Regime Based Analysis using Gated Bayesian Network

• An implementation of the gated Bayesian Network for Basketball Team written mainly in R with Rcpp extension

Abstract :

In the dynamic sport of professional basketball, a team may encounter several tangible and intangible alterations over a period of time. Regime detection, a widely used method in the domain of financial market decision-making and medical treatment planning, may assist a team management personnel to gain insight into how a team is changing with time based on historical data. The similar study has been conducted by (Bendtsen M., 2017) for the career trajectories of the baseball players . In this project, we have explored how multiple Bayesian networks could model the dynamics for a certain time frame. We have utilised basketball records starting from season 1983-84 to season 2020-21 for the NBA team Chicago Bulls. First, we identified the most important parameters to describe a team's performance using SHAP (SHapley Additive exPlanation) analysis. Next, we identify the regimes based on the Metropolis-Hastings MCMC sampling of the posterior distribution of the dataset. After identifying the regimes in the dataset, we hypothesise different regime transition structures and identify the most optimal regime transition structure. Lastly, the optimal regime transition structure is used to create a Gated Bayesian network (GBN) and parameterise the GBN using Gaussian processes distribution. We discuss the limitations of this approach and our work.Our finding has been visualised along with historical evidence, which helps to provide insight into which parameter may be important for a certain period of history and its possible application for the team officials.

Keywords: probabilistic modelling, SHAP analysis, Shapley Values, Bayesian network, directed acyclic graphs, basketball analytics, gated Bayesian network, regime-based analysis, gaussian processes optimisation, hill climbing, NBA, Chicago Bulls

Research Objectives :

The following three research objectives are thoroughly addressed in this degree project work. We list the research objectives as follows,

1. Explore the essential features from the historical basketball data that significantly impact the team’s performance.
2. Scruitinse the applicability of the Gated Bayesian Network framework to the basketball data to learn the performance dynamics of a team.
3. Validate whether the aforementioned framework enhanced the understanding of a team’s dynamics using statistical measures and historical evidence.

Scopes of this Project :

• The scope of this Master Project is bound to scrutinise the performance statistics of the NBA team Chicago Bulls between the seasons 1983-84 to 2020-21. Furthermore, in this analysis, each regular season, we consider that the individual team plays during 82 games, excluding the playoffs games. The reason for such a consideration is primarily because teams play quite differently in the playoffs than in the regular season, so the same model would not be an apt choice.
• Additionally, the non-commercial data is utilised in this project available on the basketball-reference website at gratis. Lastly, the model described in this discourse is insensitive to the alteration in the NBA regulations over the decades.

Data :

Data courtesy of Sports Reference LLC under creative commons licence, Basketball-Reference -Basketball Statistics and History. The dataset used in the experiment is composed of raw data and processed data as explained below:

Term	Description		Term	Description
Tm	Team Score		Opp	Opponent Score
FG	Field Goal		PF	Personal Fouls
FGA	Field Goal Attempts		ORtg	Offensive Ratings
FG%	Field Goal Percentage		DRtg	Defensive Ratings
3P	3 Point Goals		Pace	Pace Factor
3PA	3 Points Goal Attempted		FTr	Free Throw Attempt Rate
3P%	3 Points Goal Percentage		3PAr	3-Points Attempt Rate
FT	Free Throw		TS%	True Shooting Percentage
FTA	Free Throw Attempts		TRB%	Total Rebound Percentage
FT%	Free Throw Percentage		AST%	Assist Percentage
ORB	Offensive Rebound		STL%	Steal Percentage
DRB	Defensive Rebound		BLK%	Block Percentage
TRB	Total Rebound		eFG%	Effective Field Goal Percentage
AST	Assist		TOV%	Turnover Percentage
STL	Steal		ORB%	Offensive Rebound Percentage
BLK	Block		DRB%	Defensive Rebound Percentage
TOV	Turnover		FT/FGA	Free Throw per Free Goal Attempt

Raw Data

Regular Box Score	Advanced Box Score
Tm, Opp, FG, FGA	Tm, Opp, ORtg, DRtg, Pace, FTr
FG%, 3P, 3PA, 3P%	3PAr,TS%, TRB%, AST%, STL%, BLK%
FT, FTA, FT%, ORB, DRB, TRB	eFG%, TOV%, ORB%, FT/FGA (Offensive Four Factors)
AST, STL, BLK, TOV, PF	eFG%, TOV%, DRB%, FT/FGA (Defensive Four Factors)

Processed Data

External Influences	Player’s Contribution	Team’s Overall Performance
Home_Game	Continuing_Players_WS	Team_Prospect
Opponent_PlayOff	Incoming_Players_WS	WinsInLast15
Days_Between_Games	Leaving_Players_WS	WinsInLast10
		WinsInLast5

Team_Prospect

Team_Prospect is calculated using the running mean of score difference in a game as follows, $$\delta_{t}^{20}=\mu_{t}^{20}(Tm)-\mu_{t}^{20}(Opp) $$

• $\delta_{t}^{20}$ denotes the running mean of the opponent’s score considering twenty values up to time point t.

