## 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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