General
A thought about Defensive eFG%

While on BlogaBull yesterday, I noticed a link to a post from SBNation’s Michigan State Basketball blog, TheOnlyColors.com, which intrigued me due to my recent penchant for NCAA basketball betting :)  The writer, KJ, analyzed his team’s recent defensive eFG% lapse including their loss against my surging Illini (look who’s an 8 seed in Lunardi’s NCAA tournament projection, hey hey!) with this quote that got my wheels turning:

Offensive effective field goal % is subject to the problem Pomeroy notes above: It tells you how good a team is at scoring the basketball (when it doesn’t turn the ball over), but it doesn’t tell you whether the ability to score is the result of (1) creating and taking good shots or (2) simply being a good shooter.

With defensive effective field goal %, on the other hand, it’s a good bet that pure shooting ability is pretty randomly distributed across a team’s opponents. So a low defensive effective field goal % indicates a team excels at forcing its opponents to take difficult shots.

I’ve tried making a defensive statistical before - even using 82games player opponent data - and never got an r^2 above .55.  Perhaps an APM using opponent eFG% as the dependent variable is the factor that I’m missing?

General
I am famous

I keep this site going (loose phrase) in part because I want to submit it with my applications for a stats PhD program next Fall.  So when things comes around that involve me, best be sure it’ll wind up here with biases attached.

I post regularly on BlogABull about the team I cheer for, the Bulls.  My latest post projects Joe Johnson over the next five years using player comparisons, with an excel spreadsheet hosted here at this site.  The conclusion is that Johnson’s production will likely fall off by age 31/32, making him a bad investment for the not-ready-to-contend-yet Bulls.

Yesterday, the Chicago sportsradio show Boers and Bernstein picked up on the article, and talked about it at length here.  They had been big proponents of signing Johnson this offseason, and my article convinced them otherwise.  Take note, admissions departments.

General
Converting PER to Statistical Offensive Adjusted Plus-Minus

Last year, I followed Eli Witus’ instructions and Aaron Barzilai’s data-and-method to run 2006-2009 adjusted plus-minus (APM) numbers, split into offensive and defensive APM.

My results are a little different than others’ because I removed garbage time (defined as point spread > 10 +minutes left in game) and left each season unweighted in order to calculate a Statistical more easily.

Here’s the output, split into 2006-2009 and 2007-2009.  combining0609-and-0709.xlsx

FROM APM TO STATISTICAL APM

I’ve always been interested in figuring out what made an offense work, but the main reason I tried making a Statistical is because I didn’t like PER.  I didn’t understand it, I didn’t like how hard it was to calculate, and I figured a stat had to be organic to have meaning.  That was before I tried to beat it.

Awhile back, I created a Statistical called EOPM by regressing Ilardi/Barzilai’s 5-year weighted APM numbers against rate data from basketball-reference: TS%, AST%, OREB%, TOV%, and USG%.  I figured the ease of use (copying and pasting the whole row of advanced stats into an excel calculator) would outweigh any inaccuracies, as long is it was close.

But when I ran the r^2, it showed just .52, lower than Rosenbaum’s .57 from years back.  There were a few obvious problems with my method:

1) I used unweighed rates while Ilardi/Barzilai calcuated their APM numbers by giving extra weight to recent years.  I wasn’t sure how to quickly and accurately weight rate stats, so I lazily just left them unweighted.

2) I just used 5 rates.  Obviously that left a lot out.

3) I used TOV%, a stat I’ve come to dislike since.  Jason Collins and Dennis Rodman had enormous TOV%’s despite low Per36 turnovers because they rarely shot the ball.

EOPM didn’t work how I wanted.  But with my new unweighted APM data in hand, I decided to create a new EOPM using Rosenbaum’s Per40 stats idea. I tried to improve it further by adjusting for estimated Pace and including TS%.  In all, I made the inputs TS%, and Per36 pace adjusted (Per36 * 100/estimatedpace) OREB, DREB, AST, STL, BLK, TOV, PF and PTS.

