By Scott Kacsmar
Cold, Hard Football Facts Regressor to the Mean

A great statistical tool that works well with sports data is regression analysis. You build a model with variables so that you can analyze the relationships between them, and the model can be used to make predictions. Basically it helps us stat nerds sound like we have the necessary mathematical evidence to support the predictions we throw out there.
The regression model this stat nerd has personally used the last five years sets team win percentage as the dependent variable, and looks at five net statistics as the independent variables.
Those independent variables are:
Net Points – Points scored minus points allowed
Net Yards – Offensive yards minus defensive yards (sacks included in passing yardage for both)
Turnover Differential – Takeaways minus giveaways
Third Down Differential – Third down conversion percentage (offense) minus third down conversion percentage (defense)
Passer Rating Differential – Offensive passer rating minus defensive passer rating
All teams from 1995 to 2010 are used (n=501).
Any time you use points in your regression model, you are going to get good results. Points are what win games. Everyone knows that. The goal was not to create a great regression model without points (some other time), but to take the Bill James’ idea of Pythagorean Wins (what a team’s record should be based on points scored and allowed), and instead use regression and more data to determine the team’s theoretical win percentage.
Here is how well each stat correlates with win percentage:
Stat Win% Correlation
Net Points 0.92
Passer Rating Differential 0.80
Net Yards 0.70
Third Down Differential 0.64
Turnover Differential 0.64
The R-squared value for this model is 0.843. That essentially says that 84.3% of the variance in win percentage is accounted for by these variables. Points alone obviously make up for a lot of the variation. If we removed Net Points from the model, the R-squared value would be 0.734, but all four of the variables would then be significant. Not bad, but a better model could be made. We’ll leave that for another day.
It is worth noting that a model using nothing but Passer Rating Differential to predict win percentage produces an R-squared of 0.643. Not bad for something that does not account for the running game, sacks, fumbles, penalties, special teams or field position.
Here are the regression model results for 1995-2010, starting with the top 10 best teams based on predicted win percentage. All data is for the regular season only.

Top 10 Teams In Predicted Win%

Rk Team Year Win Loss Win% Pred%
1 New England 2007 16 0 1.000 1.041
2 St. Louis 1999 13 3 0.813 0.975
3 Minnesota 1998 15 1 0.938 0.953
4 Green Bay 1996 13 3 0.813 0.927
5 St. Louis 2001 14 2 0.875 0.871
6 New England 2010 14 2 0.875 0.868
7 San Francisco 1995 11 5 0.688 0.838
8 Indianapolis 2005 14 2 0.875 0.836
9 Indianapolis 2007 13 3 0.813 0.830
10 San Diego 2006 14 2 0.875 0.826
The ten best teams features just two Super Bowl winners (1999 Rams, 1996 Packers), as this era of football has been characterized by the best team in the regular season offer suffering a very disappointing postseason. All the teams ranked 6-through-10 lost in their first playoff game, all at home.
The 2007 Patriots were so good they were predicted to win more games than humanly possible. Guess that’s what happens when you have a formula with all positive coefficients and their performance was so good in each.
Here is how the 2007 Patriots stack up to the other 500 teams since 1995 (and just for fun: same stats included for the 2007 Giants and their .529 predicted win% season):
Stat 2007 Patriots Rank 2007 Giants Rank
Net Points 315 1st 22 213th
Passer Rating Differential 37.9 3rd -10.4 375th
Net Yards 1967 3rd 422 157th
Third Down Differential 14.5 3rd 7.0 65th
Turnover Differential 16 28th -9 408th
As the Cold, Hard Football Facts note, Super Bowl XLII is the greatest upset ever.
You may not be familiar with the 1995 San Francisco 49ers, but we have no doubt there has not been a more statistically dominant 11-5 team or defending Super Bowl champion since those 49ers set out on their title defense.
Despite losing Deion Sanders to rival Dallas and reigning MVP Steve Young for five games due to injury, the 1995 49ers led the league in points scored (457), scoring differential (+199), yards allowed (4,398), interceptions (26), and they were without a doubt the best rushing defense in the league (attempts, yards, yards/carry and touchdowns). Even with Elvis Grbac starting five games, the 49ers passed for 4,779 yards, and Jerry Rice was as dominant as ever with a record 1,848 yards receiving.
It looked like business as usual for the 49ers, but as we saw in 1987 and 1992, their statistically dominant teams weren’t always a championship team. The 1995 49ers would lose five games by just a combined total of 15 points.  In the playoffs, they fell behind 21-0 at home against Green Bay, and ultimately lost 27-17. The loss marked the beginning of a five-game losing streak to the Packers. The 49ers are just 1-13 against the Packers since, with the only win coming on Young’s last second touchdown pass to Terrell Owens in the 1998 NFC Wild Card game.
That was a look at the teams that dominated their opponents. Now for the complete opposite, the biggest doormats the league has seen since 1995.

