In my last post, I looked at how the NFL might change if the salary cap expires as it's set to do in 2010 unless extended. I looked specifically at within-season parity levels, or how close together teams are in terms of competitiveness. We saw that the salary cap era was not noticeably different from the pre-cap era.

In this post, I'll look at the cap in terms of year-to-year parity--the tendency for bad teams to improve and good teams to decline. This is the kind of parity that would tend to prevent either dynasties or perennial doormats. It's the kind of thing that gives fans of every team hope going into September. It follows that a salary cap system would prevent teams from hoarding the best players and we'd expect to see parity levels increase.

For both the pre-cap and cap eras*, I took each team's season win totals and plotted them against the improvements or decline in wins the following year. I then plotted a simple linear regression line for each era. This illustrates the "churn" of team records--how much bad teams get better and good teams get worse.

To interpret the charts, consider this example. Before the cap, a team with 2 wins one year could expect to win about 3 more wins the following season, going 5-11 on average. After the cap, a team with 2 wins can now expect to win about 4 more wins the following season, for an average record of 6-10.

Notice that the slope of the regression line for the cap era (-0.72) is singificantly steeper than the slope of the line for the pre-cap era (-0.54). This indicates that year-to-year parity has indeed improved since the salary cap. It's easier for bad teams to improve and harder for good teams to stay on top.

The R-squared for the cap era is also stronger than for the pre-cap era (0.35 compared to 0.27). This indicates that in the cap era not only do team's year-to-year fortunes change to a greater magnitude, but more reliably and predictably too.

So we can say that yes, although the salary cap has made little or no difference in the within-year parity of team strength, the cap has made a difference in the year-to-year churn of improvement and decline. The end of the salary cap would likely reduce that parity to pre-1994 levels. Whether that's a good thing or bad thing, or even if the difference is big enough to matter, depends on your point of view.

The most important thing about parity though, isn't really the effect of the salary cap, but how important is it in absolute terms. In other words, how strong is the parity of the NFL compared to what an "optimum" level is. I'm not suggesting we can determine that, but I think the idea that every fan can have realistic hope in training camp is an important ingredient in the overall success of a league.

Major League Baseball seems to be on the opposite end of the spectrum. For about 10 years, you could reliably predict the standings in the AL East, not by the All-Star break or even by opening day, but by September of the previous year. You could make the case that half of MLB's playoff spots were effectively determined before the first pitch of opening day.

There are two numbers in the NFL very important to parity I haven't mentioned yet, and those are 16 and 4. There are only 16 games in the NFL season, which helps parity because luck plays a more decisive roll in season outcomes than if the season were longer. (I often use the analogy of playing Kobe Bryant in a 3-point shooting competition. If it's 'best of 3,' sometimes I'll win. But if it's best of 100, I'll never beat him.) And 4 is the number of teams in a division. To make the playoffs, a team doesn't have to outdo 5 or 6 other teams, it just has to outdo 3. So while the cap's effect on parity levels might not be very large, the current league structure creates the illusion of greater parity.

*I defined the pre-cap era as 1978 through 1993, excluding the strike years of 1982 and 1987. I also excluded the year-pairs surrounding the strikes. In other words I did not include the improvement and decline of teams from '81 to '83 or from '87 to '89. I defined the post-cap era as 1995-2008, excluding the first transition year of 1994. Data is from PFR.

## The NFL without a Salary Cap? 2

By
Brian Burke

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Interesting post. Do you have any idea of the statistical significance of the difference in regression estimates? I agree that there is a difference, but I am not sure if it is actually a meaningful difference or just random variation, possibly attributable to other causes. Thoughts?

Cheers, Paul

Paul-Yes, the difference is statistically significant. The standard errors for both line slopes is .5, so they're about 3 and a half SEs apart.

So it's doubtful it's random, but nothing I've done here proves that it's the CBA that causes the change. For now, that has to be inferred from the timing:

'87 Free agency...'94 CBA --> greater parity

I just did a similar regression for English Premiership football, although rather than looking for year on year change I looked to see whether we can predict year X+1 points from year X points. R-squared is 0.625, which if I remember stats correctly, means that 62.5% of the points a team will score depend on how well they did the previous season.