The Formula is: EOPM = -17.173 + 18.131 * TS% + 0.317 * OREB + .190 * DREB + .716 *AST + .334 * STL  - .324 * BLK - 1.447* TOV - .280 * PF + .461* PTS

with an r^2 of .723.  Pretty good!  Next step, comparing it to PER.  (Here’s my EOPM work: eopmdata.xlsx.)

COMPARING EOPM WITH PER

I figured, for EOPM to be useful, it should accurately find Team Offensive Ratings for past years given player EOPMs and minutes played.  By multiplying each player’s EOPM by his % of minutes played during that season, then summing those products for each team, I hoped to nail each team’s Offensive Rating within a few tenths of a point.

I performed the calculations for every 2009 NBA team, regressed my estimated O-Ratings against the actual O-Ratings and got an r^2 I liked: .800.  Then I did the same using PER: .914.  Wait, what?

Whoa.  (Here’s my work: per-vs-eopm.xlsx)

After a bit of headscratching, I found that Fit is a big reason why adding EOPMs doesn’t work as well as PER.  For example, if a team is extremely good at offensive rebounding, the effect on each player’s EOPM is tiny, but for the team it leads to more shots and a higher ORating.  (When including offensive rebound rate in the team regression, EOPM’s r^2 jumped to .893.)

PER though, already considers team rebounding in its calculation, so its r^2 is unaffected when including team offensive rebound rate (jumps to .915).

So Hollinger beat me to a pulp.  And as a result, I’ve started using PER a lot more.  But sometimes I like to balance it out a bit…

COMPARING PER TO EOPM

Even though PER was a more accurate determinant of Team Offensive Rating, I still had reason to think EOPM fairly judged performance.  After all, the numbers are organic, and when adjusted for fit, its correlation nearly matches PER’s.

So my next step was seeing how the stats differed.  I regressed PER against EOPM, and the result was this formula.  EOPM = -8.4+.56* PER, with an r^2 of .736.

First off, that r^2 seemed oddly low for two stats that estimated the same thing, and I figured out why once I calculated ExpectedEOPM for each player using that formula.  Here were the players (who played >5000 minutes from 2006-2009) whose ExpectedEOPM differed most from their actual EOPM.

Biggest Overestimates:

Name	PER	ExpectedEOPM	EOPM	Difference
DeSagana Diop	11.1	-2.2	-6.6	4.4
Ben Wallace	14.5	-0.3	-4.0	3.7
Samuel Dalembert	14.9	-0.1	-3.5	3.4
Darko Milicic	13.1	-1.1	-4.4	3.3
Marcus Camby	18.6	2.0	-1.2	3.2
Dwight Howard	22.1	3.9	0.8	3.1
Joel Przybilla	13.5	-0.9	-3.8	2.9
Kendrick Perkins	12.4	-1.5	-4.3	2.8
Josh Smith	17.6	1.4	-1.4	2.8
Yao Ming	24.1	5.0	2.3	2.7
Chris Kaman	15.0	0.0	-2.7	2.6
Jason Collins	4.0	-6.2	-8.8	2.6

Biggest Underestimates:

Name	PER	ExpectedEOPM	EOPM	Difference
Jose Calderon	18.0	1.6	4.1	-2.4
Deron Williams	18.0	1.6	4.0	-2.4
Steve Nash	22.0	3.9	6.2	-2.3
Chauncey Billups	21.8	3.7	5.7	-1.9
Mike Bibby	16.4	0.7	2.5	-1.7
Michael Redd	20.3	2.9	4.6	-1.7
Raja Bell	11.6	-1.9	-0.4	-1.6
Eddie House	14.6	-0.3	1.3	-1.6
Antonio Daniels	13.8	-0.7	0.8	-1.5
Steve Blake	12.6	-1.4	0.1	-1.5
Leandro Barbosa	17.2	1.2	2.7	-1.5
Mike James	14.6	-0.3	1.2	-1.5

See a pattern?  If EOPM is to be believed, Hollinger overestimated big man stats (blocks and rebounds) to increase the PER of frontcourt players.  For a possible answer why, take a look at this chart.