Bottom 10 Teams In Predicted Win%

Rk Team Year Win Loss Win% Pred%
1 St. Louis 2009 1 15 0.063 0.053
2 Cleveland 2000 3 13 0.188 0.069
3 Detroit 2008 0 16 0.000 0.071
4 Arizona 2000 3 13 0.188 0.085
5 Detroit 2009 2 14 0.125 0.098
6 Arizona 2003 4 12 0.250 0.110
7 St. Louis 2008 2 14 0.125 0.113
8 Cleveland 1999 2 14 0.125 0.116
9 Carolina 2010 2 14 0.125 0.142
10 San Francisco 2004 2 14 0.125 0.157
A lot of the usual suspects make the list, with repeat performances by the Rams, Browns, Lions and Cardinals making up the top eight. Last year’s Carolina team shows up at nine (good luck to Ron Rivera and Cam Newton), and the bottom finally fell out on San Francisco in 2004, the season where they were only capable of beating the Cardinals 31-28 in overtime (twice). Don’t you just love the NFC West?
The following table shows the team that ranked the best and the worst in a variety of stats since 1995:
Stat Best Team Value Worst Team Value
Net Points 2007 Patriots 315 2009 Rams -261
Passer Rating Differential 1999 Rams 42.5 2009 Lions -48.9
Net Yards 2001 Rams 2208 2005 49ers -2672
Third Down Differential 1998 Vikings 17.5 1999 Browns -17.7
Turnover Differential 2010 Patriots 28 2000 Chargers -28
Offensive Passer Rating 2004 Colts 119.7 1998 Chargers 44.9
Defensive Passer Rating 2002 Buccaneers 48.4 2008 Lions 110.9
Third Down %, Offense 2006 Colts 56.1 2005 49ers 24.0
Third Down %, Defense 1998 Raiders 26.3 1995 Browns 49.6
Lastly here’s a look at the teams that were the biggest overachievers and underachievers, which are determined by the largest differences between expected wins and predicted wins. If your record is much better than your stats, you overachieved. If your record is much worse than your stats, you underachieved. This could very well aid a prediction of how a team will do the following season, which we provided the data for as well.

Top 10 Overachievers

Rk Team Year N Wins Pred. Wins Diff. Year N+1 Wins Diff.
1 Pittsburgh 2004 15 11.53 3.47 11 -4
2 Indianapolis 2009 14 10.90 3.10 10 -4
3 Atlanta 2004 11 8.11 2.89 8 -3
4 Tennessee 1999 13 10.19 2.81 13 0
5 Indianapolis 1999 13 10.25 2.75 10 -3
6 New England 2003 14 11.26 2.74 14 0
7 Minnesota 2000 11 8.44 2.56 5 -6
8 Carolina 2003 11 8.44 2.56 7 -4
9 Philadelphia 1995 10 7.54 2.46 10 0
10 Denver 2008 8 5.68 2.32 8 0
The average decline the following season was 2.4 wins. Four teams were able to put the same record together, while no one increased their win total.
In 1999 the Titans and Colts met each other in the AFC Divisional playoffs, while the 2003 Panthers and Patriots of course squared off in Super Bowl 39. The 2003 Patriots are the only Super Bowl winner on the list (2009 Colts and 1999 Titans lost the big game).
The Colts appear twice in the top five, and they routinely exceed their predicted win total. You may have noticed both the 2005 and 2007 teams made the top 10 best teams list earlier, but it was the 2006 Colts that won the Super Bowl. That team was +1.96 in wins, good for 21st since 1995.
Who were the three biggest overachievers in 2010?
Jacksonville Jaguars (+2.06 wins) – Remember when Colts’ coach Jim Caldwell called a silly timeout and Josh Scobee kicked a 59-yard game-winning field goal last year? Remember when Mike Thomas made a 50-yard game-winning catch on a deflected Hail Mary to beat the Texans? It’s only shown on NFL Network’s Redzone commercial 75 times a day.
Well, those types of moments weren’t exactly supposed to happen, hence 8-8 for Jacksonville. They drafted a new QB, but Jack Del Rio needs to win now. His pass defenses since 2007 have seem to master the art of “no rush, no coverage”. With a schedule that features Brees, Roethlisberger, Rivers, Ryan and two games each against Schaub and Manning, it could be another long year for the Jaguars.
SeattleSeahawks (+1.76 wins) – Who says Seattle backed into the playoffs? Pete Carroll’s bunch actually did better than they should have. Something this comeback aficionado hated about Seattle’s 2010 season is that they lost all nine of their games by at least 15 points, and five of their wins were by double-digits. Even with that kind of distribution, they still put up lousy stats overall in the five key variables of the model.
Now that long-time QB Matt Hasselbeck is gone, things could get ugly for Seattle in 2011 if they don’t play better. It’s time for Marshawn Lynch to move on from his “beast mode” touchdown run in the playoffs, because he’s either going to have Tarvaris Jackson or Clipboard Jesus (that’s Charlie Whitehurst in case you’ve never seen Him before) at QB now. Well, it is still the NFC West.
Chicago Bears (+1.72 wins) – The Bears essentially racked up their stolen victories before October even started. Who can forget Calvin Johnson’s game-winning touchdown catch being overturned on Detroit in the season opener? Two weeks later the Bears sat back while Green Bay committed an obscene 18 penalties for 152 yards before James Jones fumbled the ball and Robbie Gould kicked a game-winning field goal.
In 2011 the Packers are expected to be great again, Chilly is gone in Minnesota, and everyone is running towards Detroit’s bandwagon, leaving the Bears as a bit of a mystery. We don’t know yet what impact the new kickoff rules will have, but if there’s a team in the league that will be affected the most, it’s Chicago.
Which team since 1995 has posted the record closest to their predicted record? The 1997 Eagles (0.0189 wins).
Switching gears, let’s look at those teams that were putting up the stats, but could not finish games with wins for whatever the reason. Bad luck? Choked? You decide.

