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Defensive Adjusted Plus/Minus Ratings
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junkball



Joined: 24 Jun 2005
Posts: 4

PostPosted: Mon Aug 15, 2005 1:08 pm    Post subject: Reply with quote

Dan Rosenbaum wrote:
Separate regressions for all 30 teams would not make sense here. All of the data is pooled together.


Ah, I see. That's one heck of a data set.

Quote:
The "simple correlation" would probably be something like the Roland Rating. There are several reasons why a player may have a low Roland Rating, but it would not tell us much about their effectiveness. So I am not sure of the reasoning behind your statement.


The rule of thumb for multiple regression is look at the Beta values and at the simple correlation...I was presuming this also applies to basketball.

- I'm not certain why one would use b values instead of beta values, for Winval. Beta values account for differences in scale, between IVs. Might not make much of a difference because all variables are 1's and 0's, but still...

zMargin = B1*zx1 +B2*zx2 + ... + Bk*zxk

is my understanding of how WinVal rating should be done.

- The b's (WinVal) tell us the unique contribution of a player to the team. The "shared" contribution to team success doesn't say anything conclusive about the one particular player. On the other hand, this shared contribution (reflected in simple correlation) does provide an upper bound on how much a player contributes to team success.


Quote:
Accounting for the other players on the floor, I can measure how a given player affects the point differential between the two teams and the total points scored by the two teams. From that I can derive offensive and defensive ratings.


OK. So there' two regressions: one with MARGIN and one with total points scored. The offensive and defensive ratings being some function of a player's two b values.
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Dan Rosenbaum



Joined: 03 Jan 2005
Posts: 541
Location: Greensboro, North Carolina

PostPosted: Mon Aug 15, 2005 1:51 pm    Post subject: Reply with quote

junkball wrote:
The rule of thumb for multiple regression is look at the Beta values and at the simple correlation...I was presuming this also applies to basketball.

- I'm not certain why one would use b values instead of beta values, for Winval. Beta values account for differences in scale, between IVs. Might not make much of a difference because all variables are 1's and 0's, but still...

zMargin = B1*zx1 +B2*zx2 + ... + Bk*zxk

is my understanding of how WinVal rating should be done.

- The b's (WinVal) tell us the unique contribution of a player to the team. The "shared" contribution to team success doesn't say anything conclusive about the one particular player. On the other hand, this shared contribution (reflected in simple correlation) does provide an upper bound on how much a player contributes to team success.

Standardizing independent variables is an issue of how you want to present the results. In this case, I do not want the independent variables in standard deviation units. I want them to tell the effect of a player when he is in the game. Unstandardized that is what they tell me. Standardized it would be hard to interpret these coefficients, because a one standard deviation change in this circumstance has less meaning than simply leaving the variable alone and using its natural units.

In practice it always a good idea to look at simple correlations, even if they are biased estimators of what you want - as they are in this case. It is a good way to learn more about the data. But the simple correlations are a combination of the adjusted plus/minus rating that I compute and biases of different sorts. It is not really an "upper" or "lower" bound of any kind. Really it is just another estimate of player effectiveness - albeit one with lots of biases.
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kbche



Joined: 19 Jul 2005
Posts: 51
Location: washington d.c.

PostPosted: Tue Aug 16, 2005 9:31 pm    Post subject: Defensive Player Ratings Reply with quote

Hi Dan,

I looked at your top 6 defensive centers, power forwards, small forwards, shooting guards, and point guards. My observations are as follows:

1. Only 3 of the 30 players have ever won a championship (correct me if I am wrong).

2. 23 of the 30 players played on teams in the 04-05 season that made the playoffs.

3. Only 3 of the top 6 small forwards were on playoff teams in the 04-05 season. This was the lowest percentage of all categories (all other categories indicated that 5/6 played on playoff teams).

Thus the top defensive players were generally on the better teams. Are the players making the team, or are the teams making the players? How can we tell from your model?

Have you considered different OLS estimates to improve the goodness of fit? The assists made and points scored are not independent variables and should probably be treated as such in a model. A player in a particular play can not score points and an assist on the same play. Does your model account for this?

You added a appreciation/depreciation factor for players. How was this developed? A player would have to be on the same team with the same team mates for successive years, and the players' performance would have to be normalized.

Kimberly
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Dan Rosenbaum



Joined: 03 Jan 2005
Posts: 541
Location: Greensboro, North Carolina

PostPosted: Tue Aug 16, 2005 11:55 pm    Post subject: Re: Defensive Player Ratings Reply with quote

kbche wrote:
Hi Dan,

I looked at your top 6 defensive centers, power forwards, small forwards, shooting guards, and point guards. My observations are as follows:

1. Only 3 of the 30 players have ever won a championship (correct me if I am wrong).

2. 23 of the 30 players played on teams in the 04-05 season that made the playoffs.

