Sports and Numbers

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 opposite of the value of a missed field goal, since that is what his rebound is negating.
• 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)

So many things that happen on a court 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.