Introduction to Bayesian Performance Rating

The main objective of our work to assess college basketball team and player strength. We have created an advanced statistical metric, Bayesian Performance Rating (BPR), to quantify how successful a team or player is, using play-by-play data and advanced box-score metrics. This metric is predictive in nature, which means that each rating is fine-tuned to predict performance in future games. Each team and player has an offensive rating (OBPR) and a defensive rating (DBPR) which sum together to form the overall rating (BPR). You can find the more mathematical details of this metric at our main site in the How It Works tab, but we will provide a brief overview here.

Key Components

There are several key components that make Bayesian Performance Rating unique:

  • Offensive and defensive ratings are based on tempo-free efficiency statistics
  • Possessions are discarded when a particular game is out of hand
  • In-season ratings are influenced by prior predictive ratings based on historical data

There are two more distinguishing factors in the player BPR calculations:

  • Player ratings are adjusted based on the strength of all other players on the court
  • Player value is quantified both through impact on team performance and by individual efficiency statistics

Let’s look at each of these components individually.

Tempo-free efficiency statistics

Using tempo-free efficiency stats is a common approach in basketball analytics today, as it allows us to see how effective a team is, without being influenced by pace of play. A team like Duke, who generally has a lot of possessions each game and prefers to speed up the tempo, and a team like Villanova, who often slows the game down, can be fairly compared, since each team’s offensive and defensive ratings are in the form of points per 100 possessions.

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 is 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.

Prior predictive ratings based on historical data

Using historical data to form preseason predictions for each team and player gives BPR a lot of predictive power. Before a season starts, we use as much information available as we have to generate our best estimates of what each team and player’s Offensive BPR and Defensive BPR will be at the end of the season. There is a fair degree of uncertainty in these predictions, which means that the influence of these preseason estimates on the in-season ratings will diminish as more of the season is played. By the end of the season, the preseason predictions will carry almost no weight at all.

Adjusting for the strength of all players on the court

The player BPR attempts to quantify a player’s value to his team by looking at how efficiently his team performed on offense and defense on every possession he played. In order to get an accurate assessment of each player’s effectiveness, we want to 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. If we were to look at a more crude measure of player impact, like plus-minus or basic team efficiency when he is on the floor, it can be helpful, but doesn’t answer questions such as “did he play with good teammates or bad teammates?” and “Did he play so well because he only played in garbage time against inferior opponents?”. By using a model that adjusts for the strength of all players on the court, we can more accurately assess the value that a player brings to his team.

Combining team efficiency and individual efficiency statistics

Our model is centered around using play-by-play data to inform us about a player’s impact, based on his team’s efficiency when he was on the floor. However, we also want to use individual box score statistics, in the form of player efficiency metrics, to inform our model and come up with the best predictive ratings possible. A widely acknowledged advanced efficiency metric used in basketball is Player Efficiency Rating (PER), created by John Hollinger. PER uses all of a player’s individual statistics in a season in order to come up with a single number that best represents his contribution. Though PER isn’t perfect, it is easy to calculate and can give us a good starting point for evaluating a player’s statistical worth. Though we don’t want to use PER as the final representation of a player’s performance, we can still use the metric to help guide our final Bayesian Performance Ratings by creating an informative prior distribution on a player’s rating based on his PER. Essentially, when the model has a difficult time distinguishing the impact of several teammates, each player’s PER helps guide the ratings in the right direction. This technique has turned out to be incredibly beneficial at generating player ratings that more accurately represent both the value and skill of each player at the offensive and defensive end.

Here are the end-of-season Bayesian Performance Ratings from 2019-2020:

Top 20 players in BPR in 2019-2020
Top 20 Teams in BPR in 2019-2020

You can find the full Bayesian Performance Ratings for the current year and several years prior, as well as a more detailed breakdown of BPR, at

Published by Evan Miyakawa

College basketball analytics at

One thought on “Introduction to Bayesian Performance Rating

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

Create your website with
Get started
%d bloggers like this: