Tuesday, September 16, 2008

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.

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