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The Great Usage vs. Efficiency Debate
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Neil Paine



Joined: 13 Oct 2005
Posts: 774
Location: Atlanta, GA

PostPosted: Fri Nov 24, 2006 1:48 pm    Post subject: The Great Usage vs. Efficiency Debate Reply with quote

Background reading:

*How well would this team perform?
*Usage vs. Efficiency
*2006 All-NBA teams

Both of these posts deal with the very contentious matter of Usage vs. Efficiency. I missed out on these debates the first time around, but I think it's an incredibly important topic, and one that we haven't really discussed much recently.

The debate, of course, is whether or not a player can increase his usage/touches/possessions without a corresponding decrease in offensive efficiency. Many of us believe that there has to be such a decrease, if not simply from our own basketball-playing experiences -- whether we play college ball, high school, or just pick-up games at the Y, if we try to take on a bigger role in the offense than we are equipped for, our efficiency will suffer, either through increased turnovers, missed shots, or both. We feel like we know this to be true, because we've experienced it ourselves. However, Bob Chaikin made some good points in those threads I referenced above; namely, he pointed out the fact that we don't have any real evidence that this phenomenon is true at the NBA level (because players don't lend themselves to controlled experiments, and there's always a question of causality: do players shoot more because they are shooting better, or do they shoot better because they shoot more?), and he pointed out some examples of players who actually increased their usage and maintained their efficiency (David Robinson in 93-94 was one that came up). So the evidence is conflicting at best, because some players can handle the extra workload, and some can't, and we can't seem to explain why. Why could Brent Barry handle increased touches from 2001 to 2002, but we theorize that Fred Hoiberg couldn't maintain his efficiency with a similar increase in usage?

First, some theory: Think about the ways in which players go about "getting their shot"... Coaches will run plays for guys, but I agree with BobC's point in one of the threads above -- in general, players can't willfully increase their touches/min, because you can only get the ball if your teammates are willing to pass it to you (unless you're the point guard, obviously). So if you want to get any shots, it's a function of:

1. A player's teammates. You can't shoot if someone else is dominating the ball, plain and simple. But the flip-side is that playing with a great player (like Kevin Garnett in Hoiberg's case) will get you shots you wouldn't ordinarily see, because of double-teams and the D being generally fixated on the star player. Likewise, playing with great passers like Magic Johnson or Steve Nash will help you get the ball in a position to score more efficiently.
2. A player's basketball IQ. In order to get teammates to pass to you, you have to move to open spaces, free yourself of your man, use screens effectively, etc. -- be in a position to recieve the ball and do something with it.
3. A player's shooting ability. If you know you're not going to be able to make a shot from a certain area of the floor, you probably aren't going to shoot from that area. In other words, if a player's shooting range is good, it can increase how often he has the option of shooting. If it's poor, it limits his shooting opportunities to specific areas of the floor.
4. A player's ballhandling skills. This one is obvious; if you're going to create more than just catch-and-shoot opportunities, you will have to break someone down off the dribble, or at least avoid a turnover if forced to handle the ball in traffic.
5. A player's athleticism/quickness. A good first step can free you of just about any defender, and athleticism improves your ability to finish inside/alter your shot, in addition to getting you easy buckets in transition.
6. A player's size/height. Players who create matchup problems will be targeted for more usage automatically by their coaches. All other things being equal, if you can shoot over someone, you should be able to get more shots than a player whose defender is taller than them or the same size.

#1 is an issue at all levels of basketball, but probably least so in the NBA, since everybody has at least some responsibility to share the ball (even Allen Iverson passes the ball away on 50% of his touches). Numbers 2 and 3 are generally constant for veteran players, and we have to assume that every player is already using them to the maximum. However...

To increase one's usage, it will have to involve some combination of numbers 4, 5, and 6. Beyond the basic level of shot-creating (shooting only on lay-ups/open looks/catch-and-shoot type shots), you will have to employ at least one of these three tactics. You will have to beat somebody off the dribble if you're being guarded closely, which is a function of #4 and #5. If you've got a size advantage, you can shoot over guys when you would ordinarily be considered "not open"; you can also go down into the post and use your size there. Practically anybody who creates more than the basic level of shots uses either #4, #5, or #6, if not all three (although I suppose if #3 is off the charts/Reggie Miller-level, you could pull up from anywhere and not have to use 4, 5, or 6).

