## ezPM Compared with RAPM: Part II (Offense and Defense)

In a previous post, I showed the results for regressions of ezPM against 1-yr and 3-yr RAPM (regularized adjusted +/-). Now, let’s take a look at how the offensive and defensive components of ezPM correlate with their RAPM counterparts. If you are familiar with ezPM, then you know I typically calculate three separate components: O100, D100, and REB100. To enable comparison with RAPM data, I folded the REB100 into O100 and D100, to give total offense and defense components (i.e. that include offensive and defensive rebounding, respectively). Just as a quick refresher, I re-ran the regression for the overall metric comparison, this time weighting by possession number, and focusing only on the 3-yr data set:

```
RAPM as a function of EZPM (3-YR).

Call:lm(formula = RAPM ~ EZPM100, data = tot, weights = POSS)
Residuals:    Min      1Q  Median      3Q     Max
-528.06  -84.51   -7.21   64.96  613.87
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.81273    0.09070    8.96   <2e-16 ***
EZPM100      0.60519    0.03686   16.42   <2e-16 ***
---Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 142.3 on 381 degrees of freedom
Multiple R-squared: 0.4144,	Adjusted R-squared: 0.4129
F-statistic: 269.6 on 1 and 381 DF,  p-value: < 2.2e-16```

You can see that there is a slight increase in R^2 to 0.41 from 0.37 previously. Now, let’s look at the regression results for the offense:

```
RAPM vs. EZPM (3-YR Offense)

lm(formula = OFF_RAPM ~ O100, data = off, weights = POSS)
Residuals:    Min      1Q  Median      3Q     Max
-399.88  -84.15  -19.91   45.38  564.10
Coefficients:            Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.23537    0.09328  -2.523   0.0120 *
O100         0.57146    0.04266  13.395   <2e-16 ***
---Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 117.6 on 381 degrees of freedom
Multiple R-squared: 0.3201,	Adjusted R-squared: 0.3184
F-statistic: 179.4 on 1 and 381 DF,  p-value: < 2.2e-16```

The correlation between the individual offensive components of ezPM and RAPM is significant (p<2.2e-16) and R^2=0.32. As I did last time, I want to give a table showing the best and worst players according to an average of the two metrics (note Warriors guard Charlie Bell shows up on the Bottom 20):

### Top 20 Offensive Players (> 5000 Possessions)

 RANK NAME OFF_RAPM OFF_ezPM AVG 1 LeBron James 6.90 7.19 7.05 2 Steve Nash 7.80 5.56 6.68 3 Dwyane Wade 6.30 6.05 6.18 4 Chris Paul 5.10 7.07 6.09 5 Dwight Howard 3.60 6.37 4.99 6 Deron Williams 4.50 4.60 4.55 7 Chauncey Billups 3.90 4.72 4.31 8 Pau Gasol 2.90 5.67 4.29 9 Dirk Nowitzki 5.10 3.16 4.13 10 Manu Ginobili 4.20 3.74 3.97 11 Kobe Bryant 4.30 3.60 3.95 12 Brandon Roy 3.60 3.88 3.74 13 Chris Bosh 3.10 4.05 3.58 14 Kevin Martin 3.50 2.84 3.17 15 Joe Johnson 3.90 2.38 3.14 16 Nene Hilario 2.00 4.25 3.13 17 Amare Stoudemire 2.40 3.59 3.00 18 Ty Lawson 2.10 3.85 2.98 19 Carmelo Anthony 3.30 2.58 2.94 20 Kevin Love 0.90 4.94 2.92

### Bottom 20 Offensive Players (> 5000 Possessions)

 RANK NAME OFF_RAPM OFF_ezPM AVG 237 Donte Greene -1.10 -2.76 -1.93 236 Chris Kaman -2.80 -0.83 -1.82 235 Rasual Butler -2.10 -1.41 -1.76 234 Yi Jianlian -1.60 -1.87 -1.74 233 J.J. Hickson -3.30 -0.07 -1.69 232 Jonny Flynn -0.60 -2.55 -1.58 231 Corey Brewer -0.80 -2.21 -1.51 230 Brandon Rush -1.70 -1.31 -1.51 229 Dahntay Jones -2.90 0.08 -1.41 228 Darko Milicic -2.10 -0.45 -1.28 227 Jason Kapono -0.80 -1.74 -1.27 226 Tyrus Thomas -2.30 0.14 -1.08 225 Andray Blatche -1.70 -0.41 -1.06 224 Spencer Hawes -0.90 -1.08 -0.99 223 Joel Anthony -3.30 1.34 -0.98 222 Charlie Bell -0.90 -0.98 -0.94 221 Rafer Alston -0.80 -0.98 -0.89 220 Trevor Ariza -1.40 -0.32 -0.86 219 Tyreke Evans -2.10 0.46 -0.82 218 Kurt Thomas -1.80 0.18 -0.81

