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NBA Stats

July 12, 2014

NBA Estimated Impact A player rating  that uses elements from the box score only.

NBA Non Prior Informed RAPM (“NPI RAPM”) A player rating that is based on team point margins in stints where the player was on the floor. This is the most basic version of RAPM and only uses data from the year in question.

NBA Prior Informed RAPM (“PI RAPM”) A version of RAPM that uses information from previous seasons to increase stability and predictive accuracy.

NBA Boxscore Informed RAPM (“BI RAPM”) A version of RAPM that uses information from the box score to increase stability and predictive accuracy. In this version, RAPM is calculated with estimated impact, rather than 0, as the prior, then mean regressed somewhat.

Pace and Ratings (1952-2013) An estimation of each team’s possessions and the rates at which they use those possessions.

NBA Average Height by Position and Year (1952-2014)


Estimated Impact

September 16, 2013


While I initially introduced my player rating, Estimated Impact, a while ago, I recently gave it a pretty extensive makeover and I’m generally pleased with results. My goal was basically to create a box score only metric that is a) more accurate and better at predicting future team performance than other box score metrics, and b) a very reasonable snapshot of present and historical player performance. Obviously, box-score only metrics have their noted limitations. And maybe more obviously, all-in one metrics are merely a two-dimensional picture of a three-dimensional world. But I’m confident that Estimated Impact does a good job at accomplishing my goals.

I don’t want to bore you with the details so I’ll keep it basic. This metric is based on a regression of certain box score elements against long term RAPM. For each season, I fit each player’s result to the team’s efficiency differential (this is usually a pretty small adjustment).  I did the same with offense only and defense only, then fit off + def to total impact. For 1974-1977 I estimated turnovers by regression and used the same formula as I used in post-77 seasons. For pre-1974, I ran new regressions without any use of steals, blocks, etc. Needless to say, pre-74 estimates are probably less accurate. They’re certainly far from useless though, and they’re probably superior to any other measure of pre-74 production (e.g., WS/48 or PER).

In my own retrodiction testing, Estimated Impact outperforms every box score metric that I know of, and performs nearly as well as 2000s xRAPM [edit: when adjusted to give a fixed rating to very low mp players, estimated impact significantly outperforms xRAPM in retrodiction testing as well] (I’d welcome anyone to reproduce my results). And so I’m confident that it is currently the best all-in-one metric with respect to estimating historical production. For what it’s worth, the results also seem very reasonable to me. You can see all results from 1952-2013 here, or at the NBA & NCAA Stats page at the top right of the site. Or you can download the database here. Enjoy!


NBA & NCAA Stats Page

August 13, 2013

I added a new page called NBA & NCAA Stats (you can see it up in the top right corner). I’m basically using it to keep all the stats that I think are interesting or helpful but either can’t be found anywhere else or are really hard to find. You’ll notice I have RAPM from 2001-2013. I want to make it clear that this is not my RAPM, but was previously published and isn’t really publicly available anymore. I also added historical pace, which includes offensive rating, defensive rating, relative offense, relative defense, and efficiency differential for every team since 1952. I posted on this a few months ago, but I think it will be more useful to keep it in a more easily accessible place. Finally, I added Estimated Impact, my box score metric, which will get its own post soon. If there is anything else anyone would like to see (for example, I was thinking of doing a spreadsheet with substantially all available player metrics for each player), let me know and I’ll see what I can do. Anyway, enjoy!


Draft Model Update

May 24, 2013

I have made significant changes to the draft model; it’s very refined at this point and much improved from the previous iteration. To avoid confusion, I’m going to make this the go-to post and take down all posts pertaining to the earlier versions. But I’m going to use a few quotes from them so they’re not lost.

From my post called “NBA Draft Projection Model and More”:

I’ve been working on developing a model that attempts to project NBA performance of college players. Basically I ran multiple linear regressions on pretty much all the data I could collect (like pace-adjusted box score numbers, team sos, measurements, etc.) for college players from 2002-2009 against their career NBA RAPM. I removed insignificant factors, and eventually came up with a fairly reasonable predictor.

From my post called “Draft Rankings!!”:

I’m obsessive by nature, so this certainly won’t be the final iteration, but I’m pretty happy with it at this point…

…The results are far from perfect as they probably always will be – remember what we’re doing here, we’re taking stats from college kids playing against varying levels of competition in a very limited sample size and trying to project their careers. But I feel pretty confident that we can make educated guesses with this data – and do a much better job than what we’ve actually seen in the past.

I made a number of changes, but the following is a brief summary of the most significant ones:

  • I added in all players’ career numbers instead of using only their numbers from their final NCAA season. This turned out to be a very significant improvement, and I probably should have done it in the first place.
  • I went back to using ONE regression rather than three different ones (for points, wings, and bigs – an idea I had taken from Hollinger). I was able to do this because of having the career numbers. This is important because all players can be more reasonably compared to each other regardless of position, and now everyone is on a sliding scale – for example, the difference between someone who plays a bit more SF than PF and someone who plays a bit more PF than SF is very small now, which is the way it should be.
  • I refined and normalized the y values (the dependent variable for each player). Instead of using long-term RAPM, I used a RAPM-SPM blend based on the same relative period of time for each player.