3. Only 3 of the top 6 small forwards were on playoff teams in the 04-05 season. This was the lowest percentage of all categories (all other categories indicated that 5/6 played on playoff teams).

Thus the top defensive players were generally on the better teams. Are the players making the team, or are the teams making the players? How can we tell from your model?

Have you considered different OLS estimates to improve the goodness of fit? The assists made and points scored are not independent variables and should probably be treated as such in a model. A player in a particular play can not score points and an assist on the same play. Does your model account for this?

You added a appreciation/depreciation factor for players. How was this developed? A player would have to be on the same team with the same team mates for successive years, and the players' performance would have to be normalized.

Kimberly

Interesting analysis on the relationship between my highest rated defensive players and team performance. But I am not sure the patterns are strong enough to tell us much other than that teams with better defensive players tend to be better teams.

Points and assists are not independent, but the whole point of regression is to estimate the partial effect of one variable holding the effect of other variables constant; dependence between independent variables is typically the motivation for running a regression in the first place. There is no need to hold other variables constant if the other variables are independent.

Note that the points and assists variables are only in my model relating box score statistics to the basic adjusted plus/minus ratings. That data is not used to compute the adjusted plus/minus ratings. With the box score data, all that I am trying to do is identify different types of players and say something about what the average adjusted plus/minus ratings are for players of different types. It is not measuring the effect of an assist or point scored, per se.

For more details on how the adjusted plus/minus ratings are estimated, see the detailed piece I wrote on this. I think that some of the points you make about this are possibly mistaken, but I am not quite sure because I am not sure I fully understand what you are trying to say.

http://www.uncg.edu/bae/people/rosenbaum/NBA/winval2.htm
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JPOP



Joined: 07 Aug 2005
Posts: 5

PostPosted: Wed Aug 17, 2005 5:36 am    Post subject: Re: Defensive Player Ratings Reply with quote

Hey Dan,

I'm pretty impressed with the overall performance of your defensive ratings. I keep finding aberations with multiposition players although I'm only looking at a small sample. Some of these multiposition players defend out of position because of a lack of team depth, always defending the best wing or post player or to match up with the opposition.

There are quite a few players who defend well at their primary position, but don't defend well at a secondary position. Not everyone can provide the multiposition defensive flexibility of Garnett or Kirilenko to be nearly equally effective defending two positions. Just the same they may be a teams best option to defend a certain position for a length of time throughout a game.

These multiposition players are very likely to create some year to year noise defensively as their roles may change with additional personnel on their given team. Primary position defense is much less likely to spike from one year to the next than what is seen by a player having a major shift in the percentage of minutes the player needs to stray from defending their primary position.

There are quite a few examples, but here a few primary ones.

Robert Traylor is an awful defensive player when matched up with centers. At the same time he is more than adequate defending power forwards. His work at center was so bad, it pushed him into the bottom 10.

Eric Snow has made a career out of his defense. With Iverson he often cross matched defensively doing a great job at defending shooting guards. The past year in Cleveland, and generally not needing to play a cross matching game, when he defended shooting guards his defense was stellar, when defending point guards, he was incredibly average.

Darius Miles cracks the top 10 (#3) at small forward likely due to his prowess at defending the rangy fast/quick power forwards of the Western Conference. I guess some coaching genius by Cheeks and an assignment Miles never had in the past. That could explain the somewhat high Standard Error.

It seems to me having some positional ratings for multipositional players goes a lot farther than lumping together their on-court performances. There are too many players who have either offensive or defensive efficiency at one end of the court while squashing it with not enough length or bulk to be effective at the other. This is also the type of information that escapes more than a handful of coaches with their substitution practices.

Again, this is a great set of ratings and has some true promise. I look forward to seeing the whole list some day soon and believe there are quite a few coaches out there who would be shocked if they were aware of some of the shortcomings their substitution patterns bring.
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Dan Rosenbaum



Joined: 03 Jan 2005
Posts: 541
Location: Greensboro, North Carolina

PostPosted: Wed Aug 17, 2005 12:26 pm    Post subject: Reply with quote

JPOP, these points about multi-position players are another reminder of how important context is. Put a player in a role for which he is not well suited and his plus/minus rating is likely to suffer.

