Competitve Balance in the NCAA FBS

Yesterday, this article was posted positing that NCAA FBS is broken because the same top teams are in contention for the national championship game year after year.  Yet in terms of analysis the article is severely lacking. 

So, here is one take on this idea, and that is with regard to the overall level of competitive balance in all of the NCAA FBS.  I am using the Noll-Scully Competitive Balance measure.  The Noll-Scully Competitive Balance calculates the actual standard deviation of winning percent to an idealized standard deviation of winning percent, where the idealized standard deviation is measured as if wins and losses are randomly determined.  The closer the Noll-Scully Competitive Balance measure is to one, the greater the league's competitive balance.  For those that are interested in calculating this on their own, here is a step-by-step guide as to how to perform the Noll-Scully competitive balance calculation.

For a viewpoint of more than one season, I have looked at the data since 1996 (the season that overtime was instituted - and ties no longer take place).  This allows for the win/loss competitive balance measure to be used and compared from season to season.  As you can see in the chart below, competitive balance has remained rather stable since 1996, calling into question the hypothesis that college football is broke.

Competitve Balance in MLB

With the MLB's regular season in the books, I want to look at MLB over the next few days with regard to:  competitive balance, payroll inequality, payroll and performance and attendance analysis. To begin, I examine competitive balance in MLB using the regular season standings and the Noll-Scully measure of competitive balance.  For those not familiar with this measure, start here.  For those interested in calculating this on your own, try this step-by-step measure.  For the calculations below, I am using data from Yahoo! Sports.

Major League Baseball has become less competitive as the Noll-Scully increased from 2.263 in 2018 to 2.452.  In both leagues, competitive balance has decreased.  The National League Noll-Scully increased from 1.579 in 2018 to 1.884, and in the American League the Noll-Scully increased from 2.793 in 2018 to 2.924.

MLB competitive balance waxes and wanes from season to season.  Here is a graph of that in MLB since 2002.

Does the English Premier League have a Competitive Balance Problem?

Recently, the Wall Street Journal addressed concerns about the competitiveness of the English Premier League (paywall).  So let's take a look at the numbers.  First, I calculated the Noll-Scully measure of competitive balance for the last decade in the English Premier League.

Since the English Premier League has "draws" or ties, the Noll-Scully competitive balance measure must be calculated with the trinomial distribution, which as Richardson shows in his Eastern Economic Journal article, the idealized standard deviation is [(1-p)4n]^(1/2); where n is the number of games played and p is the probability of balanced teams tying.  The number of games played is simple, its 38.  The calculation of p is not as simple.  Here, I have to make a determination.  What I did was to look at the last (approximately) 20% of the season, and calculate the number of games teams that finished 9th, 10th, 11th and 12th in the EPL final table, in which those teams tied.  Then I took the average of those four teams to calculate p.

Using data from [https://datahub.io/sports-data/english-premier-league#resource-season-1819], the Noll-Scully Competitve Balance measure reveals the following:

As you can see, the English Premier League has been becoming less competitive since the 2015/16 season.  Yet, is it a problem?  That is much harder to definitively answer.  Overall, it seems to me that an economic problem exists if the league becoming less competitive results in a significant decrease in attendance, revenues and viewership.  That doesn't seem to be the case, so even with the EPL recently becoming less competitive, it is not a problem.

For those interested in the actual numbers, see below.

Season	Noll-Scully
2009/10	3.104
2010/11	2.469
2011/12	3.178
2012/13	3.141
2013/14	3.808
2014/15	3.066
2015/16	2.826
2016/17	3.507
2017/18	3.584
2018/19	4.086

2018 NCAA FBS Competitive Balance

With the end of the NCAA FBS 2018 season, I can update the how competitive the highest tier of college football was using the Noll-Scully Competitive Balance measure.  I have decided to calculate this since 1996 (the year that the NCAA FBS went to overtime to decide games), thus there are no ties and the version used by Roger Noll and Gerald Scully is used here.  For those that are interested in calculating this on their own, here is a step-by-step guide as to how to perform the Noll-Scully competitive balance calculation.

As you can see below, competitive balance slightly improved this past season as the Noll-Scully moved closer to one (a league where wins and losses randomly occur), and that for the last 20 plus years, competitive balance among NCAA FBS programs has been relatively stable.

2018 NFL Competitive Balance

With the end of the NFL regular season, let's take a look at how competitive the NFL was this past season.  I grabbed the NFL standings data from profootballreference, and then calculated the Noll-Scully measure of competitive balance.  For those interested, here is a step-by-step guide to calculating the Noll-Scully Competitive Balance measure.

For this past season the Noll-Scully measure of competitive balance for the entire league was 1.445, and for the AFC the Noll-Scully was 1.364 and the NFC the Noll-Scully was 1.569.

Recent historical perspective on competitive balance in the NFL.

Competitive Balance in Major League Baseball

With the MLB's regular season in the books, I want to look at MLB over the next four days with regard to:  competitive balance, payroll inequality, payroll and performance and attendance analysis. To begin, I examine competitive balance in MLB using the regular season standings and the Noll-Scully measure of competitive balance.  For those not familiar with this measure, start here.  For those interested in calculating this on your own, try this step-by-step measure.  For the calculations below, I am using data from Yahoo! Sports:  https://sports.yahoo.com/mlb/standings/

First, let's start with the most recent MLB regular season:  2018.  The Noll-Scully measure of competitive balance for the American League was: 2.793 and for the National League was:  1.579.  Clearly, the National League was much more competitive this season than the American League.  For MLB in total, the Noll-Scully was:  2.263.  While this is indicative that MLB was not extremely competitive, is the 2018 regular season typical, more competitive or less competitive?  To answer that, I calculate competitive balance since 2002 and display it on a graph below.



As you can see, for the National League, it is similar to previous seasons in terms of competitive balance, but for the American League, it is not.

WNBA Competitive Balance

With the Seattle Storm on the verge of sweeping the Washington Mystics in tonight's WNBA finals, I thought I would update my periodic look at the WNBA's competitive balance.  So, using the Noll-Scully measure of competitive balance and grabbing the regular season league standings from the WNBA's website, I calculated competitive balance since 2003.  (Note:  league standings data only goes back to 2011 on the website).

For those interested in how to calculate this on your own, here is a step-by-step guide to calculate the Noll-Scully measure of competitive balance.  As you can see in the graph below, competitive balance has been relatively stable from 2017 to 2018, and for this time period on the whole, the average Noll-Scully is 1.789, which is about as competitive as Major League Baseball.

Competitive Balance in the NFL

With the NFL regular season over, let's take a look at how competitively balanced the NFL was since 1981.  As a reminder, I am using the Noll-Scully measure of competitive balance which statistically measures the actual performance from the ideal performance.  An ideal level of competitive balance using the Noll-Scully measure would equal 1.000, and levels above 1.000 means that the league has some competitive imbalance, with higher Noll-Scully numbers meaning more competitive imbalance.  (Here is a step-by-step guide if you want to calculate this on your own.)  By competitive balance I am looking at how well a league's standings are in relation to a league where wins and losses are determined randomly.  In order to do this, I am going to look at the NFL season statistically as a sample and as a population - mainly for comparison purposes.  The data comes from profootball-reference.com. 

As you can see below, whether I use a sample or the population, the Noll-Scully measure of competitive balance is very similar.  Additionally, the level of competitive balance has not changed much over the last few seasons, with the Noll-Scully for a sample in 2017 equal to 1.601 and for the population equal to 1.576.  So even with the Brown's win-less season, competitive balance has not declined much from last season.