Here are the results for the defense:

```
ezPM vs. RAPM (3-YR Defense)

lm(formula = DEF_RAPM ~ D100, data = def, weights = POSS)
Residuals:    Min      1Q  Median      3Q     Max
-392.80  -51.15    6.09   61.18  372.19
Coefficients:            Estimate Std. Error t value Pr(>|t|)
(Intercept)  1.02475    0.08468   12.10   <2e-16 ***
D100         0.54199    0.04460   12.15   <2e-16 ***
---Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 102.1 on 381 degrees of freedom
Multiple R-squared: 0.2793,	Adjusted R-squared: 0.2774
F-statistic: 147.7 on 1 and 381 DF,  p-value: < 2.2e-16```

Once again the results are statistically significant (p<2.2e-16) and, perhaps, somewhat surprisingly, the R^2 value of 0.28 is only slightly lower than for the offense. This tells me that we are capturing quite a bit of the same defensive contributions as RAPM. To wrap it up, here are tables for the top and bottom players averaged by the two metrics (unfortunately, you will notice that \$15M-man David Lee shows up on the less preferred of the two lists):

### Top 20 Defensive Players (> 5000 possessions)

 RANK NAME DEF_RAPM DEF_ezPM AVG 1 Kevin Garnett 6.2 2.49 4.35 2 Dwight Howard 3.0 3.87 3.44 3 LeBron James 3.8 2.6 3.20 4 Andrew Bogut 4.1 1.88 2.99 5 Tim Duncan 3.5 2.08 2.79 6 Josh Smith 3.8 1.48 2.64 7 Gerald Wallace 3.0 2.19 2.60 8 Marcus Camby 3.0 2.03 2.52 9 Andrei Kirilenko 2.6 1.88 2.24 10 Ron Artest 3.2 0.88 2.04 11 Ben Wallace 2.5 1.37 1.94 12 Lamar Odom 3.4 0.38 1.89 13 Thabo Sefolosha 2.5 0.98 1.74 14 Kurt Thomas 2.6 0.85 1.73 15 Luol Deng 2.8 0.61 1.71 16 Trevor Ariza 2.1 1.29 1.70 17 Manu Ginobili 1.6 1.53 1.57 18 Tyrus Thomas 1.6 1.43 1.52 19 Anderson Varejao 2.1 0.81 1.46 20 James Harden 2.0 0.9 1.45

### Bottom 20 Defensive Players (> 5000 Possessions)

 RANK NAME DEF_RAPM D100 AVG 237 Andrea Bargnani -3.1 -3.07 -3.09 236 Aaron Brooks -1.8 -3.86 -2.83 235 Charlie Villanueva -2.8 -2.75 -2.78 234 Kevin Martin -3.8 -1.72 -2.76 233 Will Bynum -1.8 -3.47 -2.64 232 Jason Kapono -1.1 -3.98 -2.54 231 D.J. Augustin -0.8 -4.15 -2.48 230 JaVale McGee -1.7 -3.17 -2.44 229 Jason Maxiell -1.2 -3.61 -2.41 228 Spencer Hawes -1.6 -3.01 -2.31 227 Goran Dragic -1.1 -3.5 -2.30 226 Jose Calderon -1.7 -2.67 -2.19 225 Jeff Green -2.2 -2.14 -2.17 223 Antoine Wright -0.9 -3.43 -2.17 224 Jonny Flynn -1.6 -2.73 -2.17 222 J.J. Hickson -2.6 -1.63 -2.12 221 David Lee -1.9 -2.31 -2.11 220 Devin Harris -1.1 -3.03 -2.07 219 Ben Gordon -2.1 -1.99 -2.05 218 Maurice Evans -1.5 -2.52 -2.01

## ezPM Data

Take a look at the sidebar on the left. See anything different? That would be a .csv data file containing all the raw and calculated ezPM stats. Do with it what you will (within the constraints of the CC license, of course).

## In Defense of Counterpart Defense

(Before reading this post, make sure you have read my method for implementing counterpart defense.)

The goal for any player valuation metric is — or arguably, should be — that it estimates the player’s “true” value independent of his teammates. The player’s individual or inherent value may change from year to year due to numerous factors, for example, aging or injuries. Ideally, though, the metric will be able to do two things: 1) separate the player from his teammates and 2) have predictive value.

Predictive value is often thought primarily of as y-t-y correlation. It can also be instructive to look at player value when he switches teams during the season. This is about as close to a control experiment as we can get in the NBA, because most trades tend to involve role players who won’t significantly change the team ratings (shhh, don’t tell the GM’s). Also, in-season trades usually take place without as much accompanying personnel change as compared to y-t-y. (And even if you don’t buy these arguments, I think the following data will probably win you over, anyway.)

With the above thought process serving as underlying motivation, I wanted to look at the correlation of the new counterpart defensive component for players who were traded in-season in 2009. I found 24 players who met my pt threshold of 400 possessions with each team. Here are those players with their associated teams:

 NAME Rafer Alston (MIA, NJN) Steve Blake (POR, LAC) Caron Butler (DAL, WAS) Marcus Camby (LAC, POR) Michael Finley (BOS, SAS) Drew Gooden (LAC, DAL) Brendan Haywood (WAS, DAL) Larry Hughes (CHA, NYK) Kris Humphries (DAL, NJN) Stephen Jackson (GSW, CHA) Antawn Jamison (CLE, WAS) Jared Jeffries (NYK, HOU) Carl Landry (HOU, SAC) Kevin Martin (HOU, SAC) Eric Maynor (UTA, OKC) Flip Murray (CHA, CHI) Travis Outlaw (LAC, POR) Nate Robinson (NYK, BOS) Sergio Rodriguez (SAC, NYK) Quinton Ross (DAL, WAS) Tyrus Thomas (CHI, CHA) Al Thornton (WAS, LAC) Hakim Warrick (CHI, MIL) Eddie House (BOS, NYK)

### Individual Defensive Ratings vs. Team Ratings

Let’s look at how individual defensive ratings change as a function of change in the overall team rating before and after the trade. Team defensive ratings were gathered from basketball-reference.com. First up is the new D100 component of ezPM that incorporates counterpart defense. I should note that all regressions were done in R. For this first one, I will show the regression summary, so I can explain what values I’m looking at:

