | TB |
+0.69 | +0.71 | +0.02 wins | |

DEN |
-0.43 | -0.46 | -0.03 wins | ARZ |
-0.69 | -0.63 | +0.06 wins | |

KC |
+0.26 | +0.38 | +0.12 wins | SEA |
-0.86 | -0.89 | -0.03 wins | |

OAK |
+1.29 | +1.37 | +0.08 wins | SF |
-0.60 | -0.68 | -0.08 wins | |

SD |
+0.43 | +0.51 | +0.08 wins | STL |
+0.17 | +0.10 | -0.07 wins |

**TWIr-1:** -[0.8175 * (ToM * 4) / 38]; **TWIr-2:** [(Y_{D} / 100 * DDr) – (Y_{O} / 100 * ODr) – ToM_{S}] * 4 / 38

As the table shows, there is only a small difference from the “regression correlation coefficient” that was previously used. Albeit from a lack of strong statistical foundation, the coefficient used was fairly accurate of what the numbers from turnover rates spit out for nearly the past two decades. These new adjustments will be small on a functional level, but it’s the correct adjustment on a practical level.

Ultimately, if you want to understand the big difference between this formula and the past formula, you must look at the “slope” of the lines. Even if you go by rates for this current formula, one turnover over or under the mean is equivalent to a 0.8942-turnover difference in regression on defense and a 0.7871-turnover difference in regression on offense (along with 1-turnover difference in regression on special teams). It used to be a 0.8175-turnover difference in regression under the old formula.

The Atlanta Falcons (-0.18 differential) experienced the biggest change in 2014, given their plus-4 turnover margin on special teams. Remember we decided to regress the entirety of special teams turnovers, which proved to be accurate in this case, as the 2015 Falcons earned no takeaways and suffered no giveaways on special teams. Still, this most notable difference did not change their regression status heading into the 2015 season. However, one team did earn a change in status, as the Kansas City Chiefs (+0.12 differential to give them +1.52 EWD) would’ve been the 15th team in 2014 to face regression. They improved as expected, going from 9-7 to 11-5.

In the end, this formula change does nothing to explain the Bengals and Cardinals breaking regression. However, since we had 14 (now 15) teams on the hook as opposed to the 11 teams each of the two previous years, maybe some broken regression was bound to happen. Chalk up 2015 as an atypical year for EWD-based regression, and let’s move forward.

——————–

To calculate the Expected Win Differential and determine which teams may be in line for win-loss record regression in 2016, the **Pythagorean Win Differential (PWD)** of each team (Table 2) must first be calculated. Remember that the Pythagorean win formula used here is slightly different that what was originally constructed by Bill James and crew, as a result of the league’s recent uptick in scoring. The PWD results should give you an initial idea which teams are most at risk for regression, but turnovers could possibly explain away the scoring dynamic. Therefore, take these results with some amount of caution until the product is finished.

**Table 2: Pythagorean Win Differential, 2015 season**

Team | PythW | Record | Differential | Team | PythW | Record | Differential | |
---|---|---|---|---|---|---|---|---|

