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Assist Scoring Bias?
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Mike G



Joined: 14 Jan 2005
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PostPosted: Tue Sep 09, 2008 1:41 pm    Post subject: Reply with quote

HoopStudies wrote:

So are you saying that the arena/scorer has NO IMPACT? And that it's only about how teams play?

Not hardly. I don't see how a piece of hardware (arena, floor, lighting, ...) affects one team differently than the other. But the scorekeeping crews are going to give varying results no matter how hard they try not to.

Since we can't separate the 'scorer' from the 'arena', that's a matter of terminology, I guess. But my guess is, it's the human element that differs from one arena to the next.


Ben, of course it's the differing personalities in charge of awarding assists, that are responsible for what we call 'bias'. I just meant to say that the numbers are in the books; and it doesn't matter whether a scorekeeper decided to change his ways, or a maverick owner handed down a directive, or whatever. Each team and it's opponents registered assists, home and away; and the biases are a matter of historic record.
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HoopStudies



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PostPosted: Tue Sep 09, 2008 2:24 pm    Post subject: Reply with quote

Mike G wrote:
HoopStudies wrote:

So are you saying that the arena/scorer has NO IMPACT? And that it's only about how teams play?

Not hardly. I don't see how a piece of hardware (arena, floor, lighting, ...) affects one team differently than the other. But the scorekeeping crews are going to give varying results no matter how hard they try not to.


Then I don't understand the concern with the metric. It looks for an underlying bias for or against assists as a whole. It doesn't look for a bias for the home team. You can do that after looking for the underlying tendency to be freer or stricter with assists.

It's called Arena Scorer Factor. Throw out the Arena part if you want. I'm just saying it's a pretty similar problem that baseball already has a solution for. Why not use it?
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Harold Almonte



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PostPosted: Tue Sep 09, 2008 6:13 pm    Post subject: Reply with quote

I think we're trying to discover two different things at a time with one only metric:

The "home bookeeping privileges-in stats subject to interpretations without any league revisions" as a part of the "home advantage", and..
The way a team play (regarding passing-assists) when being at home environment, or away. Which could be, aside bookeeping, a matter of some kind of different chemistry with environment. Very rare in this "home advantaged" sport, but this could be the case for SAC, NYK, etc.. providing that the schedules are not playing a role here.

Then one thing is to look at each arenas (historical home/opponent-s differential of assists, totals or %) and another thing is to look at each team (home/away assist% performance)
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HoopStudies



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PostPosted: Tue Sep 09, 2008 7:31 pm    Post subject: Reply with quote

Harold Almonte wrote:
I think we're trying to discover two different things at a time with one only metric:


I was just trying to illustrate that there is a metric showing bias of official scorers in certain arenas for assists (and perhaps other stats) across all teams that play there.

Ben started the thread looking for this, I think (correct me if I'm wrong). If there was more to it, I am not trying to add to that, except by introducing a common basis for going beyond.
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Harold Almonte



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PostPosted: Tue Sep 09, 2008 8:39 pm    Post subject: Reply with quote

Just that there is a noise produced by team h/a performance that simple formula-s can't take off. The Mike chart gives us more information about bookeepers's judgements (even with noise), because includes (each arena's) treatment to opponents numbers (respect to the league). Then, we can see which of them see more (DEN, CLE), or less (SAC, PHO), assists than league for everybody, which of them see more for home and less for opponents (ALL MINUS ONE), or viceversa (NJN).

But, the only way to know that bkeeping bias exactlly, is a pbp replay revision by more than one people of course, after a previous agreement about the rules.

It could come one day, who knows, when the league attempts to bookeep def. atempts stats, that would need to make revisions of doubtfulness before making boxscores official.
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HoopStudies



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PostPosted: Wed Sep 10, 2008 7:56 am    Post subject: Reply with quote

I should also note that the ASFs I presented are essentially uncorrelated to playing style. I don't know what teams had new scorers in 2008, but the biggest changes in ASF are for New Orleans and Atlanta. And, hmm, New Orleans almost definitely had a new scorer because they were in OKC the year before. I might guess that Atlanta had a new scorer. But teams with the most roster turnover (and probably different style, like Boston and Minnesota) probably did not have new scorers as they were very consistent in ASF.
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Scott S



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PostPosted: Wed Sep 10, 2008 9:32 pm    Post subject: Reply with quote

This seems a pretty interesting quick study. Good observation Ben. I was also surprised by how much these bias' varied from team to team, but were consistent from year to year. I noticed initially a few people mentioned individuals they felt had benefited from generous "assists" and I thought it might be worthwhile to look into.

