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Using Adjusted +/- as a predictive measure (or, why Josh Smith is a top-ten NBA player right now)

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I'll admit, the last part of the title is a hook.  It's there to justify making you read what may end up being a very dry examination of advanced NBA statistics.  Some of you might prefer to skip the next 4 paragraphs that will be spent explaining what's going on before I get to exactly how it's relevant for the Atlanta Hawks.  The hope is that this article does not become the Hawks' blogosphere version of this because we're attempting to take Peachtree Hoops to new and exciting places.  Of course, we said the same thing about 8 months ago, so feel free to take that with a grain of salt.

HHB referred me to yet another great reference for basketball fans who are statistically minded,  Rather than just toss it up as a conversation starter and then let it lie, I'm going to explain just a bit of why this even matters.  The ultimate goal of any use of statistics is to find information that is relevant when making predictive analysis of future events.  This sounds like basic sense, but in sports, a lot of times we're looking at numbers that measure only results and attempt to quantify various levels of performance.  This also is useful since we can't watch and accurately codify 1,230 NBA games every season.  But the proprietor of Hoop Numbers spent some extra time to test and refine his measure in order to take an already useful tool and make it more accurate for predictive purposes.

Using plus/minus data from NBA games is nothing new-you can find it now in pretty much any box score.  This basically is the scoring differential for when a certain player (or in smaller samples, a 5-man unit) is on the floor.  The problem is that it does not tell the whole story-if you share the floor with 4 substandard players against Cleveland's starting 5, you're probably coming out in the negative regardless of how well you play as an individual.  That's where Adjusted Plus/Minus (APM) comes in-which you've been able to find here for quite a while.  APM is fairly context neutral and looks at +/- value for 100 possessions.  Of course, the problem is that sometimes standard Adjusted Plus/Minus tells us things that are confusing, like having Amir Johnson as the best player in the NBA in 2007-08.

If you've got a good mind for statistics, please go here for a 6,000+ word explanation of regularized adjusted plus/minus.  It took me, personally, a matter of hours to truly understand the math going on here (but hey, only 10 minutes to figure out that I'm not smart enough do it myself!)  If not, here's the basic idea.  First, you need to establish a cut-off for the minimum number of minutes a player needs in order to have any faith in the measure.  If a guy plays just 10 minutes in a season, the plus/minus data you get from that sample is not big enough to give you confidence about having established that player's true impact.  What ends up happening to those under the cutoff is that their impact fitted to a "model player," who looks similar but has enough measurable minutes.  The second thing you need to do is establish how much weight to lend to previous seasons.  A player can have a career year in any conceivable season, and it may not correlate to success in the following year, or it might indicate a break-out year.  Obviously previous seasons need to be considered to some extent.  Mike Bibby doesn't go to bed in the summer of 2010 and wake up in 2010-2011 as Ron Artest.

The third aspect is variance.  If you're new to statistics, variance is exactly what it sounds like-the amount of variety among the data points within a sample.  The difficulty is that sometimes you'll give a purely numerical sample to your statistics software, and it has no idea what a reasonable output looks like.  This can be pretty useful, in that it might reveal something you never expected, but then again, if it's all nonsense, it's basically useless.  There's a technique being used to basically limit the expected variance in the sample, and then to use those to find the best fits.  By finding this fit you can greatly improve on the overall predictive value of the measure. To find a fit, you have to actually test various combinations of the numbers to gauge its value as a predictor, which he has also done very thoroughly.

Now, what's this got to do with Josh Smith?  Well, just this: Josh Smith is clearly the player whose time on the floor is most correlated with the Hawks winning.  Of course, this shouldn't be news, right?  Other sources might tell us the same.  However, since this is meant to be used as a predictive measure, you can actually pull this out of a team context and compare it to other players around the league (with some error margin).  And here is the ranking for the 537 qualified players who are most relative to winning this season. Predictably, LeBron James tops the rankings.  As you can see, Josh Smith is sitting there at number 9.  Somewhat surprisingly, about two-thirds of that value is the offensive difference he makes. Unfortunately, Mo Evans is all the way down at # 535.

Now that's part of a four season sample where previous years are weighted much less than the current year because the researcher found that provided the best predictive value.  In this case, last season is given 25% weight, the year before is given about 6%, and the year previous is about 1.5%.  So the vast majority of that is from this year, which makes it much more relative to this particular season than next season, in which case it might make more sense to weight all years equally.  That is why you'll see links to those values as well.  Regardless of whether you weigh previous years equally or less heavily, Josh Smith is still the most valuable Hawk by a fair margin.  And if you look at just the sample size of this season, Josh Smith is ranked as the 7th best player in the NBA.

Another thing you'll notice is who is right behind him on that list-Al Horford at #8.  You might find it counter-intuitive to see that our frontcourt is way more important than everyone else, but then again, it's very noticeable how much better this team is when both are on the floor.  Joe Smith and Zaza Pachulia are both perfectly capable back-ups, but the drop-off to the bench is still huge.  Al Horford is also at #15 on the previous link-the one thatis weighted for previous seasons. A quick look at the previous seasons themselves seems a bit confusing.  His value for last season's sample doesn't paint as flattering a picture-in fact, he comes out behind Zaza Pachulia in terms of overall impact.  His APM is negative, even.  Then again, Zaza was crazy last year-he had a career year in a lot of ways-and most of his minutes were spelling Horford rather than playing alongside him.  That suggests, to me, that this measure still doesn't completely eliminate the team context from player evaluation.

So what about our man Joe Johnson?  Well, the numbers don't paint a pretty picture for him.  There's been a lot of discussion around here lately about his prospects beyond this year, and more specifically on his ability to defend other 2 guards beyond this year.  Well, right now, it already looks like he's a huge detriment on defense.  Despite ranking #5 on offensive impact, he's only #103 overall-best for 5th on the team for the Hawks.  The reason is obvious-teams simply score more points when he's on the floor.  He hasn't done nearly as good of a job staying in front of opposing twos as he did in previous seasons.

There's quite a bit of material on that site which I also recommend checking out.  One of my favorites is second-chance points resulting from player missed shots.  Unsurprisingly (once you digest what that means) Zaza Pachulia is among the perennial league leaders.  His missed shots result in nearly half a point for the Hawks. 

Another is the fast break trigger rate-basically, how often a defensive rebound from a player results in fastbreak points for his team.  Naturally, the highest %'s are with guards, since they're typically good ball handlers, passers, and end up rebounding the ball farther away from the basket than bigs-Mike Bibby is one of the league leaders here.  Josh Smith also does very well in this aspect of the game also when compared with other bigs.  He's basically the fourth best big at initiating fast breaks in the league (outside of Golden State, who simply play a completely different style).  This, of course, helps to explain some of his impact on offensive APM.  He's become a great passer, and we all know he's dangerous in the open court.

Upcoming, I have another post where I use a (very) rough projection of minutes to predict the outcomes of a playoff series against Cleveland, Orlando, and Boston.