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Glossary:

OBPR: Offensive Bayesian Performance Rating reflects the offensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the offensive strength of other teammates on the floor with him, along with the defensive strength of the opponent's players on the floor. OBPR is interpreted as the number of offensive points per 100 possessions above D1 average expected by the player's team if the player were on the court with 9 other average players. A higher rating is better.
DBPR: Defensive Bayesian Performance Rating reflects the defensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the defensive strength of other teammates on the floor with him, along with the offensive strength of the opponent's players on the floor. DBPR is interpreted as the number of defensive points per 100 possessions better than (below) D1 average expected to be allowed by the player's team if the player were on the court with 9 other average players. A higher rating is better.
BPR: Bayesian Performance Rating is the sum of a player's OBPR and DBPR. This rating is the ultimate measure of a player's overall value to his team when he is on the floor. BPR is interpreted as the number of points per 100 possessions better than the opponent the player's team is expected to be if the player were on the court with 9 other average players. A higher rating is better.
Change: Improvement in BPR over the last 30 days.
Off Poss: Number of meaningful offensive possessions played.
Def Poss: Number of meaningful defensive possessions played.
Box OBPR: Box Offensive Bayesian Performance Rating is an estimate of a player's offensive value, based only on his individual stats. This serves as a prior starting point when calculating OBPR.
Box DBPR: Box Defensive Bayesian Performance Rating is an estimate of a player's defensive value, based only on his individual stats. This serves as a prior starting point when calculating DBPR.
Box BPR: Box Bayesian Performance Rating is the sum of a player's Box OBPR and Box DBPR. This rating is an estimate of a player's overall value, based only on his individual stats.
Adj Team Off Eff: Team offensive efficiency (points scored per 100 possessions) with player on the court, adjusted for strength of opponent players faced. A higher value is better.
Adj Team Def Eff: Team defensive efficiency (points allowed by opponent per 100 possessions) with player on the court, adjusted for strength of opponent players faced. A lower value is better.
Adj Team Eff Margin: Difference between adjusted team offensive and adjusted defensive efficiency with player on the court. A higher value is better.
+/-: Number of points scored for the player's team with him on the court, minus the number of points scored by the opponent with him on the court.
Position: An estimate of a player's position based on his individual stats and team contributions. An estimated position of 1 corresponds to being a point guard, and a 5 corresponds to being a center. This estimate comes from Daniel Myers' Box Plus Minus 2.0.
Role: An estimate of a player's offensive role based on his individual stats and team contributions. An estimated role of 1 corresponds to being the “creator” in the offense, and a 5 corresponds to being the “receiver”. This estimate comes from Daniel Myers' Box Plus Minus 2.0.

BPR Interpretation Example: If Jimmer Fredette had an Offensive BPR of 4.5, a Defensive BPR of -0.5, and a BPR of 4.0, this would mean the following: If Fredette were on the court with 9 other D1 average players, his team's offense would be 4.5 points per 100 possessions better than average, or if he were not on the floor and were replaced by another D1 average player. Similarly, his team's defense would be expected to be 0.5 points per 100 possessions worse (conceding 0.5 PP100 more) while he's on the floor. Overall, his team would be expected to outscore the opponent by 4.0 points in a 100 possession game.

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Glossary:

OBPR: Team Offensive Bayesian Performance Rating reflects a team's expected offensive efficiency. This is interpreted as the points per 100 possessions better than average expected when playing against an average D1 team. A higher rating is better.
DBPR: Team Defensive Bayesian Performance Rating reflects a team's expected defensive efficiency. This is interpreted as the defensive points per 100 possessions better (lower) than average when playing against an average D1 team. A higher rating is better.
BPR: Bayesian Performance Rating is the sum of a team's OBPR and DBPR. This rating is the ultimate measure of a team's expected overall strength. This is interpreted as the number of points the team is expected to outscore an average D1 team by in an 100 possession game. A higher rating is better.
Change: Improvement in BPR over the last 30 days.
Kill Shots Per Game: The number of double digit scoring runs per game (10 points or more scored in a row without the opposing team scoring).
Kill Shots Allowed Per Game: The number of double digit scoring runs conceded per game (10 points or more scored in a row by the opponent without the team scoring).
Total Kill Shots: The total number of double digit scoring runs in the season.
Total Kill Shots Allowed: The total number of double digit scoring runs conceded in the season.
True Tempo: A measure of a team's true game pace. This number reflects the estimated number of possessions played in a game against an average paced D1 opponent.
Off Rank: A team's rank in OBPR.
Def Rank: A team's rank in DBPR.
Tempo Rank: A team's rank in True Tempo
Injury Rank: A team's overall ranking after accounting for the absence of all currently injured players.
Roster Rank: A crude ranking of each team's strength of roster. This is largely based on the individual BPR values of all players on the roster.
Resume Rank: A ranking of each team's in-season resume, treating all teams as equal at the start of the season. Think of it as a better version of the NET.
Home Rank: A team's rank in how much better they perform at home versus road games. A team ranked higher will play much better at home than on the road.