```Call:lm(formula = DELCP ~ DELTM, data = stats)
Residuals:    Min      1Q  Median      3Q     Max
-3.3559 -1.7102  0.3003  1.3137  3.7608
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.14417    0.39013  -2.933   0.0077 **
DELTM       -0.15877    0.08844  -1.795   0.0864 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.9 on 22 degrees of freedom
Multiple R-squared: 0.1278,	Adjusted R-squared: 0.08814
F-statistic: 3.223 on 1 and 22 DF,  p-value: 0.08635```

The important values here are the regression coefficient (-0.15877) and the p-value (0.08635), which is normally not considered statistically significant. The coefficient tells us that for every 1 point increase in DRTG, the player’s D100 decreases by about 0.16 pts. In other words, a player switching to a worse defensive team will have a slightly worse D100 rating. But it’s not even statistically significant. Here’s a plot of the data (click to enlarge):

Now, let’s take a look at what happens when we correlate the original D100 component of ezPM that splits credit among teammates:

For this regression, the slope is -0.144 and the p-value is 0.0515, just on the cusp of significance. The R^2 for this regression is 0.1616 compared to 0.1278. I hope you see the significance of this result. The D100 rating with counterpart incorporated is just a bit more separable from the teammate split. I assume at this point, some of you may be wondering what’s the point of all this.

For those folks, look at this plot:

This is the change in the player’s “individual” DRTG as a function of the team DRTG. Recall — or learn for the first time — that DRTG is a component of Win Shares (see basketball-reference), which is a player metric based on the work of Dean Oliver. You’re wondering about the regression? The p-value is 1.46e-13. Uh, yeah, it’s significant. The R^2 is 0.9202, which means that about 92% of the individual DRTG change is explained by the change in team DRTG. NOW DO YOU GET IT? Ok, to spell it out, the defensive component of ezPM100 (even with the split in place) does a much better job of separating player value from his teammates. That was goal #1.

### Split vs. Counterpart D100 as a Predictor

Let’s move on to goal #2, which is to have the best predictive power. We’ve already ruled out individual DRTG as a predictor, since it is almost completely tied to team rating. Therefore, we will simply focus on whether split or counterpart D100 is a better predictor. What that means is that we will correlate the player’s split or counterpart D100 before and after the trades:

You can probably eyeball it, but for the D100 with counterparts, the p-value is 0.00628 (significant). The p-value for split credit is 0.0883 (not significant). The R^2 for counterpart D100 is 0.2933 compared to 0.1263 for split credit.

### Conclusions

As stated at the top, a good metric should aim to separate player value from team value and be a good predictor. I think the data presented here present a fairly strong case that the counterpart defensive rating in ezPM is better than splitting value, and that it is better than the individual DRTG as used in Win Shares — and by extension, probably most team-based defensive metrics. If you’ve been following the development of ezPM, this is probably a) not surprising and b) still reassuring. In a future post, I will try to do the same type of analysis for offense. I think I will also add more trade data from previous seasons, and the current season when it’s (finally) over.

## Picking The Eastern All-Star Reserves

This list might be a little more controversial than the last. Ronnie Brewer appears in the table below because he has over 2000 possessions (which was my playing time filter) and he’s had a good season. But he’s not a starter, so he gets an “N” for “No, I wouldn’t pick him.” But he’s having a good season. Did I say that already?

Kris Humphries — aka Kim Kardashian’s latest boy toy — doesn’t make the list because he’s a one-dimensional rebounder, and picking him would have meant leaving Rondo off the team. You wouldn’t like me if I did that, right? (And between you and I, Humphries probably has better plans for that weekend. At least, I know who what I’d be doing.)

The “controversial” picks are obviously Iggy and Joe Johnson. Both make the team because of their defense. That’s something you won’t see other box score metrics pick out, because they don’t take into account counterparts. If you’re wondering why all the “trade Iggy” talk has died down lately, it might be that Philly realizes his worth while they’re making a playoff run.

So, who’s left off the list? Ray Allen (3.42) just misses, but with Pierce, Rondo, and Garnett, I mean, they can’t have it all, right? That would be unfair. And that team is unfair enough (to the rest of the league). After Allen, it’s a trio of “B’s” (who happen to be bigs):  Bogut (3.21), Brand (2.99), and Bosh (2.71).

Note the RANK is the overall NBA rank (for players with > 2000 possessions).

 RANK NAME MAKE? TEAM POSITION POSSESSIONS ezPM100 O100 D100 REB100 OeFG OWN OEFF USG ORR DRR 2 Paul Pierce Y BOS 3 2942 5.98 4.12 2.10 -0.25 47.82% 23.49 16.97 24.28% 10.53% 82.94% 5 Andre Iguodala Y PHI 2.5 2410 4.93 1.56 2.39 0.97 50.74% 16.56 7.63 20.51% 23.61% 86.26% 7 Ronnie Brewer N CHI 2.5 2029 4.82 -0.44 4.38 0.88 48.19% 20.50 -3.10 14.29% 25.93% 86.30% 9 Al Horford Y ATL 4.5 2893 4.41 2.81 1.58 0.02 50.40% 21.60 13.58 20.69% 29.72% 70.78% 10 Kevin Garnett Y BOS 4 2144 4.28 1.12 3.10 0.05 51.32% 18.14 5.19 21.56% 20.45% 77.88% 11 Kris Humphries N NJN 4.49 2241 4.06 -0.22 0.38 3.90 53.73% 22.18 -1.34 16.23% 43.93% 81.27% 14 Landry Fields Y NYK 2.01 2880 3.89 1.22 1.36 1.31 49.91% 21.22 9.06 13.44% 32.49% 87.34% 15 Joe Johnson Y ATL 2 2560 3.81 1.75 2.10 -0.04 45.42% 18.83 6.04 28.96% 20.92% 77.50% 16 Rajon Rondo Y BOS 1 2477 3.76 1.15 1.40 1.22 48.67% 20.91 4.94 23.18% 40.83% 84.09%

## Picking the Western All-Star Reserves

The All-Star reserves will be announced tonight on TNT, so I got to get my picks in. I’ll do the West now, and the East before tonight’s announcements are made.