Average APMs by position among players who played >5000 minutes between 2006-2009:

	Off	Def
PG	+1.2	-0.5
SG	+1.0	-0.8
SF	+0.5	-0.2
PF	+0.4	+0.9
C	-1.6	+1.5

One axiom of the NBA game is that guards generally make a bigger impact offensively because they have the ball in their hands the most, and PFs/Cs make a bigger impact defensively because they defend more shots by playing in the paint, and the chart seems to support that.

Now look at the EOPM and PER of the same sample of players:

	EOPM	PER
PG	+1.4	15.6
SG	+1.1	15.5
SF	+0.3	15.1
PF	+0.2	16.6
C	-1.4	15.9

While EOPM shows the same positional correlation as APM, PER shows the positions as equal, possibly even with a slight offensive edge to inside players.

I’m guessing Hollinger did this in an attempt to sell PER as an all-around player evaluator.  In his articles, he often analyzes transcations using only PER.  He created his Expected Wins Added statistic based purely off PER.   There’s even a Hollinger Analysis feature on the ESPN Trade Machine that estimates wins added using only PER.

But PER’s .70 correlation with Team Net Rating (Offensive Rating minus Defensive Rating) seems largely attributed to its ridiculous .914 correlation with offense.  For comparison, EOPM correlates at .69 with Team Net Rating.

By overrating Big Man categories (blocks and rebounds), Hollinger levels the positional playing field by accounting for the defensive impact of power forwards and centers.  Interestingly, that change doesn’t affect PER’s correlation with Team Offensive Rating because NBA lineups are generally built the same way, with two definite guards and two definite big men.  Therefore, each team receives roughly the same amount of over- and under-estimation.

CONVERTING PER TO EOPM

In spite of that oddity, I think PER’s pretty great.  Not only does it correlate impressively with Team Offensive Rating, but it’s widely available, and it’s easy to find PER across seasons at basketball-reference.com.

But what if you wanted to quickly estimate a player’s Offensive Statistical APM, and filter out Hollinger’s big man overestimates?

Remember that .736 correlation between PER and EOPM?  Insert Rebounds Per 36 and Blocks Per 36 into the regression, and the correlation skyrockets to .963, with the following formula:

EOPM (estimated) = -7.5 + .63 * PER - .19 * Rebounds36 - 1.22 * Blocks36

I wish it were a little easier to calculate, but it’s not bad.

General
Vinny Del Negro’s Offense

VDN was an elite midrange jumpshooter as a player. With Tim Duncan and David Robinson clogging the lane, VDN kept defenses honest with a career 49.5 eFG% over 12 seasons. But despite his shooting ability, he made just 0.3 threes and 1.3 free throws per game, leaving his career TS% at a mediocre 53.4% . Perhaps he isn’t aware of that last part, because as coach of the Bulls, he’s brought midrange shooting to his offense. Blah.

Hoopdata.com tracks shot selection like NBA HotSpots used to. According to them, NBA teams averaged 40.0 two-point jumpers per 100 possessions last year, accounting for 40.1% of total scoring attempts. The Bulls’ 42.2 and 41.9% ranked 10th and 11th highest respectively. This season, without 3pt shooters Ben Gordon, Andres Nocioni and Larry Hughes, VDN has increased 2pt jumpshots to 50.6 per 100 possessions and 50.5% of scoring attempts, both leading the league.

Chicago media has justified it by saying Vinny is working with what he’s got. It’s true in a way: Luol Deng, Derrick Rose, Brad Miller and Taj Gibson take few 3s or FTs. Vinny tried the three early on, but with the Bulls making just 26.2%, he’s scaled it back to 10.7 attempts over the past six games. The league average is 17.7.