BPR Interpretation Example: If Kansas had an Offensive BPR of 18, a Defensive BPR of 12, and a BPR of 30, this would mean the following: If Kansas was facing an average D1 team, they would be expected score 18 more points per 100 possessions than an average team would (the average points per 100 in the past has been around 104), and they would be expected to allow 12 less points per 100 possessions than an average team would. Overall, they would be expected to outscore a D1 average team by 30 points in a 100 possession game (games are often roughly around 70 possessions).

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Glossary:

OBPR: Offensive Bayesian Performance Rating reflects the offensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the offensive strength of other teammates on the floor with him, along with the defensive strength of the opponent's players on the floor. OBPR is interpreted as the number of offensive points per 100 possessions above D1 average expected by the player's team if the player were on the court with 9 other average players. A higher rating is better.
DBPR: Defensive Bayesian Performance Rating reflects the defensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the defensive strength of other teammates on the floor with him, along with the offensive strength of the opponent's players on the floor. DBPR is interpreted as the number of defensive points per 100 possessions better than (below) D1 average expected to be allowed by the player's team if the player were on the court with 9 other average players. A higher rating is better.
BPR: Bayesian Performance Rating is the sum of a player's OBPR and DBPR. This rating is the ultimate measure of a player's overall value to his team when he is on the floor. BPR is interpreted as the number of points per 100 possessions better than the opponent the player's team is expected to be if the player were on the court with 9 other average players. A higher rating is better.
Change: Improvement in BPR over the last 30 days.
Off Poss: Number of meaningful offensive possessions played.
Def Poss: Number of meaningful defensive possessions played.
Box OBPR: Box Offensive Bayesian Performance Rating is an estimate of a player's offensive value, based only on his individual stats. This serves as a prior starting point when calculating OBPR.
Box DBPR: Box Defensive Bayesian Performance Rating is an estimate of a player's defensive value, based only on his individual stats. This serves as a prior starting point when calculating DBPR.
Box BPR: Box Bayesian Performance Rating is the sum of a player's Box OBPR and Box DBPR. This rating is an estimate of a player's overall value, based only on his individual stats.
Adj Team Off Eff: Team offensive efficiency (points scored per 100 possessions) with player on the court, adjusted for strength of opponent players faced. A higher value is better.
Team Def Eff: Team defensive efficiency (points allowed by opponent per 100 possessions) with player on the court, adjusted for strength of opponent players faced. A lower value is better.
Team Eff Margin: Difference between adjusted team offensive and adjusted defensive efficiency with player on the court. A higher value is better.
+/-: Number of points scored for the player's team with him on the court, minus the number of points scored by the opponent with him on the court.
Position: An estimate of a player's position based on his individual stats and team contributions. An estimated position of 1 corresponds to being a point guard, and a 5 corresponds to being a center. This estimate comes from Daniel Myers' Box Plus Minus 2.0.
Role: An estimate of a player's offensive role based on his individual stats and team contributions. An estimated role of 1 corresponds to being the “creator” in the offense, and a 5 corresponds to being the “receiver”. This estimate comes from Daniel Myers' Box Plus Minus 2.0.
Avg Opp BPR: The average BPR of the opponent's players on the floor at the same time as the player. A higher rating indicates that the player played against tougher opposition.
Position: An estimate of a player's position based on his individual stats and team contributions. An estimated position of 1 corresponds to being a point guard, and a 5 corresponds to being a center. This estimate comes from Daniel Myers' Box Plus Minus 2.0.
Role: An estimate of a player's offensive role based on his individual stats and team contributions. An estimated position of 1 corresponds to being the “creator” in the offense, and a 5 corresponds to being the “receiver”. This estimate comes from Daniel Myers' Box Plus Minus 2.0.
On-Off Offense Splits: How much better the team played offensively with that player on the floor, compared to without them, measured in points per 100 possessions. A positive number indicates that the team was better offensively with the player on the floor.
On-Off Defense Splits: How much better the team played defensively with that player on the floor, compared to without them, measured in points per 100 possessions. A positive number indicates that the team was better defensively with the player on the floor.
On-Off Margin Splits: How much better the team played overall with that player on the floor, compared to without them, measured in points per 100 possessions. A positive number indicates that the team was better overall with the player on the floor.

