NBA Regular Season Win Prediction Based on New Metrics in Machine Learning

Abstract

In recent years, data analysis has revolutionized the way basketball is understood and managed, with the NBA leading this transformation. The development of advanced metrics and machine learning tools has enabled more accurate evaluations and predictions in the sport. Despite the success of current metrics like the Player Efficiency Rating (PER) and Pythagorean Wins (PW), they often fail to provide a complete picture due to their reliance on production data, which can lead to data leakage. This study aims to introduce new efficiency-based metrics that mitigate the risk of data leakage and improve the accuracy of predicting NBA regular season wins. The new metrics adjust traditional statistics by incorporating the team’s pace and comparing them to opponents, ensuring a more reliable prediction framework. Using machine learning models such as K-nearest neighbors, random forest, gradient boosting regression, and support vector regression, the study evaluates the predictive accuracy of the new metrics against traditional data. Results indicate that the new metrics significantly enhance prediction accuracy, particularly in random forest and gradient boosting models. This research provides a more robust methodology for predicting team performance, aiding coaches, scouts, and management in their decision-making processes.

Contents

1. Introduction
   1.1 Background
   1.2 Research Objectives

2. Methodology
   2.1 Data
     2.1.1 Data Collection
     2.1.2 Data Cleaning
     2.1.3 Training and Testing Data
   2.2 New Metrics
   2.3 Modeling
     2.3.1 Results
     2.3.2 Stability Test
     2.3.3 Model Evaluation

3. Interpreting

4. Conclusion

5. Appendix
   5.1 NBA Terms

6. References

Introduction

Background

As data analysis has become ever popular and useful across a variety of industries, NBA is no exception. In the past, coaches and audiences had to rely solely on their experience to choose team starters, make tactics, and keep track of players’ health conditions. People used to cast doubt on the credibility of predicting complex games through simple data. However, after the publication of Moneyball by Michael Lewis in 2003, crowds shifted their view. The book proved how computers and statistics successfully built a competitive team with a limited budget. In addition, the development of motion tracking technology(for example, sportVU, a system with multiple cameras can accurately capture movements of players and the basketball) allows the NBA to collect tons of motional data on the courts. As a result, data analysis gets to prevail in the basketball world.

Breakthroughs in data analysis changed the way people interpret basketball. The first breakthrough was the invention of advanced data. At the beginning of sports analytics, people could only make rough evaluations of players based on basic data(such as points, rebounds, turnovers, etc). However, data analysts in the NBA invented PER, WS, offensive/defensive efficiency, and other advanced metrics. These metrics are calculated by basic data, but dig way much further. The data reveals players’ personal skills, tactical execution, and even intuition. The second breakthrough was that through advanced tools such as AI and machine learning, team management has been able to make predictions on wins or make immediate adjustment of game tactics.

In the NBA, data is drawn to serve various purposes. The three most commonly used fields are developing tactics, managing the team, and evaluating players. First, with the help of analysis tools, coaches can grip strengths and weaknesses of the opponent team thus providing specific adjustments to win the game. The second application is to evaluate players. It could be misleading to merely judge an individual player’s performance with one set of eyes. The whole team’s performance, the strengths of the opponents, and the condition of the player that game day——It’s difficult for a scout to take all these into consideration. The recruiting process has become a laborious and intensive process that has yielded sometimes biased conclusions on potential stars. However, data analysis appears to be the ideal scout nowadays. Lastly, an application of data analysis is the management of the whole team. Through the analysis of historical and real-time data, the team’s performance can be predicted in advance. Evaluation of the team is always the final goal of sports analysis. Evaluation of players only serves this aim. Besides, the team management can adjust its ticketing, advertising, and commercializing strategies based on the team’s performance.

Research Objectives

However, current metrics in the NBA don’t always show the full picture. Let’s take PER for instance. What is PER?

The Player Efficiency Rating (PER) is an advanced basketball statistic created by John Hollinger. It is designed to assess a player’s statistical accomplishments. PER takes into account a player’s positive contributions (such as points, rebounds, assists, steals, and blocks) and negative actions (like missed shots, turnovers, and fouls). In addition, PER is adjusted to the pace of the season and thus can compare players from different eras. It allows for a comprehensive evaluation of a player’s overall efficiency on the court.

