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Ben F.
Joined: 07 Mar 2005
Posts: 390
Location: MD
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 Posted: Thu Aug 28, 2008 4:23 pm Post subject: Assist Scoring Bias? |
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We've talked about this before on the board, but I haven't really seen any larger investigation into it: the case of assist scoring bias. Since the assist is a decently subjective statistic, it depends who is scoring the game. Players may be scored very differently in different arenas, and that of course throws into question the utility of the assist as a descriptive statistic. Most fans don't really notice this, because there are few fans who are watching the play by play scoring of a game at the same time as the video itself. But in recent tracking I've come across large differences in the definition of an assist.
Take the example of a guard giving a simple bounce pass to a posted up big man. The big man will then turn and face, jab a couple of times, and pull up for a jumper. As long as he doesn't dribble, in some arenas that will be awarded as an assist to the passer. But that play doesn't square with our definition of what an assist should be: a play where the passer deserves some credit for the shot. That case is not very different from giving the ball to Kobe Bryant on the wing and then watching him break down his man off the dribble, which nobody would score an assist.
Another frequent case is whether an assist can be awarded with a dribble. Say LeBron James drives to the basket, draws the defense, kicks to Delonte West who pump fakes and then drives and hits a tough floater in the lane. Assist for LeBron or not? Some arenas will give the assist, some will not.
Seeing these differences got me interested in seeing if we can adjust for where a player is playing. If there is a consistently demonstrated effect in different arenas, we could account for this bias. (Using the term "bias" is not exactly accurate - I don't think most of the differences have to do with wanting to award assists to a specific team or a specific player more, instead the issue is with the definition of an assist. Still, "bias" is the most succinct term to describe the effect I'm talking about, so I will continue to use it.)
I decided the best first step to investigate this was to see if teams had higher rates of AST/FGM at home than away. This past year, the results were as follows:
| Code: | Team hAST% aAST% Diff
DEN 67.6% 54.8% 12.7%
BOS 66.6% 56.1% 10.6%
ATL 65.4% 55.5% 10.0%
POR 63.9% 54.0% 9.9%
LAC 66.3% 56.6% 9.7%
MIL 62.9% 53.3% 9.7%
CLE 59.9% 51.7% 8.2%
NOH 60.4% 52.4% 8.0%
DET 64.6% 57.3% 7.3%
LAL 64.8% 58.5% 6.2%
GSW 56.6% 51.0% 5.6%
PHI 57.3% 52.2% 5.1%
SAS 60.9% 55.9% 5.0%
NJN 69.7% 65.1% 4.6%
HOU 60.5% 56.5% 4.0%
WAS 55.3% 52.2% 3.1%
DAL 58.3% 55.3% 3.1%
MIN 54.3% 51.7% 2.6%
UTA 67.1% 64.9% 2.2%
TOR 62.0% 62.0% 0.0%
SEA 55.6% 56.3% -0.6%
CHI 60.1% 61.1% -1.0%
ORL 55.3% 56.3% -1.0%
IND 59.5% 60.7% -1.2%
CHA 57.8% 60.3% -2.5%
MEM 49.9% 53.1% -3.2%
MIA 56.2% 61.0% -4.7%
NYK 48.6% 54.6% -6.0%
SAC 48.1% 54.9% -6.9%
PHX 60.8% 68.3% -7.6%
hAST% = AST/FGM of team's offense while on home floor
aAST% = AST/FGM of team's offense while on an opposing floor |
The chart shows that a team like Phoenix has a 7.6% lower AST/FGM at home than on the road, and Denver has almost a 13% higher at home. The spread is quite large - certainly larger than I had anticipated. But it doesn't prove any kind of scorer bias, because perhaps these teams simply play differently at home than on the road. So the next question is to see if opponents visiting a team's arena saw the same effect. Here are last year's numbers:
| Code: | Team hAST% aAST% Diff
NJN 63.1% 58.3% 4.8%
DEN 65.2% 61.4% 3.9%
CLE 60.5% 56.7% 3.8%
LAL 59.1% 55.6% 3.5%
POR 58.4% 56.6% 1.8%
ATL 59.5% 57.7% 1.7%
MIL 61.6% 60.0% 1.5%
WAS 65.3% 64.6% 0.7%
LAC 59.2% 58.6% 0.6%
BOS 58.2% 57.7% 0.4%
GSW 59.4% 59.1% 0.3%
PHI 63.2% 63.6% -0.4%
MIN 61.1% 63.2% -2.1%
SEA 59.3% 62.0% -2.7%
NOH 57.2% 59.9% -2.8%
DET 55.9% 58.7% -2.8%
HOU 52.8% 55.7% -2.9%
TOR 58.1% 61.3% -3.2%
UTA 54.5% 57.9% -3.4%
CHI 58.4% 61.9% -3.5%
SAS 49.6% 54.6% -5.1%
IND 55.1% 62.5% -7.4%
MEM 54.0% 61.8% -7.9%
NYK 51.5% 59.7% -8.2%
DAL 49.0% 57.5% -8.5%
CHA 52.4% 62.0% -9.6%
SAC 54.9% 64.7% -9.8%
ORL 52.5% 62.9% -10.4%
PHX 42.5% 52.9% -10.4%
MIA 53.9% 66.1% -12.2%
hAST% = AST/FGM of team's opponent while on home floor
aAST% = AST/FGM of team's opponent while on an opposing floor |
So Miami's opponents have a 12% lower AST/FGM when in Miami than when Miami plays them on their home floor. New Jersey's opponents have about a 5% higher AST/FGM rate in NJN than not.