## Western Reserves

The rank is the overall NBA rank. I would pick Williams as the fifth guard over Randolph as the fifth big. The “snubs”? Gay (3.49), Hilario (3.41), Chandler (3.39), Gordon (3.35), Duncan (3.26), West (3.12), Okafor (3.04), Kirilenko (2.99), Parker (2.86), Miller (2.70), Martin (2.40), Aldridge (2.01), Westbrook (1.95).

I know that if Westbrook doesn’t make the team, he will be considered the biggest snub. I like Westbrook. But I have to say, it doesn’t seem like there is a very strong statistical case for him.

As for Monta Ellis’ case, his ezPM is 0.90. In fact, he comes in just behind Dorell Wright at 1.00.

 RANK NAME MAKE? TEAM POSITION POSSESSIONS ezPM100 O100 D100 REB100 OeFG OWN OEFF USG ORR DRR 1 Kevin Love Y MIN 4.5 3381 6.41 2.02 -0.18 4.56 54.57% 22.12 8.27 24.45% 50.65% 79.00% 3 Steve Nash Y PHX 1 2757 5.94 7.14 -1.47 0.27 47.23% 19.44 24.59 29.02% 18.46% 85.71% 4 Manu Ginobili Y SAS 2.5 2852 5.61 3.84 1.81 -0.03 54.27% 19.00 14.14 27.12% 19.64% 82.04% 6 Pau Gasol Y LAL 4.5 3259 4.90 2.04 2.15 0.71 53.05% 18.04 8.84 23.08% 40.38% 64.68% 8 Lamar Odom Y LAL 4 2919 4.68 2.48 2.09 0.11 48.88% 20.97 12.19 20.33% 30.64% 70.98% 12 Blake Griffin Y LAC 4 3249 4.04 0.47 0.67 2.90 52.00% 21.05 1.66 28.43% 45.38% 73.17% 13 Zach Randolph N MEM 4 3018 3.93 -0.10 0.00 4.03 57.13% 18.95 -0.39 26.09% 49.77% 75.83% 17 Deron Williams Y UTA 1 3133 3.74 5.13 -1.33 -0.06 50.00% 21.29 16.75 30.63% 20.41% 79.65%

## Throw Logic Out The Window: John Wall Named East Rookie of the Month in January

Landry Fields won ROM in November and December. John Wall just got the award in January. I’m not sure why. My rankings actually show him as the absolute worst rookie (with > 200 possessions). Fields would have been the better choice, though he is cooling off. Paul George has been coming on strong as a reserve. (Could be the beginning of the end for Granger in IND, eh?)

In the West? Blake Griffin. They got it right. (Phew!) And he’s getting better as the season goes on. DeMarcus Cousins is playing a lot better now, too. His season average ezPM100 is close to -4.5.

Oh, and I can’t do this without mentioning Cleveland. Manny Harris is holding his own actually. They should probably hold onto him. Samardo Samuels and Christian Eyenga, though, not so much. Did LeBron really cause all this?

