# NBA Power Rankings – November 8th

After 12 days into the NBA season, we have seen 93 NBA games; approximately 7.5% of the 1,230 total regular season games. This suggests that each team should have played an average of 6.2 games. Of these 93 games, the distribution of games played is given as follows:

• 8 Games: Atlanta (7-1)
• 7 Games: Golden State (7-0), Chicago (4-3), Houston (4-3), Milwaukee (4-3), Memphis (3-4), Orlando (3-4), Sacramento (1-6), and Brooklyn (0-7)
• 6 Games: Cleveland (5-1), Toronto (5-1), Los Angeles C (4-2), Portland (4-2), San Antonio (4-2), Utah (4-2), Dallas (3-3), Indiana (3-3), Miami (3-3), Oklahoma City (3-3), Phoenix (3-3), Washington (3-3), Charlotte (2-4), Denver (2-4), New York (2-4), New Orleans (0-6), Philadelphia (0-6)
• 5 Games: Detroit (4-1), Minnesota (3-2), Boston (2-3), Los Angeles L (1-4)

Using the first 93 games, we would like to identify the rankings of each of the thirty NBA teams. We will model the probability of winning for a particular team given any opponent by using a beta distribution dependent on the location of the game and the teams participating. We outlined the model for beta regression in a previous post on NFL games and will use this to model the previously played 93 games.

Fitted Beta model (Red) against the first 93 games played (blue) of the 2015-16 NBA season.

We see that the fit is relatively strong, with an r-squared of 0.7467. The blue line in the regression fit represents the percentage of points scored by the primary team. The primary team is merely the team given an indicator of “1”. In game 51 (Golden State versus Memphis) we severely under-predicted this value as our model expected Memphis to not lose by 50 points (119-69). The resulting percentage observed is 0.632; where our fitted value is 0.549.

However, the fitting is strong due a high r-squared value. Hence, the resulting coefficients serve as a decent indicator of who is likely to win in given match-ups; and therefore lends itself to being a decent method of ranking teams.

Rankings based on Beta distribution model after the first 93 games of the 2015-16 NBA season.

We find the top teams once again on the top of the list. While this methodology produces a decent ranking scheme, it still produces an incredibly conservative model for predicting the end of season standings. Using this model to predict the remaining 74 – 77 games of the season, we find that Golden State is expected to win only 43 more games (highest) while Sacramento is expected to win only 31 games (lowest). This effectively forces parity in the league for the remainder of the season. Instead, we propose using the possessions based model to predict outcomes of games, as done prior to the season.