(What's also interesting about these defensive numbers is that the numbers are far more negative. This makes sense though - it shows that teams on the whole have a lower assist rate on the road that at home, most likely due to fatigue from traveling and the shorter turnaround from game to game while on the road. Overall it seems that teams have about a 3.1% lower AST/FGM on the road than at home.)
So is there any consistency across the two tables? Yes, a fair amount of it. The correlation between a team's offensive bias and a team's defensive bias is 0.83.
Let's dig a little deeper, though. What specific teams have a consistent bias one way or the other in both the offensive and defensive numbers?
First let's adjust for the 3.1% average difference between home and road. So we'll add 3.1% to all the defensive numbers and subtract 3.1% from the offensive numbers. Then we'll compare the two.
After adjustment, 16 of the 30 teams see an offensive bias that is within 3% of their defensive bias, indicating a fairly consistent effect. Another 10 teams are within 4%.
So what teams see the largest and smallest overall effect?
| Code: | Team Bias Diff
DEN 8.3% 2.7%
CLE 6.0% 1.8%
POR 5.9% 2.0%
ATL 5.9% 2.0%
MIL 5.6% 1.9%
BOS 5.5% 3.9%
LAC 5.1% 2.9%
LAL 4.9% 3.5%
NJN 4.7% 6.4%
GSW 3.0% 0.8%
NOH 2.6% 4.6%
PHI 2.4% 0.7%
DET 2.2% 3.9%
WAS 1.9% 3.8%
HOU 0.5% 0.7%
MIN 0.2% 1.5%
SAS 0.0% 3.9%
UTA -0.6% 0.6%
TOR -1.6% 2.9%
SEA -1.7% 4.1%
CHI -2.3% 3.7%
DAL -2.7% 5.4%
IND -4.3% 0.0%
MEM -5.5% 1.5%
ORL -5.7% 3.1%
CHA -6.1% 0.9%
NYK -7.1% 4.0%
SAC -8.3% 3.3%
MIA -8.5% 1.3%
PHX -9.0% 3.4%
Bias = average of offensive and defensive AST/FGM differences
Diff = the difference between a team's offensive bias and defensive bias |
This table indicates that when a team plays in Phoenix they get awarded 9% less AST/FGM than when they play on the road, but when playing in Denver they get awarded 8% more AST/FGM. The most consistent arena was Indiana, where both teams saw exactly a 4.3% lower AST/FGM rate in Conseco Fieldhouse than elsewhere.
"OK", you might be saying, "but to have me really believe it I'd want to see it for multiple years. Because if the bias exists like you say, it should withstand roster moves and only make a difference based on the people in the arena scoring the games."
That's a good point, so here is the data from two years ago:
| Code: | Team Bias Diff
NJN 7.1% 4.6%
LAL 6.6% 2.7%
GSW 5.6% 2.9%
LAC 4.5% 2.1%
DEN 4.1% 2.6%
MIL 4.1% 1.2%
BOS 3.4% 1.0%
PHI 3.3% 0.2%
DET 2.4% 0.7%
MIN 1.6% 3.6%
CLE 1.6% 0.9%
CHI 1.6% 0.4%
HOU 1.5% 4.9%
WAS 1.3% 1.2%
SEA 1.2% 2.7%
POR 1.1% 0.5%
TOR -0.4% 1.7%
SAS -0.4% 4.8%
DAL -1.0% 0.3%
UTA -1.3% 0.5%
ATL -2.2% 5.8%
CHA -2.3% 2.7%
NYK -2.7% 2.1%
IND -2.7% 2.7%
NOH -3.7% 4.0%
MEM -4.4% 2.9%
ORL -5.3% 3.7%
SAC -6.8% 0.9%
PHX -8.6% 2.2%
MIA -9.3% 5.1% |
There are some definite differences, but the order of those teams is remarkably similar. I'm particularly struck by Miami being about -9% each year, since they had strongly different rosters in the last two years.
I'm very interested in what everyone has to say about this. Do you think this is sufficient proof of an assist scoring "bias"? Do you think this is worth adjusting for when looking at assist based stats? Anything else you think could improve the reliability of estimating assist bias?