BAL |
6.11 | 5-11 | +1.11 wins | CHI |
6.39 | 6-10 | +0.39 wins | |

CIN |
11.62 | 12-4 | -0.38 wins | DET |
6.94 | 7-9 | -0.06 wins | |

CLE |
4.12 | 3-13 | +1.12 wins | GB |
9.24 | 10-6 | -0.76 wins | |

PIT |
10.61 | 10-6 | +0.61 wins | MIN |
9.79 | 11-5 | -1.21 wins | |

BUF |
8.52 | 8-8 | +0.52 wins | DAL |
5.18 | 4-12 | +1.18 wins | |

MIA |
5.87 | 6-10 | -0.13 wins | NYG |
7.51 | 6-10 | +1.51 wins | |

NE |
11.49 | 12-4 | -0.51 wins | PHL |
6.75 | 7-9 | -0.25 wins | |

NYJ |
9.97 | 10-6 | -0.03 wins | WSH |
8.23 | 9-7 | -0.77 wins | |

HOU |
8.76 | 9-7 | -0.24 wins | ATL |
7.83 | 8-8 | -0.17 wins | |

IND |
6.09 | 8-8 | -1.91 wins | CAR |
12.19 | 15-1 | -2.81 wins | |

JAX |
6.34 | 5-11 | +1.34 wins | NO |
6.54 | 7-9 | -0.46 wins | |

TEN |
4.85 | 3-13 | +1.85 wins | TB |
6.13 | 6-10 | +0.13 wins | |

DEN |
9.72 | 12-4 | -2.28 wins | ARZ |
11.92 | 13-3 | -1.08 wins | |

KC |
11.13 | 11-5 | +0.13 wins | SEA |
11.75 | 10-6 | +1.75 wins | |

OAK |
6.99 | 7-9 | -0.01 wins | SF |
3.80 | 5-11 | -1.20 wins | |

SD |
5.95 | 4-12 | +1.95 wins | STL |
6.44 | 7-9 | -0.56 wins |

**PythW:** Pythagorean Wins, or (Points Scored ^ 2.4) / ((Points Scored ^ 2.4) + (Points Allowed ^ 2.4))

It comes with some degree of expectation that the two combatants of Super Bowl 50 are the first two teams on the PWD regression chopping block. However, both teams are at least two games below expectation in Pythagorean record. It could lead to some significant regression for both teams, which could mean some major changes to the power structure of the NFL. Meanwhile, the Colts return to their previous place upon the precipice of regression. This may very well mark their third time surpassing negative regression in four years. On the flip side, there is a mix of teams who could be line for notable improvement. Whether it’s bottom feeders like the Chargers and Titans, or a playoff team like Seahawks, several teams are potentially well on their way to positively surpassing the regression threshold.

Moving on to the next step, the **Turnover Win Impact regression (TWIr)** will be shown in Table 3. This will use the aforementioned new formula for each team in 2015. Adjusting for the 11.7 per-drive turnover rate in the NFL last year, the offensive and defensive linear regression lines are adjusted so y=0 when x=11.7. As a result, the offensive linear regression line for 2015 is **Y _{O} = 9.209 – 0.7871x** and the defensive linear regression line for 2015 is

**Y**. Special teams will continue to have 100 percent regression. Let’s also note that the 38 points-per game-differential equivalency holds for 2015, given the scoring-based PWD results.

_{D}= 10.462 – 0.8942x**Table 3: Turnover Win Impact Regression, 2015 season**

Team | ORate | DRate | STToM | TWIr | Team | ORate | DRate | STToM | TWIr | |
---|---|---|---|---|---|---|---|---|---|---|

BAL |
14.0% | 7.0% | -1 | +1.29 wins | CHI |
11.2% | 8.0% | +2 | +0.33 wins | |

CIN |
9.3% | 15.0% | +1 | -1.03 wins | DET |
12.3% | 9.1% | 0 | +0.54 wins | |

CLE |
15.2% | 11.7% | -3 | +0.83 wins | GB |
8.9% | 11.5% | +1 | -0.52 wins | |

PIT |
13.7% | 14.3% | +1 | -0.24 wins | MIN |
9.3% | 11.9% | 0 | -0.38 wins | |

BUF |
8.6% | 11.0% | +1 | -0.46 wins | DAL |
18.0% | 5.6% | -1 | +2.02 wins | |

MIA |
9.6% | 8.4% | -1 | +0.37 wins | NYG |
11.3% | 14.2% | +1 | -0.61 wins | |

NE |
5.7% | 10.5% | -2 | -0.53 wins | PHL |
15.3% | 11.8% | +2 | +0.38 wins | |

NYJ |
11.6% | 14.4% | +1 | -0.61 wins | WSH |
11.1% | 14.9% | -2 | -0.42 wins | |

HOU |
9.8% | 11.1% | +3 | -0.52 wins | ATL |
17.2% | 13.4% | 0 | +0.52 wins | |

IND |
14.4% | 12.4% | -1 | +0.41 wins | CAR |
9.6% | 19.4% | +1 | -1.87 wins | |

JAX |
14.0% | 8.8% | 0 | +0.90 wins | NO |
10.4% | 11.7% | 0 | -0.20 wins | |

TEN |
16.2% | 8.1% | +2 | +1.13 wins | TB |
14.8% | 12.8% | -2 | +0.48 wins | |

DEN |
15.1% | 11.9% | +2 | +0.31 wins | ARZ |
11.8% | 16.7% | 0 | -0.86 wins | |

KC |
7.1% | 15.3% | -1 | -1.21 wins | SEA |
8.6% | 13.2% | -1 | -0.59 wins | |

OAK |
10.3% | 11.5% | -1 | -0.09 wins | SF |
8.2% | 6.6% | -2 | +0.56 wins | |

SD |
12.4% | 10.0% | 0 | +0.39 wins | STL |
10.2% | 12.1% | 0 | -0.17 wins |

**ORate:** Turnover percentage per offensive drive; **DRate:** Turnover percentage per defensive drive; **STToM:** Special teams turnover margin;

**TWIr:** [(Y_{D} / 100 * DDr) – (Y_{O} / 100 * ODr) – ToM_{S}] * 4 / 38

Oh, the poor Dallas Cowboys. Without their quarterback Tony Romo for 12 of the team’s 16 games, the team was already in enough of a hole. However, the defense went from first to worst in per-drive turnover rate. That contributed by very heavily to the team’s 4-12 record. Thankfully, turnover regression alone is projected to add two wins of life onto Big D’s 2016 expectancy. What a nice remedy. On the flip side, the Panthers rode their dynamic turnover differential to the league’s best record and a Super Bowl 50 appearance. Simple turnover regression accounts for nearly two wins. No other teams come close to the extremes of these two Thanksgiving 2015 combatants.