Glossary:

Team Off Eff: Team offensive efficiency (points per possession scored) with those two player on the court at the same. A higher value is better.
Team Def Eff: Team defensive efficiency (points per possessions by opponent) with those two players on the court at the same time. A lower value is better.
Team Eff Margin: Difference between team offensive and defensive efficiency with those two players on the court at the same time. A higher value is better.
Off Poss: Number of offensive possessions with those two players on the court at the same time.
Def Poss: Number of defensive possessions with those two players on the court at the same time.
Above / Below Average: A measure of how much better the teammate played when he was on the court with the player, compared to the teammate's average play. This calculates the team's efficiency when these two players were on the court, minus the team's efficiency for all possessions when the teammate was on the court, regardless of who he played with.

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Glossary:

Team Off Eff: Team offensive efficiency (points scored per 100 possession) with those two player on the court at the same. A higher value is better.
Team Def Eff: Team defensive efficiency (points allowed by opponent per possessions) with those two players on the court at the same time. A lower value is better.
Team Eff Margin: Difference between team offensive and defensive efficiency with those two players on the court. A higher value is better.
Adj Team Eff Margin: Team Efficiency Margin, adjusted for the quality of opponent players faced by the pair of players.
Off Poss: Number of offensive possessions with those two players on the court at the same time.
Def Poss: Number of defensive possessions with those two players on the court at the same time.
Chemistry: A score that reflects how much better than average the team performs when these two players on the court together, compared to team averages when they are on the court individually.
Weighted Chemistry: This is a more reliable metric for teammate chemistry. The Chemistry score is multiplied by the number of possessions shared by the two players, to give more weight to player pairs who were on the floor more.
Avg Opp BPR: The average BPR of the opponent's players on the floor at the same time as the pair of teammates. A higher rating indicates that the players played against tougher opposition.

Glossary:

Team Off Eff: Team offensive efficiency (points scored per 100 possession) with the lineup on the floor. A higher value is better.
Team Def Eff: Team defensive efficiency (points allowed by opponent per possessions) with the lineup on the floor. A lower value is better.
Team Eff Margin: Difference between team offensive and defensive efficiency with the lineup on the floor. A higher value is better.
Adj Team Eff Margin: Team Efficiency Margin, adjusted for the quality of opponent players faced by the lineup.
Off Poss: Number of offensive possessions with the lineup on the floor.
Def Poss: Number of defensive possessions with the lineup on the floor.
Avg Opp BPR: The average BPR of the opponent's players on the floor at the same time as the lineup. A higher rating indicates that the lineup played against tougher opposition.

Glossary:

Team Off Eff: Team offensive efficiency (points scored per 100 possession) with the lineup on the floor. A higher value is better.
Team Def Eff: Team defensive efficiency (points allowed by opponent per possessions) with the lineup on the floor. A lower value is better.
Team Eff Margin: Difference between team offensive and defensive efficiency with the lineup on the floor. A higher value is better.
Adj Team Eff Margin: Team Efficiency Margin, adjusted for the quality of opponent players faced by the lineup.
Off Poss: Number of offensive possessions with the lineup on the floor.
Def Poss: Number of defensive possessions with the lineup on the floor.
Avg Opp BPR: The average BPR of the opponent's players on the floor at the same time as the lineup. A higher rating indicates that the lineup played against tougher opposition.