 RANK NAME TEAM #POSS POS ezPM100 O100 D100 REB100 OeFG OWN OEFF USG ORR DRR 1 Paul George IND 404 2.98 7.71 2.64 3.95 1.13 40.26% 27.23 13.09 20.15% 22.22% 89.19% 2 Blake Griffin LAC 970 4 5.81 1.26 1.33 3.21 49.42% 21.55 4.21 30.07% 41.18% 76.87% 3 Eric Bledsoe LAC 439 1 3.68 -2.73 4.63 1.78 40.23% 23.23 -13.56 20.15% 38.10% 86.36% 4 Landry Fields NYK 953 2.01 3.10 1.73 0.91 0.46 51.78% 22.98 13.91 12.43% 24.18% 87.32% 5 Patrick Patterson HOU 404 4 2.20 0.24 0.92 1.04 50.00% 24.26 1.52 15.87% 40.00% 63.83% 6 Ed Davis TOR 657 3.99 2.07 2.39 -1.86 1.54 59.86% 28.46 21.01 11.39% 41.84% 67.86% 7 Trevor Booker WAS 253 3.99 1.79 1.41 -1.75 2.14 56.94% 35.18 8.68 16.18% 53.13% 60.71% 8 Greg Monroe DET 842 5 1.59 1.76 0.10 -0.27 59.21% 23.28 11.97 14.67% 39.85% 56.25% 9 Omer Asik CHI 311 5 1.11 -3.36 3.68 0.79 51.35% 21.54 -23.90 14.07% 46.15% 65.22% 10 Evan Turner PHI 618 2 0.87 -0.80 1.07 0.60 47.75% 21.84 -4.29 18.62% 10.42% 88.71% 11 DeMarcus Cousins SAC 842 4.98 0.44 -3.58 2.31 1.71 52.31% 20.55 -10.57 33.86% 41.35% 67.59% 12 Derrick Favors NJN 553 4 0.42 -1.47 1.28 0.61 51.04% 26.22 -8.44 17.42% 40.96% 61.29% 13 Al-Farouq Aminu LAC 412 3.01 -0.31 -5.39 2.94 2.14 49.33% 22.57 -25.86 20.85% 38.46% 79.31% 14 Manny Harris CLE 729 1.98 -0.32 -0.35 -2.19 2.23 58.06% 20.30 -1.81 19.60% 33.90% 93.75% 15 Gary Neal SAS 614 2 -0.69 -0.48 0.41 -0.62 47.62% 21.34 -2.50 19.08% 15.00% 76.92% 16 Gordon Hayward UTA 282 2.99 -1.60 -1.49 -0.47 0.36 56.12% 21.63 -9.05 16.45% 33.33% 63.64% 17 Wesley Johnson MIN 577 2.01 -1.68 -2.01 0.48 -0.15 58.95% 20.80 -10.28 19.57% 16.00% 71.88% 18 Nikola Pekovic MIN 326 4.98 -2.26 -1.81 -1.14 0.69 51.22% 23.01 -10.04 18.02% 37.50% 60.71% 19 Larry Sanders MIL 217 4.49 -2.48 -1.92 -1.51 0.95 64.71% 28.57 -9.17 20.94% 35.14% 66.67% 20 Ekpe Udoh GSW 311 4.01 -3.37 -0.40 0.59 -3.56 57.41% 27.01 -2.94 13.76% 28.57% 44.44% 21 Quincy Pondexter NOH 270 3.01 -3.62 -2.01 -0.71 -0.91 51.72% 27.78 -14.91 13.47% 23.53% 66.67% 22 Greivis Vasquez MEM 459 1.01 -5.08 -0.91 -3.77 -0.40 50.60% 25.05 -4.44 20.38% 11.54% 79.17% 23 Luke Harangody BOS 273 3.5 -5.44 -3.00 -2.12 -0.33 53.64% 27.84 -22.39 13.38% 33.33% 65.71% 24 Eugene Jeter SAC 470 0.99 -5.64 -0.71 -4.50 -0.43 52.91% 22.98 -3.91 18.03% 8.33% 83.33% 25 Samardo Samuels CLE 409 4.49 -5.66 -4.33 -0.82 -0.51 55.80% 23.96 -21.76 19.91% 35.29% 54.35% 26 Christian Eyenga CLE 551 1.99 -6.78 -4.34 -1.78 -0.66 55.61% 25.59 -24.43 17.75% 23.40% 69.23% 27 Gary Forbes DEN 234 3.99 -7.90 -3.25 -5.10 0.46 65.12% 25.21 -13.96 23.31% 28.57% 68.42% 28 John Wall WAS 1055 1 -8.37 -1.49 -6.37 -0.51 60.53% 22.84 -5.38 27.78% 8.77% 81.43%

## Does Tim Duncan Still Have “The Stats”?

I (literally) just read an article “debating” whether Tim Duncan will or should make the All-Star team. I immediately had a sense of deja vu. According to the author, Brian Mahoney:

Tim Duncan’s championship credentials will someday mandate a spot in the Hall of Fame.

“He’s a pillar, one of the few pillars of this league,” Houston’s Shane Battier said.

One who is having a mediocre season statistically, the kind that would normally warrant a long weekend off next month.

Duncan barely cracks the top 20 in scoring among a stellar class of Western Conference forwards. So as coaches submit their ballots this week for All-Star reserves, they’ll have to look elsewhere if they choose to consider Duncan for a 13th straight appearance.

Huh. What exactly does Mr. Mahoney mean when he says “mediocre season”? He goes on to mention Duncan’s career low 13.6 points per game and 9.4 rebounds in “only 29 minutes” per game. Here, “only” is used as a derogatory modifier, not because it would make those numbers appear more impressive. Now, I cannot argue with Mr. Mahoney about his facts. Those are career lows. But if we look at the totality of Duncan’s game this season, the case is quite strong for him making the All-Star team. Here are my latest rankings with the new defensive counterpart data incorporated (player with > 2000 possessions):

 RANK NAME TEAM POSITION ezPM100 O100 D100 REB100 OEFF USG ORR DRR 1 Dwight Howard ORL 5 7.57 -0.39 4.51 3.45 -1.32 29.40% 46.24% 77.54% 2 LeBron James MIA 3.5 7.04 3.98 3.32 -0.26 11.18 35.61% 19.54% 77.08% 3 Chris Paul NOH 1 6.59 6.32 0.22 0.04 24.07 26.27% 14.29% 82.72% 4 Dwyane Wade MIA 2 6.07 3.03 1.13 1.90 9.00 33.68% 38.51% 87.50% 5 Steve Nash PHX 1 5.93 6.97 -1.41 0.37 23.95 29.12% 18.75% 86.36% 6 Kevin Love MIN 4.5 5.90 1.61 -0.38 4.67 6.50 24.73% 51.40% 78.66% 7 Kobe Bryant LAL 2 5.78 2.56 1.94 1.29 6.91 36.99% 29.41% 84.51% 8 Paul Pierce BOS 3 5.45 4.18 1.51 -0.24 17.51 23.89% 9.46% 83.48% 9 Manu Ginobili SAS 2.5 5.41 3.45 1.99 -0.03 12.69 27.18% 19.14% 82.50% 10 Pau Gasol LAL 4.5 5.25 2.32 2.40 0.53 10.03 23.13% 39.79% 64.46% 11 Tim Duncan SAS 4.5 5.06 -0.19 3.24 2.02 -0.83 23.10% 39.30% 74.37% 12 Lamar Odom LAL 4 4.75 2.47 2.25 0.03 12.12 20.35% 29.57% 71.16% 13 Kris Humphries NJN 4.49 4.28 -0.16 0.31 4.12 -0.98 16.21% 45.16% 81.54% 14 Landry Fields NYK 2.01 4.22 0.95 1.73 1.54 7.07 13.44% 33.33% 89.04% 15 Al Horford ATL 4.5 4.17 2.49 1.91 -0.23 11.61 21.45% 29.74% 69.51% 16 Rajon Rondo BOS 1 3.96 1.32 1.36 1.28 5.81 22.71% 43.00% 83.64% 17 Andre Iguodala PHI 2.5 3.95 0.97 2.13 0.86 4.68 20.67% 20.61% 86.98% 18 Zach Randolph MEM 4 3.88 -0.42 0.28 4.02 -1.62 25.94% 49.49% 75.98% 19 Blake Griffin LAC 4 3.79 0.20 0.54 3.05 0.70 28.63% 46.57% 73.18% 20 Nene Hilario DEN 4.51 3.78 4.29 0.91 -1.42 22.43 19.15% 22.26% 67.97%