Last edited by Ben F. on Thu Aug 28, 2008 11:29 pm; edited 1 time in total |
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Ryan J. Parker
Joined: 23 Mar 2007
Posts: 685
Location: Raleigh, NC
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| Posted: Thu Aug 28, 2008 6:36 pm Post subject: |
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I'm tracking data from the 2008 playoffs, and over a small sample (I'm on game #10 now) I've seen game 1 of Boston vs Atlanta be very generous with assists, and I've seen game 2 of Toronto vs Orlando be very stingy with assists. I wouldn't, however, say there was any bias. I'd say they were just scored in different ways.
As for your method, this is a good way of looking at this I think. After a quick thought, it might be worthwhile to look and see if shot location varies to determine if there are specific inconsistencies with the way the assists are awarded and/or the way the teams are playing from arena to arena. I'm not sure that would be worth the effort but it might give some more insight.
Even assist "bias" aside (aka giving Nash more credit than he might deserve), it is also worth trying to discover the inherent difference between the way assists are scored from arena to arena (more specifically a "team" of scorers; are these scoring teams consistent for every game or do teams score in multiple locations)?
Clearly we can't have the same guy break down every shot to credit assists, but if we know the people behind each game maybe we can determine their self bias (or rather the way they determine how credit should be given).
I guess a question I have is, is there any way to know who scored games? That might prove beneficial.
I know I'm all over the place with this post, but lastly I'd also take a look at specific units of players to see if there is a bias. Every unit is going to play differently, so when you have different lineups used in each game we have to try and find something specific to look at. In this case games on a whole might not be best. |
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dsparks
Joined: 22 Feb 2008
Posts: 61
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| Posted: Thu Aug 28, 2008 8:03 pm Post subject: |
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This is a good idea that I've been meaning to check out for sometime. Thank you for being the catalyst. Looking at each game from 1986-08, I attempted to regress game location (factors) on visiting team as/fgm, controlling for home team quality (winning percentage), season (because I figured as/fgm might experience a secular change over time), and percent of made field goals that were three pointers (because these are assisted at a different rate than are F2Ms):
The results:
| Code: |
lm(formula = visitasfgm ~ location + homestrength + factor(gameseason) +
visit3pf)
Residuals:
Min 1Q Median 3Q Max
-0.431254 -0.064029 0.003417 0.067128 0.374519
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.837e-01 5.031e-03 116.026 < 2e-16 ***
locationBOS 3.947e-02 4.642e-03 8.503 < 2e-16 ***
locationCHA 4.363e-02 8.413e-03 5.185 2.17e-07 ***
locationCHH 9.897e-02 5.300e-03 18.673 < 2e-16 ***
locationCHI 8.803e-02 4.646e-03 18.948 < 2e-16 ***
locationCLE 8.921e-02 4.639e-03 19.229 < 2e-16 ***
locationDAL -2.292e-02 4.644e-03 -4.936 8.03e-07 ***
locationDEN 3.591e-02 4.640e-03 7.738 1.05e-14 ***
locationDET 2.532e-02 4.645e-03 5.451 5.07e-08 ***
locationGSW 3.400e-02 4.641e-03 7.325 2.46e-13 ***
locationHOU 3.143e-02 4.655e-03 6.753 1.48e-11 ***
locationIND 5.167e-02 4.641e-03 11.132 < 2e-16 ***
locationLAC 2.023e-02 4.649e-03 4.351 1.36e-05 ***
locationLAL 7.178e-02 4.663e-03 15.393 < 2e-16 ***
locationMEM 2.333e-02 6.701e-03 3.481 0.000500 ***
locationMIA -5.745e-03 4.763e-03 -1.206 0.227756
locationMIL 3.956e-02 4.640e-03 8.525 < 2e-16 ***
locationMIN 9.392e-02 4.841e-03 19.401 < 2e-16 ***
locationNJN 2.482e-02 4.641e-03 5.348 8.99e-08 ***
locationNOH 7.602e-02 8.406e-03 9.044 < 2e-16 ***
locationNOK -2.251e-02 1.144e-02 -1.968 0.049064 *
locationNYK 2.779e-02 4.641e-03 5.987 2.16e-09 ***
locationORL -3.393e-03 4.832e-03 -0.702 0.482555
locationPHI 3.143e-02 4.643e-03 6.770 1.32e-11 ***
locationPHO 6.634e-02 4.654e-03 14.256 < 2e-16 ***
locationPOR 3.496e-02 4.643e-03 7.530 5.27e-14 ***
locationSAC 2.335e-02 4.640e-03 5.031 4.91e-07 ***
locationSAS 2.827e-02 4.657e-03 6.070 1.29e-09 ***
locationSEA 1.581e-02 4.649e-03 3.401 0.000674 ***
locationTOR 4.608e-02 5.438e-03 8.474 < 2e-16 ***
locationUTA 1.088e-01 4.664e-03 23.332 < 2e-16 ***
locationVAN 7.584e-02 7.317e-03 10.365 < 2e-16 ***
locationWAS -1.904e-03 5.757e-03 -0.331 0.740832
locationWSB -9.489e-03 5.694e-03 -1.667 0.095600 .