Key Findings :

Trends in 3 Points Attempt with Time

• The goal scored outside the 3-point line earns the team 3 points, which is denoted by 3P, and the number of 3-point attempts by the team is denoted by 3PA. Furthermore, the percentage of successful 3 points goals made out of all 3-point attempts is represented by 3P% or 3PPer.

• In the figure, we have visualised how the trends in 3 points attempts have changed with the season, as not all the seasons had the same number of matches, we have chosen to plot 3 point attempts per game for the each of the 38 seasons.

• We also include points per game in each season for comparison. It is evident that although the number of 3-point attempts increased each season, the points per game in the seasons have fluctuated but have not seen an increasing trend. These points to changes in playing style over the years, where players choose to shoot 3-point goals, possibly because it is more attractive to the spectators.

SHAP Analysis

• Here the feature that has the highest effect on Team_Prospect is WinsInLast15, i.e. the number of wins in the last fifteen games; this is unsurprising as the Team_Prospect takes into account the running mean of score difference for the last twenty games, so there is likely a higher correlation between these two events.

• We observed a similar result for another feature WinsInLast10, which accounts for several wins in the last ten games, albeit the feature importance is less than that of WinsInLast15.

• The next three most important features are related to the player’s individual contribution. As described previously, the first category of the players are those who are going to continue playing in the next season; these players have a higher impact on the Team_Prospect than the contribution from the players who either have newly joined the team in the current season or the players from the current season who are going to be leaving the team in the next season.

Roster Continuity

• Roster Continuity measures the percentage of the current season roster made up of players from the previous season. In this figure, the roster continuity is plotted on the y-axis ranging between 0 to 1 (or 0% to 100%) along with the corresponding season on the x-axis.
• The season where a team only played in the regular season is marked with grey coloured bars, and when the team is advancing to other levels, such as playing in Conference 1st Round, Conference Semi-Final, Conference Final or Championship Final represented by green, blue, turquoise and red colours accordingly. We can visually observe that seasons, where Chicago Bulls had advanced to the Conference Semi-Final or above are described by blue, turquoise and red bars, which correspond to more than 50% roster continuity value (except for season 2010-11 for which roster continuity is 49%), which means that there is a significant correlation between roster stability of a team and team’s performance.
• Now, if we consider the stability of the roster in terms of players who continue to play in the next season, this would translate into the player’s contribution towards win share.

Gated Bayesian Network for Chicago Bulls

• Chicago Bulls was a rather mediocre team in the early 1980s; from the season 1980-81 to the season 1983-84, they did not even qualify for the playoffs and the team was ranked 19th out of 23.

• The first regime $R_1$ began in the season 1983-84, which brought several changes; the team had a new coach Kevin Loughery along with four rookies and only two players with experience of five years maximum. In the following season, the team had a new executive, Jerry Krause and a rookie Shooting Guard Michael Jordan; this made several long-lasting impacts on the franchise. Chicago Bulls started qualifying for the playoffs from 1984-85. The first regime started from the season 1983-84. We can observe that winning the previous games and the players’ win share have an impact over the Team_Prospect; this has been consistent through all the regimes.

• Chicago Bulls had hit their stride in the regime $R_2$, which started in season 1988-89 and lasted until season 1994-95. The distribution of Team_Prospect here has a left tail indicating their consistent domination on the court; the performance during this period was exemplary, which earned the Chicago Bulls their first threepeat (three consecutive wins)of NBA title. After the sudden departure of Michael Jordan from the team before season 1993-94, Scottie Pippen helmed the leadership, but the team had a performance dip in two consecutive seasons in the absence of Michael Jordan.

• The next regime $R_3$ Michael Jordan’s 2nd retirement coincided with this era, and multiple prominent players like Dennis Rodman and Scottie Pippen were traded-off to another team; this was a volatile time; the team hired several rookies from NCAA, Ed Curry and Tyson Chandler, and the team had one of the worst seasons in 2001 with 16 consecutive losses in the regular games, in the following years the franchise underwent several different coaches, it was only in the season 2004-05, the Chicago Bulls appeared in the play-off after six years.

• Regime $R_4$ started in the season 2004-05 and lasted until the season 2017-18; this was the era of resurgence; three coaches who coached the team over the years, Scott Skiles (for four years), Tom Thibodeau (for five years) and Fred Hoiberg (for four years). This regime covered 13 seasons; Chicago Bulls had advanced to Playoffs in 11 seasons.

• The last era is made of only three seasons;the home-game advantage is not evident in this regime. After the season 2016-17, Chicago Bulls did not appear in the playoffs in the following seasons.

Ethical Consideration

• The data set utilised here is hosted on the website basketball-reference.com which seems to operate on a combination of ad revenue based freemium model, we have only accessed the available data without any cost.
• We have adhered to the Terms of Use and Information Sharing guidelines laid out by the parent company of the data hosting website, Sports Reference LLC, to the best of our knowledge.
• Primarily, the data is utilised for academic research purposes. Furthermore, the research we conducted here is intended for constructive development in the sports analytics community (if any) without any commercial ambition.

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