The metric of PER is very complex. Firstly, uPER(unadjusted PER) is calculated, which converts data in total into data per minute and puts different weight on the data. Secondly, aPER(adjusted PER) is calculated, which is able to compare players in different eras by adjusting the data according to league paces. Thirdly, PER is calculated based on uPER and aPER, playing a role of standardizing.

Of course, you don’t have to fully understand the complex formulas, but still, it’s essential to know basic terms in the basketball world to continue our discussion, which you can refer to in the appendix.

Let’s look at the following example in a specific season: Player A drops 27.5 points, 6.3 rebounds, 3,8 assists, 1.9 steals, 0.8 blocks, and 2.2 turnovers, with 52.9% 2-point goal percentage and 38% 3-point goal percentage per 36 minutes; player B drops 25.2 points, 8.2 rebounds, 8.3 assists, 1.2 steals, 0.6 blocks, and 3.9 turnovers, with 61.1% 2-point goal percentage and 36.3% 3-point goal percentage per 36 minutes.

From all perspectives, you’ll conclude that player B is the more versatile player. To have a better understanding of that fact, let’s make a radar chart to reinforce the idea.

It is obvious. However, PER, an advanced metric of comprehensive evaluation of players, favors player A to player B. In fact, player A is Kawhi Leonard; player B is LeBron James; both data is collected from season 2016-2017. What’s wrong with PER? Here’s another example in season 2023—2024:

Ayo Dosunmu drops 14.9 points, 3.5 rebounds, 4 assists, 1.1 steals, 0.6 blocks, and 1.6 turnovers, with 56.9% 2-point goal percentage and 40% 3-point goal percentage per 36 minutes; Bogdan Bogdanović drops 20.2 points, 4.2 rebounds, 3.7 assists, 1.3 steals, 0.5 blocks, and 1.6 turnovers, with 50% 2-point goal percentage and 37.6% 3-point goal percentage per 36 minutes.

In this season, Ayo has a PER of 13.3, and Bogdan has a PER of 14.8. The difference of their PERs is 1.5. Let have a look at basic stats from radar charts:

We conclude that there is only a slight difference between their stats. And such a difference in basic stats is enough to result in a difference of 1.5 in PERs. However, let’s compare Russel Westbrook’s performance in season 2014-2015 to that in season 2016-2017.

It is clear from the radar chart that Russell has much better performance in season 2016-2017 than season 2014-2015. But surprisingly, PER of Russell in season 2016-2017 is 30.6, 29.1 in season 2014-2015. The difference in Russell’s PERs is exactly 1.5, the same as that of Ayo and Bogdan.

It seems that the progress made by Russell in PER does not match the progress in his stats. What’s the relative disadvantage of Russell? We spot his relative higher turnover rate and lower shot percentage than Ayo and Bogdan. However, that’s mainly because Russell shoots a lot more than the former. Russell made 842 baskets in season 2016-2017, and 647 in season 2014-2015. By contrast, Ayo made 339 baskets and Bogdan made 428 baskets in season 2023-2024.In the basketball world, no player can make a higher shot percentage with more shots.

In conclusion, players who make less mistakes are unreasonably favored by PER. They have higher PERs than players who have more versatile data but make more mistakes.

In addition, in a same season, players in a slow-paced team tend to have higher PERs:

We conclude from the formula that when LgPace is constant, the lower the LgPace, the higher the aPER(and thus higher the PER).

The shortcomings of PER and other metrics inevitably mislead people’s evaluation of players, leading to a distorted assessment of the entire team based on individual performances. This raises the question: What are the issues with current methods of predicting seasons wins? Is it possible to predict season wins more accurately through a different set of criteria? By exploring various team statistics, this study aims to develop a precise prediction of NBA regular season wins.

Methodology

Data

Data Collection

All data comes from the NBA. The data includes Team_Toals, Opponent_Totals, Team_Summaries, and Per36Mins.

Team_Totals includes 1845 entries and 28 columns. The columns are: season, league, team, abbreviation, playoffs, g, mp, fg, fga, fg%, x3p, x3pa, x3p%, x2p, x2pa, x2p%, ft, fta, ft%, orb, drb, trb, ast, stl, blk, tov, pf, pts.