Top 10 Underachievers

Rk Team Year N Wins Pred. Wins Diff. Year N+1 Wins Diff.
1 San Diego 2001 5 8.29 -3.29 8 3
2 Green Bay 2008 6 9.28 -3.28 11 5
3 Carolina 2001 1 3.83 -2.83 7 6
4 Tampa Bay 2004 5 7.78 -2.78 11 6
5 Baltimore 2009 9 11.63 -2.63 12 3
6 Indianapolis 1997 3 5.62 -2.62 3 0
7 St. Louis 1999 13 15.60 -2.60 10 -3
8 Jacksonville 2006 8 10.55 -2.55 11 3
9 San Diego 2008 8 10.53 -2.53 13 5
10 Jacksonville 2002 6 8.52 -2.52 5 -1
The average increase the following season was 2.7 wins. Seven teams increased their win total by at least three games. The Colts stayed at the same win total in Peyton Manning’s rookie season, while the 2000 Rams and 2003 Jaguars suffered a small decline.
It is awkward seeing the 1999 Rams, a 13-3 Super Bowl winner, on a list of underachievers, but it’s because they were the second most dominant team in this era, and it’s the way they lost the three games.
In a Super Bowl preview, the Rams went to Tennessee and fell behind 21-0 in the first quarter. They were able to get within a field goal, 24-21, only to watch kicker Jeff Wilkins miss a 38-yard field goal that would have tied the game with 0:07 left.
The following week in Detroit, Kurt Warner threw a go ahead touchdown pass with 2:42 left. On the next drive, the Lions converted a 4th & 26 (Gus Frerotte was the quarterback), and were able to get the game-winning touchdown with 0:28 left. The Rams lost 31-27.
In the week 17 finale at Philadelphia, the Rams rested some starters late in a 24-24 game. The Rams would then turn the ball over five times in the fourth quarter (seven for the game), as the Eagles won 38-31.
When you look at these three losses, you can see why the stats say they should have really challenged the perfect season.
Notice both the Chargers and Packers make the list for the 2008 season. Keep that in mind.
Who were the three biggest underachievers in 2010?
Tennessee Titans (-2.20 wins) – In case you forgot, the Titans were 5-2 last year. After coming off an impressive win over the Eagles, where Kenny Britt exploded for 225 yards and 3 touchdowns, the Titans finished just 1-8 and long-time coach Jeff Fisher stepped down.
With a brand new coaching staff the Titans don’t seem like a great pick for a team to improve in 2011. However, many of the league’s great turnarounds coincide with the arrival of a new coach and quarterback, and the Titans do have that in Mike Munchak and Matt Hasselbeck. They also have one of the better offensive lines in the league, so the running game should still be productive, and a reenergized veteran QB like Hasselbeck could prove to be a valuable signing.
It’s also good news that a blindfolded Roger Goodell used his “Jump to Conclusions” mat and landed on “No Suspension” for Kenny Britt this season.
Green Bay Packers (-2.11 wins) – Nice, another Super Bowl champion leading the underachiever list. You have to remember the Packers were a 10-6 team that claimed the sixth seed on tie-breakers over the 10-6 Buccaneers and Giants. Had Tampa Bay not lost that game in overtime to Detroit late in the year, we are probably talking about Green Bay getting their players back healthy this year after that disappointing 2010. Instead we’re talking about the defending Super Bowl Champions.
Green Bay shows up here because of how great they were statistically, but also for how bad they were (and have been) at winning close games. Remember, the Packers never trailed by more than seven points all season long. We have a whole feature planned on this topic for next week, so be sure to come back for that in-depth analysis.
San Diego Chargers (-2.11 wins) – If only special teams were devalued a year earlier, we would have seen the Chargers shake up the AFC playoffs for sure. They outgained their opponents by 1,984 yards, which is 17 more than the 2007 Patriots. The only variable they weren’t exceptional at was their -6 turnover differential. They won six games by at least 21 points, but they struggled to win the close games, then had a shocking December with double-digit losses to the Raiders and Bengals.
With the way San Diego starts seasons under Norv Turner, it makes you wonder if every calendar in the facility is a month behind. Slow start or not, the Chargers are a heavy favorite to regain the AFC West crown in 2011. The last time they were in this position they went 13-3 and claimed the AFC’s #2 seed. Now if they could just figure out what to do in January.
For all the new Detroit fans, the Lions came in fifth (-1.92 wins).
We’ll chime in around midseason to report on what the model says about the teams of 2011.