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:
|Chicago||25||19||7||4th||Los Angeles C||30||16||11.5||4th|
|Milwaukee||20||27||13.5||Los Angeles L||9||38||33|
Once we apply the aforementioned rankings model, we obtain the following power rankings:
|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.
Using this model, we are able to predict the final standings.
|Chicago||52||30||7||3rd||Los Angeles C||55||27||11.5||4th|
|Milwaukee||32||50||13.5||Los Angeles L||15||67||33|
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.