Reliving the 2015 NBA Playoffs

By Hans Chen

Explanation of the Method:

In this paper, we are going to look at how each player’s individual contribution affects the overall performance of the team. We collected Player Efficiency Ratings (PER[1]) and playing time for each player during last year’s regular season from ESPN.com. We are going to modify the PER to create new statistic, Weighted Player Efficiency Rating (WPER), which measures the efficiency of a player given how much time he plays throughout the season. This statistic aims to measure a player’s “true” contribution to the team. PER does not take playing time into account, so there can be players with high PER and minimal playing time, which translates to a very small contribution to their teams. Let’s take a look at some examples of how WPER is calculated:

Player Name Game MPG Player Minutes Player Min / Total Min PER WPER
L. James 69 36.1 2490.9 0.125889 26 3.27311
K. Irving 75 36.4 2730 0.137973 21.6 2.980214
K. Love 75 33.8 2535 0.128118 18.9 2.421424
J.R. Smith 46 31.8 1462.8 0.073929 14.5 1.071973
T. Mozgov 46 25 1150 0.05812 18.8 1.092664
D. Waiters 33 23.8 785.4 0.039694 12.3 0.488233
A. Varejao 26 24.5 637 0.032194 17.7 0.569828
T. Thompson 82 26.8 2197.6 0.111066 15.7 1.74373
I. Shumpert 38 24.2 919.6 0.046476 11.2 0.520533
S. Marion 57 19.3 1100.1 0.055599 11 0.611584
M. Dellavedova 67 20.6 1380.2 0.069755 8.6 0.59989
J. Jones 57 11.7 666.9 0.033705 11.1 0.374123
J. Harris 51 9.7 494.7 0.025002 5.6 0.140011
K. Perkins 17 9.8 166.6 0.00842 4.8 0.040415
M. Miller 52 13.5 702 0.035479 4.6 0.163202
A. Price 11 7.9 86.9 0.004392 7.7 0.033818
W. Cherry 8 8.6 68.8 0.003477 5.9 0.020515
B. Haywood 22 5.4 118.8 0.006004 9.1 0.054637
L. Amundson 12 6.6 79.2 0.004003 3.8 0.01521
A. Kirk 5 2.8 14 0.000708 8.5 0.006014
Total     19786.5     16.22113
Figure 1: A sample calculation of WPER for the Cleveland Cavaliers in 2014-2015 Regular

Season. The team combined for a total of 19786.5 minutes played. We created the column Player Min / Total Min to measure the ratio of each player’s playing time to their total playing time. Then we multiplied that column by the PER column to calculate each player’s WPER. Finally, we sum over each player’s WPER in order to determine their total Team Efficiency Rating (TER).

With this method, we calculated TER for each team and collected each team’s winning percentage in the regular season.

Team TER Winning Percentage Team TER Winning Percentage
Bulls 15.56385 0.609756 Warriors 17.26468 0.817073
Cavaliers 16.22113 0.646341 Clippers 16.89853 0.682927
Pistons 14.98546 0.390244 Lakers 14.28295 0.256098
Pacers 14.15951 0.463415 Suns 14.95527 0.47561
Bucks 14.55201 0.5 Kings 14.42513 0.353659
Celtics 14.59825 0.487805 Mavericks 16.17429 0.609756
Nets 14.60623 0.463415 Rockets 15.1276 0.682927
Knicks 13.16042 0.207317 Grizzlies 15.46248 0.670732
76ers 12.30276 0.219512 Pelicans 16.07248 0.54878
Raptors 16.20265 0.597561 Spurs 16.28095 0.670732
Hawks 16.29142 0.731707 Nuggets 14.30349 0.365854
Hornets 13.77095 0.402439 Timberwolves 14.1462 0.195122
Heat 14.58467 0.45122 Thunder 15.45037 0.54878
Magic 13.98673 0.304878 Blazers 15.63608 0.621951
Wizards 14.70004 0.560976 Jazz 15.21007 0.463415
Figure 2. 30 Teams’ Team Efficiency Rating (TER) and their winning percentage in 2014-2015 regular season.

Next we’ll use linear regression to model the relationship between TER and winning percentage.ChenArticleBBall

Figure 3: Scatterplot of TER vs. Win Percentage

As the graph demonstrates, the r-squared value is large – roughly 0.76 – meaning 76% of the variance of winning percentage can be explained by the change in TER. The graph and the regression line show a strong relationship between a team’s winning percentage and TER. Therefore, the higher the Team Efficiency Rating, the more likely a team is going to win.

Analysis of Strengths and Weaknesses of the Model:

Strengths:

  1. This method allows us to view a player’s “true” contribution to a team’s victory. The model can help us identify some superstars who play many minutes, but whose inefficient performances actually hurt the team.
  2. This method allows us account for a player’s inability to contribute whenever he is injured or he doesn’t get a chance to play. The overall TER will decrease and thus negatively affect a team’s performance.

Weaknesses:

  1. We assume that a player’s PER is constant through both the regular season and playoffs.
  2. There are many other factors affecting a player’s performance such as pressure, emotions, and personal business.
  3. One player’s PER can be affected by another player’s PER because they may play particularly well in the presence of one another. These factors may affect each player’s PER and thus affect the overall TER.

 

If the 2015 Playoffs reset…

Taking all the injuries into account from the 2015 playoffs and using this method to predict the 2015 NBA Playoff games, would result in the following bracket:

ChenPic2Bball.png

Overall, we got 12 of the 15 series correct, which is 80% accurate. Our confidence percentage is close to the r-squared value obtained earlier, which suggests that this method can accurately account for roughly 3/4 of all matchup victories.

Conclusion:

In this paper, we introduced the method of using Weighted Player Efficiency Ratings (WPER) to predict NBA playoff games. We collected Player Efficiency Rating (PER) data from ESPN and weighted it according to each player’s playing time. WPER tells us about the real contribution of a player to the team victory. The results show that there is a strong relationship between the sum of each player’s WPER and a team’s performance. This method helps us predict each team’s performance in playoffs based on the players’ contributions to the team in regular season with an accuracy around 76%. In the future, this model can be further modified by considering the factors that change Player Efficiency Rating (PER), such as pressure, emotions, and playing conditions.

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