FanPost

Yet Another Rating System

                There seems to have been quite a bit of discussion lately about the value of various statistical evaluations of NBA teams, especially the Blazers. This most likely is due to the Blazers 2nd best point differential, despite their slow pace. This usually leads to observations about strength of schedule and general doubt about what the future holds.

                As has been observed by many people, point differential is a flawed metric. Most other metrics have similar problems, or are shrouded in such mystery (Hollinger), that it is impossible to tell what is going on. Being a mathematically inclined individual, I've been working on devising a metric that meets several standards:

1)   Predictive: Ratings are great, as are a myriad of statistics. However, if we are searching for some single number, it would be best if it allowed us to give a prediction of future games. That is, if given the ratings for two teams, the system would calculate an expected margin.

2)   Sensitivity To Games: Once a game's margin is predicted, a team will either exceed this margin or not. If it does exceed it, then the team is better than expected, and the rating should adjust itself upward. The same idea applies to not meeting the margin.

3)   Dependent on Strength of Schedule: This is really the whole point of this post. If everyone knows that the metric needs to be viewed through a SOS lense, then why not just incorporate SOS into the metric in the first place. Note that if the 1st two characteristics are incorporated, this one should be taken care of as well.

4)   Pace-Adjusted: This is true of almost all basketball statistics. The Blazers play slowly, and we really want to know how a team performs over 100 possessions, not 48 minutes.

With these in mind, I proceeded to construct a theory of skill as relates to basketball. The metric encompasses the first 3, but is not paced adjusted, as I was unable to find pace calculations for individual games (if you have any tips, please let me know). The basic idea is that each team has a given rating, and the expected margin is merely,

TeamOneRating-TeamTwoRating = Margin,

where, since this is time based, the margin would be the expected margin after 48 minutes. However, I noticed that, on average, home teams outscore visiting teams by a margin of about 3.8. Thus, the margin that the Home team is expected to win by, MarginExpected, is given by

MarginExpected = 3.8 + HomeRating-VisitingRating.

From this formula and the scores of the last 221 basketball games, I was able to compute the ratings for all 30 teams. This was done using a least squares approximation. For each game, there is an error given by

Error = ExpectedMargin-ActualMargin.

The least squares method finds the values of the ratings such that the sum of the errors is minimized. Additionally, because all of the values are relative to each other, you can constrain them so that the average rating is 0. Then it becomes a constrained minimization problem in a quadratic of 30 variables, which computer software can solve quite easily.

                The following table shows the calculated ratings, both with and without home-court advantage factored in. As you can see, this does move some teams around, such as the Lakers, who have only played 3 road games, but it leaves the general ordering unchanged, and the Blazers at number 2.

Team

Home Advantage Rankings

Home Advantage

No Home Advantage Ranking

No Home Advantage

Dallas Mavericks

1

6.442

3

6.383

Portland Trail Blazers

2

6.372

2

6.458

Atlanta Hawks

3

6.035

1

6.584

Orlando Magic

4

5.965

6

5.67

Denver Nuggets

5

5.964

7

5.256

Boston Celtics

6

5.574

4

6.1416

Phoenix Suns

7

5.09

9

4.286

Oklahoma City Thunder

8

4.28

10

3.931

Los Angeles Lakers

9

4.264

5

6.128

San Antonio Spurs

10

3.93

8

5.18

Houston Rockets

11

2.999

11

2.954

Cleveland Cavaliers

12

2.748

12

2.394

Utah Jazz

13

1.748

13

1.986

Milwaukee Bucks

14

0.618788

16

0.682

Miami Heat

15

0.223

14

1.1

Detroit Pistons

16

-0.087

17

-0.958

Sacramento Kings

17

-1.146

18

-1.164

Golden State Warriors

18

-1.246

21

-2.167

New Orleans Hornets

19

-1.259

15

0.8966

Toronto Raptors

20

-1.269

20

-1.783

Charlotte Bobcats

21

-1.363

19

-1.429

Indiana Pacers

22

-3.259

22

-2.399

Chicago Bulls

23

-3.358

24

-4.296

Washington Wizards

24

-3.648

23

-3.906

Philadelphia 76ers

25

-4.847

26

-5.34

Los Angeles Clippers

26

-5.097

25

-4.648

Memphis Grizzlies

27

-5.5607

27

-5.92

New York Knickerbockers

28

-7.565

28

-7.1002

New Jersey Nets

29

-9.752

29

-10.5322

Minnesota Timberwolves

30

-12.8

30

-12.689

If you have any questions about methodology, math, thought-process or anything else please just post a response. This is my first post, so I will be watching it closely. Hope you enjoy it.

To read the table, just subtract the visiting team rating from the home team and add 3.8. Thus, we expect the Blazers to win by roughly 6.372-(-5.5607)+3.8 = 15.7 pts. Go Blazers.

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