Prediction of the “All Nba Team” Players in a National Basketball Association Season Using Probabilistic Models

Ângelo Ghigiarelli Majeau; Ítalo João Bolqui Dutra

DOI: 10.22167/2675-6528-202602672

Article derived from a Final Course Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

The selection for the National Basketball Association (NBA) All-NBA Team is a prestigious, traditionally subjective individual recognition. This work aimed to develop a predictive model to identify players selected for the All-NBA Team, using statistical data and probabilistic methods. To this end, real player data from the 2014/15 to 2022/23 seasons were analyzed, excluding periods impacted by the pandemic. The main model was built with the XGBoost algorithm, with hyperparameters tuned via K-Fold cross-validation (k=5) and Randomized Search, using RMSE as the optimization metric. The developed model showed performance similar to the best benchmark model in identifying the elected players, correctly identifying 13 out of 15 players in 2022 and 2023. However, it demonstrated superiority in the correct allocation of players among the teams (9 correct selections in both seasons) and in the quality of errors, without registering predictions of players who did not receive official votes. It was concluded that probabilistic models are capable of capturing relevant patterns in the selection process, offering important insights for understanding the factors that influence sports voting, even without fully replicating human subjectivity.

Keywords: ALL-NBA Team; Basketball; Predictive modeling; XGBoost.

1. Introduction

The National Basketball Association (NBA) is globally recognized as the premier North American professional basketball league. Founded in 1946, the league consists of 30 teams and brings together approximately 450 players who compete in an 82-game regular season, followed by playoffs that culminate in the crowning of the champion.

Among the various honors awarded to athletes, inclusion in the “All-NBA Team” represents one of the most prestigious individual recognitions, reflecting each player’s technical performance and impact on their team (Kubatko et al., 2007; Oliver, 2012). This award is divided into three teams – First Team, Second Team, and Third Team – each composed of five players, totaling 15 athletes selected at the end of each season. The choice is made by a panel of journalists and sports experts after the end of the regular season, before the conclusion of the playoffs.

The distinction of being named to an All-NBA Team transcends individual recognition, possessing significant contractual relevance. It serves as an eligibility criterion for the awarding of financial bonuses and for the celebration of contracts with higher value and duration, such as supermax contracts. Consequently, this is a highly coveted distinction by athletes, being even one of the factors that define a player as a “star” by the league itself (NBA Board of Governors, 2023).

Traditionally, the selection of players for the All-NBA Team is based on expert voting, incorporating subjective elements. However, with the increasing availability of sports data and the advancement of analytical and statistical methods, it has become feasible to apply probabilistic models to predict this selection. Such models can consider a variety of variables, including players’ individual statistics (such as points, rebounds, assists, and efficiency) and contextual factors, like the team’s collective performance and its standing in the league table (Cervone et al., 2016; Sampaio & Janeira, 2003).

The relevance of this research lies in the possibility of anticipating results that are, by nature, traditionally subjective. By identifying which performance metrics influence athletes’ choices and evaluating the predictive capacity of probabilistic models, the study seeks to contribute to strategic analyses of sports performance and to the growing use of Data Science in team sports.

Thus, this work investigates the prediction of players who integrate the “All-NBA Team” in an NBA season, using probabilistic models based on historical data and specialized literature in sports statistics and predictive analysis.

2. Material and Methods

This study, of a quantitative nature and predictive modeling approach, aimed to identify the players selected for the “All-NBA Team”. 4,694 player participations in National Basketball Association (NBA) seasons, from 2014/15 to 2022/23, were analyzed. The 2019/20 and 2020/21 seasons were excluded due to the impacts of the COVID-19 pandemic, and periods prior to 2014/15, due to structural transformations observed in league basketball.

The data were collected from the Basketball Reference portal (BASKETBALL REFERENCE, 2026). The initial database, with 84 variables and 4,694 observations, was structured into four sets: basic statistics, advanced statistics, final team standings, and results of the All-NBA Team voting. Data treatment and analysis were performed in the Jupyter Notebook environment, using the Python language and the pandas, numpy, and scikit-learn libraries.

The preprocessing excluded players who played for more than one team in the same season, to avoid inconsistencies in collective performance variables (GLOBO ESPORTE, 2025). Normalized metrics, such as averages per game and per minute, were created from basic statistics, complementing the explanatory variables. The response variable adopted was “Share”, a continuous indicator between 0 and 1, representing the proportion of votes received by a player in relation to the maximum possible total.