Opponent_Totals includes 1845 entries and 28 columns. The columns are: season, league, team, abbreviation, playoffs, opp_g, opp_mp, opp_fg, opp_fga, opp_fg%, opp_x3p, opp_x3pa, opp_x3p%, opp_x2p, opp_x2pa, opp_x2p%, opp_ft, opp_fta, opp_ft%, opp_orb, opp_drb, opp_trb, opp_ast, opp_stl, opp_blk,opp_tov, opp_pf, opp_pts.

Team_Summaries includes 1845 entries and 31 total columns. The columns are: season, league, team, abbreviation, playoffs, age(mean age), wins, losses, pw, pl, mov, sos, srs, o_rtg, d_rtg, n_rtg, pace, f_tr, x3p_ar, ts%, e_fg%, tov%, orb%, ft_fga, opp_e_fg%, opp_tov%, opp_drb%, opp_ft_fga, arena, attend, attend_g.

Per36Mins includes 31853 entries and 34 columns. The columns are: season id, season, player id, player, birth year, position, age, experience, league, team, g, gs, mp, fg, fga, fg%, x3p, x3pa, x3p%, x2p, x2pa, x2p%, ft, fta, ft%, orb, drb, trb, ast, stl, blk, tov, pf, pts.

Data Cleaning

First, this study only includes the data from season 1981-1982 to season 2023-2024.The three-point line was introduced from the ABA in season 1980-1981. At that season, teams considered the three-point line as a temporary experiment, so players didn’t attempt much three-pointers. But since season 1981-1982, the three point line is set permanently and widely-accepted. Season 2023-2024 only completed about 70 games at the time the report is written, which is harnessed in the stability test.

Second, I remove some columns in the datasets. For the Team_Totals dataset, this study only keeps these columns: fg%, x3p%, x2p%, ft%, orb, drb, ast, stl, blk, tov, pf. For the Opponent_Totals, this study only keeps opp_fg%, opp_x3p%, opp_x2p%, opp_ft%, opp_ orb, opp_drb, opp_ast, opp_stl, opp_blk, opp_tov, opp_pf. For the Team_Summaries dataset, this study only keeps these columns: w, orb%.

Third, since some NBA teams changed their names through history, I change the names in my datasets into the team names now. That is: SEA-OKC, KCK-SAC, CHA-CHO, SDC-LAC, WSB-WAS, NJN-BRK, CHH-CHO.

Training and Testing Data

In order to apply our machine learning model, the data is split into training and testing data. The training set and test set are split in chronological order; the newest 25% in terms of time is the test data, while the oldest 75% is the training data.

New Metrics

The current predictive metric of regular season wins is Pythagorean Wins(PW). The metric estimates team’s expected wins based on its points scored and allowed over a given period. .

The fundamental premise underlying PW asserts that a team’s winning percentage can be approximated using a formula derived from the Pythagorean theorem. Formally expressed as(Here, k represents an exponent typically around 13.91 for basketball): \[ PW = \frac{\text{Games Played} \times \text{Tm Pts}^{13.91}}{\text{Tm Pts}^{13.91} + \text{Opp Pts}^{13.91}} \]
The accuracy of PW is extremely high. We can tell it from its MAE(Mean Absolute Error):

## [1] "MAE of PW 2.37404580152672"

The result indicates that the average prediction error of PW is around 3 games. Since PW is already so accurate, why attempt to predict the number of wins? Let me explain.

The principle of choosing predictors is the nonexistence of data leakage. In machine learning models, data leakage refers to the situation where information from outside the training dataset is used to create the model. This can lead to overly optimistic performance estimates during model training and evaluation. To prevent data leakage, it’s essential to ensure that the training data strictly represents the information that would be available at the time of prediction, maintaining the integrity and reliability of the machine learning model. For example, it’s risky to provide models points data, because the team who wins the most probably scores the most points. The data should be defined into two categories: one indicating production and the other reflecting efficiency. We should not use production data, especially scoring-related data such as three-pointers made (3PM), which directly influences team scoring. For instance, teams with higher 3PM scores more three-pointers, increasing their total score and likelihood of winning games. By contrast, only efficiency data, such as three-point percentage and offensive rebounding rate, should be used as predictors. This approach helps mitigate the risk of data leakage. So, through the PW formula, it can be seen that PW calculations are directly based on total points scored by the team and total points allowed, which fall under production data. This poses significant risk of data leakage.