homestrength 1.942e-03 4.345e-03 0.447 0.654936
factor(gameseason)1988 -4.013e-05 4.497e-03 -0.009 0.992880
factor(gameseason)1989 -1.611e-02 4.415e-03 -3.648 0.000265 ***
factor(gameseason)1990 -1.777e-02 4.342e-03 -4.092 4.29e-05 ***
factor(gameseason)1991 -2.198e-02 4.343e-03 -5.061 4.19e-07 ***
factor(gameseason)1992 -2.603e-02 4.347e-03 -5.989 2.14e-09 ***
factor(gameseason)1993 -1.512e-02 4.357e-03 -3.470 0.000522 ***
factor(gameseason)1994 -6.025e-03 4.366e-03 -1.380 0.167596
factor(gameseason)1995 -2.418e-02 4.469e-03 -5.411 6.32e-08 ***
factor(gameseason)1996 -3.270e-02 4.447e-03 -7.353 1.99e-13 ***
factor(gameseason)1997 -3.691e-02 4.466e-03 -8.266 < 2e-16 ***
factor(gameseason)1998 -2.523e-02 4.372e-03 -5.771 7.96e-09 ***
factor(gameseason)1999 -3.082e-02 4.941e-03 -6.239 4.48e-10 ***
factor(gameseason)2000 -3.255e-02 4.391e-03 -7.412 1.29e-13 ***
factor(gameseason)2001 -3.291e-02 4.398e-03 -7.484 7.43e-14 ***
factor(gameseason)2002 -3.668e-02 4.412e-03 -8.314 < 2e-16 ***
factor(gameseason)2003 -3.974e-02 4.425e-03 -8.981 < 2e-16 ***
factor(gameseason)2004 -3.800e-02 4.426e-03 -8.585 < 2e-16 ***
factor(gameseason)2005 -5.338e-02 4.427e-03 -12.058 < 2e-16 ***
factor(gameseason)2006 -7.072e-02 4.435e-03 -15.948 < 2e-16 ***
factor(gameseason)2007 -6.323e-02 4.463e-03 -14.169 < 2e-16 ***
factor(gameseason)2008 -6.718e-02 4.474e-03 -15.017 < 2e-16 ***
visit3pf 2.429e-01 9.540e-03 25.466 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.09764 on 24653 degrees of freedom
Multiple R-Squared: 0.132, Adjusted R-squared: 0.13
F-statistic: 66.96 on 56 and 24653 DF, p-value: < 2.2e-16
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The intercept estimates would appear to apply to teams visiting ATL in 1987, and the rest of the coefficients indicate difference from the intercept.
Here are the location coefficients in order of magnitude, without regard to significance:
| Code: |
locationUTA 0.108817646
locationCHH 0.098970521
locationMIN 0.093924373
locationCLE 0.089209815
locationCHI 0.088029529
locationNOH 0.076021971
locationVAN 0.075842199
locationLAL 0.071777463
locationPHO 0.066343463
locationIND 0.051668802
locationTOR 0.046080497
locationCHA 0.043626702
locationMIL 0.039560112
locationBOS 0.039472811
locationDEN 0.035906043
locationPOR 0.034959965
locationGSW 0.033995296
locationPHI 0.031432244
locationHOU 0.031430868
locationSAS 0.028268067
locationNYK 0.027786008
locationDET 0.025317975
locationNJN 0.024820167
locationSAC 0.023347566
locationMEM 0.023327291
locationLAC 0.020230792
locationSEA 0.015808264
locationATL 0.00 * intercept, so all other terms are relative to this.
locationWAS -0.001904240
locationORL -0.003392909
locationMIA -0.005744619
locationWSB -0.009489497
locationNOK -0.022513653
locationDAL -0.022922881
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I hope some of those with post-graduate degrees in statistics will assist me (no pun intended) with the interpretation of these results, but it appears to me that:
Utah is the easiest place for visiting teams to get credit for an assist. One possible implication is that Utah may have inflated all assist numbers, including those of John Stockton.
The two different names for Washington teams have very similar coefficients, which I think is a good thing as far as implications for this model's validity. I could have done this a lot more thoroughly, and combined those two, as well as looked at situations in different arenas (focusing on the building itself), but I didn't have that data, and I assumed that it's franchise philosophy, rather than physical location itself, that determines the variance.
Scorers in the Southeast (ORL, ATL, MIA) are stingy with assists.
Oddly enough, Ryan J. Parker's two cases, at Boston (in the top half) and at Orlando (toward the bottom), would appear to fit with the above results.
I welcome any comments or critiques.