To define eligibility and restrict the sample to athletes with a plausible voting profile, additional filtering was applied. The criteria were: i) participation in more than 45 games in the season; ii) an average of more than 25 minutes per game; and iii) starting in more than 95% of the games played. The final dataset, after filtering, consisted of 624 observations, of which 225 corresponded to players who received at least one vote in their respective seasons.

Prior to model construction, the data were segmented into two samples: “DES” (development) and “OOT” (out-of-time). The “OOT” sample, comprising the two most recent seasons, was reserved for evaluating the model’s performance in a future scenario (HASTIE; TIBSHIRANI; FRIEDMAN, 2009; KUHN; JOHNSON, 2013). The “DES” sample was used for fitting and calibration. The XGBoost (Extreme Gradient Boosting) algorithm was employed for the development of the predictive model, recognized for its efficiency in classification and regression problems (Chen & Guestrin, 2016).

To optimize the use of observations and obtain a robust estimate of the generalization error, K-Fold cross-validation was used, with K = 5 (Kohavi, 1995). Hyperparameter search was performed via Randomized Search, with RMSE (root mean squared error) as the optimization metric, aiming to mitigate overfitting. The calibrated hyperparameters included n_estimators (25 to 150), max_depth (3 to 5), and learning_rate (0.005 to 0.1). The final model was composed of 52 predictor variables, and their importance was evaluated by the information gain method (Friedman, 2001).

After development with the “DES” sample, the model was applied to the observations of the “OOT” sample, generating the predicted value of the “Share” variable for each player. For evaluation, the prediction of “Share” ranked the players in descending order. The 15 players with the highest predicted values were selected to compose the All-NBA Team: the first five for the First Team, those from sixth to tenth position for the Second Team, and those from eleventh to fifteenth for the Third Team.

The model’s performance evaluation also included the analysis of three types of prediction errors. Type 1 Error occurred in the allocation to an incorrect adjacent time slot, even with correct identification as All-NBA. Type 2 Error involved allocation with a two-level difference or prediction as All-NBA for a player with votes, but not selected. Type 3 Error was characterized by predicting a player as All-NBA who received no official votes. The model’s quality was compared to two benchmark models, referred to as “guess models” (Provost; Fawcett, 2013).

The “guess model 1” selected the 15 players with the highest total score in the season, requiring a minimum of 41 games, without the main model’s eligibility filters. The “guess model 2” ranked players by points per game, applying the same eligibility criteria as the developed model, and an additional filter to include only players selected for the All-Star Game in the respective season.

3. Results and Discussion

The research culminated in the development and application of a predictive model to identify players selected for the All-NBA Team. This work aimed to anticipate traditionally subjective decisions, employing a quantitative approach based on statistical data and probabilistic methods. The analysis covered a dataset of 4,694 player participations, collected between the 2014/15 and 2022/23 seasons, with the strategic exclusion of the 2019/20 and 2020/21 periods, which were significantly impacted by the COVID-19 pandemic. The results obtained demonstrate the model’s ability to capture relevant patterns in the selection process, offering valuable insights into the factors influencing sports voting and enhancing the understanding of elite performance in the NBA.

The exploratory analysis stage was fundamental to understanding the profile of the players that make up the final database and to identifying the distinctive characteristics of the athletes elected to the All-NBA Team. This analysis focused on widely recognized basketball statistics, such as points per game, Player Efficiency Rating (PER), and team winning percentage. A consistent pattern was observed: players selected for the All-NBA Team generally presented superior performance levels in all these metrics, indicating a positive correlation between high statistical performance and individual recognition. This behavior reinforced the premise that quantifiable performance is a preponderant factor in the voters’ decision, even in a process with subjective elements.

Specifically, players elected to the All-NBA Team exhibited a median of approximately 25 points per game, with a relatively consistent distribution across quartiles, suggesting notable stability in their offensive performance. The presence of lower outliers, with averages below 15 points per game, indicated that selection is not based solely on scoring volume, but also on other factors, such as defensive impact and efficiency. In contrast, players who only received votes or did not receive any showed lower medians and greater variability. Similarly, in Player Efficiency Rating (PER), elected athletes presented the highest values, with a median close to 25, reflecting a high and consistent level of individual efficiency. The groups of unelected players showed lower medians and greater dispersion, evidencing lower levels of overall efficiency.

The analysis of the team’s win rate revealed that players elected to the All-NBA Team were associated with the highest median, around 0.62, and a concentrated distribution between quartiles. This suggests a strong link between elite individual performance and the team’s collective success, indicating that the competitive context and team performance are important factors for eligibility and voting. Players who received votes but were not elected, and those without votes, showed progressively lower win rate medians and greater variability. This consistent pattern across all analyzed variables corroborates the idea that “star” players stand out not only individually but also contribute significantly to their teams’ success, which is an implicit criterion in the All-NBA Team voting.