To check this, I wanted to see how MPG, PER and APG impacted this bias. I found home splits from nba.com for the 2008 season and adjusted the them based on the "PF_ast" figures posted by Dean. In order to weigh factors of 5 and .2 similarly, I applied the following formula for my analysis (Ast_h - Ast_r)/Max(Ast_h,Ast_r). Performing regression analysis, I found that this value for players varies according to the following coefficients:

Code:

Intercept   0.001912812
MPG           0.001979137

Intercept   -0.009871184
PER           0.004245436

Intercept   0.031264237
APG           0.007863901

Intercept   -0.012437351
MP            0.000975041
AST            0.001849118
PER           0.002487489


The final model loses some validity and has a smaller value for F. The p-stats of the PER and APG coefficients on the 2nd and 3rd models are about 0.17. MPG in model 1 is .28.

Consider the following examples of players good enough to average 10 road assists per 48 minutes based on the projections of the 1st 3 models. (These examples ignore correlation of the 4 stats, which definitely exist.)
Someone with a PER of 10 would be expected to have 10.34 home assists per 48 minutes on an average team. A PER of 30 produces an expectation of 11.31 AST48. When looking at MPG, 10 MPG produces an expectation of 10.22 AST48 compared to someone averaging 45 MPG expecting 10.99 AST48. 1 APG produces an expectation of 10.41 AP48 while 12 APG produces an expectation of 11.41 based on each respective model.

Based on the previous messages in this post, these results should not come as a surprise. I still think it is interesting. Perhaps the increase in the factor in New Orleans is partially due to Chris Paul's "chase" of Steve Nash's assist title. (I wouldn't be surprised if the stat keepers cared more about it than him.) I don't know how many other stats could be impacted by such factors. You hear this suggested all of the time in other sports. Even if you don't buy it, you probably consider it plausible. Would have error have been called if it wasn't a record hit, etc.? I guess in every sport you can consider the increase/decrease in a player's performance as he nears a significant mark. Contract years are a big one. I haven't looked into this, but considering how often it is mentioned, I wonder what the exact effect is.

Back to home/road assists, here is a summary of the top 5 assisters per home game:
Code:

Chris Paul , NOH        11.9
Deron Williams , UTA    11.2
Jason Kidd , DAL-NJN   10.2
Steve Nash , PHX    10.1
Baron Davis , GSW    8.6

Road assists
Code:

Steve Nash , PHX    12.1
Chris Paul , NOH    11.2
Jason Kidd , DAL-NJN    9.9
Deron Williams , UTA    9.8
Jamaal Tinsley , IND    8.3

Note that I did not include players who played for multiple teams or those who played less than 100 minutes in the year for my models.

I know it doesn't exactly address your original post, Ben, but hopefully this helps contribute to the assist bias aspect you brought up.

(How do you get the code to line up exactly?)
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Mike G



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PostPosted: Thu Sep 11, 2008 8:31 am    Post subject: Reply with quote

I've often wondered about John Stockton's anomalous 1989, when his assist rate was interrupted from it's steady rise. In 1988, he had become a starter, and Utah's (road) assist rate jumped to the next level.
Factor = (1+AAst%/HAst%)/2 :
Code:
 Utah Jazz                    John Stockton
year   HAst%  AAst%   Fac.   Ast36   Ast%   Adj%
1987   .671   .616   .959    13.0   .476   .457
1988   .715   .665   .965    14.3   .548   .529
1989   .668   .657   .992    12.7   .543   .539
1990   .666   .662   .997    14.0   .574   .573
1991   .713   .665   .966    13.5   .575   .556
1992   .659   .634   .981    13.5   .537   .527

http://www.basketball-reference.com/players/s/stockjo01.html
The drop in raw assists/36 minutes is some 11% (14.3 to 12.7) from '88 to '89.
Justin K's (new/improved) Ast% corrects most of that, as the new (and current) coach, along with Mark Eaton's career year, made Utah the league's top defensive team.

But the Jazz scorekeepers also handed out fewer assists, relative to the rest of the league. In '89 and '90, Stock got no more assists in Utah than he did elsewhere.
The Adj% = Ast% x Fac , and it yields a smooth trajectory tracking Stockton's prime passing seasons. There is no blip at all in 1989, but a continued rise, topping out in the next season.


