• ## RE: [APBR_analysis] Re: Team Ratings (adjusted for schedule strength)

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• Thanks, clearly my figure of 2/3 home wins was based on 1970s-1980s memories, in recent years the figure s been more like 3/5. There s a lot of little detailed
Message 1 of 18 , Jan 6, 2004
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Thanks, clearly my figure of 2/3 home wins was based on 1970s-1980s
memories, in recent years the figure's been more like 3/5.

There's a lot of little detailed questions to be answered, such as
which Home Win% figure to use, let's just pick this year's current
value of 62%.

Using ssims' ORate and DRate numbers, that corresponds to a team
having approximately a 3.5 point advantage, in terms of ORate -
DRate difference.

So if a team has played 12 home games and 8 away games, it's got
a 4-game imbalance, worth a cumulative 4*3.5 point ORate-DRate
difference = 14, which spread over its 20 games is 0.7 points
of ORate-DRate differential.

So if the initial rating has the team appearing to be a .500
team with ORate = 100 and DRate = 100, an estimate which
corrects for its excessive home games would be ORate = 99.3
(or, the .7 points could be split evenly between ORate and DRate).

This is a crude measure of course;, if we had home-road splits
of O and D, we could do separate corrections for ORate and DRate.

And for theoretical correctness we should apply the same Home-
Road correction to the Opponent's ratings, as well as the
Opponents' Opponents' ratings.

Better still would be to apply the correction to individual
game scores, rather than each team's aggregate totals; and
to base the ratings on the outcomes of the individual games
rather than the aggregate season totals; and to permit
individual teams to have differing home bonuses instead of
assigning all teams a 3.5 home bonus; and to solve the
simultaneous equations for looking at opponents'
opponents' opponents' ... ad infinitum; and etc. etc.

But those procedures would require a lot more data and a lot
more work. This crude home-road correction is simple and
I would guess cleans up a good chunk of the home-road bias.

--MKT

-----Original Message-----
From: Dean LaVernge [mailto:deanlav@...]
Sent: Monday, January 05, 2004 8:24 PM
To: APBR_analysis@yahoogroups.com
Subject: RE: [APBR_analysis] Re: Team Ratings (adjusted for schedule
strength)

On 5 Jan 2004 at 9:43, Michael Tamada wrote:

>
> I was thinking of a simpler, cruder home-away correction. Although
> some teams seem to thrive at home and wilt away from it (Utah) and
> others seem to be road warriors as good on the road as at home (Boston,
> Seattle), I was thinking in terms of simply giving a single universal
> home-away correction that would be applied to every home team's offense
> rating or defense rating (or both, but I think this wouldn't really matter,
> because it'd simply be a constant to be added or subtracted).
>
> We would still need some home-away split data, but even if that's
> unavailable we could estimate what the home bonus should be: in
> most years, NBA teams win about 2/3 of their home games (I haven't
> looked at this year's data). Comparing a .667 team to a .500 team,
> how much better would its offense have to be to move it from .500
> to .667? (Or equivalently, how much better would its defense have
> to be?) Whatever that figure is, that's the home bonus to give
> to the home team's offensive rating (or defensive rating).
>
> Crude but simple and I think it would significantly help correct
> for teams which have had schedules which were either (a) unbalanced
> with respect to home and away games or (b) balanced with respect
> to home and away, but unbalanced in terms of having tough or easy
> road opponents, and vice-versa at home.
>
>
> --MKT
>

Here is the Home/Away records for the NBA (2004 Season through games of 1/4/2004)