_________________
David
http://arbitrarian.wordpress.com |
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Brian M
Joined: 25 Nov 2006
Posts: 40
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| Posted: Thu Aug 28, 2008 11:00 pm Post subject: |
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| For this sort of stuff I think it would be useful to have a supposedly more objective stats, like rebound rate or fg%, as controls. If assists are more subjective than those stats, and different locations score them differently, you should get an interaction such that only assists/fgm show an effect of location. |
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John Hollinger
Joined: 14 Feb 2005
Posts: 169
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| Posted: Tue Sep 02, 2008 12:03 am Post subject: |
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| Very interesting stuff. Another area to check is assists with regard to the point guards in particular. some home-team scorers seem to think it's their job to pad the PGs assist #s ... when Jason Williams was in Memphis it was fairly blatant, and I also witnessed first-hand (from about three seats away from the scorer) some absolutely ridiculous assists given to Chris Paul during the playoffs. My suspicion was that Hilton Armstrong doesn't get the benefit of the doubt on those, but it would be great topic to study, somehow. |
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Galen D
Joined: 26 Aug 2008
Posts: 1
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| Posted: Tue Sep 02, 2008 6:37 pm Post subject: |
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I think this is a really interesting line of pursuit. It amazes me that the differences are so large.
If anyone has the data, I would absolutely love to perform the same analysis on collegiate statistics. |
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Harold Almonte
Joined: 04 Aug 2006
Posts: 616
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| Posted: Tue Sep 02, 2008 7:27 pm Post subject: |
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| Would it be too much work, to split players's assists by location, and apply an adjust to them according to a league average bookepers's h/a biasing? |
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Sandy Weil
Joined: 19 Jun 2008
Posts: 20
Location: Boulder, CO
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| Posted: Tue Sep 02, 2008 11:48 pm Post subject: |
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In looking at dsparks regression results, I was struck by a few things.
(1) The coefficients for all the seasons were negative and almost all were significant. In 1987 (the year built into the constant term) and 1988 (coef is near zero), visiting teams were credited with assists on about 58% of made field goals. In every year since then, the percentage has been more like 51-56%. 1987 and 1988 are the high water mark in this data set and there is a general downward trend. I wonder how long ago this downward trend began. I'm going to bet that is didn't start in 1987.
(2) In looking at the annual data more closely, there is a drop-off between pre-2004 (coefs were consistently around 3%) and post-2005 (coefs are all between 5.3 and 7.1). An obvious interpretation of that is that the hand-check rules have had an effect on assist rates.
(3) I understand why the Charlotte Hornets scoring could be different from the New Orleans Hornets (new city, possibly new scorer). I'm not sure that this is a necessary change, but I can't argue against it. But it is not clear to me what is gained by keeping separate the two Washington coefficients.
(4) As you mentioned, a scorer (like Utah in the Stockton era) could get so used to looking for assists for his own guy that he starts to see borderline assists for the other side, too. I think that this regression could be extended to try to measure that influence. I'd look to see if the visiting team ast/fgm % difference can be predicted by the home team's ast/fgm % for the season. That is, if you include the home team's mean ast/fgm ratio into the regression, what would the coefficient on that term look like? And, would it account for some of the visiting team effect?
I'm thinking along the lines of:
lm(formula = visitasfgm(for this game) ~ location + homestrength + factor(gameseason) + visit3pf + homeasfgm(season mean) )
It seems like this mean homeasfgm term should be for just the home team's away games. The advantage of using the away games is that it would better account for the home team's "style of play". The home games would include the same bias that we are trying to look at.
It also seems like new variable would be easier to interpret if it were zero-mean. Maybe something like: (HomeTeam's #Ast on road that season / Home Team's #FGM on road that season) - (NBATotal #Ast that season / NBATotal #FGM that season). I suppose that this variable is not truly zero-mean, but it is probably more meaningful than one that uses data across seasons to get to a true zero-mean.
If you did, then an interpretation of a positive, significant coef on this new variable would be that teams that assist on a high % of their own baskets on the road have scorers at home that look for high % at home in general for both teams-- that scorers are indeed influenced by the play of their home team. |
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kjb
Joined: 03 Jan 2005
Posts: 842
Location: Washington, DC
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| Posted: Thu Sep 04, 2008 10:44 am Post subject: |
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| John Hollinger wrote: | | Very interesting stuff. Another area to check is assists with regard to the point guards in particular. some home-team scorers seem to think it's their job to pad the PGs assist #s ... when Jason Williams was in Memphis it was fairly blatant, and I also witnessed first-hand (from about three seats away from the scorer) some absolutely ridiculous assists given to Chris Paul during the playoffs. My suspicion was that Hilton Armstrong doesn't get the benefit of the doubt on those, but it would be great topic to study, somehow. |
I've witnessed this effect as well. I saw it particularly when Jason Kidd was in NJ. He got credited with some preposterous assists as well as some borderline assists when teammates (such as Mikki Moore) were not credited for nearly identical passes. |
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Sandy Weil
Joined: 19 Jun 2008
Posts: 20
Location: Boulder, CO
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| Posted: Thu Sep 04, 2008 1:44 pm Post subject: |
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| I (Sandy Weil) wrote: | (4) As you mentioned, a scorer (like Utah in the Stockton era) could get so used to looking for assists for his own guy that he starts to see borderline assists for the other side, too. I think that this regression could be extended to try to measure that influence. I'd look to see if the visiting team ast/fgm % difference can be predicted by the home team's ast/fgm % for the season. That is, if you include the home team's mean ast/fgm ratio into the regression, what would the coefficient on that term look like? And, would it account for some of the visiting team effect?