Using the same logic, we must also discard TS%, eFG%, MOV, SOS, SRS, O_Rtg, D_Rtg, and N_Rtg. These metrics directly utilize scoring production data such as Tm PTS, and some even directly use win-loss records, which we can tell from their formulas:

MOV: Margin of Victory
\[ MOV = \text{Tm Pts} - \text{Opp Pts} \]

SOS: Strength of Schedule
\[ SOS = \frac{\text{Opp W} - \text{Opp L}}{\text{Games}} \]

SRS: Simple Rating System
\[ SRS = MOV + SOS \]

O_Rtg: Offensive Rating
\[ O\_Rtg = \frac{\text{Points}}{\text{Possessions}} \times 100 \]

D_Rtg: Defensive Rating
\[ D\_Rtg = \frac{\text{Opp Points}}{\text{Opp Possessions}} \times 100 \]

N_Rtg: Net Rating
\[ N\_Rtg = O\_Rtg - D\_Rtg \]

This study aims to invent new metrics to get the essence of the game. We’ll compare the accuracy of machine learning models trained by new metrics and basic data to tell whether there is an improvement. The fundamental idea is, in basketball (and any other sports), the higher a team’s production, the harder it is to maintain efficiency. Pace serves as an efficiency metric which reflects a team’s offensive rhythm. Therefore, we use 0.01 times pace as an adjuster to adjust team data. The adjusted metrics are as following:

adj \[ \text{adjuster} = 0.01 \times \text{Pace} \]

opp_adj \[ \text{opp_adjuster} = 0.01 \times \text{opp_Pace} \]

aORB% It’s data on offensive performance so it’s multiplied by adj. \[ \text{aORB%} = \text{ORB%} \times \text{adj} \]

aDRB% The more offensive possessions the opponent has, the harder it is to maintain a high defensive rebound percent, so it’s multiplied by opp_adj. \[ \text{aDRB%} = \text{DRB%}\times \text{opp_adj} \]

aTOV% The more offensive possessions the team has, the harder it is to maintain low turnovers, so it’s divided by adj. \[ \text{aTOV%} = \frac{\text{TOV%}}{\text{adj}} \] aSTL% The more offensive possessions the opponent team has, the harder it is to maintain high steal rate, so it’s multiplied by opp_adj. \[ \text{aSTL%} = \text{STL%}\times \text{opp_adj} \]

aAST% It’s data on offensive performance so it’s multiplied by adj. \[ \text{aAST%} = \text{AST%}\times \text{adj} \]

aPercent Adjusted Field Goal Percent(aPercent) takes all ft%, x2p%, and x3p% into consideration. The idea is to weight ft%, x2p%, and x3p% according to their point values; According to John Hollinger, each free throw attempt is counted as 0.44 two-point attempt; Each three-point attempt is counted as one two-point attempt. In this way, we can compute adjusted statistics aft%, ax2p%, and ax3p%. We calculate the harmonic mean of these data and multiply it with a adjuster. \[ aPercent = \frac{3 \times adj}{aFT\% + aX3P\% + aX2P\%} \] We also took the natural logarithm of the ratios of aPercent to opp_aPercent, Pace to opp_Pace, aTOV% to opp_aTOV%, and aAST% to opp_AST%. We put these variables into the train datasets to find out how the relative differences in these variables contributed to the number of wins.

Modeling

In this study, we will employ K-nearest neighbors regression, random forest, gradient boosting regression, and support vector regression for predicting the number of wins. Subsequently, we will evaluate the prediction accuracy and model stability to select the final model for win prediction.

Results

We first train the model using a training set constructed with new metrics and obtain its MAE(We are using MAE here because the highest regular season win in NBA history is 73, and it’s not an outlier). Then, we train the model using a training set constructed with traditional data and obtain the fitting accuracy. Finally, we take the natural logarithm of the ratio of the accuracy from the two training sessions to evaluate the model’s improvement.