Season Wins Losses % Wins Losses %
1947 202 129 0.610 129 202 0.390
1948 107 85 0.557 85 107 0.443
1949 212 132 0.616 132 212 0.384
1950 351 167 0.678 167 351 0.322
1951 254 85 0.749 85 254 0.251
1952 213 80 0.727 80 213 0.273
1953 195 83 0.701 83 195 0.299
1954 151 84 0.643 84 151 0.357
1955 139 59 0.702 59 139 0.298
1956 141 80 0.638 80 141 0.362
1957 172 76 0.694 76 172 0.306
1958 150 85 0.638 85 150 0.362
1959 148 80 0.649 80 148 0.351
1960 149 84 0.639 84 149 0.361
1961 156 85 0.647 85 156 0.353
1962 166 107 0.608 107 166 0.392
1963 184 109 0.628 109 184 0.372
1964 185 126 0.595 126 185 0.405
1965 178 125 0.587 125 178 0.413
1966 197 89 0.689 89 197 0.311
1967 193 128 0.601 128 193 0.399
1968 241 182 0.570 182 241 0.430
1969 315 206 0.605 206 315 0.395
1970 312 207 0.601 207 313 0.398
1971 402 262 0.605 262 402 0.395
1972 385 277 0.582 277 385 0.418
1973 393 268 0.595 268 393 0.405
1974 410 262 0.610 262 410 0.390
1975 472 266 0.640 266 472 0.360
1976 484 254 0.656 354 484 0.422
1977 634 268 0.703 293 609 0.325
1978 610 292 0.676 292 610 0.324
1979 600 302 0.665 302 600 0.335
1980 588 314 0.652 314 588 0.348
1981 586 357 0.621 357 586 0.379
1982 565 378 0.599 378 565 0.401
1983 585 358 0.620 358 585 0.380
1984 640 303 0.679 303 640 0.321
1985 601 342 0.637 342 601 0.363
1986 617 326 0.654 326 617 0.346
1987 627 316 0.665 316 627 0.335
1988 640 303 0.679 303 640 0.321
1989 694 331 0.677 331 694 0.323
1990 713 394 0.644 394 713 0.356
1991 730 377 0.659 377 730 0.341
1992 689 408 0.628 408 699 0.369
1993 676 431 0.611 431 676 0.389
1994 677 430 0.612 430 677 0.388
1995 661 446 0.597 446 661 0.403
1996 718 471 0.604 471 718 0.396
1997 684 505 0.575 505 684 0.425
1998 708 481 0.595 481 708 0.405
1999 452 273 0.623 273 452 0.377
2000 726 463 0.611 452 737 0.380
2001 711 478 0.598 478 711 0.402
2002 703 486 0.591 480 709 0.404
2003 747 442 0.628 442 747 0.372
2004 297 179 0.624 179 297 0.376
NBA 25136 14716 0.631 14824 25139 0.371

DeanL

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• I did a few calculations of my own on a schedule strength modifier. ... I used .625 (or 5/8). Using the Pythagorean approximation, and assuming Offense = 1,
Message 2 of 18 , Jan 8, 2004
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I did a few calculations of my own on a schedule strength
modifier.

wrote:
> There's a lot of little detailed questions to be answered, such as
> which Home Win% figure to use, let's just pick this year's current
> value of 62%.
>
I used .625 (or 5/8). Using the Pythagorean approximation, and
assuming Offense = 1, then

0.625 = (1 ^ EXP) / ( 1 ^ EXP + DEF ^ EXP)

where EXP is the exponent you are using. I use 14, since it is
about average for the last few seasons. Solving for DEF (the team
defensive rating as a percentage):

DEF = ( ( 1 / 0.625 ) - 1 ) ^ ( 1 / 14 )

or DEF = 0.9641701. Balancing the defensive and offensive ratios
around 100, I get Offense = 101.82417 and Defense = 98.20851.
These are the expected offensive and defensive ratings for an
average team at home. On the road, reverse the two. This gives a
3.6 point difference, pretty close to what you found.