Glossary:

Team Off Eff: Team offensive efficiency (points scored per 100 possession) with the lineup on the floor. A higher value is better.
Team Def Eff: Team defensive efficiency (points allowed by opponent per possessions) with the lineup on the floor. A lower value is better.
Team Eff Margin: Difference between team offensive and defensive efficiency with the lineup on the floor. A higher value is better.
Adj Team Eff Margin: Team Efficiency Margin, adjusted for the quality of opponent players faced by the lineup.
Off Poss: Number of offensive possessions with the lineup on the floor.
Def Poss: Number of defensive possessions with the lineup on the floor.
Avg Opp BPR: The average BPR of the opponent's players on the floor at the same time as the lineup. A higher rating indicates that the lineup played against tougher opposition.

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Glossary:

Non-Garbage Score: The team's score after filtering out possessions when the game was already decided. See “How It Works” for details
Non-Garbage Opp Score: The opponent's score after filtering out possessions when the game was already decided.
Off Eff: The team's offensive efficiency (points scored per 100 possessions), adjusted for home court advantage. A higher value is better.
Def Eff: The team's defensive efficiency (points allowed by opponent per 100 possessions), adjusted for home court advantage. A lower value is better.
Non-Garbage Off Eff: The team's offensive efficiency after filtering out possessions when the game was already decided. This is a more accurate assessment of how the team played on offense than Off Eff.
Non-Garbage Def Eff: The team's defensive efficiency after filtering out possessions when the game was already decided. This is a more accurate assessment of how the team played on defense than Def Eff.
Off Poss: Number of offensive possessions
Def Poss: Number of defensive possessions
Non-Garbage Off Poss: Number of offensive possessions after filtering out possessions when the game was already decided.
Non-Garbage Def Poss: Number of defensive possessions after filtering out possessions when the game was already decided.

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Year:

Glossary:

Adj Team Off Eff: Team offensive efficiency (points scored per 100 possession) with the lineup on the floor, adjusted for the strength of opposing players faced. A higher value is better.
Adj Team Def Eff: Team defensive efficiency (points allowed by opponent per possessions) with the lineup on the floor, adjusted for the strength of opposing players faced. A lower value is better.
Adj Team Eff Margin: Difference between adjusted team offensive and adjusted defensive efficiency with the lineup on the floor. A higher value is better.
Off Poss: Number of offensive possessions with the lineup on the floor.
Def Poss: Number of defensive possessions with the lineup on the floor.
Avg Opp BPR: The average BPR of the opponent's players on the floor at the same time as the lineup. A higher rating indicates that the lineup played against tougher opposition.
Team Off Eff: Team offensive efficiency (points scored per 100 possession) with the lineup on the floor, not adjusted for strength of opposition. A higher value is better.
Team Def Eff: Team defensive efficiency (points allowed by opponent per possessions) with the lineup on the floor, not adjusted for strength of opposition.. A lower value is better.
Team Eff Margin: Difference between team offensive and defensive efficiency with the lineup on the floor. A higher value is better.

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Glossary:

MVP Score: An overall score that rates players by how worthy they are to be called the “most valuable player”. This combines the Indispensability Score and some of the Bayesian Performance Rating and Box BPR metrics.
Indispensability Score: A value that quantifies how much worse off the player's team would be if he were not available. This is a good starting point for evaluating how valuable a player is to his team, without being biased towards players on better teams.
OBPR: Offensive Bayesian Performance Rating reflects the offensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the offensive strength of other teammates on the floor with him, along with the defensive strength of the opponent's players on the floor. OBPR is interpreted as the number of offensive points per 100 possessions above D1 average expected by the player's team if the player were on the court with 9 other average players. A higher rating is better.
DBPR: Defensive Bayesian Performance Rating reflects the defensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the defensive strength of other teammates on the floor with him, along with the offensive strength of the opponent's players on the floor. DBPR is interpreted as the number of defensive points per 100 possessions better than (below) D1 average expected to be allowed by the player's team if the player were on the court with 9 other average players. A higher rating is better.
BPR: Bayesian Performance Rating is the sum of a player's OBPR and DBPR. This rating is the ultimate measure of a player's overall value to his team when he is on the floor. BPR is interpreted as the number of points per 100 possessions better than the opponent the player's team is expected to be if the player were on the court with 9 other average players. A higher rating is better.
Box OBPR: Box Offensive Bayesian Performance Rating is an estimate of a player's offensive value, based only on his individual stats. This serves as a prior starting point when calculating OBPR.
Box DBPR: Box Defensive Bayesian Performance Rating is an estimate of a player's defensive value, based only on his individual stats. This serves as a prior starting point when calculating DBPR.
Box BPR: Box Bayesian Performance Rating is the sum of a player's Box OBPR and Box DBPR. This rating is an estimate of a player's overall value, based only on his individual stats.

