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Scheduling in the 2015 NFL Season: An Application of Graph Theory

In 2015, the New England Patriots and the Carolina Panthers dominated the National Football League regular season. Football analysts and armchair general managers alike credited the success of these two organizations to their talent, coaching, and powerhouse quarterbacks. However, a recent discovery by Professor Stephen Miller at Rutgers University provides a new perspective on exactly why these teams fared so well last season: they had abnormally weak schedules.

In a single season, each NFL team plays a total of 16 games. Six of these games are against three division rivals, four are against the teams of another division in the conference, four are against the teams of a division in the other conference, and the final two are individual pairings based on prior season performance. Traditionally, the divisions that play each other are based on a simple cycle-shaped network. For example, the following network represents the divisional matchups for the current 2016 season.

2016-divisional-matchups

Each node represents a division, while the edges connect divisions that are scheduled to play against each other. For example, the NFC South is slotted against the AFC West and NFC West this year.

In 2015, however, this large single network structure was broken. Professor Miller observed that the divisional matchups were instead divided into two separate clusters. Put another way, the network was divided into two separate connected components, which are shown below.

2015-two-components

On its own, this decomposition of the network into two components should not have resulted in any inconsistencies in the level of difficulty of each team’s schedule. If the distribution of high-quality and low-quality divisions had been even between the two components, there would not have been any unbalanced schedules. However, the orange component had two strong divisions, the AFC East and NFC South, playing against two weak divisions, the NFC East and AFC South. Combined, the NFC East and AFC South won a league-worst 39.8% of their games in 2014. As a result, the Patriots and Panthers, the leaders of the AFC East and NFC South, respectively, essentially had eight weak matchups each throughout the season. In fact, the Patriots and Panthers went on to win 15 of these 16 games, which strongly boosted their overall regular season performance.

Looking at the orange component through the lens of structural balance within networks, the impact of the Panthers’ and Patriots’ weak schedules is abundantly clear. Using the diagram below, define solid orange edges as “positive” ties and dotted orange edges as “negative” ties. In this context, “positive” indicates a matchup and “negative” indicates no game.

orange-component

Clearly, the NFC South-AFC South-NFC East and AFC East-AFC South-NFC East triads are unbalanced with two positive ties and one negative tie each. Conceptually, this lack of balance is captured by the dominance of the NFC South and AFC East over the other divisions.

Overall, looking at NFL scheduling with a networks-oriented perspective uncovers novel insights and provides another layer of data for analysts and fans to consider when developing opinions about specific teams. I am excited to see if the NFL considers Professor Miller’s discovery when building schedules in the future.

 

Source: http://www.nj.com/education/2016/01/nfl_schedule_unfair_rutgers_professor_says.html

 

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