The Study Of Parity Has Been Very Uneven

The second the NFL Championship games were over and we knew the Super Bowl match-up, I knew it was coming. It's like the swallows returning to Capistrano or Jets fans hating their first round pick -- you can set your clock to it (assuming you had one of those clocks that counts in years).

What I'm referring to is the inevitable story about how baseball has more parity than football because of the higher number of repeat champions in the NFL. Normally, Jayson Stark is the one championing the cause (and I actually like Stark), but this year Tom Verducci beat him to it.

Now, normally, this is one of those things that I wouldn't really care much about. I mean, I love baseball and I love football, so it's kind of like deciding which kid you love the most or which is your favorite IPA, but I'm always bothered by the analysis. Simply looking at the different number of champions over a given time frame is like judging a pitcher or quarterback only by win-loss record.

So I decided to take a crack at it. While the ever accurate sniff test tells me that the NFL has more parity, I made a strong effort to stay intellectually honest and not let my suspicion guide the analysis.

But I must warn ye, there be math ahead.

Before getting into any analysis, we're going to start with a step that is usually overlooked in these things. Namely, we're going to define what "parity" means.

As I said pre-jump, I don't believe that parity can simply be explained by looking at how many champions a league has had over a given time. In my mind the question of parity isn't so much an issue of whether or not a multitude of teams have successfully won the league, but rather one that looks at the opportunity each team has. In other words, "does each team have the same opportunity for success?"

For example, the American sports "league" with the absolute least parity in my mind is Division I NCAA Football. There are 119 teams that play for a single championship, but because of varying schedules, AQ vs. non-AQ conferences, an economically driven bowl system, and this absurd notion that there should be a pre-season poll (which ultimately drives decisions in the BCS rankings), not all teams are given an equal opportunity to win said championship. If, in the upcoming season, my beloved Northwestern Wildcats went undefeated, but two SEC schools also went undefeated, the Wildcats would likely be on the outside looking in. Similarly, though, the ‘Cats would be in a better position than, say, Boise St.

Individual sports such as the PGA Tour or WTA, however, have the ultimate parity. Sure, some players have better equipment, coaches, sponsorships, etc, but the advantages that those provide are minimal. All players have the same opportunity to play in the same number of events at the same venues and for the same purse.

As it pertains to MLB and the NFL, however, it's tougher to define opportunity. We can debate all day the pros and cons of the NFL's salary cap system vs MLB's luxury tax approach, but in order to retroactively evaluate which one has had better success, I'm going to use playoff appearances in place of league champion.

I'm doing this because I subscribe to the theory that the playoffs are a bit of a crap shoot -- especially when you consider the one-and-done model in the NFL -- so I feel that playoff appearances give us a better view as to whether teams have been given the opportunity to adequately improve themselves over time. I understand that this is not the perfect model, as it ignores the inequities in divisions (i.e., AL East vs NL Central) or rules (i.e., a 7-9 Seahawks team making the playoffs over a 10-6 Giants team), but hopefully we can agree that it is a superior model to simply looking at champions.

Lastly, to close the preliminaries, I would ideally have used 20 years or more worth of data, but considering the changes in CBAs and league structures, I questioned how valid the older data might be. As a result, I decided that the most relevant data set would be the past 10 years.

Now, if you disagree with this premise, you're probably better off saving yourself some time and just skipping down to the comments to complain, but if you agree or are just totally bored, let's move on to the good stuff. Of course, considering I've taken nearly 700 words to get to this point, you may want to go get a cup of coffee first. Don't worry, I'll still be here when you get back.

The obvious place to start is to look at how many playoff appearances each team has had in their respective leagues.

This data is neither surprising, nor particularly interesting. It tells us that the Yankees and Colts have both dominated post season appearances in their respective leagues. Oooohhh (/waves hands)! The standard parity analysis would ignore this fact and only point to the fact that both teams have a measly one championship each and claim victory. We, on the other hand, know better.

But how do we draw conclusions from this data?

Well, first off, it would be irresponsible (and a bit boring) for us to simply look at totals without considering the fact that 12 out of the 32 NFL (38%) teams make the playoffs each year while only 8 out of 30 MLB teams (27%) make the playoffs. The Yankees' 9 playoff appearances are not the same as the Colts' 9 playoff appearances.

What we need to do is compare how the number of playoff appearances that each team has had to the expected number of playoff appearances in a totally equitable league. Let's take the concept of parity to the extreme. In this scenario, every team would start each season with exactly the same probability of making the playoffs. In baseball, each team would start with a 27% probability of making the playoffs and every NFL team would start with a probability of 38%. In such a league, over a ten year span, we would expect each NFL team to make the playoffs 3.8 times and each MLB team 2.7 times.

Now, obviously some of you are thinking that the extreme leagues are stupid because it's impossible to make the playoffs a fraction of a time. This is true, and even if you played out this fake league and randomly selected the playoff teams out of a hat, the probability that all teams would reach the playoffs an equal amount of time is virtually zero. Just by chance, you're going to have some teams go to the playoffs more than others.

So in order to test for parity, what we can do is see what is the probability that performing such an exercise would result in the actual results above. In other words, in this completely random extreme league, what are the chances that the Colts would actually reach the playoffs nine times and the Texans just once?

If we do this for both the MLB results and the NFL results, we should be able to see which one is closest to true parity, right?

Right! Fortunately for us, the world of statistics provides us with such a tool to perform this test. It's called a Pearson's Chi-Squared test.

In an effort to retain the few readers who have actually made it this far, I'm going to save you from the statistical analysis and just give you the results. Ready?!?!

The probability that the extreme NFL parity league would result in the actual playoff appearances seen above is 5.2%. The probability that the extreme MLB parity league would result in the actual playoff appearances seen above is a measly 0.3%.

What this tells us is that the NFL is actually closer to a fully equitable league than is MLB. Yay, argument over!!

Well, sort of. See, the issue is that we're not really supposed to use the Chi-Squared test when the expected frequencies are below 5 (remember, we're at 3.8 and 2.7). We're in better shape because of the amount of teams we're dealing with (which gives us a high degree of freedom), so the results aren't invalid, but it's still not a slam dunk.

Ultimately, as with any statistical analysis, after we've performed our calculations, we need to step back and look at this intelligently. Ideally, we would be able to run this analysis over a 20-30 year period in order to improve the statistical results and weed out generational issues. For example, the Colts had more playoff appearances over this time in part because they were able to retain Peyton Manning and had a lot of consistency. Conversely, the Yankees sustained playoff success stems from the fact that they have the resources to replace and add players constantly.

Over time, it's not a stretch to presume that the Yankees' approach is more sustainable. We've already seen this year that the Colts are in store for a few playoff-less years, but the Yankees still have the resources to continue their dominance. More likely than not, the Yankees are not on the precipice of a drought.

In the end, we can say that the NFL has more parity, but it's also not to the extreme that some would like to think. It will be interesting to see how this continues as the years go on and to see if the differences become more glaring.