Sports and Numbers

One of the things I wanted to do by rating player performance with the PSAN system was to find some relationship between player performance and team performance.  That is, when KU performed better as a team, did it happen to coincide with certain players having better games?  There are a couple of ways I'm going to break this down.

First, I'll look at correlations between individual player game ratings and KU's performance.  Each player will be compared to the team separately.  This may be the easiest to understand, but I don't believe it is the most accurate.

The second way will be to look at every player's performance each game and find a "best fit" for how to quantify how much each player's rating contributes to the team performance.  So, each player's rating is taken into the broader context of how all players performed.  As you'll see, the results of this analysis show that most of KU's performance variability could be attributed to just a handful of players.

Method 1: Correlation Coefficient

The first way I'll analyze player performance compared to team performance is simple linear correlation between player cPSAN rating and corresponding KU game performance (using power rating of opponent).  The value of a correlation coeffecient ranges from -1 to +1.  A value of +1 means that an increase in cPSAN rating of that player coincides with an exactly proportional increase in KU's game performance (and vice versa).  A value of -1 means that the two are perfectly inversely proportional (as one goes up the other goes down).  And a value of 0 means there is absolutely no linear relationship between the two variables -- it's random.  Now, let's look at the results:

What does this mean?  Simply put, games where KU performed its strongest coincided most with Hawkins' best performances.  It also means that there were no players who played significant minutes whose performance was negatively (inversely) correlated with KU performance.  That's a relief.  Can you imagine being the player whose success always seemed tied to bad games?  But let's talk about a few concepts before you rush to any judgments about this analysis, and let's do it in FAQ style:

Does this mean Jeff Hawkins was responsible for KU's performance more than any other player?

No.  Correlation merely implies that two things occur simultaneously.  It does not prove causality.  As an example, does the fact that you hold your umbrella over your head cause it to rain?  No, but the two events are very well correlated.  Now, this doesn't mean that it's inconsequential that Hawkins (and others) had high correlations to team performance.  We'll just have to come up with some theories as to why.

Does this imply that Hawkins was the most valuable player?

No.  This statistic measures how well the change in player performance tracks with team performance.  Put it another way.  If you played 2-on-2 with Kobe Bryant as your partner against some fairly decent regular players, you'd probably end up winning lots of games pretty handily.  And Kobe would be dominant every single time on a very consistent basis.  There's no doubt that it's because of Kobe that you're winning, not you.  But because your own performance is so variable, your team performance probably closely follows your personal performance more than it does Kobe's.  Capice?

What can we learn from this analysis?

When looking at individual player performances each game, without putting into context what the other players were doing, KU performed best when Hawkins, Rush, and Robinson were playing well and, to a lesser extent, some other players.  Giles and Kaun (basically, the center position) did not account for much of the variability in KU's team performance.  This analysis does not imply that Giles and Kaun did not play well or that good play was not needed from them ... only that it didn't appear to fluctuate in tandem with team performance.  If I knew nothing about Kansas and saw this analysis, I'd guess that the team lived and died mostly by its perimeter game.