Sports and Numbers

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., Sagarin) 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 75.00, and the opponent grades out to a 70.00.
2. Take the margin of the game (Team - Opponent), add that to the opponent's strength in #1 above.  Subtract the 75.00 (grade for an average team) to get the team's performance for the game.

Example:  Team A plays road game against Team B (rated 73.00), 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 (77.00)
• Team A beat Team B by 8 points, so add 8.00 to Team B's strength (77 + 8 = 85.00)
• Subtract 75 from the result (85-75 = 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-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.

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 weighs 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.