> Using ssims' ORate and DRate numbers, that corresponds to a team
> having approximately a 3.5 point advantage, in terms of ORate -
> DRate difference.
>
> So if a team has played 12 home games and 8 away games, it's got
> a 4-game imbalance, worth a cumulative 4*3.5 point ORate-DRate
> difference = 14, which spread over its 20 games is 0.7 points
> of ORate-DRate differential.
>
> So if the initial rating has the team appearing to be a .500
> team with ORate = 100 and DRate = 100, an estimate which
> corrects for its excessive home games would be ORate = 99.3
> (or, the .7 points could be split evenly between ORate and DRate).
>
> This is a crude measure of course;, if we had home-road splits
> of O and D, we could do separate corrections for ORate and DRate.
>
> And for theoretical correctness we should apply the same Home-
> Road correction to the Opponent's ratings, as well as the
> Opponents' Opponents' ratings.
>

What I will do when I have the time is change the weights in the
formulas that calculate the schedule strength. Instead of each game
being weighted as 1, a home game will weigh as .982 for offensive
strength and 1.018 for defensive strength, and road games will weigh
as the opposite.

> Better still would be to apply the correction to individual
> game scores, rather than each team's aggregate totals; and
> to base the ratings on the outcomes of the individual games
> rather than the aggregate season totals; and to permit
> individual teams to have differing home bonuses instead of
> assigning all teams a 3.5 home bonus; and to solve the
> simultaneous equations for looking at opponents'
> opponents' opponents' ... ad infinitum; and etc. etc.
>
> But those procedures would require a lot more data and a lot
> more work. This crude home-road correction is simple and
> I would guess cleans up a good chunk of the home-road bias.
>
>
>
> --MKT
>
• The team ratings are updated through Jan. 27. I didn t have time to include a home/away modifier, so all ratings are calculated the same as before. ... with
Message 3 of 18 , Jan 28, 2004
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The team ratings are updated through Jan. 27. I didn't have time
to include a home/away modifier, so all ratings are calculated the
same as before.

--- In APBR_analysis@yahoogroups.com, "ssims22000" <ssims2@i...>
wrote:
> These ratings use a pythagorean approximation (exponent 14),
with
> offensive & defensive ratings adjusted as follows:
>
> ORate = Base ORate * Opp. Opp. ORate / Opp. DRate
> DRate = Base DRate * Opp. Opp. DRate / Opp. ORate
>
> the ORates and DRates listed are adjusted to leage average = 100.
> XWins is expected wins out of 82. Ratings are through Jan. 27.

I've also included a Floor Rating (basically, team floor %
adjusted for strength of schedule and league average. You can
really tell the teams that rely heavily on the three (their floor
ratings are much lower than their offensive ratings).

Team ORate DRate XWins OFlR DFlR
SAN 97.3 90.7 59.6 98.9 91.8
SAC 108.1 101.0 59.3 105.9 102.0
MIN 103.6 98.0 56.1 105.3 97.7
LAL 102.8 98.1 54.2 104.8 98.4
HOU 98.1 93.5 54.2 96.2 93.0
IND 99.3 94.7 54.1 98.8 95.8
DAL 108.9 103.9 54.1 107.3 102.9
DET 99.5 95.3 53.2 100.4 96.0
MEM 102.4 99.6 48.8 102.3 100.0
DEN 100.7 98.3 47.8 101.5 99.6
MIL 102.2 100.7 45.0 102.2 100.9
NJN 96.7 95.4 44.8 97.1 95.0
NOR 99.5 99.1 42.2 98.1 98.8
UTA 101.4 101.6 40.6 104.1 101.1
BOS 100.1 100.4 40.2 97.9 99.1
SEA 104.1 105.1 38.3 99.9 104.0
GSW 100.3 101.7 37.0 100.3 101.1
LAC 102.3 103.8 36.9 102.9 104.4
NYK 98.2 99.8 36.3 96.7 99.9
PHI 97.3 99.3 35.4 97.9 98.4
PHO 98.3 101.0 33.5 98.5 100.4
POR 102.4 105.8 31.6 103.7 105.6
CLE 97.5 100.8 31.5 99.7 100.2
MIA 97.0 100.8 30.3 96.5 100.6
TOR 93.9 98.1 28.7 93.3 99.8
ORL 101.8 108.0 24.8 101.2 107.7
WAS 94.5 100.9 23.6 95.5 100.8
ATL 96.2 102.8 23.2 97.1 102.8
CHI 95.1 102.1 22.3 95.4 102.1