It’s nothing new to argue that an excess of 2pt jumpshots is a bad idea. Just 40.5% of 2pt jumpers shot last year went in, falling well short of the league’s 54.4 TS%. Advanced game charting presents more bad news: 82games says just 7% of all shooting fouls occur on 2pt jumpshots and the Rockets’ Eli Witus says that the 2pt jumpshot is the shot least likely to be offensively rebounded. The data shows that offenses relying heavily on the 2pt shot would be better off penetrating, or even easier, taking a couple steps back to shoot a 3. I want to focus on the jumpshots here, because it’s easier to shift 2pt jumpshots to 3s than to layups.

For the Bulls, there’s little incentive to keep doing what they’re doing. Their shot selection is so bad that even if they shot league average from each location (60.5% inside, 40.1% on 2pt jumpers, 34.7% on 3s), their TS% would be just 51.3%, ranking them 27th in the NBA. Add in their poor shooting, and an ugly 96.9 Offensive Rating results.

But if you’re Del Negro, what can you do? Your team is shooting poorly from 2s, but they’re making just 26.2% 3s. Is there another option?

To try to answer this, I’ll define Percentage of Jumpers as the percentage of your team’s jumpshots that are two-pointers. The league average this year and last was 67%. The Bulls are currently at 80%. What would happen if the Bulls moved to 67%, and the field goal percentages stayed the same?

Using Excel, I ran 100,000 simulations of the following matchup: Team A takes 80 two-pointers and 20 threes each game, and Team B takes 67 two-pointers and 33 threes each game. To start, each 2pt shot has a 39.1% chance of going in, and each 3pt shot has a 26.2% chance of going in - the current rates for the Bulls.

The results:

100,000 Simulations, 80/20 ratio vs. 67/33 ratio 2pt jumpshot FG% = 39.1%, 3pt jumpshot FG% = 26.2%
Team	Win%	PPG	StDev
Team A (80 2s)	50.0%	78.30	10.50
Team B (67 2s)	50.0%	78.32	11.02

Conventional wisdom says that taking more 3s at a 26.2% rate is a bad idea. At the very least, the game to game variability would be chaotic. But the math shows differently. Even with a 26.2 3pt%, the Bulls can maintain their winning% by taking more threes, average the same PPG, and barely affect their StDev. With the offensive rebounding increase and the potential for improved floor spacing, this is likely at least a wash scenario for a team in need of a spark offensively.

But the added benefit is, due to practice or simply having more chances to regain their shooting stroke, their 3pt% should improve over time. After all, the lowest team 3pt% in the past five years was 31.2% by the ‘05 Hawks, so 26.2% is probably an anomaly. Here’s how the simulations play out if the Bulls make 29% of threes:

100,000 Simulations, 80/20 ratio vs. 67/33 ratio 2pt jumpshot FG% = 39.1%, 3pt jumpshot FG% = 29.0%
Team	Win%	PPG	StDev
Team A (80 2s)	47.0%	79.94	10.65
Team B (67 2s)	53.0%	81.08	11.18

Here we see a distinct advantage in Win% and in PPG. Moving to the 31.2% the lowly Hawks shot a few years back:

100,000 Simulations, 80/20 ratio vs. 67/33 ratio 2pt jumpshot FG% = 39.1%, 3pt jumpshot FG% = 31.2%
Team	Win%	PPG	StDev
Team A (80 2s)	44.9%	81.29	10.70
Team B (67 2s)	55.1%	83.26	11.34

The PPG difference of 1.97 per 100 jumpshots translates to about 1.25 per 63 jumpshots, which is the Bulls’ per game average. 55.1% of the time they’d score more points than they would taking 80% 2pt jumpers. Over the course of the season, that shift should add about 3 extra wins.

Personally, I think the Bulls might have better 3pt shooters than the media gives them credit for. Kirk Hinrich and John Salmons both made over 40% last year. Luol Deng leads the league with 8.8 jumpshots per game from 16-23 feet, and makes 38%. Derrick Rose makes 41% of his 6.4 per game, and both their percentages are consistent with last year. If Deng and Rose step back, can they hit 30% of their 3s? It still wouldn’t be efficient, but the numbers say it would improve the Bulls offense. If their shooting more 3s also helps them improve, all the better.