I'm thinking along the lines of:
lm(formula = visitasfgm(for this game) ~ location + homestrength + factor(gameseason) + visit3pf + homeasfgm(season mean) )
It seems like this mean homeasfgm term should be for just the home team's away games. The advantage of using the away games is that it would better account for the home team's "style of play". The home games would include the same bias that we are trying to look at.
It also seems like new variable would be easier to interpret if it were zero-mean. Maybe something like: (HomeTeam's #Ast on road that season / Home Team's #FGM on road that season) - (NBATotal #Ast that season / NBATotal #FGM that season). I suppose that this variable is not truly zero-mean, but it is probably more meaningful than one that uses data across seasons to get to a true zero-mean.
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I've reconsidered this idea that I posted a day or two ago and think that this mught be less enlightening that something like the average number of assists per game for the team's top assist man. It is harder to see a good way to mean-zero this but it seems like it would get more directly at the Jason Kidd / Jason Williams phenomena that others mentioned. |
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dsparks
Joined: 22 Feb 2008
Posts: 61
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| Posted: Thu Sep 04, 2008 5:04 pm Post subject: |
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Thanks all for sharing your ideas. I am in the midst of preparing for preliminary exams, and as such, have little time for APBR stuff... but when I get a free moment, I'll follow through on some of your excellent suggestions. Thanks for your thoughts and patience.
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http://arbitrarian.wordpress.com |
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Mike G
Joined: 14 Jan 2005
Posts: 3294
Location: Delphi, Indiana
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| Posted: Sun Sep 07, 2008 7:53 am Post subject: Re: Assist Scoring Bias? |
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Ben, this is a great study. I've had very little time to analyze it deeply, and only now an opportunity to reply.
| Ben F. wrote: | ..."bias" is the most succinct term to describe the effect I'm talking about, ...
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I'd say there are 2 distinct factors at work, perhaps unrelated:
1) Scorekeeper 'generosity' in awarding assists.
2) Scorekeeper 'favoritism' toward the home team or certain players.
| Code: |
Team hAST% aAST% Diff
DEN 67.6% 54.8% 12.7%
BOS 66.6% 56.1% 10.6%
... ...
SAC 48.1% 54.9% -6.9%
PHX 60.8% 68.3% -7.6%
hAST% = AST/FGM of team's offense while on home floor
aAST% = AST/FGM of team's offense while on an opposing floor |
The 'Diff' column would seem to be the sum of the two effects I refer to above. Denver players' home assists were 12.7% higher than they'd be if they were distributed randomly to other venues. If league norms are 'correct', the Nuggs 'really' assisted only 54.8% of their FG.
| Quote: | ...But it doesn't prove any kind of scorer bias, because perhaps these teams simply play differently at home than on the road. ..
...teams on the whole have a lower assist rate on the road that at home, most likely due to fatigue from traveling and the shorter turnaround from game to game... |
Why would teams play differently on the road? Fatigue, etc, may produce fewer FG. But would you be less likely to pass the ball if you are tired? I'd guess the home/away bias is due to simple homerism. It's explainable by human nature.
In any case, I'm curious about the availability of an 'adjustment factor' we can apply to players' assist rates. As mentioned above, the rest of the NBA (scorekeepers) seem to think the Nuggets only assist 55% of their FG, so I'd hit every Nugget's assist rate with a 548/676 = .81 factor. But that would apply to just their home games; since that's half their schedule, split the difference: Each Denver assist is worth .905 NBA assist.
So Iverson was credited with 586 assists, but with an average NBA scorekeeper, he'd have gotten 530. His 6.2 Ast/36 (28th in the league) should be downgraded to 5.6 (40th).
On the other end, Steve Nash's league-best 11.6 Ast/36 (#26 alltime) could be upgraded 6.2%, to 12.3 (#17, or higher if others should be demoted) .
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Ben F.
Joined: 07 Mar 2005
Posts: 390
Location: MD
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| Posted: Sun Sep 07, 2008 10:52 am Post subject: Re: Assist Scoring Bias? |
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| Mike G wrote: | I'd say there are 2 distinct factors at work, perhaps unrelated:
1) Scorekeeper 'generosity' in awarding assists.
2) Scorekeeper 'favoritism' toward the home team or certain players.
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This is a good way to break it down. In my first post, I defined "generosity" as difference in definition of assists. For example, if Luis Scola enters the ball to Tracy McGrady posted up at the elbow, and Mcgrady turns and jabs and fakes and then shoots a fadeaway jumper, some scorers will say that it was an assist because the player shot after a pass without dribbling. Others will say it's not an assist because the pass didn't directly lead to the shot. From my limited tracking of this issue, the "definition problem" seems to be the largest component of the "bias". Although that tracking is quite limited so I don't know if that's true in all cases.