Comments: I mentioned Sacramento's very high offensive efficiency
(110 a month ago) and San Antonio's excellent defensive efficiency
(90 a month ago) as being unsustainable. Well, Sacramento's offense
has fallen off by two points (and their sub-par defense improved by
one), so I was right there. San Antonio's defense has yet to fall
off significantly, though, and their offense continues to be among
the NBA's least efficient. San Antonio also faced the weakest first
half schedule of any Western team (Sacramento faced the second-
weakest), so the true test will be the second half. These two teams
have yet to play each other, so we have four games between the
irresistable force and the immovable object to look forward too.

Other strong offenses & defenses: Houston has improved its numbers
by about two in either direction, much of that presumably
attributable to Yao's continued development. Anyone else think this
team could be very dangerous come playoff time? Their achilles heel
is their low offensive floor% - when it comes to crunch time, can
their offense come through with the needed buckets? Dallas is back
on top of the NBA's offenses, though they're doing it differently
this year. Their shooting is down (with Walker throwing up all
those bricks, that's a given), but their offensive rebounding is way
up, thanks to Jamison, Fortson, and Howard, primarily. That makes
their offensive numbers much more sustainable, in my mind, than
Sacramento's, which are based on continued amazing shooting from
within and without the arc.

Other notes: Orlando's defense is on pace to be one of the worst in
NBA history. Seattle is taking 30% of their shots behind the arc,
resulting in a floor rating of 100 and an offensive rating of 104.
• ... From: ssims22000 To: Sent: Wednesday, January 28, 2004 5:08 PM Subject: [APBR_analysis] Re: Team
Message 4 of 18 , Jan 28, 2004
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----- Original Message -----
From: "ssims22000" <ssims2@...>
To: <APBR_analysis@yahoogroups.com>
Sent: Wednesday, January 28, 2004 5:08 PM
Subject: [APBR_analysis] Re: Team Ratings (adjusted for schedule strength)

> The team ratings are updated through Jan. 27. I didn't have time
> to include a home/away modifier, so all ratings are calculated the
> same as before.
>

I may have missed this the first time around, but how are you adjusting for
opponent strength? Just this season's performance, or are you including
previous season(s)?

ed
• ... I m curious whether your ratings add anything beyond what Jeff Sagarin offers: http://www.usatoday.com/sports/sagarin/nba0304.htm He uses
Message 5 of 18 , Jan 29, 2004
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--- In APBR_analysis@yahoogroups.com, "ssims22000" <ssims2@i...>
wrote:
> The team ratings are updated through Jan. 27. I didn't have time
> to include a home/away modifier, so all ratings are calculated the
> same as before.

Sagarin offers:

http://www.usatoday.com/sports/sagarin/nba0304.htm

He uses point-differential, rather than off/def efficiencies. It
seems to me a team's scoring differential is going to be equivalent
to their efficiency differential. Whether they are better on
offense or on defense is another matter; but whether team A is
better than team B, does one need that distinction?

Sagarin does use home/away in his SOS deduction. He ranks the
Kings' SOS as #24 in the league (Spurs at #17).

In your eXpected Wins column, I guess you are assuming a balanced
schedule for everyone ?