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Glossary:

Transfer Ranking: The quality of the transfer based on a 5-star ranking system, using our projections for each player.
OBPR 2024*: A player's projected Offensive BPR for the upcoming season. Offensive Bayesian Performance Rating reflects the offensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the offensive strength of other teammates on the floor with him, along with the defensive strength of the opponent's players on the floor. OBPR is interpreted as the number of offensive points per 100 possessions above D1 average expected by the player's team if the player were on the court with 9 other average players. A higher rating is better.
DBPR 2024*: A player's projected Defensive BPR for the upcoming season. Defensive Bayesian Performance Rating reflects the defensive value a player brings to his team when he is on the court. This rating incorporates a player's individual efficiency stats and on-court play-by-play impact, and also accounts for the defensive strength of other teammates on the floor with him, along with the offensive strength of the opponent's players on the floor. DBPR is interpreted as the number of defensive points per 100 possessions better than (below) D1 average expected to be allowed by the player's team if the player were on the court with 9 other average players. A higher rating is better.
BPR 2024*: A player's projected BPR for the upcoming season. Bayesian Performance Rating is the sum of a player's OBPR and DBPR. This rating is the ultimate measure of a player's overall value to his team when he is on the floor. BPR is interpreted as the number of points per 100 possessions better than the opponent the player's team is expected to be if the player were on the court with 9 other average players. A higher rating is better.
HS Recruit Ranking: The quality of the player as a high school prospect based on high school composite recruiting rankings.
Poss: Number of non-garbage time possessions played in the most recent season.
OBPR: A player's Offensive BPR for the most recent season played. See OBPR 2023* for a full definition.
DBPR: A player's Defensive BPR for the most recent season played. See DBPR 2023* for a full definition.
BPR: A player's BPR for the most recent season played. See BPR 2023* for a full definition.
Box OBPR: A player's Box OBPR for the most recent season played. Box Offensive Bayesian Performance Rating is an estimate of a player's offensive value, based only on his individual stats. This serves as a prior starting point when calculating OBPR. It also usually aligns closely with the general public consensus on a player's offensive ability based on common stats.
Box DBPR: A player's Box DBPR for the most recent season played. Box Defensive Bayesian Performance Rating is an estimate of a player's defensive value, based only on his individual stats. This serves as a prior starting point when calculating DBPR. It also usually aligns closely with the general public consensus on a player's defensive ability based on common stats.
Box BPR: A player's Box BPR for the most recent season played. Box Bayesian Performance Rating is the sum of a player's Box OBPR and Box DBPR. This rating is an estimate of a player's overall value, based only on his individual stats.
+/-: A player's plus-minus for the most recent season played. It is the number of points scored for the player's team with him on the court, minus the number of points scored by the opponent with him on the court.
Adj Team Off Eff: A player's Adj Team Off Eff for the most recent season played. It is the team's offensive efficiency (points scored per 100 possessions) with player on the court, adjusted for strength of opponent players faced. A higher value is better.
Adj Team Def Eff: A player's Adj Team Def Eff for the most recent season played. It is the team defensive efficiency (points allowed by opponent per 100 possessions) with player on the court, adjusted for strength of opponent players faced. A lower value is better.
Adj Team Eff Margin: A player's Adj Team Eff Margin for the most recent season played. It is the difference between adjusted team offensive and adjusted defensive efficiency with player on the court. A higher value is better.
Role: An estimate of a player's offensive role based on his individual stats and team contributions. An estimated role of 1 corresponds to being the “creator” in the offense, and a 5 corresponds to being the “receiver”. This estimate comes from Daniel Myers' Box Plus Minus 2.0.

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Bracketology

Play-in teams are denoted in italics. Autobids are denoted in red. Bracketology projections are computed using a deep learning neural network machine learning algorithm.