We can plot a grouped bar chart to visualize the difference. Remember, the lower MSE and MAE, the more accurate the model is.

From the plot, we conclude that based on new metrics, random forest and gradient boosting regression significantly reduced the error; KNN clustering remained the same; surprisingly, svr increased the error.

Stability test

In order to give a comprehensive evaluation of the model, we’ll conduct a stability test. The stability test involves determining whether the model has potential overfitting risks by reducing the sample size. We will retrain and test the models using half of the previously used test and training data (which still adhere to the chronological order). We continue to represent the relative change in model accuracy using the natural logarithm of the MAE ratio.

Model Evaluation

Random forest achieved the highest prediction accuracy. Gradient boosting regression and support vector regression followed closely. After conducting the stability test, gradient boosting regression proved to be the most stable, with a negligible difference from random forest; these two models exhibited nearly identical prediction accuracy with 0.5 times the sample size. Although support vector regression displayed good accuracy, its stability was significantly lower than that of random forest and gradient boosting regression. K-nearest neighbors regression showed the poorest prediction accuracy and stability, suggesting it may not be suitable for our modeling. In summary, we select the random forest model as the final model for predicting NBA regular season wins.

Interpreting

##                   IncNodePurity
## orb_percent            6868.225
## drb_percent            6709.932
## tov_percent            7237.946
## tov_percent_ratio      7191.032
## pace_ratio            14778.341
## pace                   5238.042
## stl_rate               4583.314
## stl_rate_ratio        12119.507
## ast_percent            5174.947
## ast_percent_ratio     14123.544
## apercent               8303.162
## apercent_ratio        46339.843

The inc node purity plot demonstrates the contribution each feature makes to the random forest model’s predictions(The higher the inc node purity, the greater the feature’s contribution).

Firstly, we observe that the most notable feature in the chart is that the relative differences in the same metrics between teams and their opponents contribute more to the model than the metrics themselves (except for aTOV%, which is almost equal to its ratio). This is reasonable because victory requires outperforming the opponent. Specifically, the most significant contribution is from aPercent_ratio, indicating that the key to winning lies in the difference in overall shooting efficiency between the two teams (here, “overall” also considers the team’s pace and the proportion of possessions taken by free throws). Next is Pace_ratio, showing that the number of possessions per unit time for both teams affects win prediction, possibly because differences in pace greatly impact the team’s regular tactics and stamina distribution. The third most significant contributor is aAST%, highlighting that smoother team cooperation and offense compared to the opponent significantly contribute to winning in modern basketball. The fourth is aSTL%_ratio, reflecting a team’s strong defensive style. Compared to blocks, steals can directly lead to a transition from defense to offense, clearly disrupting the offensive rhythm and flow of the opponent.

Given the significant drop in inc node purity between the fifth and fourth values, the contribution beyond the fourth-ranked value to the model is not high. Therefore, we provide partial explanations for only a few values. Without considering the relative differences between the team and the opponent, aPercent is just a numerical value, but maintaining a reasonably high shooting percentage is more important than controlling turnovers and rebounds for winning a game. ORB% and DRB% have low contribution values, possibly because they are not necessarily related to shooting efficiency and team cooperation or have minimal impact on the opponent’s pace. Given the high contribution value of aSTL%_ratio, a potential explanation for the lower ranks of aTOV% and aTOV_ratio is that the proportion of turnovers not caused by the opponent’s steals is relatively high, leading to a lack of proportionality between steal-related data and turnover-related data. It is also possible that aSTL% reflects strong team defense, while TOV% is neither a defensive efficiency indicator nor necessarily related to low overall shooting efficiency.

Conclusion

This research introduces a novel approach to NBA win prediction by developing new efficiency metrics that mitigate data leakage issues inherent in traditional metrics like PER and PW. By incorporating adjustments for team pace and opponent comparisons, our proposed metrics offer a more nuanced evaluation of team performance. The application of these metrics in machine learning models, particularly random forest, has demonstrated significant improvements in predictive accuracy.