Here are some observations about what player projections mean:

  • Like before, players +2 or better are very likely to be all-star caliber NBA players. The +2 club is more exclusive than before, and so if there’s a +2 on the board when your team is picking, take him.
  • +1 or better means the player is very likely to be a solid NBA player. In some cases – usually if the player has behavioral or work ethic issues – +1s won’t pan out, but more often than not, they will.
  • Players in the positive or slightly negative range are more likely than not to be solid contributors.
  • Players more than slightly negative will be hit and miss. You probably won’t find may great players here, and the more negative, the less likely it is the player will be any good.

Finally, here are all the out-of-sample (2010 to 2012) results for drafted players:

And as always, the current draft rankings can be found at the top bar.


It’s a Good Year to Move Up in the Draft

April 29, 2013


Generally speaking, I would discourage any team from trading its assets to acquire a higher draft pick. This is because, frankly, there just isn’t a lot of value in most drafts. Only a handful of good players will come out of any given draft, including about five all-stars per year. And teams generally perceive their high picks (especially when we’re talking top five) to be more valuable than they really are. In fact, the only pick that more often than not turns out to be a high impact player is #1. So trading up is usually a bad idea unless it either allows you to get a large, unwanted contract off your hands or you trade up a spot or two and it doesn’t cost you much.

But this year is a bit peculiar. It is almost universally considered to be a “weak” draft, especially after the decisions of a number of high profile potential draftees (Marcus Smart in particular). More specifically though, it’s viewed as a draft with a handful of solid players but no sure-bet all-star types. Accordingly, a pick in the two to five range isn’t viewed as that much better than a pick in the six to fourteen range this year, at least if you believe the prominent media, who purportedly have a great deal of contact with the general managers who actually make the decisions.

And that’s exactly where you can pull a fast one this year. In the three to eight range sits a man named Otto Porter. Now, I’m not Miss Cleo or John Titor, but my draft model has Otto as better than a +3. And if you recall, I consider +2 or better to be as close to a sure thing as you’ll see.

In other words, I believe Otto Porter has a pretty good chance to be an all-star caliber NBA forward a few years down the road. Don’t let Georgetown’s poor performance in the tournament fool you, Otto’s supporting cast was not particularly impressive, and the fact that they rode his coattails to the Big East’s best record is remarkable in itself. I think it’s actually a testament to Otto’s ability to lift an average team to elite levels. And that shouldn’t be a surprise if you watched him play this year. He is a do-everything type player who puts up superb numbers across the board and adds plenty of intangibles that don’t show up in the box score. He is a very good shooter (and scorer) in spite of his shooting form. He’s also an excellent if underrated passer who has a LeBron-esque ability to find the open man anywhere on the court. And while he lacks elite athleticism, he makes up for it with craftyness, a high basketball IQ, and a great overall feel for the game. He is also valuable because of his ability to play either forward position on both offense and defense and have a matchup advantage against most of the league because of his size-skill combination. This is a 6-8 guy with a 7-2 wingspan who shot 42% from long range and showed a terrific ability to steal the ball, block shots, and simply menace opponents on defense. Because of all this, I think that he’s arguably the best player in this class.

And that’s why I think it’s worth taking a shot to try to move up to a position where you can draft Porter. Of course this is easier said than done, but if your team has assets of some value, it’s worth making some calls to see what you  might be able to get for them, especially if the assets are either expiring contracts or reasonably expendable given their relative value or redundancy. Because of the overall lukewarm attitude toward this draft, I’m willing to bet that someone will listen. And if you can spin this kind of asset into Otto Porter, I’m confident it will have been well worth it.

Pre-1974 Pace And More

April 10, 2013


Before 1974 they didn’t track turnovers or offensive rebounds for NBA teams. Because of this, we are missing pieces necessary to estimate pace, which can be super helpful in understanding team strengths and even player contributions. However, it’s possible to get a reasonable estimate of pace by using regression analysis and making reasonable inferences. I was particularly intrigued by the methods employed by ElGee, who posted his results a year or so ago. Unfortunately, something went wrong with his site, and none of his data is available anymore. Luckily, Opposing Views reblogged his post, and I was able to find his formula, which is as follows:

Pre-1974 Pace = (FGA + 0.4 * FTA – ORB% * (FGA – FG) + (-TOV% * (FGA + 0.44 * FTA) / (TOV% – 1))/G), where ORB% = 0.319 for1971-1973 and 0.303 for before 1971, and TOV% = 0.158 for 1971-1973 and 0.161 for before 1971.

Using this information, I figured I’d post the estimated pace for all teams from 1951-1973 (before 1951 we don’t have rebounds, so there’s no way we’re gonna be able to estimate further back than that). Additionally, with pace (possessions per game by the way, though I’ll probably add possessions per 48 soon), I can calculate Offensive Rating and Defensive Rating – points scored per 100 possessions and points surrendered per 100 possessions, respectively. And with Offensive and Defensive Ratings I can estimate Relative Offense (Ortg – League Avg Ortg), Relative Defense (League Avg Drtg – Drtg), and Efficiency Differential (Ortg – Drtg). So I made a spreadsheet and included all this stuff for anyone interested in finding all these numbers, including the post-1973 estimates, in one place.