Similar to Dwight Howard, Duncan does his damage on defense and on the glass. But aren’t those really, really important? I think Blake Griffin is great. But this season…if you ask me who I’d rather have to help me win games, it would still be Duncan. Same as it ever was. (Ok, not quite the same, but pretty much.)

## ezPM v.2.0: Incorporating Counterpart Defense or “The Biggie”

This is going to be epic, so pull up a comfy chair.

Anybody who knows anything about basketball metrics knows that there are two major areas of improvement sought: 1) defense; and 2) “the little things”. Unfortunately, play-by-play data doesn’t really tell us much about “the little things”, but it can tell us something about defense. Currently, ezPM distributes credit or blame equally among teammates when the defense denies a bucket or allows one, respectively. The formula looks like this:

$DEF = 1.06*STL+OFT_PTS-0.2*(2-1.06)*OPP_2PTM-0.2*(3-1.06)*OPP_3PTM+1.06*0.74*0.2* OFG_MISS+0.2*1.06*TEAM_TAKE+1.06*0.74*BLK$

All the terms with “0.2” represent distributed credit/blame (for opponent 2pt FG, 3pt FG, missed FG, and non-steal turnovers). Because credit/blame is distributed equally, some players won’t get the credit they deserve, and other players will get more credit than they deserve for defense.

To begin to address this, I modified “the code” to keep track of the counterpart data for shots and assists. Once the data are collected, we can then modify the formula for defense. Here’s one way to do it (perhaps, the most obvious way):

$DEF' =1.06*STL+OFT_PTS-(2-1.06)*AFG2CP-(3-1.06)*AFG3CP-(2-1.06)*UFG2CP-(3-1.06)*UFG3CP+1.06*0.74*CPMISS+0.5*0.2*1.06*TEAM_TAKE+0.5*1.06*TOVCP+1.06*0.74*BLK$

Here, I’ve made no distinction between assisted and unassisted field goals. The “CP” refers to “counterpart”. Note that now every term, except for “TEAM_TAKE” (50% weight to non-steal opponent turnovers), is attributed to an individual counterpart. In theory, this should enable more accurate player valuation.

An alternative to the above formula that is worth considering is to distinguish between assisted and unassisted field goals, just as we do for offense:

$DEF''=1.06*STL+OFT_PTS-0.3*(2-1.06)*AST2CP-0.3*(3-1.06)*AST3CP-0.7*(2-1.06)*AFG2CP-0.7*(3-1.06)*AFG3CP-(2-1.06)*UFG2CP-(3-1.06)*UFG3CP+1.06*0.74*CPMISS+0.5*0.2*1.06* TEAM_TAKE+0.5*1.06*TOVCP+1.06*0.74*BLK$

Here, just as for the offense, I’ve split blame between the defender who “gives up” the assist and the one who allows the made field goal.

Now, it’s time to look at some of the results. Here are the top defenders as defined by $DEF'$ (greater than 1500 possessions):

$D100' = DEF'*100/POSSESSIONS$

 RANK NAME TEAM POSITION D100’ 1 Ronnie Brewer CHI 2.5 3.95 2 Dwight Howard ORL 5 3.70 3 Andrew Bogut MIL 5 3.43 4 Rajon Rondo BOS 1 3.24 5 Tim Duncan SAS 4.5 3.01 6 Anderson Varejao CLE 4.5 2.80 7 LeBron James MIA 3.5 2.74 8 Chris Paul NOH 1 2.67 9 Tony Parker SAS 1 2.65 10 Andre Miller POR 1.02 2.59 11 Kevin Garnett BOS 4 2.57 12 Eric Bledsoe LAC 1 2.55 13 Rudy Gay MEM 3 2.55 14 Jason Kidd DAL 1 2.46 15 Marc Gasol MEM 4.98 2.40 16 Jose Barea DAL 1.02 2.40 17 C.J. Miles UTA 4.5 2.15 18 Jodie Meeks PHI 1.98 2.11 19 George Hill SAS 1.01 2.06 20 Derrick Rose CHI 1 2.04 21 Luol Deng CHI 3 2.03 22 Taj Gibson CHI 4 2.00 23 Pau Gasol LAL 4.5 2.00 24 Andrei Kirilenko UTA 1.99 1.99 25 Tracy McGrady DET 2.51 1.89

Note that the average position for the top 25 above is 2.56 (between SG and SF). Here are the 10 players who improve the most with $DEF'$ over the original defense formula:

