Just above these words, it says “posted by Chase.” And it was literally posted by Chase, but the words below the line belong to Bryan Frye, a longtime reader and commenter who has agreed to write this guest post for us. And I thank him for it. Bryan lives in Yorktown, Virginia, and operates his own great site at http://www.thegridfe.com/, where he focuses on NFL stats and history.

---

With six weeks behind us, we should be at the point where we can figure out who teams are. ^[1]For a counter view, see this post by Chase. However, this season seems to be a parity lover’s dream. Although many teams near the poles are who we thought they were, others (such as New Orleans and Dallas and perhaps San Diego) are far from their preseason projections. The middle ranks are a jumble of average and indiscernible teams, and no team was even able to make it to 4-0. ^[2]Think that’s crazy? In 1961, the Cowboys, Lions, and Eagles were the last undefeated teams in the NFL, at 2-0. With half of the NFL’s teams lingering around 1-2 losses, how can we tell the petty tyrants from those with legitimate claims to the throne? I recently began working on a model to do just that.

[continue reading…]

Just above these words, it says “posted by Chase.” And it was literally posted by Chase, but the words below the line belong to Bryan Frye, a longtime reader and commenter who has agreed to write this guest post for us. And I thank him for it. Bryan lives in Yorktown, Virginia, and operates his own great site at http://www.thegridfe.com/, where he focuses on NFL stats and history.

---

In February, Chase used a regressed version of Football Outsiders’ DVOA metric to derive 2014 expected wins. If you are reading this site, you probably have some familiarity with Football Outsiders and DVOA, FO’s main efficiency statistic. Given the granularity of DVOA, it is no surprise that Year N DVOA correlates more strongly with Year N + 1 wins (correlation coefficient of .39) than Year N wins does (correlation coefficient of .32).

By now, even casual NFL fans probably have at least heard of Pythagorean wins, and regular readers of this site are certainly familiar with the concept. Typically, an analyst uses Pythagorean records to see which teams overachieved and underachieved, which can help us predict next year’s sleepers and paper tigers. Well, I wondered what would happen if we combined the two formulae to make a “DVOA-adjusted Pythagorean Expectation” (or something cooler sounding; you be the judge).

Going back to 1989, the earliest year for DVOA, I used the offensive, defensive, and special teams components of DVOA to adjust the normal input for Pythagorean wins (points). Because DVOA is measured as a percentage, I adjusted the league average points per team game accordingly (I split special teams DVOA between offense and defense). Let’s use Seattle, which led the league in DVOA in 2013, as an example.

In 2013, the league average points per game was 23.4. Last year, Seattle had an offensive DVOA of 9.4% and a defensive DVOA of -25.9% (in Football Outsiders’ world, a negative DVOA is better for defenses).  The Seahawks also had a special teams DVOA of 4.7%.  So to calculate Seattle’s DVOA-adjusted points per game average, we would use the following formula:

23.4 + [23.4 * (9.4% + 4.7%/2)] = 26.15 DVOA-adjusted PPG scored

And to calculate the team’s DVOA-adjusted PPG allowed average, we would perform the following calculation: [continue reading…]

For years, sports analysts have used Pythagorean records as more granular measure of team strength than pure record. We’re not exactly at the point where Pythagorean records are mainstream, but I think, at least with respect to readers of this blog, people are pretty comfortable using Pythagorean records.

For the uninitiated, the use of Pythagorean records in sports dates back at least 30 years, and probably longer. Bill James is generally credited with popularizing this approach in baseball, and the same analysis has since been applied to just about every other spot. The formula to calculate a team’s Pythagorean winning percentage is always some variation of:

(Points Scored^2) / (Points Scored ^2 + Points Allowed^2)

My research has discovered that for football, the best-fit exponent is 2.57. However, football is subject to points inflation.  The best-fit exponent for the NFL in 1972 is not necessarily the best one for 2002 or 2013. This is particularly relevant now, as the 2013 season was the second highest scoring in history. ^[1]In fact, it came in just four hundredths of a point behind the 10-team, 12-game 1948 schedule Moreover, the same exponent that works for a Broncos game does not necessarily work for a Panthers game. [continue reading…]

The Jets beat the Browns 24-13 today, bringing New York’s record up to 7-8. With Rex Ryan on the hot seat — more on this in a few hours — some have defended the controversial head coach by lauding his work this season. After all, if the Jets are one of the least talented teams in the NFL, isn’t it the product of great coaching that the Jets got to 7-8?

