February 26, 1998

I was recently asked how closely NBA teams' Smallworld Points (SWP) correlate with their won-loss percentage. My initial reaction was that, at the team level, points scored probably provided the best correlation, while the SWP formula was more appropriate for comparing individual players. Then someone pointed out that this season, points scored only shows a 55% correlation with winning percentage over the first three months of the season, while team SWP's showed a correlation coefficient of 70%. (A "correlation coefficient" measures how closely one statistic tracks another. A 100% correlation coefficient would mean the two stats track each other perfectly. A coefficient of 0% means there is no apparent relationship between the two.)

Fantasy geek that I am, this was all it took to get my analytical jets fired up. I wondered if one could develop a better correlated formula by changing the multipliers (but keeping the same eight statistical categories used in Smallworld's formula). Surprisingly, I found it was pretty simple to solve for a new formula which produced an 88% correlation coefficient vs. team winning percentage.

This "team success" formula is quite simple:

Not only is this formula much simpler than the Smallworld formula, but it holds up much better from year to year. I mentioned above that the Smallworld formula showed 70% correlation with winning percentage this season, but the corresponding correlations for each of the past two seasons were only 49% and 65%. The team success formula not only showed correlation of 88% with winning percentage for this season, but remained similarly high at 90% and 92% for each of the past two seasons.

First, notice the lack of influence that points, missed free throws, assists, and blocks seem to have. There has been no material linkage between any of them and winning percentage. Lack of correlation for blocks is probably understandable, since only a few players tend to dominate this category, but it's not necessary to have a good shot blocker to win. (Name a great shot blocker on the Bulls!) The other categories are a little more difficult to rationalize, but the linkages are just not there - or if there are measurable correlations, they are not signficant, nor are they stable from year to year.

Note that missed FG's have the same impact as turnovers, which makes sense, since a missed FG is tantamount to a turnover - unless there's an offensive rebound. And the rebound factor directly compensates for that eventuality. Steals have the opposite impact of a turnover - another intuitive relationship. So the formula essentially measures the number of times a team takes control of the ball without the other team scoring. Come to think of it, maybe that does make sense.

What would happen if we ranked individual players using this formula? Using cumulative stats through the All Star break, here are the top 20 players using each formula:

Rank	Smallworld Rating	Team Success Rating
1	D Robinson	D Rodman
2	K Malone	J Williams
3	R Strickland	C Barkley
4	G Payton	D Mutombo
5	G Hill	C Oakley
6	M Jordan	A Green
7	K Garnett	K Garnett
8	T Duncan	A Mason
9	C Webber	D Garrett
10	A Walker	T Duncan
11	T Hardaway	D Robinson
12	D Stoudamire	D Marshall
13	D Mutombo	Z Ilgauskas
14	J Kidd	T Hill
15	S Abdur-Rahim	C Webber
16	C Barkley	B Williams
17	V Baker	P Brown
18	M Finley	A Walker
19	J Williams	K Willis
20	T Gugliotta	L Wright

So what should we make of this? Are points, blocks, and assists really overrated statistics? When comparing player performance, I certainly don't think you'd want to ignore those factors. Clearly, the player rankings based on the team success rating don't fit our intuitive sense of relative value, while the Smallworld ratings seems to make sense. So, I can't say that the Smallworld formula is inappropriate as a comparative measure at the player level. But at the team level, these stats just don't seem to differentiate the good teams from the bad.

If anyone has some additional insights to offer on this, as Ross Perot says, I'm all ears!"

Return to Guru's Hoop Pointers index