NBA Power Rankings: Normalized Ranking Model

In this article, we come back from a month hiatus and introduce a normalized rankings model for ranking every team in the NBA. By normalized ranking, we set all rankings to a score between zero and one, where one is a perfect ranking and zero is the worst possible ranking.

To build the model we consider several factors: location of each game, time (hours) between games for respective teams, the resulting score of the game with diminishing returns, game statistics, and (obviously) the teams playing in each game. We then apply a bernoulli exponential family model to obtain a probability of winning a particular game. The resulting coefficients, with whitening from the resulting variance-covariance matrix, yields a ranking. Transforming to a [0,1] scale, we obtain our rankings. Feel confused? Don’t worry; all the work has been done already.

 

Current Standings and Rankings

As of the afternoon of January 27th, 682 of the 1230 NBA games have been played; approximately 55% of the season has been completed. The Golden State Warriors are still on stellar pace for the 72-10 record, currently with a 41-4 record; with a rematch with Dallas looming later tonight. The San Antonio Spurs, despite being dismantled by Golden State two days ago, maintain a phenomenal 39-7 record; a mere 2.5 games behind the hottest team in the NBA. Obviously, these two teams should be one and two, respectively.

First, we give the current standings:

 

Atlantic Wins Losses GB   Northwest Wins Losses GB
Toronto 30 15 2nd Oklahoma City 35 13 3rd
Boston 26 21 5 5th Portland 21 26 13.5 8th
New York 22 25 9 Utah 20 25 13.5
Brooklyn 12 34 18.5 Denver 17 29 17
Philadelphia 7 40 24 Minnesota 14 33 20.5
Central Wins Losses GB   Pacific Wins Losses GB
Cleveland 32 12 1st Golden State 41 4 1st
Chicago 25 19 7 4th Los Angeles C 30 16 11.5 4th
Detroit 25 21 8 6th Sacramento 20 25 21
Indiana 23 22 9.5 8th Phoenix 14 33 28
Milwaukee 20 27 13.5 Los Angeles L 9 38 33
Southeast Wins Losses GB   Southwest Wins Losses GB
Atlanta 27 20 3rd San Antonio 39 7 2nd
Miami 25 21 1.5 7th Memphis 26 20 13 5th
Charlotte 22 24 4.5 Dallas 26 21 13.5 6th
Washington 20 23 5 Houston 25 23 15 7th
Orlando 20 24 5.5 New Orleans 16 28 22

Once we apply the aforementioned rankings model, we obtain the following power rankings:

Rank Team Ranking Record
1 Golden State 1.0000 41 – 4
2 San Antonio 0.8116 39 – 7
3 Cleveland 0.6183 32 – 12
4 Oklahoma City 0.5898 35 – 13
5 Toronto 0.5639 30 – 15
6 LA Clippers 0.5574 30 – 16
7 Atlanta 0.5017 27 – 20
8 Dallas 0.5005 26 – 21
9 Detroit 0.4983 25 – 21
10 Chicago 0.4897 25 – 19
11 Memphis 0.4616 26 – 20
12 Indiana 0.4615 23 – 22
13 Houston 0.4523 25 – 23
14 Boston 0.4484 26 – 21
15 Charlotte 0.4377 22 – 24
16 Miami 0.4268 25 – 21
17 New York 0.3973 22 – 25
18 Sacramento 0.3928 20 – 25
19 Washington 0.3905 20 – 23
20 Milwaukee 0.3814 20 – 27
21 Utah 0.3545 20 – 25
22 Orlando 0.3464 20 – 24
23 Portland 0.3407 21 – 26
24 New Orleans 0.3325 16 – 28
25 Denver 0.3277 17 – 29
26 Minnesota 0.2410 14 – 33
27 Phoenix 0.2180 14 – 33
28 Brooklyn 0.1842 12 – 34
29 LA Lakers 0.0905 9 – 38
30 Philadelphia 0.0151 7 – 40

We see immediately that the Warriors and Spurs are indeed the two best teams in the league. However, we find that the Cavaliers is ranked third, with the Oklahoma City Thunder sitting at fourth. This makes sense as Cavaliers are 1-0 against the Thunder. Of the remaining games, which each team has lost 12 apiece; the losses are against similar teams. Thus the offset between these teams is a mere 0.0285 points separating these two teams. Toronto and the Los Angeles Clippers round out the elite teams status with ranking scores of 0.55 and higher.