Of course if you want to assume that there is no difference in the way teams play at home and on the road with regards to AST/FGM, you can tease out the two elements (definition and favoritism) by looking at offensive numbers versus the defensive numbers. So Denver's offense is +12.7% at home, while teams visiting Denver are +3.9%. We could then say that the definition factor adds about 4% and the bias factor adds about 9%.
The problem with this is that I would assume that playing on the road does have an effect on a team's AST/FGM. We have numbers that demonstrate that teams play worse on the road, most likely due to fatigue factors (not only does the travel affect the players, but games are much more frequent on road trips). I would guess that fatigue factors could result in less fast breaks (which have a high rate of assists) as well as players not running the offense as effectively.
Overall we saw that home teams got 3.1% more AST/FGM last year than road teams. How much of that is due to favoritism by scorers and how much is due to fatigue is hard to tell. And since I would think that fatigue would affect teams differently, trying to assign home team favoritism based on these numbers becomes a tricky business.
| Mike G wrote: | | In any case, I'm curious about the availability of an 'adjustment factor' we can apply to players' assist rates. |
Yeah, that is part of what I was looking for when I started this study. I think you have to be careful applying it, however. I'd be much more comfortable applying it to Phoenix's numbers than Denver's - Phoenix over the last two years has been right around 9% lower AST/FGM for both teams (Phoenix and their opponent). That consistency (between years and teams) makes me think that we can be pretty sure that the scorers in Arizona are just stingy, and therefore, were we to import some other scorers Nash (and the whole team) would have more assists than they were actually awarded.
But with a team like Denver, the "bias" was pretty different between last year and the year before. So that makes me a lot less certain that it has to do with the scorers. |
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Mike G
Joined: 14 Jan 2005
Posts: 3294
Location: Delphi, Indiana
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| Posted: Mon Sep 08, 2008 6:43 am Post subject: Re: Assist Scoring Bias? |
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| Ben F. wrote: | | ... the "definition problem" seems to be the largest component of the "bias". |
Ah, see, you haven't been consistent with your terms. Is 'definition' a component of 'bias', or is it separate? -- | Quote: | ...Denver's offense is +12.7% at home, while teams visiting Denver are +3.9%. We could then say that the definition factor adds about 4% and the bias factor adds about 9%.
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This 2nd statement agrees with what I was calling 'generosity' and 'favoritism'. I like your terms better, but didn't want to use 'bias' in a different way.
But then I'm still unclear, because in your opening post: | Code: | Team Bias Diff
DEN 8.3% 2.7%
... |
This was after adding +/- 3.1, and I never got what this list represented. But if we go with 'bias' defined as the difference -- in 'definition/generosity' -- between what scorekeepers give the home team vs the away team, then teams rank like this:
| Code: | team assists opponent assists bias
Team hAST% aAST% Diff hAST% aAST% Diff B1
Dal .583 .553 .031 .490 .575 -.085 .116
NOH .604 .524 .080 .572 .599 -.028 .108
Bos .666 .561 .106 .582 .577 .004 .102
SAS .609 .559 .050 .496 .546 -.051 .101
Det .646 .573 .073 .559 .587 -.028 .101
Orl .553 .563 -.010 .525 .629 -.104 .094
LAC .663 .566 .097 .592 .586 .006 .091
Den .676 .548 .127 .652 .614 .039 .088
Atl .654 .555 .100 .595 .577 .017 .083
Mil .629 .533 .097 .616 .600 .015 .082
Por .639 .540 .099 .584 .566 .018 .081
Mia .562 .610 -.047 .539 .661 -.122 .075
Cha .578 .603 -.025 .524 .620 -.096 .071
Hou .605 .565 .040 .528 .557 -.029 .069
Ind .595 .607 -.012 .551 .625 -.074 .062
Uta .671 .649 .022 .545 .579 -.034 .056
Phl .573 .522 .051 .632 .636 -.004 .055
GSW .566 .510 .056 .594 .591 .003 .053
Mem .499 .531 -.032 .540 .618 -.079 .047
Min .543 .517 .026 .611 .632 -.021 .047
Cle .599 .517 .082 .605 .567 .038 .044
Tor .620 .620 .000 .581 .613 -.032 .032
Sac .481 .549 -.069 .549 .647 -.098 .029
Phx .608 .683 -.076 .425 .529 -.104 .028
LAL .648 .585 .062 .591 .556 .035 .027
Chi .601 .611 -.010 .584 .619 -.035 .025
Was .553 .522 .031 .653 .646 .007 .024
NYK .486 .546 -.060 .515 .597 -.082 .022
Sea .556 .563 -.006 .593 .620 -.027 .021
NJN .697 .651 .046 .631 .583 .048 -.002
avg .599 .568 .031 .568 .598 -.030 .061
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The Nets were the only team that seemed to be more generous to their opponents than to their own guys. NJ opponents got .048 more assists in NJ than at their own places (when playing NJ), and the Nets got just .046 more.
At the top end, the Mavs gave their own players the league average of .031 more assists at home. But visitors to Dallas had their assists skimmed by a whopping -.085 .
