- Forgive me if this has already been done, and as usual, pardon my

inarticulate method of explaining all things mathematical.

Standard deviation is something I've been playing around with. I've

been calculating "z-scores" (standard deviations above or below the

mean -- the "standardize" function in Excel) of winning percentages

and point differential for every BAA/NBA team just to see if I

discovered anything interesting.

I'm not sure I did, but one thing that occurred to me is that you

could use the z-score for point differential to determine an expected

winning percentage, rather than using an exponent of 13.5 (or whatever

it is) which should be a mutable number depending on league conditions

anyway. You could really do this for any level of basketball, or any

sport for that matter without having to work out an exponent.

You determine the point differential z-score for each team, multiply

it by the standard deviation of winning percentage (.142 last year)

and add it to the mean (.500) and you'll come up with an "Expected

winning percentage" based on point differential. For example, here it

is for the 2002-03 season. This will probably look like crap, but the

columns are supposed to be: team, point differential per game, point

differential z-score, expected win-loss record, and actual win-loss

record (in paren).

Team Pt Dif. Z-score Expected W-L (Actual W-L)

ATL -3.6 -0.85 31-51 (35-47)

BOS -0.4 -0.09 40-42 (44-38)

CHI -5.1 -1.22 27-55 (30-52)

CLE -9.6 -2.29 14-68 (17-65)

DAL +7.8 +1.85 62-20 (60-22)

DEN -8.3 -1.97 18-64 (17-65)

DET +3.7 +0.88 51-31 (50-32)

GSW -1.1 -0.27 38-44 (38-44)

HOU +1.5 +0.35 45-37 (43-39)

IND +3.5 +0.83 51-31 (48-34)

LAC -4.1 -0.98 30-52 (27-55)

LAL +2.3 +0.55 47-35 (50-32)

MEM -3.2 -0.77 32-50 (28-54)

MIA -5.0 -1.20 27-55 (25-57)

MIL +0.2 +0.06 42-40 (42-40)

MIN +2.1 +0.49 47-35 (51-31)

NJN +5.2 +1.24 55-27 (49-33)

NOH +2.1 +0.50 47-35 (47-35)

NYK -1.4 -0.32 37-45 (37-45)

ORL +0.1 +0.03 41-41 (42-40)

PHI +2.3 +0.55 47-35 (48-34)

PHO +1.1 +0.27 44-38 (44-38)

POR +2.6 +0.62 48-34 (50-32)

SAC +6.5 +1.55 59-23 (59-23)

SAN +5.4 +1.29 56-26 (60-22)

SEA -0.1 -0.03 41-41 (40-42)

TOR -5.9 -1.40 25-57 (24-58)

UTA +2.4 +0.57 48-34 (47-35)

WSW -1.0 -0.24 38-44 (37-45)

I would be curious to find out how this matches up with the 13.5

exponent. So what do you think? Is there some bias that I'm missing

that invalidates this method? Too much work for too little payoff?

Moné - --- In APBR_analysis@yahoogroups.com, "monepeterson" <mone@s...> wrote:
> --- In APBR_analysis@yahoogroups.com, "Michael Tamada" <tamada@o...>

Both work equivalently. These days, I prefer using the offensive and

> > This is somewhat following along the lines of what DeanO does with

> > his "basketball's bell curve stuff", although instead of looking at

> > z-scores per se he looks at points scored means and standard

> > deviations, points allowed means and standard deviations, and

> > perhaps most crucially, the covariance between them.

>

> Ah, interesting. Time to dig out the book again. Dean, do you use

> points per 100 possessions or raw points for the means and SDs (anyone

> who knows may answer)?

defensive ratings because pace adds a significant correlation to pts

and dpts. That then hides whether turnovers lead to points or whether

offensive rebounds hurt a defense (which both are rather important to

know for teams).

DeanO

www.basketballonpaper.com

"Dean Oliver looks at basketball with a fresh perspective. If you

want a new way to analyze the game, this book is for you. You'll

never watch a game the same way again. We use his stuff and it helps

us." Yvan Kelly, Scout, Seattle SuperSonics