With this in mind, let's look at the Barry/Hoiberg situation to see why Barry could handle an increase, while Hoiberg might not be able to. First off, Barry is bigger (6'6" versus 6'4"), but I don't see that being a huge advantage. Numbers 4 and 5 are big advantages in Barry's direction, though: Hoiberg may have had low turnover rates, but it's because he never dribbled the ball. When he was put into situations where he had to take on more usage (and, thus, put the ball on the floor more often), his turnover rates went up, because he didn't have the requisite ballhandling ability. Barry, on the other hand, was playing de facto point guard for Seattle for years, and was pretty well-known for his floor game. In terms of athleticism, Barry was a former slam-dunk contest winner, while Hoiberg was simply not very athletic. In light of this, it explains what many people had voiced in the other threads -- that asking Hoiberg to take on a higher percentage of a team's offense would result in his efficiency taking a (pretty major) hit, because his potential to add usage without penalty was limited by his lack of dribbling skills, size, and athleticism.

How big a hit would his efficiency take, though? I'm a firm believer in BobC's notion that players gravitate towards a usage they feel comfortable with, and that asking them to do more/less would take them out of their comfort zone, and probably hamper their efficiency. But, clearly, some guys have room to add possessions to their usage while maintaining their efficiency (they haven't reached their "maximum usage", if you will), while others have "maxed out", and any increase in usage would cause their efficiency to drop precipitously. Who is who? Not only that, but what happens when a bunch of low-usage guys get together on a team? Now somebody has to shoot... how will their efficiency be impacted?

We can quantify height. John Hollinger once suggested that atheticism could be approximated by looking at a player's rebounds, blocks, dunks, and steals. Can we quantify ball-handling ability so that guys who never dribble (cough, Hoiberg) don't get credit for not committing turnovers? Those last two are trickier. However, if we can, it might be theoretically possible to use those three factors to determine a player's "peak usage", or the maximum possible usage they can take on without a catastrophic drop in efficiency. What do others think of this? Am I way off base? Are people tired of this debate? Any suggestions on quantifying athleticism and/or dribbling ability?


Last edited by Neil Paine on Fri Nov 24, 2006 7:47 pm; edited 1 time in total
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Mike G



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PostPosted: Fri Nov 24, 2006 6:18 pm    Post subject: Reply with quote

I was just thinking it was time for another thread on this issue. Many topics seem to converge here, or at least have tangential aspects that do.

The causality issue is vital. Finding players whose shooting and/or passing increase because Someone needs to step up, we need to look at certain scenarios; not just games in which players took more shots.

How about last year's Rockets? Yao and McGrady missed 25 and 35 games, respectively. How did #3 man Juwan Howard do when one or both guys were out? Between 1/10 and 1/18, in his game log I see 4 games in which he played 40+ minutes, in which neither superstar appeared. He shot 13-26, 9-22, 9-20, 8-17; then 3-9 in 31 min. Then McGrady returns.

One instance of one player who steps up -- then shoots progressively less/worse as the week goes on -- doesn't indicate anything. Does anyone have boxscores in a database, such that they could segregate the shooting (or assists/turnovers) of Howard, Wesley, Alston, Head -- for games with/without TMac/Yao?
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Harold Almonte



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PostPosted: Fri Nov 24, 2006 7:00 pm    Post subject: Reply with quote

That was a very good explanation about scoring and usage. I´m agree with the argument that there must be a "player´s top efficient usage" depending on his skills, but an on date performance rating, a bad night, wrong teammates, can hide that. If this "top usage" could be measured, it could be taken as a player offensive performance-reference. What would be Kobe´s top?, his 81 points game?, his carreer average?, his two or three better seasons? upper than that?
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bballfan72031



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PostPosted: Fri Nov 24, 2006 7:42 pm    Post subject: Re: The Great Usage vs. Efficiency Debate Reply with quote

davis21wylie2121 wrote:

Can we quantify ball-handling ability so that guys who never dribble (cough, Hoiberg) don't get credit for not committing turnovers? Those last two are trickier. However, if we can, it might be theoretically possible to use those three factors to determine a player's "peak usage", or the maximum possible usage they can take on without a catastrophic drop in efficiency. What do others think of this? Am I way off base? Are people tired of this debate? Any suggestions on quantifying athleticism and/or dribbling ability?