 RANK NAME TEAM POSITION DIFF’ 1 Jose Barea DAL 1.02 2.61 2 Anderson Varejao CLE 4.5 2.43 3 Rodney Stuckey DET 1.5 2.24 4 Steve Nash PHX 1 2.05 5 Jodie Meeks PHI 1.98 1.91 6 Eric Bledsoe LAC 1 1.80 7 Tony Parker SAS 1 1.74 8 Ty Lawson DEN 1 1.51 9 Nenad Krstic OKC 5 1.51 10 Brandon Rush IND 2 1.51

I was not expecting Steve Nash to be helped by counterpart defense. I suspect my readers share my surprise. Moving on, here are the 10 players hurt the most by $DEF'$:

 RANK NAME TEAM POSITION DIFF’ 178 Charlie Villanueva DET 4 -2.71 177 Steve Blake LAL 1.01 -2.44 176 DeJuan Blair SAS 4.02 -2.23 175 Joakim Noah CHI 4.99 -2.18 174 Nicolas Batum POR 3 -1.95 173 Brandon Jennings MIL 1 -1.88 172 Amare Stoudemire NYK 4 -1.69 171 Reggie Williams GSW 3.01 -1.64 170 Dirk Nowitzki DAL 4.02 -1.55 169 Paul Millsap UTA 4 -1.51

Noah? That was not expected.

Let’s look at what happens when we take into account assists. Here are the top 25 defenders according to $DEF''$:

$D100' = DEF''*100/POSSESSIONS$

 RANK NAME TEAM POSITION D100’’ 1 Ronnie Brewer CHI 2.5 4.78 2 Dwight Howard ORL 5 4.51 3 Andrew Bogut MIL 5 3.59 4 LeBron James MIA 3.5 3.32 5 Tim Duncan SAS 4.5 3.24 6 Kevin Garnett BOS 4 2.97 7 Rudy Gay MEM 3 2.95 8 Anderson Varejao CLE 4.5 2.86 9 Taj Gibson CHI 4 2.79 10 Marc Gasol MEM 4.98 2.77 11 Josh Smith ATL 4 2.75 12 C.J. Miles UTA 4.5 2.65 13 Andrei Kirilenko UTA 1.99 2.47 14 Trevor Ariza NOH 3 2.40 15 Pau Gasol LAL 4.5 2.40 16 Elton Brand PHI 4.5 2.32 17 Luol Deng CHI 3 2.31 18 Ben Wallace DET 4.99 2.31 19 Lamar Odom LAL 4 2.25 20 Jodie Meeks PHI 1.98 2.24 21 Tracy McGrady DET 2.51 2.24 22 Gerald Wallace CHA 3.5 2.18 23 Andre Iguodala PHI 2.5 2.13 24 Corey Brewer MIN 2.5 2.10 25 Glen Davis BOS 3.99 2.04

The average position here is 3.7 (between SF and PF). Maybe I’m crazy, but this actually makes more sense to me than the first metric, as big guys do tend to have more impact on defense — at least, that’s the conventional wisdom, right?

Here are the 10 players who improve the most:

 RANK NAME TEAM POSITION DIFF’’ 1 Anderson Varejao CLE 4.5 2.49 2 Jodie Meeks PHI 1.98 2.03 3 Nenad Krstic OKC 5 1.80 4 Kobe Bryant LAL 2 1.75 5 Landry Fields NYK 2.01 1.75 6 Joe Johnson ATL 2 1.65 7 Tayshaun Prince DET 3 1.58 8 Brandon Rush IND 2 1.58 9 Dwight Howard ORL 5 1.54 10 Lamar Odom LAL 4 1.40

And here are the players who lose the most with $DEF''$:

 RANK NAME TEAM POSITION DIFF’’ 1 Steve Blake LAL 1.01 -4.29 2 John Wall WAS 1 -3.90 3 Brandon Jennings MIL 1 -3.87 4 Derek Fisher LAL 1 -3.67 5 Ramon Sessions CLE 1.01 -3.22 6 Raymond Felton NYK 1 -3.11 7 Devin Harris NJN 1 -2.98 8 Mike Conley MEM 1 -2.93 9 Mike Bibby ATL 1.01 -2.90 10 Chris Paul NOH 1 -2.81

All point guards on this list. Now, the interesting thing is that I’m not sure that’s bad. Why? Because ezPM appeared to have a preference for point guards before. Why? For the same reason that point guards appear on this list. They get a lot of credit for assists, but don’t get debited for “missing” assists (or potential assists, which aren’t recorded). It’s sort of a win-win situation for point guards. So, in a way, you can think of this as a defensive correction.

Anyway, there are some really interesting questions that can and should be raised. I’ll leave you with this particular question. We know, or at least, the conventional wisdom is that assisted field goals are “easier” to make. That’s why I give an assisted field goal 70% of the credit that an unassisted field goal would receive. This raises an important question: On the defensive side, should we give more or less credit for giving up an assisted or unassisted field goal? If the assisted field goal on offense was easier to make, it would seem to follow that the defender should be debited a little less, right? That would justify debiting the player guarding the passer as well as the one defending the shooter. On the other hand, one could make the argument that the defender enabled the counterpart to get open and in a position where he could be assisted. See where I’m going with this? These are not simple questions in my mind. But we’re getting somewhere now, I think. To be continued…obviously.

## More on Non-Steal Counterpart Turnovers

My last post suggested the idea of tabulating counterpart turnovers that are not the result of steals — in other words, not explicitly attributed to a particular player according to the box score (or play-by-play data). In the current iteration of ezPM, the credit for these turnovers are split amongst teammates. The question is whether we should, indeed, give some or all of the credit for these non-steal turnovers to their counterparts.

