# NFL Even MORE Competitively Balanced (Yet Again)

Further to an earlier post one year ago to the day, the same result occurred upon conclusion of the 2011 NFL season as in EVERY previous season since the re-alignment to 32 teams in 2002 – that the NFL is even more competitively balanced when the standings are adjusted for strength of schedule (than on the basis of raw standings) .

Even though this season was noticeably less balanced than (the recent) average without adjustment, the difference from the adjustment was even more pronounced than any other season during this period (with the exception of 2003), making adjusted competitive balance about average over the same period.

On this occasion, the actual-to-idealized standard deviation ratios are 1.611 (unadjusted) and 1.462 (adjusted); the Gini coefficients are 0.292 (unadjusted) and 0.260 (adjusted); and the Herfindahl indexes of CB are 1.162 (unadjusted) and 1.134 (adjusted).

Ultimately, this result reinforces further the need to account for strength of schedule in producing standard competitive balance metrics for various empirical studies!

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It has always amazed me that the NFL has as high a ratio of actual to ideal standard deviation as it does, even after adjusting for unbalanced schedules across teams. The idealized standard deviation for winning percentage for the NFL is roughly 0.125 which means a range of actual winning percentages of 0.375 to 0.625 for parity. Yet the actual range is far larger than this, despite the fact the NFL uses extensive revenue sharing and a hard salary cap. Economic theory suggests that the NFL should be much closer to parity with these revenue and payroll devices. Yet we see teams that are consistently good performers (Patriots for example) and teams that are consistently poor (Browns for example) and this should not happen according to theory. If it comes down to bad coaching and management, then the poor performing teams should be able to fire the poor managers and hire good ones so that parity is once again achieved. But this does not seem to happen, or alternatively, bad coaching and management is not the explanation. Multiple equilibria could be an explanation, but perhaps not.

One can always point to injuries of key players in increasing the variance of winning percentages but this is probably not enough to explain the excessive volatility either. I don’t know the answer, but as a start to finding one, it would be useful to investigate the factors that account for the excessive volatility from the ideal somehow.

Thanks for the post, Liam.

Duane: Switching between end of season uncertainty and between season uncertainty is bound to be confusing. The theory of sharing impacts, as far as I know the theory, is only developed for winning percent, relevant to end of season. And for a closed league like the NFL, there are reasonable conditions where sharing has no impact on balance. This seems to me characteristic of the history of the NFL, especially since its sharing approach hasn’t changed in some time.

The cap can only have small impact in the first place and remains quite soft anyway.

I don’t know of any theory of between season uncertainty (edging toward the question of dynasties). Rottenberg never addressed it, for example. So, for me, it remains that there is still important revenue variation in the NFL and sharing simply takes money from players and distributes it among owner’s by a formula that does not contain any incentives to alter the distribution of talent. So end of season balance can improve for other reasons (growing market equality over time), and there can still remain enough revenue variation to drive a large part of the observed outcome. Finally, NFL football is still a league with very few games and the game itself allows a greater chance for truly large and small winning percentage values. Management matters. But so do all of these other factors.

Maybe somebody will (or has and I am uninformed) give us the theory of between season incertainty so we have something to test. Go get ’em sports economists!

Yes Rod, you are quite right that, in theory, revenue sharing has minimal effects on parity. Also the NFL salary cap system allows a sufficient range in payrolls that it is not very effective (although that range will be tightened up in the 2013 season), although some of the lowest payroll clubs (Patriots) consistently outperform some of the higher payroll clubs (Giants, Redskins, Vikings).

It is not hard to understand why the NFL has the smallest standard deviation ratio compared to the NBA, NHL and MLB: revenue certainty. This is where your idea of between season uncertainty is important and a fruitful area for research. For most NFL clubs, the majority of game tickets are sold before the season starts, TV and media revenues are already contracted and other revenue sources can be accurately estimated. Performance on the field does not matter as much for season revenue as it does in the other 3 leagues. It would be interesting to try to isolate this effect, and other potential factors such as market sizes, on these ratios across the 4 leagues. I have not seen this in the literature, although I could be uninformed.