But I am not sure the year-to-year variation in adjusted plus/minus ratings is greater for multi-position players. Players who are well suited to just one position are often forced to play a different position, and for that reason their plus/minus ratings can be all over the map. Dwight Gooden is a good example. Memphis and Orlando tried to play him a lot at the 3 and he had horrible plus/minus ratings. Put almost exclusively at the 4 with Cleveland and he looked a lot better.

Recogninzing the roles which a player can excel most at is where a good coach or a good stats analyst can be of tremendous value.
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Ben



Joined: 13 Jan 2005
Posts: 266
Location: Iowa City

PostPosted: Wed Aug 17, 2005 1:32 pm    Post subject: Reply with quote

Dan Rosenbaum wrote:
Dwight Gooden is a good example.


I see you're a baseball fan too. Personally, I was a big fan of those mid 80's Mets teams.
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Nikos



Joined: 16 Jan 2005
Posts: 346

PostPosted: Wed Aug 17, 2005 2:30 pm    Post subject: Reply with quote

Ben wrote:
Dan Rosenbaum wrote:
Dwight Gooden is a good example.


I see you're a baseball fan too. Personally, I was a big fan of those mid 80's Mets teams.


Laughing

I was a Met Fan too.
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JPOP



Joined: 07 Aug 2005
Posts: 5

PostPosted: Wed Aug 17, 2005 5:19 pm    Post subject: Reply with quote

Dan Rosenbaum wrote:
But I am not sure the year-to-year variation in adjusted plus/minus ratings is greater for multi-position players. Players who are well suited to just one position are often forced to play a different position, and for that reason their plus/minus ratings can be all over the map. Dwight Gooden is a good example. Memphis and Orlando tried to play him a lot at the 3 and he had horrible plus/minus ratings. Put almost exclusively at the 4 with Cleveland and he looked a lot better.

Recogninzing the roles which a player can excel most at is where a good coach or a good stats analyst can be of tremendous value.


Drew Gooden probably isn't a good example as his inability to rotate defensively prompted his move to small forward where he couldn't defend the perimeter. Place him on a team with Ilgauskas and all of a sudden Gooden looks like he has some game with cleaner looks and defenses making their best efforts to keep Ilgauskas off the offensive boards. Not much different than how Boozer's talents seemed to be minimized in Utah, after leaving Ilgauskas' shadow.

The premise still remains the same. Despite having defensive shortcomings at one position and success at another, the results of an overall defensive rating not considering the position played in part will provide some noisy results. If the percentage of overall minutes is proportional from one season to the next, the numbers likely don't vary much. If the same player is afforded a larger percentage of overall minutes at a position they don't play well, their defensive rating suffers.

The caveat of this is if you don't break out the primary position defense, is you've piled these multiposition players with players who only need to posess the skills to play a single position.
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back2newbelf



Joined: 21 Jun 2005
Posts: 274

PostPosted: Thu Aug 18, 2005 3:42 am    Post subject: Reply with quote

@dan rosenbaum:
-could we get the numbers for artest from the seasons he played? just the ballbark would be alright...
-would the defensive adjusted +/- ratings and the "normal" adjusted +/- ratings make it possible to accurately guess the offensive adjusted +/- ratings? for example: if michael redd has an average "normal" rating, could we say that he is an outstanding offensive player, and if so...get an accurate offensive rating?
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kbche



Joined: 19 Jul 2005
Posts: 51
Location: washington d.c.

PostPosted: Thu Aug 18, 2005 10:07 pm    Post subject: Re: Defensive Player Ratings Reply with quote

In a regression analysis, you are assuming that Y is some function of a set of X variables. A regression can be performed with any set of variables. It is up to the developer to verify that Y is actually a function of X variables, and the type of function must be specified.
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Eli W



Joined: 01 Feb 2005
Posts: 402

PostPosted: Tue Aug 30, 2005 12:00 pm    Post subject: Reply with quote

One thing I've often wondered is how well the players themselves can tell who plays the best defense. The all-defensive teams give us a sense of the general perception, but what about a player's teammates, opponents, and coaches? What do someone like Ben Gordon's teammates think about his defense?

In Dan's rankings, Darius Miles rated as the third best SF defender. He has a high defensive statistical +/- and has had a very good defensive adjusted +/- each of the last three years. But here's what his new assistant coach Maurice Lucas had to say about his defense:

Quote:
blazers.com: If you could successfully accomplish one thing this season, what would it be?

ML: Teach Zach [Randolph] and Darius [Miles] that playing defense will make them better offensive players.


http://www.nba.com/blazers/news/Trail_Blazers_Add_to_Coaching_-147848-41.html
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