Here's the same treatment for Chris Paul's career:
Code:
      New Orleans Hornets       Chris Paul
year   HAst%  AAst%   Fac.    Ast36   Ast%   Adj%
2006   .534   .539   1.005     7.8   .382   .384
2007   .525   .510    .986     8.7   .413   .407
2008   .604   .522    .932    11.1   .522   .487

In his rookie year, the Hornets weren't giving any freebie assists. Last year, they gave a lot. Consequently, CP3 didn't really assist 37% more than his rookie year, but merely 27% more (487/384).

These adjustments make the assumption that a team's Away Ast/FG ratio (AAst%) is their true Ast/FG ratio.
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HoopStudies



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PostPosted: Thu Sep 11, 2008 9:04 am    Post subject: Reply with quote

Scott S wrote:
...

Based on the previous messages in this post, these results should not come as a surprise. I still think it is interesting. Perhaps the increase in the factor in New Orleans is partially due to Chris Paul's "chase" of Steve Nash's assist title. (I wouldn't be surprised if the stat keepers cared more about it than him.) I don't know how many other stats could be impacted by such factors. You hear this suggested all of the time in other sports. Even if you don't buy it, you probably consider it plausible. Would have error have been called if it wasn't a record hit, etc.? I guess in every sport you can consider the increase/decrease in a player's performance as he nears a significant mark. Contract years are a big one. I haven't looked into this, but considering how often it is mentioned, I wonder what the exact effect is.

...


I should note that the Hornets ASF for assists went like this:

2005 1.044 in NOR
2006 0.903 in OKC
2007 0.934 in OKC
2008 1.067 in NOR

That would suggest to me that the more likely factor is that the Hornets got their old scorer back, who was more generous with assists than the OKC scorer.

There may have been some element of "chase" to it also, as the late season factor was higher than the early season factor. But that was true also in Phoenix.
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Dean Oliver
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Harold Almonte



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PostPosted: Thu Sep 11, 2008 9:38 am    Post subject: Reply with quote

Quote:
These adjustments make the assumption that a team's Away Ast/FG ratio (AAst%) is their true Ast/FG ratio.


Quote:
2005 1.044 in NOR
2006 0.903 in OKC
2007 0.934 in OKC
2008 1.067 in NOR


Would the next step be, if possible, to know how much of this (AST)ASF is due to bookeeping, and how much due to generally "teams better home performance"? (with exceptions at passing assists, since some teams have anyway a negative factor, but all teams, even worsts, perform better at home)

But, bookeeping should be the biggest factor, since just half of top12 teams at FG%diff. (not splitted h/a), appear as more biased top teams. Why aren't the other good teams (some of them with top assist PGs) top biased too?. Also a lot of top biased are negative, or almost even, at total assist diff.

PD: How about h/a SOS?
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HoopStudies



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PostPosted: Thu Sep 11, 2008 10:54 am    Post subject: Reply with quote

Harold Almonte wrote:
Quote:
These adjustments make the assumption that a team's Away Ast/FG ratio (AAst%) is their true Ast/FG ratio.


Quote:
2005 1.044 in NOR
2006 0.903 in OKC
2007 0.934 in OKC
2008 1.067 in NOR


Would the next step be, if possible, to know how much of this (AST)ASF is due to bookeeping, and how much due to generally "teams better home performance"? (with exceptions at passing assists, since some teams have anyway a negative factor, but all teams, even worsts performs better at home)


Let me clarify. The ASF shouldn't be due to "better home performance" as it looks at how many assists a team gets and gives up at home vs how many they get and give up on the road. So if a team is equally better on O at home as on D, it washes out because their astrate goes up on O and down on D (the numerator).

AFTER you adjust by this, then you can start looking for bias by a scorer just for their team or for teams "better home performance."
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Harold Almonte



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PostPosted: Thu Sep 11, 2008 11:21 am    Post subject: Reply with quote

OK, my fault. The formula adds the opponents's assists, I was all the road thinking as it was substracting them, like a kind of differential.

It appears that having a lot of teams that give up more assists than they give, even at home (and bkeep-biased against the opponents), and that give less assists at home than on road; that, home and more assists are not correlated, although they should be (from the first factor).
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Scott S



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PostPosted: Thu Sep 11, 2008 1:13 pm    Post subject: Reply with quote

HoopStudies wrote:

I should note that the Hornets ASF for assists went like this:

2005 1.044 in NOR
2006 0.903 in OKC
2007 0.934 in OKC
2008 1.067 in NOR

That would suggest to me that the more likely factor is that the Hornets got their old scorer back, who was more generous with assists than the OKC scorer.