>
>
>
> Team ORate DRate XWins OFlR DFlR
> SAN 97.3 90.7 59.6 98.9 91.8
> SAC 108.1 101.0 59.3 105.9 102.0
> MIN 103.6 98.0 56.1 105.3 97.7
> LAL 102.8 98.1 54.2 104.8 98.4
> HOU 98.1 93.5 54.2 96.2 93.0
> IND 99.3 94.7 54.1 98.8 95.8
> DAL 108.9 103.9 54.1 107.3 102.9
> DET 99.5 95.3 53.2 100.4 96.0
> MEM 102.4 99.6 48.8 102.3 100.0
> DEN 100.7 98.3 47.8 101.5 99.6
> MIL 102.2 100.7 45.0 102.2 100.9
> NJN 96.7 95.4 44.8 97.1 95.0
> NOR 99.5 99.1 42.2 98.1 98.8
> UTA 101.4 101.6 40.6 104.1 101.1
> BOS 100.1 100.4 40.2 97.9 99.1
> SEA 104.1 105.1 38.3 99.9 104.0
> GSW 100.3 101.7 37.0 100.3 101.1
> LAC 102.3 103.8 36.9 102.9 104.4
> NYK 98.2 99.8 36.3 96.7 99.9
> PHI 97.3 99.3 35.4 97.9 98.4
> PHO 98.3 101.0 33.5 98.5 100.4
> POR 102.4 105.8 31.6 103.7 105.6
> CLE 97.5 100.8 31.5 99.7 100.2
> MIA 97.0 100.8 30.3 96.5 100.6
> TOR 93.9 98.1 28.7 93.3 99.8
> ORL 101.8 108.0 24.8 101.2 107.7
> WAS 94.5 100.9 23.6 95.5 100.8
> ATL 96.2 102.8 23.2 97.1 102.8
> CHI 95.1 102.1 22.3 95.4 102.1
>
• ... time ... the ... equivalent ... The purpose of my ratings is a little different than Sagarin s. If you just want to look at which team is better, and that
Message 6 of 18 , Jan 29, 2004
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--- In APBR_analysis@yahoogroups.com, "Mike G" <msg_53@h...> wrote:
> --- In APBR_analysis@yahoogroups.com, "ssims22000" <ssims2@i...>
> wrote:
> > The team ratings are updated through Jan. 27. I didn't have
time
> > to include a home/away modifier, so all ratings are calculated
the
> > same as before.
>
> Sagarin offers:
>
> http://www.usatoday.com/sports/sagarin/nba0304.htm
>
> He uses point-differential, rather than off/def efficiencies. It
> seems to me a team's scoring differential is going to be
equivalent
> to their efficiency differential. Whether they are better on
> offense or on defense is another matter; but whether team A is
> better than team B, does one need that distinction?
>
The purpose of my ratings is a little different than Sagarin's.
If you just want to look at which team is better, and that is all
you care about, use his ratings - his rating model is a lot more
sophisticated. After all, I am just using a clunky Pythagorean
approximation. A bell curve like Dean uses would be more accurate,
but it would require me to use a matrix of game scores, and that's a
bit too time-consuming for me right now. All I want out of my
overall team ratings is an approximation of how well each team is
doing. One small note - the results are a bit different because I
don't set a team's possessions equal to its opponents' possessions.
So a team which, for some reason, has 0.7 fewer possessions / game
than its opponents will rate better than it would if pure
differential were used. I do this because using pure possessions
like this gives more accurate offensive & defensive ratings, and
that's what I'm really after here.
Offensive and Defensive ratings, in my opinion, give more useful
information about a team than just a rating saying how "good" the
team is. These ratings start to answer the question of how a team
is good (or bad). For instance, someone just looking at the Sagarin
ratings for Orlando might be bewildered as to how a team that was in
the playoffs a year ago could be so bad. Look at their defensive
rating, though. Here we see some epic-level bad defense. OK, that
explains things. If you want to know why they are so bad
defensively, you'd have to go deeper than this. I have some other
quick stats that can help elucidate the factors that make an offense
or defense perform the way it does (I took most of these from Dean's
book, as well): true shooting percentage (we're all familiar with
this one, right?), free throw ratio (as Dean defines it, free throws
MADE / field goals attempted - you could combine these first two
into a scoring efficiency number, as well, though looking at them
separately tells you more about how they score), offensive
rebounding percentage & turnover percentage (turnovers /
possessions). These cover all of the factors going into an
offensive (or defensive) rating. The floor percentage (or floor
rating, as I have it here - a modification of Dean's formula) is an
alternate efficiency rating that measures how often a team scores.
Sometimes consistency counts more than pure efficiency (points per
possession).
I didn't include the extra indicators for space reasons, but here
are some for a few interesting offenses & defenses (league average
floor percentage (Flr%) is 48.2, true shooting percentage (TSP)
46.8, free throw ratio (FTR) 22.1, offensive rebound % (Off) 28.7 &
turnover percentage (TO%) 16.7):

