From Elite to Poor and Back: A Lesson in Stability and Transiency in the NFL

Math equations on chalk board


Free agency is almost (officially) a week old, and we at SumerSports have had you covered from the jump. Thomas Dimitroff and I went through the tampering period and the first few hours of the league year on the SumerSports Show:

Free agency, the draft, and the offseason are often hailed as transitional phases for NFL teams. Chicago, coming off a season where they had the worst record in football, is attempting to transition into an era of contention with Justin Fields at quarterback. Teams like Tampa Bay and the Los Angeles Rams appear to be transitioning into an era of rebuilding and retooling after winning two of the last three Super Bowls.

While the idea that there are seasons of transition can be scary, they are unmistakable when looking at team strengths. Teams move from elite to above or even below average frequently, while many stay in the poor category for some time. The question is which states are more stable and which states are more transient – and hence not a reasonable goal – than the other ones. 

For the last two offseasons, I used Markov matrices to look at the probability of transition from one of four different stages: poor, below average, above average, and elite.

In those articles, I used PFF’s team-level metric, PFF Elo, to determine the phase a team was in. While I really like that metric (I am a little biased, I built it), we are going to use something more public for this article, Football Outsider’s DVOA. Depending on which side of zero they were on, a team with a DVOA over/under 12.5% was considered elite/poor, while those closer to zero were considered above or below average. These happen to be the quartiles when you look at the history of FO’s DVOA data.

We looked at DVOA immediately after the regular season for each year after the new CBA was enacted (2011) to create our transition probabilities. We put these transition probabilities into a matrix, which, given the last twelve years of data, looks like this:

Math equations

Along each row is the probability of a team “entering” that category, and along each column is the probability of a team “leaving” that category into another category. Notice here that, maybe surprisingly given the league’s supposed slant towards parity, the most stable category for teams year-to-year is being elite. An elite team remains in that category year-to-year with a probability of 0.45, which is a fair bit higher than the 38% percent likelihood that a team stays poor.

It is remarkable that a team is almost just as likely to go from being above average to below average (27%) than it is to stay above average (28%). The opposite, however, is not true as staying below average occurs 36% of the time. A team that is categorized as above average one year is almost as likely to jump all the way to poor (22%) as they are to make the jump to elite (23%). In other words, being above average is the most transient state in the NFL.

Markov matrix models are tools often used to understand the long-term steady-state solution of an iterative system of probabilities like this one. You can view my linear algebra course to see how it is used in the world of genetics. If one seeks a vector modeling the likelihood that a team is elite, above average, below average, or poor each year (t), one can use the Markov matrix above to iterate upon such a vector through matrix multiplication:

Math equations

From here, it is interesting to look at the powers of the Markov matrix. If the matrix to the first power (just the matrix) tells us the likelihood of transitioning from one state to the next, the square of the matrix tells us what the likelihood is of transitioning from state to state in two years:

Math equations

While the first power of the matrix sheds light on the transiency of being above average (but not elite), the square of the matrix shows the absorbency of being below average. For each classification other than being elite, the most likely state after two years is being below average. For elite teams, it is more likely that they are below average in two years than above average (but no longer elite). Teams that are poor and below average have the exact same likelihood (29%) of being below average in two years and very similar likelihoods of being above average or elite (43% to 46%). Above average and below average teams have about the same likelihood of being poor (24% to 25%) in two years.

The stability of below average teams is found in the stable-stage distribution of this matrix, which is what you would get if you iterated on the matrix a large number of times and looked at the resulting probability vector. This can be found by normalizing the eigenvector associated with the matrix’s first eigenvalue (which is always 1 for this matrix type). We have the helpful Perron-Frobenius theorem to thank for this. This stable-stage distribution is:

Math equations

Long term, the largest group of teams is below average, while the second highest classification is elite teams represented at 25%. Teams that are classified as above average have the smallest representation at 23% followed by teams classified as poor.

Lessons for Team Building

While every situation is different, it can be instructive to know the base rates associated with team strengths in the NFL.

For teams that have earned an elite distinction, such a distinction is stickier than any other on a year-to-year basis. This is likely due to a great quarterback, a great head coach, or in the case of Kansas City, both. Almost half of the teams that are elite one year are elite the next, and almost a third are elite two years in the future.

Being above average in the NFL is a difficult goal as it is the most transient state according to this research. In two years, an above average team is more likely to be below average (28%), elite (25%), or poor (24%), than it is to stay in that classification (23%). Some of this is probably good; elite teams can backslide for a period of time due to regression or injury to important positions, but it is more likely that a team is above average for unsustainable reasons (e.g., defense, a pop-up season by a previously mediocre quarterback, or turnovers). Decisions made to stay above average should thus be viewed with skepticism. 

Below average is the most absorbent state in the league. This is interesting because, for most Markovian systems, the two edges (in this case elite and poor) in finite systems are the most absorbent. Mechanically, this happens for a few reasons. The NFL lends instruments such as schedule differences and the rookie wage scale (which, when applied to a quarterback, is a huge edge) to the worst teams to help bring them from the depths of the league to at least a measure of respectability:

How NFL teams should attack the quarterback position despite a down class | NFL Draft | PFF

There are also more things that can go wrong in the NFL than can go right. For teams without an elite head coach and/or elite quarterback, there can be more drift downward from above average or even elite to below average than upward, and hence the result we see.

While we have seen some serious futility in the NFL, sustained poor play is the exception and not the rule; this research shows the poor category is more of a transient state than an absorbent one. The instruments at the league’s disposal aimed at making bad teams better and the natural deterrents that prevent above average teams from both becoming elite and staying above average give rise to the main point of this article, which is in the pursuit of being elite, don’t be afraid to be poor for a little while.


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