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Bracket Simulation

Quick Overview

Welcome to EvanMiya College Basketball Analytics! The main objective of our work is to assess college basketball team and player strength. We have created an advanced statistical metric, Bayesian Performance Rating (BPR), which quantifies how effective a team or player is, using advanced box-score metrics, play-by-play data, and historical information. This metric is predictive in nature, which means that each rating is fine-tuned to predict performance in future games.

There are several pages of analysis (plus several more that appear when appropriate):

Team Ratings: We assess the strength of each team by calculating offensive and defensive ratings that reflect the team's offensive and defensive efficiency, while accounting for other factors, such as game pace and opponent strength.
Player Ratings: We quantify the value of each player to his team on both offense and defense. A player's ratings incorporate his individual efficiency statistics, along with his impact on the court for his team, which is assessed by looking at how successful his team was in every possession he played. These ratings account for the strength of all other players on the floor with that player in each of his possessions that he played.
Team Breakdown Tool: This tool provides a more detailed look into player and lineup metrics for each team.
Lineup Ratings: We rate all two, three, four, and five man lineups across all of Division 1 basketball, adjusted for the strength of opposing players faced by each lineup.

Now for some more detail into how we get these numbers:

Collecting Data

We have box score data available for every game played in the each college basketball season, along with play-by-play data, which includes substitutions. The possession by possession data is the main component used to drive our analysis.

Discarding unhelpful possessions

One key step that we take to gain the best predictions from our data is to only look at possessions in a game that “mattered”. Analyzing possessions when the game is already well out of hand isn't as valuable to us as possessions when the winner hasn't been decided yet. We use the in-game naive win probability (which assumes that teams are equally matched) in order to assess when a game was out of hand. Once a team has a win probability of at least 99%, we start down-weighting the possessions until the win probability is greater than 99.99%, at which point we discard all possessions entirely. In the rare situation where the losing team mounts a comeback and the win probability of the winning team sinks below 99%, we start giving each possession full weight again.

From a coach's perspective, every possession matters, even when your team has seemingly won or lost with minutes to spare. However, for predictive purposes, we can't properly assess the strength of a team when both teams aren't putting their normal lineups in or aren't playing as hard as they might if the outcome of the game were still in question.

Adjusting for the strength of opposition

At both a team and player level, our BPR metrics adjust for the strength of opposition for every possession played. For players, this includes an adjustment for the individual level of every single opposing player on the floor for a possession, along with the strength of teammates as well.

Tempo free statistics

All of our metrics adjust for the pace of play in a game by looking at efficiency on a per-possession basis.

Bayesian Performance Rating

We have created an advanced statistical metric, Bayesian Performance Rating (BPR), which quantifies how effective a player is, using advanced box-score metrics, play-by-play data, and historical information (for the basketball metric nerds, this is a highly technical version of an adjusted plus-minus). This metric is predictive in nature, which means that each rating is fine-tuned to predict performance in future games.

BPR quantifies the value of each player to his team on both offense and defense. A player's ratings incorporate his individual efficiency statistics, along with his impact on the court for his team, which is assessed by looking at how successful his team was in every possession he played. These ratings account for the strength of all other players on the floor with that player in each of his possessions that he played. Each player has an Offensive BPR and a Defensive BPR, which are added together to make the player's overall BPR. Very good players will have higher positive offensive and defensive ratings, with the average D1 player having an Offensive BPR and Defensive BPR of 0. Like other adjusted plus-minus metrics, BPR values are interpreted as the expected points per 100 possessions better than a D1 average player while on the floor.

The BPR statistical model is trained on data going back to 2011, making it the most fine-tuned player evaluation metric in college basketball.

First Stage: Historical Stats

The first stage in forming a player's rating is in the form of a projection for the season, based on that player's statistics and metrics in previous seasons, along with other predictive information, such as recruiting ratings. Though the historical information does not influence BPR much by the end of a season, it is incredibly useful as it allows for Bayesian Performance Rating to be effective in assessing a player's impact, even when he hasn't played much (or at all) in the current season.

Second Stage: Individual Stats

The second stage in forming a player's rating is his Box Bayesian Performance Rating (Box BPR), which is an estimate of a player's impact on both ends of the court, using only his individual box score statistics. Box BPR, which is essentially our own version of a Box-Plus-Minus, can give us a good initial estimate of a player's statistical worth. Though we don't want to use Box BPR as the final representation of a player's effectiveness, we can still use the metric to help guide our final ratings by using it as a starting point.