After a significant 0.05+ point drop, there is a logjam of four teams: Atlanta, Dallas, Detroit and Chicago. These four teams are all contained within 0.0120 points. A curious note is that the Chicago Bulls are behind the Detroit Pistons despite being a full game ahead. This is typically due to the strength of wins on top of the records. The two teams do not have identical schedules, so a pure record cannot be used to distinguish the teams; despite the playoffs being dictated so. It should be noted the difference in schedules is only in 3-4 games difference: Detroit plays an extra game each against Boston, Brooklyn, and Washington; Chicago plays an extra game each against Charlotte, New York, and Toronto. While Chicago’s schedule seems tougher; indicating a better record would dictate a higher ranking, the Detroit Pistons are one of the four teams to defeat the Golden State Warriors and are 2-1 against the Bulls.

In these rankings, there no major surprises. The biggest difference between the 16 teams slated for the playoffs and the rankings is that the Portland Trailblazers are ranked 23rd, despite hanging on to the 8th spot in the Western Conference.

So who should we expect for the playoffs?

Predicted Final Standings

Using the Beta distribution for predicting home team percentages of points scored, we found that the fitted r-squared for the original 682 NBA games is 0.6621. This indicates a fairly good fit. In fact, retroactively fitting the model to the percentage of points scored, all 682 games are imputed correctly: 682-0.

Screen Shot 2016-01-27 at 8.57.50 PM

Beta regression fit (red) to the true proportion of points scored by the home team (blue) over all 682 NBA games (x-axis) in the 2015-2016 NBA season.

Using this model, we are able to predict the final standings.

Atlantic Wins Losses GB   Northwest Wins Losses GB
Toronto 58 24 2nd Oklahoma City 60 22 3rd
Boston 47 35 5 5th Utah 36 46 13.5
New York 37 45 9 Portland 32 50 13.5
Brooklyn 23 59 18.5 Denver 29 53 17
Philadelphia 13 69 24 Minnesota 23 59 20.5
Central Wins Losses GB   Pacific Wins Losses GB
Cleveland 61 21 1st Golden State 70 12 1st
Chicago 52 30 7 3rd Los Angeles C 55 27 11.5 4th
Detroit 44 38 8 7th Sacramento 37 45 21 8th
Indiana 41 41 9.5 Phoenix 24 58 28
Milwaukee 32 50 13.5 Los Angeles L 15 67 33
Southeast Wins Losses GB   Southwest Wins Losses GB
Atlanta 48 34 4th San Antonio 67 15 2nd
Miami 45 37 1.5 6th Memphis 50 32 13 5th
Charlotte 42 40 4.5  8th Dallas 44 38 13.5 6th
Washington 40 42 5 Houston 43 39 15 7th
Orlando 32 50 5.5 New Orleans 30 52 22

Here, we see that nothing major changes with the standings except a couple positions switches. For instance, the Chicago Bulls are expected to climb to third in conference from fifth, leap-frogging the Atlanta Hawks and Boston Celtics.

Similarly, we expect the Portland Trailblazers to fade for the remainder of the season, allowing for either the Utah Jazz or Sacramento Kings to sneak in as a the 8th seed. Unfortunately the 8th seed will have to face off an insanely high-octane Golden State Warriors, who are still predicted to fall just short of the 72-10 record; predicted to fall at 70-12.

As the season draws nearer to a close, we will start to run the Markov Chain Monte Carlo systems to predict probabilities of making the playoffs. However, there are still over 500 NBA games remaining for the season. So we can still sit back and enjoy the games. Such as a Golden State Warriors 20 point win over the Dallas Mavericks.

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