The development of the predictive model began with the structuring of a comprehensive database, containing 84 variables and 4,694 observations of players across the analyzed seasons. Data collection was performed from the Basketball Reference portal, ensuring the use of detailed statistical information. A crucial preprocessing step involved excluding players who played for multiple teams in the same season, as such situations could introduce inconsistencies in the predictor variables related to team performance and are historically disregarded in voting. Additionally, normalized metrics, such as per-game and per-minute averages, were created to complement the total statistics, enriching the set of explanatory variables for the model.

The central response variable of the study was “Share”, a continuous indicator representing the proportion of votes received by a player relative to the maximum possible total votes in a season. This voting system assigns distinct weights to each selection (five points for the First Team, three for the Second, and one for the Third Team), justifying the continuous nature of “Share”. A strong imbalance was observed in the response variable, with only 6.65% of players receiving at least one vote in a season, which required an additional filtering step. To define a minimum eligibility criterion, the sample was restricted to athletes who participated in more than 45 games, had an average of over 25 minutes per game, and started as a starter in more than 95% of the games played, resulting in 624 eligible observations.

The main model was built with the XGBoost (Extreme Gradient Boosting) algorithm, an optimized implementation of Gradient Boosting that stands out for its ability to build robust predictive models by sequentially combining multiple decision trees (Chen & Guestrin, 2016). XGBoost incorporates L1 and L2 regularization techniques, tree complexity control, and training parallelization, mitigating the risk of overfitting and improving the model’s generalization ability. The hyperparameter search was conducted using the Randomized Search method and K-Fold cross-validation (k=5), utilizing RMSE as the optimization metric to identify the configuration that presented the best average performance. The final model hyperparameters included n_estimators = 100, max_depth = 4, learning_rate = 0.05, subsample = 0.7, colsample_bytree = 0.8, and random_state = 42.

The evaluation of the importance of the variables in the final model was performed using the information gain method, which quantifies the contribution of each variable to the improvement of predictive performance (J. H. Friedman, 2001). Among the ten most relevant variables, five belonged to the set of advanced statistics, accounting for 62.2% of the model’s total importance. Traditional NBA statistics, such as points, rebounds, and assists, represented 33.2% of the importance, while variables related to the team’s campaign contributed 4.6%. After the development and calibration of the model on the “DES” sample, it was applied to the “OOT” (out-of-time) sample, composed of the two most recent seasons, for a prospective and realistic evaluation of its performance on data not used in training.

Comparative Results

The comparative analysis of the results obtained by the developed model was performed based on specific metrics and in relation to two reference models, the “guess models”. The first, “guess model 1”, selected the 15 players with the highest total score, with a minimum of 41 games played, without applying the eligibility filters of the main model. The second, “guess model 2”, considered the players with the highest score per game, applying the same eligibility criteria as the main model and an additional filter for players selected for the All-Star Game. The evaluation focused on the correct identification of the 15 players elected to the All-NBA Team and the accuracy of the allocation of these players to specific teams (First, Second, and Third Team), in addition to a detailed analysis of the types of prediction error.

In the 2022 season, the developed model demonstrated remarkable performance in identifying the players selected for the All-NBA Team. It correctly identified 13 out of 15 players, corresponding to an 87% accuracy rate, matching the performance of the prediction model 2 and surpassing prediction model 1, which achieved 12 correct selections. However, the superiority of the developed model became more evident in the metric of exact player allocation to their respective teams. The developed model correctly allocated 9 players (60%), while prediction model 1 only got 3 players right (20%) and prediction model 2 achieved 5 correct selections (33%). This difference highlights the model’s capability not only to identify elite players but also to classify them with greater precision within the three All-NBA teams.

The analysis of error types for the 2022 season revealed a favorable pattern for the developed model. It registered 4 Type 1 errors, in which the player was correctly identified as All-NBA but allocated to an incorrect adjacent team, and 2 Type 2 errors, which involve a two-level difference in allocation or the prediction of a player who was not All-NBA but received votes. Crucially, the developed model presented no Type 3 errors, meaning it did not predict players who did not receive any official votes. In contrast, the guess model 1 presented 8 Type 1 errors and 2 Type 3 errors, while the guess model 2 had 6 Type 1 errors and 1 Type 3 error. The absence of Type 3 errors in the developed model indicates greater reliability in its predictions, avoiding the inclusion of players without any official recognition.