I went about trying to answer this question. First, I took the list of the top 50 players from the last post and calculated their rates for 2009. I restricted the comparison to players who had above average playing time (possessions), which left 36 players. Here are their ranks in ascending order by last season’s rank:

 NAME TEAM 2010 2009 Andrew Bogut MIL 19 3 Ersan Ilyasova MIL 32 5 D.J. Augustin CHA 21 7 C.J. Watson CHI 5 9 Brad Miller HOU 31 17 Ben Wallace DET 28 21 Jose Barea DAL 1 29 T.J. Ford IND 22 31 Mike Conley MEM 15 35 Jared Dudley PHX 46 37 Ty Lawson DEN 36 51 Josh Smith ATL 29 55 Spencer Hawes PHI 49 61 Brandon Jennings MIL 18 62 Channing Frye PHX 30 69 Luc Mbah a Moute MIL 42 80 Steve Nash PHX 25 83 Andrea Bargnani TOR 13 84 Jason Richardson PHX 41 86 Zydrunas Ilgauskas MIA 45 89 Serge Ibaka OKC 50 91 Beno Udrih SAC 11 114 Jameer Nelson ORL 24 119 Jason Thompson SAC 47 120 Emeka Okafor NOH 14 134 Kevin Love MIN 38 136 Anderson Varejao CLE 12 141 Rodney Stuckey DET 9 148 Shaquille O’Neal BOS 35 158 C.J. Miles UTA 27 159 Corey Brewer MIN 39 162 Joel Anthony MIA 48 164 Zach Randolph MEM 26 167 Hedo Turkoglu PHX 7 201 Amare Stoudemire NYK 40 206 Marcus Camby POR 20 215 AVERAGE 27.6 93

Recall that the ranks in the first column were from the top 50 players this season, so the average rank is obviously close to 25 (it would be exactly 25 if those 14 other players were not excluded). The average rank for these players in 2009 was 93 out of about 215 players, which is just a little bit better than what we might expect a random sample of 34 players to have, which suggests that the year-to-year correlation for this statistic is very low.

One might imagine that these non-steal counterpart turnovers are correlated to steal rates. Interestingly, there doesn’t appear to be any significant correlation:

Another thing to look at is whether the counterpart turnover rate is correlated to the currently calculated DEF100, which splits credit among teammates. Somewhat surprisingly, once again, I did not find any significant correlation:

Ok, so the case for counterpart turnovers being due to skill is so far very weak, if not non-existent. Is it even worth worrying about? The answer is probably not. If we look at DEF100 calculated with individuals getting full credit for counterpart turnovers or split amongst teammates, there is very little difference:

This was a good exercise. It may be that certain players are better at forcing non-steal turnovers (i.e. traveling, double-dribble, etc.), but I don’t think we’re going to capture it with the PBP data. Going forward, I think it makes sense to give 50/50 weight to teammates and counterparts. It won’t hurt, and it’s probably the safe middle ground.

## Single Game Prediction: CHA vs. GSW

Given the +/- for two teams, we can make some prediction about the probability of each side winning. For example, if each team has a +/- equal to zero, there is a 50/50 chance on each side of winning. In the NBA, there is a home court advantage (HCA), which amounts to roughly +3.34 pts per 100 possessions. Therefore, given two average teams (+/- = 0.0), the home side is predicted to be +3.34. This point differential equates to a win probability of approximately 60.3%, as follows:

$100*(3.34*2.54+41)/82$

The 2.54 comes from regressing wins on point differential, as I discussed in a previous post.

Let’s use this approach to calculate the win probabilities for tonight’s game against Charlotte. To do this, I’ve calculated ezPM100 data over the past month for both teams, figuring that recent play is probably more important than season average. (This could probably be improved by regressing the data to the mean, but I’ll leave that for another time.) I project how many possessions each player will have by calculating the percentage of team possessions they have used over the past month, and to make the math work out with the “win formula” above, I project the total +/- data for each team on to 100 possessions. Then I add in the HCA for the Warriors. Here are the results:

 NAME TEAM ezPM100 Projected #POSS Projected +/- D.J. Augustin CHA 4.75 73 3.46 Stephen Jackson CHA -2.73 73 -1.99 Boris Diaw CHA -2.79 68 -1.89 Kwame Brown CHA 0.81 56 0.45 Gerald Henderson CHA 0.37 50 0.19 Gerald Wallace CHA 2.07 41 0.86 Tyrus Thomas CHA -2.98 32 -0.97 Shaun Livingston CHA 2.25 32 0.72 Dominic McGuire CHA 6.27 20 1.27 Nazr Mohammed CHA -1.54 17 -0.26 Matt Carroll CHA 2.43 15 0.37 Eduardo Najera CHA -5.46 13 -0.69 Derrick Brown CHA 7.67 9 0.71 Sherron Collins CHA 30.85 1 0.18 TOTALS 56.84% 2.42 Monta Ellis GSW 1.20 89 1.06 Dorell Wright GSW 1.33 81 1.07 Stephen Curry GSW 3.27 67 2.20 David Lee GSW -2.79 65 -1.82 Andris Biedrins GSW -2.94 39 -1.14 Vladimir Radmanovic GSW -3.58 36 -1.29 Acie Law GSW 0.52 29 0.15 Reggie Williams GSW -8.94 29 -2.57 Ekpe Udoh GSW -1.27 24 -0.31 Louis Amundson GSW -7.32 21 -1.52 Brandan Wright GSW 4.96 9 0.47 Dan Gadzuric GSW 5.84 9 0.53 Rodney Carney GSW -7.50 2 -0.14 TOTALS 43.16% 0.21

### Win Probabilities

CHA 56.84%

GSW 43.16%

Projection: CHA wins

Let’s see how this works out.