Offense Rating Flr% TSP FTR Off TO%
Dallas 108.90 51.6 48.3 20.7 31.3 13.1
Sacramento 108.15 51.5 51.2 24.6 27.3 15.1
Seattle 104.08 48.0 49.8 19.9 26.7 16.0
Minnesota 103.62 50.9 49.1 19.5 26.2 14.1
AVERAGE 100.00 48.2 46.8 22.1 28.7 16.7
San Antonio 97.25 47.8 46.3 22.0 29.0 16.9
Toronto 93.85 45.2 45.3 20.3 24.2 16.7

Defense Rating Flr% TSP FTR Off TO%
San Antonio 90.70 44.2 42.3 21.0 25.7 17.0
Houston 93.51 44.9 42.5 22.7 25.9 15.2
Indiana 94.71 46.0 45.5 22.0 26.2 18.2
Detroit 95.25 46.0 44.6 18.8 28.0 17.1
AVERAGE 100.00 48.2 46.8 22.1 28.7 16.7
Dallas 103.88 49.8 49.3 19.8 29.1 15.7
Orlando 108.03 51.4 49.2 22.0 31.8 15.5

Note that these other indicators are not adjusted for schedule
strength.

> Sagarin does use home/away in his SOS deduction. He ranks the
> Kings' SOS as #24 in the league (Spurs at #17).
>
I don't use home & away for two reasons: 1) it would be too much
work and 2) I intend these rating primarily as whole-season analysis
tools, and over a whole season, each team plays a balanced or close
to balanced schedule with respect to home and away. The Spurs'
schedule rates worse in my system because they have played more road
games than home games against the better East teams (this will
eventually even out).

> In your eXpected Wins column, I guess you are assuming a balanced
> schedule for everyone ?
>
Yes. It's simply the projection based on offensive & defensive
ratings, everything else being equal.
• ... adjusting for ... including ... Just this season s.
Message 7 of 18 , Jan 29, 2004
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--- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
<igorkupfer@r...> wrote:
> I may have missed this the first time around, but how are you
> opponent strength? Just this season's performance, or are you
including
> previous season(s)?
>
Just this season's.

> ed
• ... time ... the ... Sagarin s stuff is a little bit of overkill for the NBA. Doing simple evaluation of schedule strength and home/road easily accounts for
Message 8 of 18 , Jan 31, 2004
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--- In APBR_analysis@yahoogroups.com, "Mike G" <msg_53@h...> wrote:
> --- In APBR_analysis@yahoogroups.com, "ssims22000" <ssims2@i...>
> wrote:
> > The team ratings are updated through Jan. 27. I didn't have
time
> > to include a home/away modifier, so all ratings are calculated
the
> > same as before.
>
> Sagarin offers:
>
> http://www.usatoday.com/sports/sagarin/nba0304.htm
>
> He uses point-differential, rather than off/def efficiencies. It
> seems to me a team's scoring differential is going to be equivalent
> to their efficiency differential. Whether they are better on
> offense or on defense is another matter; but whether team A is
> better than team B, does one need that distinction?
>

Sagarin's stuff is a little bit of overkill for the NBA. Doing
simple evaluation of schedule strength and home/road easily accounts
for things well enough. Sagarin's evaluation goes above and beyond
and makes sense for college where varying schedules are huge.

So, yeah, Sagarin's overall evaluation should be roughly comparable.
It's just more interesting to look at the offensive and defensive
ratings separately. Tells a better story.

DeanO