For fun, here are some top tens:

Top Ten Efficiency Differentials:

  1. 1996 Bulls, +13.4
  2. 1997 Bulls, +12.0
  3. 2008 Celtics, +11.3
  4. 1992 Bulls, +11.0
  5. 1971 Bucks, +10.9
  6. 1972 Lakers, +10.5
  7. 1972 Bucks, +10.1
  8. 2009 Cavs, +10.0
  9. 1994 Sonics, +9.6
  10. 1997 Jazz, +9.6

Top Ten Relative Offenses:

  1. 2004 Mavs, +9.2
  2. 2005 Suns, +8.4
  3. 1971 Bucks, +7.8
  4. 1997 Bulls, +7.7
  5. 2010 Suns, +7.7
  6. 2002 Mavs, +7.7
  7. 1998 Jazz, +7.6
  8. 1996 Bulls, +7.5
  9. 2007 Suns, +7.5
  10. 1982 Nuggets, +7.4

Top Ten Relative Defenses:

  1. 1964 Celtics, +10.9
  2. 1965 Celtics, +9.5
  3. 2004 Spurs, +8.8
  4. 1963 Celtics, +8.6
  5. 2008 Celtics, +8.6
  6. 1962 Celtics, +8.5
  7. 1993 Knicks, +8.3
  8. 1973 Celtics, +8.2
  9. 1994 Knicks, +8.0
  10. 1961 Celtics, +7.7

Again, the pre-1973 estimates aren’t as accurate as their modern counterparts, but they come reasonably close, and that’s what we’re going for. What I find particularly interesting is the number of Nash offenses and Russell defenses in their respective top tens (5 each).


The Importance of Position on Offense and Defense

March 27, 2013


Perimeter players aren’t as important on defense as bigs. And bigs aren’t as important on offense as perimeter players. I’ve heard this assertion made quite a few times. I’ve even made it myself. But is it true? When I wrote the post arguing that Trey Burke should be an early lottery pick rather than a mid-first-round pick , I noted that Burke’s “troubles” on defense are not particularly concerning because he is a point guard, not a big. This got me to thinking: sure, certain bigs have way more impact on defense than any perimeter player could ever hope to, but does that mean bigs are more “important” on defense? Instead, isn’t the difference between a good big on defense and a bad big on defense the same as the difference between a good guard and a bad guard? The best defensive guards have much less of an impact than the best defensive bigs, but aren’t the worst defensive guards as substantially worse than the worst defensive bigs? On the other hand, isn’t the discrepancy between Garnett and Bargnani (or Larry Sanders and David Lee, if you’re a Goldsberry fan) a lot bigger than the discrepancy between say, Rajon Rondo and Steve Nash? Then again, maybe it isn’t.  I decided to investigate.

In order to answer my questions, I looked at J.E.’s 12 year RAPM data, which includes every player’s regularized APM from 2001 to 2012. I excluded players who played less than 20,000 possessions because their RAPM values are much more uncertain. I separated all players by position with an assist from basketball-reference. Then I looked at the offensive and defensive ranges for each position.

I found the following:

On defense,

  • ~95% of point guards fall between -4.1 and 2.3 per 100 possessions (a range of 6.4)
  • ~95% of shooting guards fall between -3.6 and 2.3 (a range of 6.0)
  • ~95% of small forwards fall between -3.5 and 3.3 (a range of 6.8)
  • ~95% of power forwards fall between -3.5 and 4.2 (a range of 7.7)
  • ~95% of centers fall between -2.4 and 5.7 (a range of 8.1)
  • While there is a bit of a difference across positions – i.e., centers may be a bit more important than guards – the difference is not statistically significant (e.g., the hypothesis that each position will have the same range is accepted). This is true even if we include the entire range for each position and not just two standard deviations from the mean.

On offense,

  • ~95% of point guards fall between -3.4 and 4.2 per 100 possessions (a range of 7.5)
  • ~95% of shooting guards fall between -3.8 and 4.3 (a range of 8.1)
  • ~95% of small forwards fall between -3.8 and 3.8 (a range of 7.6)
  • ~95% of power forwards fall between -4.2 and 2.7 (a range of 6.9)
  • ~95% of centers fall between -5.2 and 2.6 (a range of 7.8)
  • Again, the variance on offense among positions is not statistically significant.

Here are a couple of graphs for those who like visualizing data:



So, basically, as we expected, the big guys are better on average on defense and worse on average on offense. But when we look at their ranges, their relative importance is pretty much the same. Now, of course, more work needs to be done here. 12 year RAPM is likely a good overall indicator, but it’s certainly not the ultimate source for everything (nothing is). It would be interesting to see a study like this replicated using other data, whatever it may be. But, for now at least, it doesn’t appear that certain positions are significantly more “important” than others on either side of the ball, though they can certainly be more impactful. Starting a little guy at center, for example, is obviously a bad idea. But the difference between a bad center and a good center doesn’t seem to be significantly different from the difference between a bad guard and a good guard.