Sports and Numbers

So often, a team's performance is keyed by the performance of a select group of players.  One way of analyzing this is by doing a correlation analysis between a player's performance and the team performance for each game of the season.

In this analysis, I will use cPSAN to measure player performance, because it controls for quality of the opponent.  The cPSAN is meant to measure the "total impact" a player has on the game, and so it does not account for playing time.  But in this analysis, the point is to see which players, when they impact the game most, are associated with better team results.

For team performance, I used a formula that takes the actual margin of the game (Kansas points minus opponent points) and compared it to the expected margin of the game using Pomeroy Ratings.  This represents how much better/worse than expected KU's performance was.  This way, we can compare across games.

Correlation Coefficient Defined

The definition of "correlation coefficient": A numerical value that identifies the strength of relationship between variables.

It is used to determine a linear relationship between two sets of values.  The value can range anywhere from -1 to +1, where -1 means there is a perfectly inverse relationship (if you adjust a value in the first set downward, the corresponding value in the other set will be up by the same proportion), whereas a +1 value indicates a perfect linear relationship (increasing numbers in one set correspond to proportionally increasing numbers in the other set).

Bottom Line:  The closer a correlation coefficient is to +1, the stronger proportional relationship there is between the two sets of numbers you're measuring.  A value of 0 would indicate no relationship at all.

In this analysis, I did a series of calculations, using one player's cPSAN performances as one set of numbers, and compared it to the team performance (as described above) as the other set of numbers.  I derived a correlation coefficient to compare those two sets of numbers, which is the value you see below.  I repeated this for every player.

Note:  Data uses only games in which the player logged at least 5 minutes.  Here are the basic results of the analysis for the season overall:

Analysis

Some very interesting things all shake out when you break the correlation up into non-conference vs conference play.  I will be providing that analysis as an exclusive feature in an upcoming newsletter.

Some key things to remember about this.  Correlation coefficient measures a relationship between two sets, but it cannot prove causality.  These results don't argue that Jeff Hawkins' good play is causing KU to perform better.  Only that KU's best (worst) games have corresponded most closely with Hawkins' best (worst) games, and to a slightly lesser extent Rush and Robinson's best (worst) games.

This is very interesting, because Kaun, Giles, and Jackson have some of the better efficiency ratings on the team (cPSAN70).  Yet, it looks as though this team is performing best when its contributions are mostly coming from wing players.

I'm not really sure what to make of Hawkins' team-leading correlation.  But it does seem that when he has an "on" shooting night, KU performs well.

Rush and Robinson are no-brainers, because they each bring something uniquely valuable to the team.  Russell has the tremendous defense and passing.  Brandon provides that midrange game and deadly long-range shooting.  Without each one performing well in those categories, it is easy to see that KU typically is not doing well.

Two surprises are Kaun and Chalmers.  Kaun is rated as #1 on the season in efficiency.  But he is near the bottom in correlation to team performance.  I'm not sure this represents a Kaun-specific reason so much as a team style-of-play reason.  This season, KU has performed best when the team plays pressure defense, forces turnovers, and runs the break.  Those games usually benefit the wing players.  Thus, when Kaun performs well, it may mean KU isn't getting as many opportunities to showcase its strengths.

Chalmers may be the biggest surprise here.  Everyone points to the time when Robinson was assigned the point guard duties and Chalmers was moved over to shooting guard as the turning point of the season.  And the fact that Chalmers has played better in the second half of the season than the first (much better) would imply that he should be at the top of this correlation list.  But, it turns out, when you look at it on a game-by-game basis, not just a span of games, that Chalmers' performance hasn't really been that positively correlated to team performance.  This is baffling, because Chalmers' style is to force steals and get out and run on the fast break.  But for whatever reason, this relationship hasn't really come to fruition.  For example, he was the only player with a good rating in the Missouri game (one of our lowest rated performances), but he had one of his worse outings against Nebraska in Lawrence (the team's best performance).

Again, these don't imply causality.  Nor do I have the answers for causality.  I am merely showing you the results that may help you answer some of those questions in your mind.