Good one Liam. In your research on this I know you’ve calculated correlations of divisional rank orderings and/or WPCT from season t-1 to t . How did they shape up this year?

On a broader point, another often overlooked reason why competitive balance varies between leagues is the randomness of the sporting contest itself. Have a look at most of the popular sporting contest success functions and they will have a variable controlling for the ‘discriminatory power’ of the contest. While people occasionally discuss rule changes such as how a contest is restarted after a score, the effect of technology change (balls, bats, etc.) changes I’ve seen little formal modelling of how such things might improve the closeness of individual matches and thus make it more or less likely for a result to be uncertain – such things could arguably flow through to seasonal CB.

In a season where from afar it seemed the NFL tinkered with a lot of rules that perhaps made it a “QB’s league”. If the focus is more upon the skill of a specialist then maybe the worsening of CB can be explained by the “short supply of Mannings?” (or just that as erratically good as he is, Tim Tebow cannot be omnipresent)

Re: Salary Cap Not Making Much Difference —

You know, I’ve always wondered if there is a “Moneyball” out there waiting to be written for football. As discussed, (roughly) equal money does not equal parity of performance.

NFL teams, like their MLB brethren, can and do: (1) grossly overpay certain players, while (2) grossly underpaying other players on their roster who are giving them more bang for their buck, which the market addresses when they become free agents, where they they can be overpaid by another team instead. Meanwhile, the overpaid players become boat anchors whose contracts they cannot get out of, at least not easily. Agents are getting smarter lately, and demanding their clients get more quasi-guaranteed money in the form of front loading early years of contracts, signing bonuses, etc.

There must be some way to overcome this whipsawing and keep better-than-average players tied to fairly priced contracts. All positions have metrics, including offensive linemen.

Equal league revenue does not address unequal costs of doing business (New York = expensive, Kansas City = cheaper, Green Bay = cheap cheap) but I am not sure if that difference is significant, though I could be wrong.

Thoughts? Is there a GM out there waiting to turn the league on its ear?

Adjusting for the strength of competition is a nice innovation. It’s interesting that this consistently reduces the SD of winning percentage.

However, using the actual-to-idealized standard deviation ratio greatly overstates the amount of competitive balance in the NFL (i.e. it understates the amount of variation in teams’ true talent). The problem with using the ratio method is that while a shorter season does increase variance, it ADDS variance rather than multiplying it. So while the NFL’s short season does indeed increase the SD of team winning percentage compared to other sports, it does not do so proportionately. In fact, the NFL is quite “unbalanced,” much more so than baseball for example (but not quite so much as the NBA). It’s low ratio is entirely a function of the denominator (.125) being so large.

Imagine that the NBA, MLB and NFL all had the same level of true competitive balance, such that with infinitely long schedules all 3 leagues would have a SD of .100. That gives us variance of .01 from “true” differences in team strength. Now, add the variance contributed by length of schedule: .0156 for NFL (.125^2), .0015 for MLB, and .0030 for NBA. To get the observed variance when these leagues play we simply add the variances, and then take sqrt to get the SD. For example, the NFL is .01 (true strengh) + .0156 = .0256, and the SD we would observe is .160. In MLB we would see a SD of .107 (just slightly more than the true difference among teams, due to the long 162 game season), and in the NBA .114. And this would in turn give us the following actual:idealized ratios:

NFL 1.28

MLB 2.75

NBA 2.07

As you can see, the ratio method will make the NFL appear to be highly competitive, even though we know that all three leagues in this hypothetical have (by definition) the same differences in team strength. This is why you cannot rely on the ratio to measure league competitiveness. (The good news for you is that, since you are always using the same denominator for the NFL, your findings about adjusting for strength of schedule, and year-to-year comparisons, should all remain valid.)

Given your finding of an adjusted SD of .182, we can estimate the true SD for team strength in the NFL at .133. This is quite large, about twice what exists in baseball (where a .633 win% is relatively rare).