That would be true if the Jets were playing like a 7-8 team. But that’s not the case. The Jets have been outscored by 110 points this year, which makes them a bottom five team, a level of production more in line with the team’s talent. If Ryan is getting bottom five production out of a team that’s bottom five in talent, well, that’s not nearly as impressive.

But perhaps you want to argue that the Jets have overachieved in record (but not anywhere else) because of Ryan? Let’s investigate that claim. New York has just 4.45 Pythagorean wins, which means that they’ve won 2.55 more games than expected. The table below shows the 24 teams to exceed their Pythagorean record ^[1]Among teams in 16-game seasons by at least two wins while posting a negative points differential. [continue reading…]

The Patriots and Pythagoras

With the exception of a blowout win over Tampa Bay, each Patriots game this year has been in doubt until the final minute. Against Buffalo, Stephen Gostkowski hit the game-winning 35-yard field goal with nine seconds left. In week two, the Jets had the ball, trailing by three, with 56 seconds remaining at their own 29-yard line, but a Geno Smith interception ended the comeback attempt. The Falcons failed on 4th-and-7 from the Patriots 10-yard line, trailing by a touchdown, with 41 seconds remaining. And last week, Tom Brady had not one, not two, but three chances to win the game in the final three minutes; eventually, he hit Kenbrell Thompkins with 10 seconds left for the game-winning touchdown.

To be fair, the Patriots sole loss was a nail-biter, too: it wasn’t until Adam Jones intercepted a Tom Brady pass at the Bengals three-yard line with 26 seconds remaining that Cincinnati sealed the 13-6 win. Still, New England has “only” outscored its opponents by 28 points so far this year. That’s a pretty low number for a 5-1 team.

From 1920 to 2012, 222 teams started the season with a 5-1-0 record. In an odd bit of trivia, the only one of those teams with a negative points differential through six games was a Super Bowl champion: the 1976 Oakland Raiders, who were blown out by the Patriots in week four but finished the year 16-1 (including a controversial revenge victory against New England in the playoffs).

If we limit ourselves to just post-merger teams, there are 148 teams that started 5-1-0 prior to 2013. If we throw out the strike seasons, that leaves us with 139 teams. This is the part of the post where you’d expect the teams with the highest points differential to perform the best over the rest of the season, but that actually hasn’t been the case.
[continue reading…]

Last year’s article on the Lions was somewhat negative. Detroit went 4-12 in 2012, but the Lions are going to win more games this year. This is the type of article that Jason Lisk, Bill Barnwell, Brian Burke, or Aaron Schatz could write in their sleep. But I’m writing it while watching TV, writing a more complicated article, working out, taking out the trash, and tweeting. Let’s see Lisk do that!

The Lions went 3-9 in games decided by 8 or fewer points last year, giving them the most losses and the worst winning percentage of all teams in one-possession games. While this might imply that the Lions lack the mental fortitude to win close games, you might recall that in 2011, the Minnesota Vikings (2-9) and the Indianapolis Colts (1-7) were the worst two teams in such situations and then made the playoffs last year.

Another way to convey similar information is to look at each team’s Pythagorean record, which is calculated based on a team’s points scored and points allowed and is a better predictor of future winning percentage than past winning percentage. The table below shows each team’s number of wins, points scored and allowed, and number of Pythagorean wins for 2012, using 2.57 as my exponent(which produced the best fit for recent years). The table is sorted by the difference between actual wins and Pythagorean wins:
[continue reading…]

No, this article isn’t an article about quarterbacks squaring off against ancient Greek mathematicians. Today, we’re going to look at quarterback win-loss records and see how they compare to their Pythagorean win-loss records.

Over 30 years ago, Bill James wrote that, on average, baseball teams’ true strengths could be measured more accurately by looking at runs scored and runs allowed than by looking at wins and losses. Since then, sports statisticians have applied the same thinking to all sports. The formula to calculate a team’s Pythagorean winning percentage is always some variation of:

(Points Scored^2) / (Points Scored ^2 + Points Allowed^2)

With the exponent changing from 2 to whatever number best fits the data for the particular sport. In football, that number is 2.53. We can look, for example, at the Pythagorean records for each team in the league last season, and line it up against their actual record:

[continue reading…]