That would be disparity (although wikipedia has a better example. Portuguese football has had 3 teams win 71 of the past 73 championships)

Ian-That's amazing about the Portuguese teams.

You're a little off on interpreting r-squared. R^2 is the amount of statistical variance shared by two variables. It's not correct to say 62.5% of goals scored depend on previous year goals.

R, the correlation coefficient, is about .8 if the r^2 is .625. So it would be more precise to say 'for every standard deviation above average a team is any year, we'd expect it to be .8 standard deviations above average the next year.'

I think that's a better real world interpretation. In this case, the units of R^2 is "goals squared." I like using both the regression slope and R^2 to think about the relationship, but in a univariate regression, they're both reporting the same information.

Either way you interpret it, it seems the Premier League doesn't have much year-to-year parity at all.

By the way, I just read a great article on the subject of correlation and regression today:

http://www.hardballtimes.com/main/article/statistical-shenanigans/

Thanks for the reply, Brian. I guess we better hope for the salary cap to stay put...

You can see even more of an increase in churn if you look at several consecutive years. I ran a regression a while ago predicting NFL teams' Year X performance (winning percentage, I believe) based on performance in Year X-1, Year X-2, and Year X-3. Year X-1 and Year X-2 both had significant coefficients for the early seasons, but for recent seasons only Year X-1 was significant. In other words, teams used to be stable enough for multiple years of previous data to be predictive, but they aren't any more.

I could try to find the data to give you more details, or maybe you could run the analysis on your data set.

-Vince

I think free agency started in 1994, so free agency may confound the analysis. Free agency and the salary cap makes the pro scouting and the general manager more important.

I think you mean 1987.

My memory may be failing me as I get older, but this source

http://bleacherreport.com/articles/18183-nfl-history-the-road-to-free-agency

claims a "plan B" free agency (with each team protecting 37 players) from 1989 to 1992 with free agency as we know it today starting in 1993. Close enough to the dates in your analysis to confound the analysis. How do you separate the salary cap effects from the free agency effects?

At this point, FA and the cap go hand in hand regarding parity. FA without the cap would make for a very unstable system--i.e. "rich get richer," just like the MLB now.

I can rerun the pre-cap regression without 89-92 and compare the slopes. But that creates another problem. That period would have fewer years, which makes luck a larger part of the variance, which in turn would make the slope appear shallower than it should.

Were you plagiarized?

http://www.bigcatcountry.com/2009/3/10/787605/the-nfl-salary-cap-facts-m

Thanks for the heads up. Yeah, I noticed that a couple days ago. I think the writer just isn't aware of the rules more than deliberately ripping me off. Further down in the comments, he freely links to this article as "one of the sites I used to research the post," so I assume he just neglected to cite the source of the graph.

Just to be clear, I don't mind if people use my stuff as long they properly attribute it. In fact, anyone can literally copy and paste an entire article if they want, as long as they attribute it. It's when guys repeatedly rip off my articles/ideas and don't link to them that really ticks me off.

I think you would find a wider gap by studying how quickly and/or often teams with 4 or fewer wins become playoff and/or Super Bowl teams in a 3-5-year span, before and after the salary cap.

What any study like this is really telling us is that the salary FLOOR is the most important difference between NFL parity (which didn't make it impossible to create a dynasty, as evidenced by the Patriots, Steelers, and maybe even the Rams). There have been no Johnny Damon/Carlos Beltran fire sales in the NFL.

Some have misinterpreted this sort of data (including the bigcatcountry blogger and many of his readers) as suggesting that the loss of the NFL salary cap will be no big deal and nothing will change significantly (+/-1 win to bad teams is never going to sound significant to anyone, even if it is statistically significant). But if the cap/floor are no more, then the NFL won't be worth watching soon afterward, many small market teams will see their owners line their pockets with revenue sharing checks rather than use franchise and transition tags at all. 1/3 of the NFL will be like the past 15 years of Kansas City Royals history.