The final step in today’s study involves putting it all together. The **Expected Win Differential (EWD)** for each team in 2015 (Table 3) uses the sum of the Pythagorean Win Differential and the Turnover Win Impact regression (**PWD + TWIr**). With a new formula for TWIr, we’ve decided to also change how we determine the regression threshold. Given that TWIr totals aren’t significantly different under the new formula, we use the previous three seasons of data to get our threshold. Data from 2012 to 2014 yields an EWD standard deviation of 1.551 wins, which will become our regression threshold. Note that the EWD to Win Differential correlation of 0.5758 suggests a moderate positive relation, meaning that teams with a greater absolute EWD (re: further from zero) generally are more likely to have a greater absolute win differential the following season. In other words, we have good reason to believe in using a regression threshold to classify the teams expected to regress. Teams in line for improvement are denoted in blue, while teams in line for decline are denoted in red.

**Table 4: Expected Win Differential, 2015 season**

Team | PWD | TWIr | EWD | Team | PWD | TWIr | EWD | |
---|---|---|---|---|---|---|---|---|

BAL |
+1.11 | +1.29 | +2.40 wins | CHI |
+0.39 | +0.33 | +0.72 wins | |

CIN |
-0.38 | -1.03 | -1.41 wins | DET |
-0.06 | +0.54 | +0.48 wins | |

CLE |
+1.12 | +0.83 | +1.95 wins | GB |
-0.76 | -0.52 | -1.28 wins | |

PIT |
+0.61 | -0.24 | +0.37 wins | MIN |
-1.21 | -0.38 | -1.59 wins | |

BUF |
+0.52 | -0.06 | +0.06 wins | DAL |
+1.18 | +2.02 | +3.20 wins | |

MIA |
-0.13 | +0.37 | +0.24 wins | NYG |
+1.51 | -0.61 | +0.90 wins | |

NE |
-0.51 | -0.53 | -1.04 wins | PHL |
-0.25 | +0.38 | +0.13 wins | |

NYJ |
-0.03 | -0.61 | -0.64 wins | WSH |
-0.77 | -0.42 | -1.19 wins | |

HOU |
-0.24 | -0.52 | -0.76 wins | ATL |
-0.17 | +0.52 | +0.35 wins | |

IND |
-1.91 | +0.41 | -1.50 wins | CAR |
-2.81 | -1.87 | -4.68 wins | |

JAX |
+1.34 | +0.90 | +2.24 wins | NO |
-0.46 | -0.20 | -0.66 wins | |

TEN |
+1.85 | +1.13 | +2.98 wins | TB |
+0.13 | +0.48 | +0.61 wins | |

DEN |
-2.28 | +0.31 | -1.97 wins | ARZ |
-1.08 | -0.86 | -1.94 wins | |

KC |
+0.13 | -1.21 | -1.08 wins | SEA |
+1.75 | -0.59 | +1.16 wins | |

OAK |
-0.01 | -0.09 | -0.10 wins | SF |
-1.20 | +0.56 | -0.64 wins | |

SD |
+1.95 | +0.39 | +2.34 wins | STL |
-0.56 | -0.17 | -0.73 wins |

**EWD:** PWD – TWIr; **Note: **The threshold for regression is ±1.551 wins.

These are much of the expected or even obvious teams to face regression. On the plus-side, the Browns and Titans come off of sharing the league’s worst record with a 3-13 record each in 2015. Then there’s the Chargers, Cowboys and Ravens. Each team dropped at least five games in the standings last year after losing a combined 24 one-possession games. All three teams have more than capable quarterbacks, with Tony Romo (Cowboys) and Joe Flacco (Ravens) returning from season-ending injuries. EWD regression seems like a mere formality. On the minus-side, the Panthers and Broncos come off of Super Bowl appearances. Carolina’s 15-1 record obviously plays a big role as well, given that no team has ever won 15+ games in consecutive seasons. Note that they are more than three(!) standard deviations away from zero. Then there’s the Cardinals and their 13-3 season that ended in an NFC Championship Game appearance. Sure, they broke regression last year, but perhaps there’s no place to move up in 2016.

Truly, the only remotely unexpected teams facing regression are the Jaguars and Vikings. Jacksonville got here thanks in much part to Blake Bortles’ 29 touchdown passes when trailing, which was the highlight of his unusually trailing-waited success in 2015. Minnesota got here mostly because of its grounded offense in 2015, as Teddy Bridgewater still hasn’t taken full control of his offense. The regression at play makes for an interesting wrinkle as Bortles and Bridgewater both enter their third season, respectively. Given that Minnesota has a six-game head start from last season, perhaps these tales converge to share a similar script in win-loss record in 2016.

Hopefully, the formula change and a seemingly calm results table lead to a return to glory for Expected Win Differential.