## predicting W-L record based on team point differential

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• 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
Message 1 of 9 , Oct 9 10:47 AM
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@...

• ... 82 games ... similar), you ... differential is ... (actually ... for the ... wins, and ... winning six ... put won a ... two ... their ... plus or ... our
Message 2 of 9 , Oct 9 12:17 PM
--- In APBR_analysis@y..., bchaikin@a... wrote:
> 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....
>

Yup, lots of ways to do this. But all of them show that the '94
Bulls record was a little lucky given their point differential.

DeanO
• Have also seen that Bill James pythagorean method applied to the NBA to, to do this. The exponent, of course, is radically different. ... From:
Message 3 of 9 , Oct 9 7:01 PM
Have also seen that Bill James pythagorean method applied to the NBA to, to do this.  The exponent, of course, is radically different.
----- Original Message -----
Sent: Thursday, October 10, 2002 3:17 AM
Subject: [APBR_analysis] predicting W-L record based on team point differential

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.
• ... And then there s DeanO s normal probability model approach. All of them I m sure lead to similar results, I wonder if some of them are more accurate than
Message 4 of 9 , Oct 10 6:22 AM
On Thu, 10 Oct 2002, Richard Scott wrote:

> Have also seen that Bill James pythagorean method applied to the NBA to, to do this. The exponent, of course, is radically different.

And then there's DeanO's normal probability model approach. All of them
I'm sure lead to similar results, I wonder if some of them are more
accurate than others? Or if some are more accurate at the extremes,
others more accurate at predicting teams with "average" stats. There's
different functional forms one can use in the linear regressions too:
ratio vs difference, logarithms or straight points, etc.

--MKT
• ... NBA to, to do this. The exponent, of course, is radically different. ... them ... There s ... I once compared the normal probability approach to different
Message 5 of 9 , Oct 10 8:20 AM
>
>
> On Thu, 10 Oct 2002, Richard Scott wrote:
>
> > Have also seen that Bill James pythagorean method applied to the
NBA to, to do this. The exponent, of course, is radically different.
>
> And then there's DeanO's normal probability model approach. All of
them
> I'm sure lead to similar results, I wonder if some of them are more
> accurate than others? Or if some are more accurate at the extremes,
> others more accurate at predicting teams with "average" stats.
There's
> different functional forms one can use in the linear regressions
too:
> ratio vs difference, logarithms or straight points, etc.

I once compared the normal probability approach to different
pythagorean exponents and the normal approach is always better. Not
by enough to worry about, though. I'd expect any linear form or
ratio to be similar to the pythagorean. Since the normal approach
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.

DeanO
• ... I found that an exponent somewhere around 13 (unfortunately, I don t have my notes with me; I m at school and they re at home) works really well.
Message 6 of 9 , Oct 10 12:33 PM
On Thu, 10 Oct 2002, Richard Scott wrote:

> Have also seen that Bill James pythagorean method applied to the NBA to, to do this. The exponent, of course, is radically different.

I found that an exponent somewhere around 13 (unfortunately, I don't have
my notes with me; I'm at school and they're at home) works really well.
Obviously, it's not perfect; just like baseball, factors other than point
differential (like luck) impact won-lost records.

John Craven

> ----- Original Message -----
> From: bchaikin@...
> To: APBR_analysis@yahoogroups.com
> Sent: Thursday, October 10, 2002 3:17 AM
> Subject: [APBR_analysis] predicting W-L record based on team point differential
>
>
> 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.
>
>
• ... NBA to, to do this. The exponent, of course, is radically different. ... don t have ... well. ... point ... 13 works well for the current slow pace.
Message 7 of 9 , Oct 10 1:46 PM
--- In APBR_analysis@y..., john wallace craven <john1974@u...> wrote:
>
>
>
> On Thu, 10 Oct 2002, Richard Scott wrote:
>
> > Have also seen that Bill James pythagorean method applied to the
NBA to, to do this. The exponent, of course, is radically different.
>
> I found that an exponent somewhere around 13 (unfortunately, I
don't have
> my notes with me; I'm at school and they're at home) works really
well.
> Obviously, it's not perfect; just like baseball, factors other than
point
> differential (like luck) impact won-lost records.

13 works well for the current slow pace. Higher numbers work better
with older higher scoring games (16 worked better in the '80's).
WNBA exponent is around 9.

>
> John Craven
>
> > ----- Original Message -----
> > From: bchaikin@a...
> > To: APBR_analysis@y...
> > Sent: Thursday, October 10, 2002 3:17 AM
> > Subject: [APBR_analysis] predicting W-L record based on team
point differential
> >
> >
> > 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.
> >
> >
• ... [...] ... Good points. What is both a strength and weakness of the normal probability approach is: it uses more information and thus can make more
Message 8 of 9 , Oct 15 6:48 PM
On Thu, 10 Oct 2002, Dean Oliver wrote:

[...]

> I once compared the normal probability approach to different
> pythagorean exponents and the normal approach is always better. Not
> by enough to worry about, though. I'd expect any linear form or
> ratio to be similar to the pythagorean. Since the normal approach
> 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.

Good points. What is both a strength and weakness of the normal
probability approach is: it uses more information and thus can make more
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, but the
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.

As usual, there's a choice of the quick-and-dirty vs the more-accurate-
but-more-work calculations.

--MKT
• ... Not ... approach ... points ... little ... any ... Pythagorean ... to ... make more ... mean ... takes ... Yup. The covariance is actually quite
Message 9 of 9 , Oct 15 6:59 PM
> [...]
>
> > I once compared the normal probability approach to different
> > pythagorean exponents and the normal approach is always better.
Not
> > by enough to worry about, though. I'd expect any linear form or
> > ratio to be similar to the pythagorean. Since the normal
approach
> > 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.
>
> Good points. What is both a strength and weakness of the normal
make more
> 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.
>
> As usual, there's a choice of the quick-and-dirty vs the more-
accurate-
> but-more-work calculations.
>
>
> --MKT
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