Tuesday, April 28, 2009

WNBA Seasons and the Noll-Scully Measure

One of the ways that you can measure the competitveness of any league - basketball, baseball, football, whatever - is through something called a Noll-Scully measure. I decided that I would apply the Noll-Scully measure to the history of the WNBA.

The way Noll-Scully is developed is to look at a "perfectly competitive" league and compare the league in question to this imaginary league mathematically. We will define perfectly competitive league as a league where "all teams are equal". They are equally competitive to the point that when any two teams play each other on a neutral court, you literally cannot predict who will win. Neither team has a discernable edge and you could predict just as accurately by flipping a coin.

So if such a league existed, and that league was set up the same way as the WNBA where every team played 34 games, what would we expect the league standings to be? You might be tempted to say, "every team will have a 17-17 record at the end of the year"...but you'd be wrong, and the reason you'd be wrong is that you have to take into account what randomness really means. To claim that every team would finish 17-17 for the year would be akin to claiming that for every trial in which you flipped a coin 34 times, you would always get 17 heads and 17 tails. As an experiment, make a trial of flipping a coin four times. Do you always get two heads and two tails with each trial.

The answer is "no": this perfectly competitive league will be affected by a random scatter. (I'll just simply say "binomial distribution" and "standard deviation" and let you go to sleep.) For any of the teams in this perfectly competitive league, the chances are 68 percent that the team will win between 14 and 20 games in a year. (After all, if you were to flip a coin 34 times, you might not get 17 heads but you'll probably get something pretty close to it.) The chances are 95 percent that the team will win between 11 and 23 games. For such a team to either win 10 or less games or 24 or more games would be very rare - the chances would be 4.6 percent or less.

If we know something about how the distribution of wins in a perfectly competitive league "scatter", we can compare the scatter of our test league to this perfectly competitive league and come up with the Noll-Scully measure.

Noll-Scully measure = (standard deviation of wins in test league)/(standard deviation of wins in perfectly competitive league).

Binomial distributions - "random chance distributions" - have a rather tight and regular scatter. If our test league is exactly like a perfectly competitive league, the numerator and denominator become equal, and the Noll-Scully measure becomes equal to 1.00. 1.00 is perfection; non-perfect leagues - in other words, every league - will have a Noll-Scully higher than 1.00.

Here are some commonly accepted Noll-Scully measures for professional leagues:

National Football League: 1.48
National Hockey League: 1.70
National League (baseball): 1.76
American League (baseball) 1.78
National Basketball Association: 2.89

These numbers sort of make sense. The NFL's low Noll-Scully indicates that the NFL is a very competitive league. Every year, it takes until the very last week of play to eliminate some of the teams from playoff contention. The NBA, however, is a very low-competitive league, which is divided into "have" teams and "have-not" teams - except maybe for the #8 playoff spot, one can usually tell right away which teams will be competitive and which teams won't.

And now, the heart of the matter: Here are the year-per-year Noll-Scully measures for the WNBA:

1997 1.40
1998 2.14
1999 1.62
2000 2.22
2001 1.96
2002 1.64
2003 1.65
2004 1.26
2005 2.00
2006 2.12
2007 1.53
2008 1.84

Using a "weighted mean", where the weight of 2008 is "12", the weight of 2007 is "11", etc., the weighted Noll-Scully measure of the WNBA is 1.78.

This is very surprising. This indicates that the WNBA is much more competitive than the NBA - it's a lot harder to tell right away who the best teams are in the WNBA. It takes longer to sort out the playoff picture in the WNBA than it does in the NBA, where at the beginning of the year you can usually pencil the Celtics and Lakers in automatically.

Some observations:

1. 1997 was the most competitive year of WNBA history. If you look at the final regular season standings, it was a 28-game season and no team won more than 18 games. Only three games separated the first place team from the last place team in the Eastern Conference.
2. You would expect the N-S measure to increase every year of league expansion. In 1998, the measure jumped to 2.14 as weak, non-competitive teams were thrown into the mix. With another 1999 expansion, there's an aberration as the N-S measure falls, but in 2000 with the advent of a 16-team league, the NS goes up again as four teams are added to the WNBA. Indeed, 2000 was the least competitive year according to N-S.
3. All other things being equal, after an expansion you would expect an immediate decline in the N-S. From 2000 to 2002 - the years of the 16-team WNBA - the N-S measure goes down every year. The bad teams are given a chance to sort themselves out and become competitive.
4. From 2005 on, the league hasn't been very competitive. In 2005, Charlotte and San Antonio finished in the dog house. In 2006, the league expanded which weakened competitive balance. (Chicago finished 5-29.) The league's balance got better in 2007 when Charlotte was contracted out of the league, but the addition of Atlanta in 2008 made things less competitive again - the Eastern Conference, for example, was much weaker than the Western.

Does this prove anything? No, but it's an interesting way to look at changes from year to year. My prediction is that with the strengthening of the Atlanta Dream in the off-season and with the tightening of roster sizes necessitated by the recession that the league will become more competitive and the N-S measure will drop. We shall see.

Note: This isn't the first time I've written about Noll-Scully - I also wrote about it last year. That's the problem with the flu, it fries your brain.


Greg Finley said...

Thanks for computing these numbers! I've linked to your results here.

jpbenney said...

Interesting point. From what I have read about human biology I have imagined that women’s sporting leagues would have an inherent tendency to be less competitive than those for men. This is because the physical variation in women is less than in men, so the women at the extremes would be scarcer and stand out more.

The results do not suggest this. However, an interesting alternative way to measure competitive balance would be to compare with a perfectly unequal league; ie, where team A wins every game, team B wins all games except against team A, and so on. One can calculate the standard deviation for such a league (it is cumbersome on my old Casio FX-82MS, but I love doing it) and compare it with the observed results.

For the WNBA these are the Noll-Scully divided by approximately 3.60555:

1997 0.388
1998 0.594
1999 0.449
2000 0.616
2001 0.544
2002 0.455
2003 0.458
2004 0.349
2005 0.555
2006 0.588
2007 0.424
2008 0.510

I have estimated that for the men’s NBA the figures must be around 0.60 or 0.65 of the perfectly unequal league.

It raises an interesting question about sports for women since the results are not what I imagined. It may reflect that, as Berri says, the NBA has been too lenient in adding teams that may not be competitive even if they make money off the court.