*This is pretty radical. Does anyone know what team ppg differential*

typically produces in terms of W-L record? My guess is 6.3 ppg and

57-25 is closer to normal, like Bob says, than 3.1 ppg and 55-27 is.

yes.....using just the two variables of "wins" and "point differential", you can do a least squares fit (curve fitting) assuming a linear regression (that's a mouthful, huh?). sounds complicated but its really not....

remember the old algebra equation y = ax + b for determining the slope of a straight line? if you plot on a graph "Wins" versus "Point Differential", you can calculate, assuming a linear distribution, a formula to predict one paramater if you have the other, based on a mound of data supporting it (technically this is not a linear distribution, as not each team plays every other team an equal amount of times each season, but for our purposes here i think its close)....

we have the "mound of data", all the historical nba team stats. for this example, looking at the nba team data only for seasons where teams played 82 games (all years back to 67-68 except the strike year of 98-99, and 82 games because to calculate this properly you need all events to be similar), you get the equation:

Y = aX + b where a = 2.61 and b = 41

or

Y = (2.61 times X) + 41

or

Wins = 2.61 times (point diff) + 41

41 is the b parameter because, you guessed it, if your point differential is zero, you should be a .500 ball club (W-L of 41-41)...

so for the 92-93 bulls with a pt diff of 6.3, historical data (actually includes the test data) predicts 57.4 wins, and they won 57 games. for the 93-94 bulls with a pt diff of 3.1, historical data predicts 49.1 wins, and they won 55 games. so you could say the 93-94 bulls were lucky in winning six more games than they "should have" based on their stats, or simply put won a few more close games than the odds would have suggested......

over the time period of 1967-68 to 2001-02 (not including 1998-99), two thirds of the teams were within plus or minus 3 wins or losses of their predicted W-L record based on the above equation, 80% were within plus or minus 4 games, and 90% within plus or minus 5 games, so again for our purposes i think the above formula gives you a good indication of what a team's W-L record should be based on point differential....

an analogy would be flipping a coin 82 times - how often would you get 41 heads and 41 tails, which is what you would expect? you know you "should" get 41 heads, so if 90% of the time you were within 5 (36 heads to 46 heads), i'm guessing that's pretty good, because 82 is really not that large of a sample population size...

bob chaikin

bchaikin@...

- --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:
> [...]

Not

>

> > I once compared the normal probability approach to different

> > pythagorean exponents and the normal approach is always better.

> > by enough to worry about, though. I'd expect any linear form or

approach

> > ratio to be similar to the pythagorean. Since the normal

> > takes into account a little more than just points scored and

points

> > allowed (how variable they were in doing so), it should be a

little

> > more accurate. It also allows it to work without modification in

any

> > league, whereas you need to change the exponent on the

Pythagorean

> > approach from the WNBA to the NBA to college men to college women

to

> > HS, etc.

make more

>

> Good points. What is both a strength and weakness of the normal

> probability approach is: it uses more information and thus can

> accurate predictions. But one needs to have data on, not just the

mean

> points, but also the variance of points (and I think your formula

takes

> covariance into account too?). These are very easy calculations,

Yup. The covariance is actually quite important. It shows how much

teams play up or down to opponents. Teams definitely play up or down

to opponents in the NBA. Not as clear in other leagues (or other

sports). Basically there is no reason to blow a team out by 45 when

you can win by 10 safely. That's also why you can't do a correlation

of Jordan's minutes to how well his team performed. If he's injured

and plays 20 minutes, the team could do poorly. But if he plays so

well that the team is up by 35 after 20 minutes and he doesn't play

again, the team can do well. I tried correlating playing time to

team success (by game, not by season) and found this to be an

impossible barrier to overcome. So, the correlation definitely

matters.

DeanO

> data are a bit less easy to get. Available, but a little more

hunting and

> a little more work to do, compared to just looking at points scored

and

> allowed.

accurate-

>

> As usual, there's a choice of the quick-and-dirty vs the more-

> but-more-work calculations.

>

>

> --MKT