Please let me know if I'm misinterpreting this somehow.
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Ben F.
Joined: 07 Mar 2005
Posts: 390
Location: MD
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| Posted: Mon Sep 08, 2008 8:31 am Post subject: Re: Assist Scoring Bias? |
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| Mike G wrote: | | Ah, see, you haven't been consistent with your terms. Is 'definition' a component of 'bias', or is it separate? |
Yeah, this was the problem I thought I would run into - the terms I used were poorly chosen and are creating confusion.
You can see in my first post I noted that I was using "bias" not to mean any intentional favoritism, but rather just as a concise term to represent the phenomenon I was talking about: assists being awarded differently in different places. I didn't want to have to keep typing "assists awarded differently in different places" so I substituted in "bias" instead, with the risk that it might create confusion. My apologies.
So to belatedly correct myself, the two components I see of assists being awarded differently in different places are: definition and favoritism.
| Mike G wrote: | | This was after adding +/- 3.1, and I never got what this list represented. |
The idea behind that list was to try and check the consistency of the assists being awarded differently in different places. But the problem with using the straight numbers to check consistency is that there is a structural difference in the way teams get AST/FGM at home vs. on the road. (Whether that difference is due to favoritism or fatigue is still a matter of debate.) I wanted to correct for that difference to compare the home and away numbers. So Miami was -4.7% in Miami. Their opponents were -12.2% in Miami. That seems fairly inconsistent. But because we would assume Miami opponents in Miami (i.e. road teams) would be 3.1% lower, we can adjust those numbers and see that beyond the home/road effects, really it's -7.8% for Miami in Miami and -9.1% for opponents in Miami. Those numbers are much more consistent.
(Note that if you just look at correlation between the two numbers, moving things by 3.1% doesn't change anything, the correlation stays the same. I'm saying this just to be clear that by adjusting things by 3.1% I'm not artificially creating consistency. I'm just trying to resolve the reason for these two fairly disparate but consistent numbers, and in the process come up with one number that better represents the total difference in the way scorers award assists.)
| Mike G wrote: | But if we go with 'bias' defined as the difference -- in 'definition/generosity' -- between what scorekeepers give the home team vs the away team, then teams rank like this:
| Code: | team assists opponent assists bias
Team hAST% aAST% Diff hAST% aAST% Diff B1
Dal .583 .553 .031 .490 .575 -.085 .116
NOH .604 .524 .080 .572 .599 -.028 .108
Bos .666 .561 .106 .582 .577 .004 .102
SAS .609 .559 .050 .496 .546 -.051 .101
Det .646 .573 .073 .559 .587 -.028 .101
Orl .553 .563 -.010 .525 .629 -.104 .094
LAC .663 .566 .097 .592 .586 .006 .091
Den .676 .548 .127 .652 .614 .039 .088
Atl .654 .555 .100 .595 .577 .017 .083
Mil .629 .533 .097 .616 .600 .015 .082
Por .639 .540 .099 .584 .566 .018 .081
Mia .562 .610 -.047 .539 .661 -.122 .075
Cha .578 .603 -.025 .524 .620 -.096 .071
Hou .605 .565 .040 .528 .557 -.029 .069
Ind .595 .607 -.012 .551 .625 -.074 .062
Uta .671 .649 .022 .545 .579 -.034 .056
Phl .573 .522 .051 .632 .636 -.004 .055
GSW .566 .510 .056 .594 .591 .003 .053
Mem .499 .531 -.032 .540 .618 -.079 .047
Min .543 .517 .026 .611 .632 -.021 .047
Cle .599 .517 .082 .605 .567 .038 .044
Tor .620 .620 .000 .581 .613 -.032 .032
Sac .481 .549 -.069 .549 .647 -.098 .029
Phx .608 .683 -.076 .425 .529 -.104 .028
LAL .648 .585 .062 .591 .556 .035 .027
Chi .601 .611 -.010 .584 .619 -.035 .025
Was .553 .522 .031 .653 .646 .007 .024
NYK .486 .546 -.060 .515 .597 -.082 .022
Sea .556 .563 -.006 .593 .620 -.027 .021
NJN .697 .651 .046 .631 .583 .048 -.002
avg .599 .568 .031 .568 .598 -.030 .061
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The Nets were the only team that seemed to be more generous to their opponents than to their own guys. NJ opponents got .048 more assists in NJ than at their own places (when playing NJ), and the Nets got just .046 more.
At the top end, the Mavs gave their own players the league average of .031 more assists at home. But visitors to Dallas had their assists skimmed by a whopping -.085 .
Please let me know if I'm misinterpreting this somehow. |
You're not misinterpreting at all, this is a great chart, and very interesting. I didn't think to remix the data in this way.
In response to New Jersey being the only place to have road teams have a higher AST/FGM, I think that's fairly good proof that something pretty extreme is going on. Either road teams play differently with regard to AST/FGM, or there's an incredible structural favoritism going on. I'm more inclined to believe the former, but again, it's almost impossible to tease out the proof for either one. |
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