For the 2023 season, the developed model maintained its consistency, correctly identifying 13 out of the 15 players elected to the All-NBA Team, with an accuracy rate of 87%. This year, the developed model surpassed the guess model 2, which identified 12 players, and guess model 1, which achieved 10 correct identifications. In the metric of exact player allocation to teams, the developed model again demonstrated robust performance, with 9 correct identifications (60%), matching guess model 2, which also achieved 9 correct identifications. Guess model 1, in turn, identified 8 players (53%). The 2023 season showed a more direct association between total points and selection for the First Team, which slightly favored the allocation of the guess models, but the developed model maintained its superior performance in general identification.

The analysis of errors in the 2023 season reinforced the quality of the developed model. It registered 4 Type 1 errors and 2 Type 2 errors, and, as in 2022, presented no Type 3 errors. This means that all its All-NBA player predictions were of athletes who actually received official votes, even if they were not correctly selected or allocated. The guess models, on the other hand, concentrated their errors predominantly in Type 2, with guess model 1 registering 5 Type 2 errors and 2 Type 1 errors, and guess model 2 with 4 Type 2 errors and 2 Type 1 errors. The persistence of the absence of Type 3 errors in the developed model, in both seasons, is a crucial indicator of its robustness and the quality of its predictions compared to the benchmark approaches.

The summarization of the results from the 2022 and 2023 seasons offers a consolidated view of the models’ performance. The developed model correctly identified a total of 26 out of the 30 players elected to the All-NBA Team (87%), surpassing predictive model 1 (22 correct, 73%) and predictive model 2 (25 correct, 83%). This consistency across both seasons underscores the model’s effectiveness in identifying elite athletes. More significantly, in the exact allocation of players to teams, the developed model achieved 18 correct selections out of 30 (60%), demonstrating a clear advantage over predictive model 1 (11 correct, 37%) and predictive model 2 (14 correct, 47%). This accuracy in team classification is an important differentiator, as it reflects a more granular understanding of the selection criteria.

The analysis of the representativeness of the consolidated error types for the two seasons highlights the qualitative superiority of the developed model. It presented 8 Type 1 errors and 4 Type 2 errors, but, notably, zero Type 3 errors. This means that 66.67% of the model’s errors were Type 1, indicating that the incorrect classifications occurred in adjacent teams, with small magnitude, such as the 17th and 23rd positions in 2022, and 16th and 21st in 2023. In contrast, the guess model 1 registered 10 Type 1 errors, 7 Type 2 errors, and 2 Type 3 errors, while guess model 2 had 8 Type 1 errors, 7 Type 2 errors, and 1 Type 3 error. The absence of Type 3 errors in the developed model is a critical indicator of its reliability, as it ensures that all its All-NBA predictions correspond to players who, in fact, received some official recognition, even if they were not selected.

In summary, the results demonstrate that the predictive model based on XGBoost is effective in identifying the players of the All-NBA Team, presenting a performance comparable or superior to the reference models in terms of total accuracy. Its main contribution lies in the greater precision of player allocation to specific teams and, crucially, in the quality of errors, which were predominantly of lesser severity and never involved predicting players without official votes. This suggests that, although human subjectivity in voting is complex, probabilistic models can capture robust statistical patterns that influence selection decisions, offering a valuable tool for the analysis and understanding of elite sports performance in the NBA.

4. Conclusion

This work sought to develop a predictive model to identify players selected for the All-NBA Team, employing statistical data and probabilistic methods. It was found that the main model, built with the XGBoost algorithm and calibrated with data from the 2014/15 to 2022/23 seasons, demonstrated a high accuracy in identifying the elected athletes. In the 2022 and 2023 seasons, the model correctly identified 13 out of 15 players each year, surpassing or matching the benchmark models. Additionally, a superiority was observed in the exact allocation of players to their respective teams, with nine correct predictions in both seasons, and in the quality of errors, with no recorded predictions of players who did not receive official votes. The variable importance analysis revealed that advanced statistics were the most relevant for predictive performance. The main contribution of the study lies in offering insights into the patterns that influence sports voting and in providing a valuable tool for the analysis of elite performance in the NBA.

However, it is recognized that the prediction of sports votes, such as the All-NBA Team, involves a subjective component inherent in human judgment, which was not explicitly modeled in this work. Factors such as reputation, narrative, and voters’ personal bias can influence decisions, even in the presence of objective criteria. For future studies, the application of other statistical methodologies is suggested, such as approaches based on rankings and multicriteria ordering. Such methods could complement the results obtained, offering an alternative view on player evaluation and selection, by combining multiple performance indicators more directly among athletes.

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Article originating from the Final Course Work of the Specialization in Data Science and Analytics of the MBA USP/Esalq

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