The findings highlight the critical role of efficiency-based metrics in enhancing the reliability of NBA win predictions. These metrics provide a comprehensive assessment of team performance, offering valuable insights for coaches, analysts, and management in their strategic decision-making processes. The enhanced predictive accuracy achieved through these metrics underscores their potential to revolutionize performance evaluation in professional basketball.

Future research should explore further refinements of these efficiency metrics and their application across different contexts within basketball analytics. Additionally, investigating the integration of these metrics with other advanced analytical techniques could yield even more robust predictive models, paving the way for more sophisticated approaches to understanding and managing team performance in the NBA.

Appendix

NBA Terms

Tm (prefix): Statistics of the Team
Lg (prefix): Statistics of the League
Opp (prefix): Statistics of the Opponent Team
G: Games Played
MP: Minutes Played
Pos: Position
3PM/x3p: 3-Point Field Goals
2PM/x2p: 2-Point Field Goals
AST: Assists
FGM: Field Goal Made
FGA: Field Goal Attempts
FTM: Free Throw Made
FTA: Free Throw Attempts
TOV: Turnovers
DRB: Defensive Rebounds
ORB: Offensive Rebounds
TRB: Total Rebounds
BLK: Blocks
STL: Steals
PF: Personal Fouls
W： Wins
l: Losses
AST%
\[ AST\%\frac{\text{AST}}{\text{Tm FGM}} \]

TOV \[ TOV\%=\frac{\text{Tov} \times 100}{\text{Tm Possessions}} \]

VOP: \[ VOP = \frac{\text{Lg Total Points}}{\text{Lg Total Possessions}} \]

Possessions \[ Possessions=0.5 \times (fga + 0.4 \times fta - 1.07 \times \left( \frac{orb}{orb + opp\_drb} \right) \times (fga - fg) + tov) \]

Pace: 48×(Tm possessions)/(Tm MP)
\[ Pace = 48 \times \frac{\text{Tm possessions}}{\text{Tm MP}} \]

F_Tr: Free Throw Rate
\[ F\_Tr = \frac{\text{FTA}}{\text{FGA}} \]

x3p_Ar: Three-Point Attempt Rate
\[ x3p\_Ar = \frac{\text{3PA}}{\text{FGA}} \]

TS%: True Shooting Percentage
\[ TS\% = \frac{\text{Points}}{2 \times (\text{FGA} + 0.44 \times \text{FTA})} \]

e_FG%: Effective Field Goal Percentage
\[ eFG\% = \frac{\text{FGM} + 0.5 \times \text{3PM}}{\text{FGA}} \]

TOV%: Turnover Percentage
\[ TOV\% = \frac{\text{TOV}}{\text{FGA} + 0.44 \times \text{FTA} + \text{TOV}} \]

ORB%: Offensive Rebound Percentage
\[ ORB\% = \frac{\text{ORB}}{\text{ORB} + \text{Opp DRB}} \]

ft_Fta: Free Throws Per Field Goal Attempt
\[ ft\_Fta = \frac{\text{FT}}{\text{FGA}} \]

MOV: Margin of Victory
\[ MOV = \text{Tm Pts} - \text{Opp Pts} \]

SOS: Strength of Schedule
\[ SOS = \frac{\text{Opp W} - \text{Opp L}}{\text{Games}} \]

SRS: Simple Rating System
\[ SRS = MOV + SOS \]

O_Rtg: Offensive Rating
\[ O\_Rtg = \frac{\text{Points}}{\text{Possessions}} \times 100 \]

D_Rtg: Defensive Rating
\[ D\_Rtg = \frac{\text{Opp Points}}{\text{Opp Possessions}} \times 100 \]

N_Rtg: Net Rating
\[ N\_Rtg = O\_Rtg - D\_Rtg \]

PW: Pythagorean Wins
\[ PW = \frac{\text{Games Played} \times \text{Tm Pts}^{13.91}}{\text{Tm Pts}^{13.91} + \text{Opp Pts}^{13.91}} \]

PL: Pythagorean Losses
\[ PL = \frac{\text{Games Played} \times \text{Opp Pts}^{13.91}}{\text{Tm Pts}^{13.91} + \text{Opp Pts}^{13.91}} \]

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