Third Stage: Play-by-Play Impact

The third stage looks at every possession a player played, attempting to quantify his value to his team by looking at how efficiently his team performed on offense and defense for those plays. In addition, we also adjust for the strength of his teammates on the court with him, along with the strength of opposing players for each possession he was on the court. Essentially, our model finds the offensive and defensive rating for each player that can best explain the results from every possession that occurred from the season, for all players. The Box BPR is the starting point for a given player, but the rating will move up if he had more of an impact than his individual stats suggested, or vice versa. In some cases, the final BPR will be very close to the Box BPR, and in other cases they will be very different. Players who look really good on the stat sheet often evaluate well, but equally so, guys who control the game beyond what their stats convey will also be credited accordingly.

Team Ratings

The purpose behind the Bayesian Performance Rating at a team level is to provide each team a true offensive and a true defensive rating that best explains all of the real game results that we observed from the season, while also incorporating other predictive statistics, such as four factors and team historical information. These can be used, along with the BPR ratings of the opposing team, to estimate each team's expected offensive and defensive efficiency (points scored per 100 possessions) in a game. These coefficients are designed to have 0 as the national average. Thus, very good teams will have higher positive offensive and defensive ratings. A team's overall BPR is just the sum of its OBPR and DBPR.

Our team ratings also incorporate team-specific home court advantages, and adjust for each team's pace of play, seen in the True Tempo metric, which is the adjusted pace of play for each team, based on if they were playing the D1 team with the average tempo.

How To Use BPR

The purpose of Bayesian Performance Rating is to identify the players who are having the biggest impact on the offensive and defensive side of the ball. BPR cannot provide everything that an eye-test can, but is a very helpful tool to either confirm what we thought was true of a player, or provide insight into trends we could have missed. By sorting a roster by BPR, the order will often be close to what you might have expected after watching the games. However, it is helpful to note which players evaluate much higher or lower than we might have expected, and to try to explain why. When I am trying to understand why a player has the rating that he does, I look at three stats, in order, which are all listed in the Team Breakdown Tool - Players page for each player.

Box Plus Minus
- Box Offensive BPR and Box Defensive BPR sum up a player's individual efficiency stats into one number that estimates effectiveness on that side of the court. Since this serves as the starting point for the final BPR calculation, it's the first place I look if I am trying to explain a particular player's evaluation. If a player's Box BPR is higher than expected, it might be because he was more efficient in some statistical category on a per possession basis than I realized.
Adjusted Team Efficiency
- The metrics in this category tell how many points per 100 possessions a team scored or conceded with that player on the floor. This does a calculation of efficiency on both sides of the court on a per possession basis, and adjusts for the strength of opposition players faced by that lineup. Often, a player who has a higher BPR on his team also has one of the higher Team Efficiency Margins, since this is a huge component to the calculation of the rating.
Average Opponent BPR
- This shows the average rating of the individual opponents faced by a player when he was on the floor. If a player has a higher Avg Opp BPR than other teammates, this indicates that he had to play against better players when he was on the floor, and his BPR will be adjusted higher accordingly.

Additionally, we have also included each player's estimated position and offensive role in the Team Table, which is based on individual stats and team contributions. An estimated position of 1 corresponds to being a point guard, and a 5 corresponds to being a center. An estimated offensive role of 1 corresponds to being the “creator” in the offense, and a 5 corresponds to being the “receiver”. These can be helpful see if a player's statistical contribution was similar to how they were envisioned to be helping the team. Bayesian Performance Rating is not biased based on position or offensive role.

About Me

My name is Evan Miyakawa, and I have my doctorate in statistics. I graduated with my Ph.D. from Baylor in 2022, and my Bachelor's Degree in 2017 from Taylor University. You can find out more on my LinkedIn page.

My college basketball research has been featured in articles by Sports Illustrated, CBS Sports, ESPN, the AP, and others.

Contact

Feel free to email me at evanmiyainfo@gmail.com with any questions or requests. I occasionally appear on radio shows and podcasts to talk about college basketball. I also work with college basketball coaches who want to utilize analytics for their teams.

You can also follow me on Twitter.

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Access the EvanMiya blog here.

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