Measuring Competitive Balance

I play fantasy basketball. Yes I realize it is akin to Dungeon and Dragons for jocks, but I have no shame. Did I mention that I have read Twilight, but I regress, and I just lost my credibility for all topics sports. Let me try to earn that back. 

In the league, genealogically known as the Harris Ballers, it was brought to the attention of the league by Guy on a Longhorn! that

- There are 5 teams in the top half of the leader boards that are within 1 game of each other

- There are 4 teams in the bottom half of the leader boards that are within 3 games of each other

- Besides first and last place (you know who you are), everyone appears to be very evenly matched so far.

What Guy is saying is that the league is experiencing competitive balance, most notably when measuring competitive balance using the standard deviation of winning percentage. More specifically, the following equation:

Simple enough for all you stats geeks. Here are the league standings:

TEAM	W	L	T	PCT	GB
Stu- Boyz	63	37	0	.630	--
Gotham's Reckoning	54	42	4	.560	7
Not the Batum of the league	53	44	3	.545	8.5
More Wins than the Jazz	53	45	2	.540	9
Eagletown Farmboys	53	45	2	.540	9
Wenatchee Skookums	53	46	1	.535	9.5
Guy On A Longhorn!	50	46	4	.520	11
SR Puak Chomneah	48	50	2	.490	14
Los Conquistadors	45	49	6	.480	15
Wichikansistan Shazam	45	52	3	.465	16.5
Gladiators Win	41	56	3	.425	20.5
Flying Tortilla Chips	26	72	2	.270	36

Thus the standard deviation of winning percentage is approximately = .085

How does this compare to other leagues historically? First, we need to standardize it using what is called the Null-Scully measure of standard deviation of winning percentage. Simple equation, just divide the previous equation by .500/(square root of the number of games).

Meaning that the standardized winning percentage for the league is 1.71

Compared other sports

	the standardized winning percentage
MLB	1.69
NFL	1.66
NBA	2.71

So our fantasy bball league seems comparable to MLB.

But who cares about how close all the losers are? All that matters is the championship, and that seems to be already determined.

So thanks for making us losers feel like we are in good company. You have done a lot to make my day way better, about as much as that parking ticket improved my day.