There may have been some element of "chase" to it also, as the late season factor was higher than the early season factor. But that was true also in Phoenix.


I didn't notice the yearly progession. While I think both factors contribute, I would tend to agree, based on the above figures, that a potential scorer change would have the higher impact, at least in this specific instance.

As for the issue at hand, overall bias in assists, I think that much of the error is related to lack of a clear definition of assists. To me, a pass directly leading to a field goal (my understanding of the definition of an assist) is still very difficult to assess. How direct do we need to be? How does someone shooting immediately or dribbling meaninglessly or making a slight fake or making a strong move change how directly an assist reflects on a field goal? If someone feeds a scorer where he has a very favorable position, say feeding Duncan down low with minimal coverage, Nash for a wide open 3 pointer or Lebron for a 2 on 1 fast break and they make a move to further increase thier chances of scoring by a slight margin, it bothers me to not have an assist rewarded (but I realize consistency is the most important factor here). Whereas, if you feed Ben Wallace for a long 2 at the top of the key and he is double covered with 1 second left on the shot clock and he happens to bank it in (like the bank shot makes it more feasible), I cringe at awarding an assist for that because the assist lowered your team's expected scoring by making that pass. In reality (or theory) every PASS has an expected value added or subtracted. Some just happen to lead to scores. This expected value would be nearly impossible to track, I would imagine.

Mostly to make myself feel better, I came up with a couple altered versions of assists that might work better and be easier to distinguish:

Assist1: A pass, with more than 3 seconds remaining on the shot clock, to one of the following three types of field goal scorers:
(1) any open shooter who shoots within 1 foot away from the three point line,
(2) any shooter who is within 5 feet of the basket or
(3) any shooter who has a numerical player advantage on the opponents end.
An Assist1 can only occur when no attempt to avoid a defender has been made by the shooter.

Assist2: Any pass resulting in a score that is not categorized as an Assist1 pass and improves his teams expectation for scoring compared to the expectation prior to the passer obtaining the ball.

These can definately be futher clarified. Assist2 is obvoiusly more subjective and can include "Free Throw Assists" and "Secondary Assists", among others but should still exclude the Ben Wallace assist above (this is the difficult part and I hope the impact would be minimal since the value might be near 0). The value of assist2s should be less than assist1s, but still above 0. I would imagine that the average other pass might even correlate negatively with expected value. Can anyone further clarify what could be included in this definition (not that I would be able to track this in bulk anyway, but just out of curiosity)?

There are an infinite number of ways to define assists, what is the consensus "best" way?
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Harold Almonte



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PostPosted: Thu Sep 11, 2008 5:00 pm    Post subject: Reply with quote

Good points.
I think that things should be put on easilly (binarial) to bookeepers: assist or no assist. But the conditional towards a consensed rule and (to be further clarified by somebody) should be one, and only one of these: zero move, just one move, or two, to avoid a defender (and the definition of what is an individual shot creation move, of course).

The weight of assists (between 0 and 1 full assist) is a metricians's job (and decision). The "assistfigure" figure, was already invented for this kind of question.
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Scott S



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PostPosted: Thu Sep 11, 2008 8:55 pm    Post subject: Reply with quote

I understand that this could be somewhat confusing to track. I was thinking along the lines of how 82games.com tracks close shots, tips, and jumpers and box scores track fade aways and hook shots.

I definately agree that a binary statistics are needed, at least for now. I intended to say that there could be 2 types of assists, like in hockey and a count of passes, which may already exist.

And, certainly there are many ways to approximate the value of the average assist in the current form. I just think that if we can better measure what we are looking at, the variations of our estimates will lower and the accuracy of any models will improve, not to mention the decreases in the occurances of bias' (which would actually have more to do with consistency in measure). For example, adjusted plus-minus measures can approach almost exactly what an individual's point value,above a certain level, is as data and permuations of lineups approach infinity, but, a full season often produces poor measurements due to lack of credibility (or a high coefficient variances). I imagine that over a smaller period this statistic could be nearly useless (such as the NBA Finals or a measure of adjusted plus minus turnovers or something). However, if you improve the accuracy of your measurements, I think you can better estimate true value and better assess value a shorter sample.

That said, I don't really know how feasible or helpful this would be. It is difficult to track statistics to test and there are probably better ways for the many people like me who limited time in their schedule.
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