Analysis: Relationship Between Kansas Player Performance
and Team Performance 2005-06

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.

Method 2: Multiple Regression

Note: For this method, I used only data from Game 9 onward to account for the addition of Darnell Jackson.  Given that he played significant minutes, it made most sense to analyze the dynamics of the team after he joined.  Having done this for the analysis in Method 1 above would not have made significant changes (i.e., Kaun and Giles still at bottom, Hawkins and Rush still at top).

A more comprehensive way of looking at the relationship between player performance and team performance is to look at every player's performance each game compared to team performance.  Then, let the computer calculate a "best fit" model to predict team performance based on each player's performance.  When you do this, some players are more significant to the calculation than others.  Using a 95% confidence interval for determining whether a player's fluctuations are significant, I performed a stepwise regression analysis to build a list of players whose variability in performance matter in determining variability in KU's performance.  Again, I can't stress enough that this does NOT imply who is the best performer or most praise-worthy of KU victories.  It just implies which players' change in performance from game to game best explains KU's performance from game to game.  Let's look at the results.

Hold on one second!  Didn't Kaun have the lowest correlation in the first method?  He sure did.  But that didn't take into account what was happening to all the other players' ratings in each game.  At first glance, one may think Kaun's success didn't matter to the team, but the more robust multiple regression adds evidence that it did.

In a nutshell, this second method tells us that you could reasonably account for a good or bad KU performance compared to its baseline by looking at whether Rush, Hawkins, Robinson, and Kaun were having good games compared to their baselines.  Anyone surprised?

Rush was the leading scorer and shooter on the team.  An off night from him put a lot of pressure on the team to score.  Besides, he played more minutes than anyone else, so fluctuations in his game impact rating mattered more.  Hawkins is a bit more challenging to interpret.  My guess is that his streaky shooting was extremely important to the team.  Robinson handled the ball an awful lot and played a lot of minutes.  Given that Kaun and Giles basically split duties at center, it is very telling that Kaun's fluctuations were significant in this analysis and Giles' were not.  One might speculate that Kaun's efforts actually made a difference.  That is, he played well against teams that KU needed to beat inside, while Giles did not ... although Giles' game against Cal's Leon Powe was a major exception.  It's not an exact science.  But for whatever reason, KU's performance hinged more on these four players' ability to have a good game that day.

Bottom Line: Who is MVP?

What I take away from this is that KU's performance depended heavily upon strong games from key perimeter players (Rush, Hawkins, and Robinson) and that the inside game's effectiveness depended more on whether Kaun had a good or bad game.  But it's extremely important to note that this analysis does not imply these four players were most responsible for wins/losses.  The best players are ultimately most responsible for victories (ePSAN ratings indicate that Chalmers contributed the most).  But the ups and downs the team experienced were mostly a result of the ups and downs of the four players highlighted.

Combining the list of those who contributed most to the season (ePSAN) and those whose ups and downs mattered the most could be one way of ascertaining the true MVP of the team.  The highest-rated ePSAN on the list of four players in the multiple regression analysis is ... Russell Robinson.

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