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.

Parity in the WNBA

A poster named "bluesky" over at the Rebkell Message Board complained that the 2008 playoffs were not very interesting. The argument was that these were the same teams as last year. bluesky furthermore complained about "parity" in the WNBA.

What is "parity"? "Parity" refers to an equal playing field where all teams have an equal chance to compete regardless of financial circumstances. Is there a way to mathematically measure parity? Yes. Back from my baseball days, I used something called the "Noll-Scully Measure" to determine how much parity existed in any given league.

In a perfectly competitive WNBA, all teams would be clones of each other. They'd all have the same talent, suffer the same injuries, having the same coaching, the same finances, whatever. Teams would be so evenly matched that on neutral grounds, a gambler would be shafted - trying to determine which of the two teams would win would be similar to flipping a coin.

However, not every team will finish at 17-17 because of the random chance factor. Random chance is always a determinant, because if you flip an unbiased coin ten times, you don't expect five heads and five tails. Sometimes you get six heads and four tails, or either greater "deviations". (Remember this term.) So there would be some deviations from a 17-17 record.

With a lot of games, the "number of wins" variable approaches a bell curve distribution. Our imaginary "pure average" team will win between 14 and 20 games about 68 percent of the time. It will win between 11 and 23 games about 95 percent of the time! A "perfectly .500" team winning 10 or less games or 24 or more games would happen very infrequently, less than 5 percent of the time.

What the Noll-Scully measure does it that it compares the "scatter" of a perfectly matched league to the "scatter" of any league you give it. The actual measure is (standard deviation of wins in given league)/(standard deviation of wins in perfect league) = (standard deviation of wins in given league)/[(1/2)*(square root of games played)]. The denominator comes from what one would expect the standard deviation of wins to be in a binomial, or "coin-flip" distribution.

A "perfectly competitive" league would have a Noll-Scully measure of 1.0, since the numerator would be equal to the denominator.

Here are some Noll-Scully measures for various leagues:

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

There isn't a lot of parity in the NBA. The good teams tend to stay good for long periods of time, and bad teams tend to remain bad - just ask the Los Angeles Clippers. Now, let's look at the Noll-Scully Measure for the WNBA over its history.

WNBA Noll-Scully Measures:

1997: 1.400
1998: 2.605 - expansion
1999: 1.624 - expansion
2000: 2.086
2001: 1.962
2002: 1.638
2003: 1.704 - contraction
2004: 1.299 - contraction
2005: 2.061
2006: 2.188 - expansion
2007: 1.581 - contraction
2008: 1.896 - expansion

Average Noll-Scully: 1.953

In short, there isn't as much parity in the WNBA as in baseball, football or hockey, but there's a lot more parity in the WNBA than there is in the NBA, where you can expect the same teams to march to the playoffs every year.

Remember: low numbers equal more parity.

Was "bluesky" right? Yes,there wasn't as much parity this year than there was in 2007, but it was a better than average year in terms of parity. The year when the WNBA had the most parity was 2004, where there were a huge number of teams clumped around the middle. The worst year was 1998, when you had Houston's historic high of 27-3 and the Mystics low of 3-27. You had 10 teams and three of them didn't really have a chance, losing at least 20 games each. (Sacramento, Utah, and Washington.)

One great thing we can do with the standard deviation work is attempt to determine the best teams all time and worst teams all time in the WNBA. That will come as a later post.