Possession-based Sports and Numbers (PSAN) Ratings

Evaluating the performance of basketball players using only the information available in boxscores is a very daunting task.  The explanation behind every single calculation in the ratings presented here would take up way too much space.  But this page is an attempt to explain the concepts behind the ratings, enough to help you decipher what they are all about.

Visual Conceptual Overview of PSAN-Related Ratings

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Expected Points per Possession (EPP)

The basis for much of the PSAN system is comparing the contribution of a player's actions against what his team expected to do (or opponent was expected attain) on each possession.  The EPP is calculated as "points divided possessions."  If you're looking at a PSAN-related score for just a game, it would be the points and possessions from that game.  If you're looking at a season, it would be the entire season's points and possessions.

Possessions are calculated using a formula that is well-established in basketball statistical analysis: FGA - OREB + TO + 0.44*FTA

The bottom line here is that we can look at how a player's actions translate into points, and then compare each of his actions' point values to what was expected to happen on that possession.  That forms the basis for the value a player brings to his team.

Tangible Contributions (Unadjusted)

The boxscore provides the following statistics from which we can calculate tangible contributions of players:

• Minutes (MIN) and Points (PTS)
• Rebounds (TREB) - Offensive Rebounds (OREB) and Defensive Rebounds (DREB)
• Assists (AST), Steals (STL), Blocks (BLK), Turnovers (TO) and Personal Fouls (PF)
• Field Goals, Three-Point Field Goals, and Freethrows Attempted & Made (FGA, FGM, 3FGA, 3FGM, FTM, FTA)

The reason for using the term "unadjusted" is that these statistics do not account for the fact that PTS, for example, attributed to a player are not 100% a result of that player's contribution.  Others have made it possible for him to score those points.  Similarly, turnovers aren't completely the fault of the player but also to the credit of the opposition for stealing it.  These kind of complexities require a more sophisticated use of the available data to rate players.  That's why each event that is captured in the boxscore is assigned a weight factor to account for such complexities.

These weights are derived on the fundamental concept of possession-based rating.  That is, analyzing what each player contributes to each possession.  The simplest way to describe this is to say that we will compare what a player's actions provide to the team (in terms of points) on each possession and compare that to the team's Expected Points / Possession (EPP).  EPP is simply derived from taking the number of points a team scores divided by the number of possessions.  This can be done over a game or a season, depending on what the analysis is trying to determine.

Let's take a look at one example:

• Turnovers - When a player turns the ball over, he is basically taking away the chance for his team to score.  Where the team expected to score EPP points, now they will score zero.  But it's not that simple.  In college basketball, half of turnovers are the result of a steal.  So, not all the "blame" can be assigned to the player who turned it over.  In the PSAN rating system, when the ball is stolen, 80% of the credit goes to the stealer and 20% blame goes to the player who turns it over.  Thus, any turnover is assigned a weight as follows:  0.5*(-1*EPP)+0.5*(-0.2*EPP).  What does this mean?  Half the time (when the player simply causes a turnover by himself), the player's contribution is simply "negative EPP" and the other half (when it's a steal) the contribution is "20 percent of negative EPP."  Those other 80 percent of the EPP go to the stealer's PSAN rating.

Every category has a weight that has been meticulously crafted from an analysis of what the player's action contributes to the team's possession.  Some of the factors taken into account include:

• AST - Some excellent passes result in a player getting fouled and then making freethrows.  Such passes are not given credit as an AST.  But the PSAN system adjusts for this in its weighting factor for assists.
• Rebounds - The value of a DREB is very different than that of a OREB.  The value of a DREB is based on what the EPP of the opposition is, because that's what it is negating.  The value of a OREB is the EPP of the player's own team, since that is what his rebound is giving to his team.
• PF - Personal fouls are worth more or less depending on how many freethrows it nets the opposition and how well the opposition is converting those freethrows.  This does mimic the real-world situations.
• BLK - Blocks result in negating the opposition's chance to score, but only when it results in a change of possession.  About half of blocks are assumed to stay with the opposition, so the value of a block is effectively 0.5*EPP(opponent)

Intangible Contributions (added to Tangibles to get PSAN)

There are so many things that happen on a court that simply do not show up in any of these categories.  What about screens, picks, poise, leadership, the pass that led to an assist, tapping out the ball on offensive rebounds, energy, etc?  There's really no way to reward each of these behaviors, but presumably if those things are positive, then they must be resulting in better team performance.

To capture intangible contributions, the PSAN rating distributes the margin of victory (or loss) to the players on the team according to playing time.  But not the entire margin.  If a team wins by 25 and the "tangible contributions" discussed above add up to 15, then only the remaining 10 points are divided up amongst the players.  And even then, only players who played at least 5 minutes are the ones who benefit from the distribution of these points (or penalized in a loss).  The net result is that all points in the margin of victory (or loss) are accounted for by PSAN scores.

PSAN is the best score to use for single-game MVP honors.  It can also be applied to the season cumulative stats, but it will not be as detailed in capturing how important rebounds, assist, etc., were in each particular game as they will be lumped together.  However, every team is still different and the PSAN for the season will still clearly capture the team's dynamics to rate the players. 

Adjusting for Quality of Opponent (cPSAN = comparative PSAN)

PSAN works great to see how well players performed in a game, but it would also be useful to be able to compare player performance across multiple games and to compare them with players from other teams.  This can be accomplished by adjusting for the quality of the opponent.

The cPSAN uses power ratings that are readily available (i.e., Pomeroy) to then adjust the PSAN in a two-step process:

1. Determine the opponents' strength level as compared to the average team.  Let's the say the average team is 50.00, and the opponent grades out to a 45.00.
2. Take the margin of the game (Team - Opponent), add that to the opponent's strength in #1 above.  Subtract the 50.00 (grade for an average team) to get the team's performance for the game.

Example:  Team A plays road game against Team B (rated 48.00), and Team A wins 75-67.

• Add 4 points (estimated homecourt advantage) to Team B's rating to get their true strength for the game (52.00)
• Team A beat Team B by 8 points, so add 8.00 to Team B's strength (52 + 8 = 60.00)
• Subtract 50 from the result (60-50 = 10.00)
• Team A's performance for the game is actually +10.00 (i.e., 10 points better than the average team)
• Divide the +10.00 points amongst the players on Team A according to playing time (skip any players who played less than 5 minutes)
• Add these points to the PSAN scores for each player to get their cPSAN scores, which are used for comparisons to other games that player has played in, or to other players' ratings on other teams.  (preferable to do this on a per-possession or per-70-possessions basis)

cPSAN70 is just the cPSAN score for a player per 70 possessions (the number of possessions in an average college basketball game).

cPSAN70 is the best score to use for comparing players from different teams to each other.

Weighting Recent Games More (ePSAN = enhanced PSAN)

This feature is currently available only for Kansas (my alma mater) because of the level of detail it requires.  In the future, it may be rolled out to other teams, or from time to time, select teams may be showcased with ePSAN ratings for their players.

ePSAN uses data from individual games to come up with each game's cPSAN score for players.  Then, it weights each of these cPSAN according to how recently that game took place.  The final result is ePSAN, which can then be expressed on a per-70-possession basis, or ePSAN70.

The ePSAN70 is the most powerful use of the PSAN-related scores, but it would be somewhat inaccurate to compare one player's ePSAN70 score to another's cPSAN70 ... not completely inaccurate, but perhaps misleading.  ePSAN70 weights recent games more, so it's a better measure of how a player is performing today, whereas the cPSAN70 treats all the games of the season equally and would measure how a player has performed all season long.

A player who's ePSAN is higher than his cPSAN is playing better recently.

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