Greg's Contribution and Refuting Plus-Minus

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Over the past couple weeks we've seen people use the plus minus stat to basically say that the blazers play worse when Greg is on the floor as opposed to Joel.  Usually they then go on to say something along the lines of "this is entirely Greg's fault" or in some way imply that Greg is a bad team player or somesuch.

First off as a disclaimer let me say that I am a pro-numbers guy (engineering graduate).  And I do like my statistics.  Preferably cold hard absolute numbers.  Also, for most of this I won't be crunching numbers, so don't be afraid of seeing standard deviations and statistical methods.

Let's break down this stat to see what it means.  From nba.com:

"What is the AutoTrader.com +/- Stat?
The AutoTrader.com +/- stat shows the power of teamwork. It's a way of showing the best-engineered/best combination of players on the court. The +/- stat is a statistic that looks at the point differential when players are both in and out of the game, to see how the team performs with various combinations."

Okay, so (plus minus) = (total pts scored by good guys) - (total pts scored by bad guys)

This is a combined total offensive production of all 10 guys on the floor.  In concept this is a good idea for showing trends in the game for certain periods of time.  Where this breaks down is in applying this TEAM trend into an INDIVIDUALS performance.  Why? We need to dig deeper into its constituents. 

The points scored are a hard figure without dispute.  However there are a variety of factors that figure into whether or not points are scored.  (I know you're thinking "thank you, captain obvious!" but bear with me, this is a development of logic).

Factors for scoring on an individual possession (not all inclusive):

*Shooting Skill of offensive player taking the shot

*Whether or not the shot falls within the category of the shooters skillset.

*The origin of the offensive possession: half court set or turnover induced fast break?

*If it's a set: efficiency of the offensive scheme.

*Efficiency of defensive scheme.

*Defensive skills of player guarding the ball.

These are just a few and don't even begin to cover things like getting rebounds and turnovers to create additional possessions, pace of game, garbage time, etc.

As you can see, when totaled together for a team, this creates a lot of factors.  Any one individual is only responsible for a segment of these factors and certainly not enough to be able to contribute the entire plus minus score to his doing.  The plus minus is perfectly valid when applied TO THE WHOLE TEAM ONLY.  To apply 100% of this statistic to someone making 10% of the contribution to it is obviously a flawed method.

Furthermore, just for fun, I'm going to look at the biggest assumption that must be made for the plus minus stat to have any meaning.  Quite simply, for the plus minus stat to be meaningful when applied to Greg, the goal of the team must be to outscore the opponent for the duration of time that Greg is on the floor.  This is not always (indeed one might argue it could be never up to this point in the season) the case.  The overall goal is obviously to have the most points on the scoreboard before time expires.  However, KP, Nate, etc. said that the goal this year with Greg is to develop his skills.  If the team has a comfortable lead, WHY NOT give Greg a couple possessions to give him a chance to practice his post up skills?  He needs practice.  The team could run more effective offensive schemes when he's on the floor, yes.  However, they are giving him valuable time to hone his skills.

Plus minus conclusions:  Attaching significance to the plus minus stat when applying it to Greg (or any other individual) is logically unsound, mathematically faulty, and based on a usually false assumption.

Also, I don't plan on offering a complete mathematical refutation of the plus minus, but take a look at the following link and you can probably figure out why I don't attach much value to it, or many other composite stats such as wins produced, the defensive side of PER, etc.

Links:

Blazers plus minus from last year

Analysis of an adjusted plus minus

Greg's Stat Page

Joel's Stat Page

Efficiency Stats

More player stats

Greg's Contributions:  Now that I'm done being negative and ragging on the plus minus stat, I'd figure I'd share some numbers with you.  After all the skepticism about Greg's play I think it's a good idea to look at something helpful.  I've been keeping track of a lot of blazers statistics in a spreadsheet this year so I can chart both Greg's and the teams growth.  I was going to post this after our 24 game brutal stretch and then again at midseason.  I can't do a full defensive analysis until years end because I need teams season averages to calculate differences, but here we go.

I've just got 2 graphs for you today since this thread is ridiculously long.  Both of these are just hard numbers and not adjusted for time.  First we have points in the paint over 15 games, which should be entirely self-explanatory.

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Notice that while Greg is out we are getting schooled.  Even with Greg back, opponents are getting far too many buckets close in, but with him back these have decreased slightly, while ours have risen somewhat, albeit erratically.  These data points are a little spread out so I wouldn't read much more into it than a general trend.

The 2nd chart is rebounds.

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Yes, these points are all over the place and a little hard to look at, but this graph is more informative.  Our team has been winning the battle of the boards for the most part.  Our bigs have also done a good job of out rebounding the bad guys starting center.  Notice that Joel is a beast.  There are only 2 games where he has really bad numbers on the boards, and one of those was thanks to Orlando's zebra unit.  Also notice that except for the last 2 games, Greg has also grabbed more boards than the opposing starting center.  We are also doing a good job holding down the opposed big guy, the only 2 spikes in that chart are called Dwight and Shaq.

In conclusion, I think it is a little premature to be criticizing Greg.  I also think there's a lot of over analyzing going on by media types looking for stories.  People really need to just let the guy play and enjoy it.  Other than the last 2 games, his initial numbers are probably better than expected, and I don't think there's any reason for worry or concern whatsoever.

What do you think of the numbers so far?  Are there any other numbers, charts, graphs, etc. you want to see?  And how awesome would a Greg Oden beard night be if they handed out fake beards on strings to the fans?

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And why do these garbage lines of code keep showing up even after i delete them?