I think that including the percentage of a player's shots that are assisted would be a good step.

And it would be good to take offensive fouls out of the turnovers.

It seems to me to be that turnover rate and assisted% are the best ways to quantify one's ability to increase one's possession usage. Plus however you would measure athleticism.

(Although I suppose it would be nice to just include assisted% in usage rate)
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bchaikin



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PostPosted: Sat Nov 25, 2006 12:40 am    Post subject: Reply with quote

couple of points:

Hoiberg may have had low turnover rates, but it's because he never dribbled the ball.

i can only surmise anyone truly believing this hasn't seen hoiberg play much...

in 00-01 hoiberg led the bulls in total assists. not many mind you (just 263), and the team wasn't very good (just 15-67), but it had the likes of elton brand, ron artest, ron mercer, brad miller, and others. are there alot of players that lead their team in assists than never dribble? did the players on this 00-01 bulls team dribble even less than hoiberg?...

the stats of dan majerle his last 6 seasons in the league (with miami and phoenix) are virtually identical to those of hoiberg over the past 10 years. same low touches/min (0.80 for hoiberg, 0.75 for majerle), both shot the ball with less than 1/3 of their touches, both turned the ball over with just 1 out of every 25 touches. similar rebounding rates, rates of steals, rates of blocks. was majerle another player who - like hoiberg - simply never dribbled the ball and was not athletic (his last 6 seasons in the league)? how about raja bell, hubert davis, and eric piatkowski (other SGs with similar low touches/min like hoiberg and majerle)?...

When he was put into situations where he had to take on more usage (and, thus, put the ball on the floor more often), his turnover rates went up, because he didn't have the requisite ballhandling ability.

on the contrary that same 00-01 season hoiberg had his highest touches/min, and played his most total minutes in a season, yet had one of his lowest rates of turnovers per touch at just 3% (about 1 turnover for about every 30 touches on offense)...

In terms of athleticism, Barry was a former slam-dunk contest winner, while Hoiberg was simply not very athletic.

guess that depends on your definition of athletic. have there been alot of unathletic players to have played in the league for a decade, and been one of it's best shooters? he shot close to 40% on 3s (just under 1000 attempts), and his career ScFG% of 56.4% was one of the top 20 or so in the league during the 10 years that he played. i'd say that for a player to play that long and shoot that well against the best players in the world, he'd have to be in pretty good shape athletically...

It assumes players convert shots on the margin at the same rate as their average shot. And so if we remove those players who shoot a lot (and draw a lot of the focus of the defense), the shooting percentages of remaining players will not change. Wins Produced is very similar to Bob Chaikin's simulator along those lines. Coming from a sports economics literature dominated by baseball, it is very natural to make this assumption, since this issue does not come up in a sport where every player gets his turn at bat.

this statement was made in another thread (the recent wages of wins thread), but is also talking about efficiency and usage. it states that the idea that "...the shooting percentages of players will remain the same if a player who shoots alot and thus draws the focus of the defense is removed..." is an assumption...

i can't speak for the wins produced people, but as for the simulator, this is not an assumption. what's the best way to look at this? well you can look at the stats of players who play alongside these high scoring star players who draw defenders, and then look at their stats when that star is on the bench. unfortunately those star players that score alot play a ton of minutes, and the sample size of data for when they don't play is small. would that data be significant? hard to say...

but what you can also do is to look at the players who played with the high scoring, defender drawing stars, and then look at those same players when they were not playing alongside those same high scoring, defender drawing stars - as in when they were on different teams from those stars...

the two players to have attempted the most scoring opportunities (FGA + FTA/2) this past decade are allen iverson and kobe bryant. both have played 10 years in the league, and both for the same team all that time (76ers/lakers). during the time iverson played for the 76ers 95 other players played on the 76ers, and of those 95 players 81 also played on other teams during those 10 years. here are the stats of those 81 players on the 76ers and on other teams during that decade:

team--------min------ScFG%--pts/0ptposs
76ers----162129-----.504--------1.87
others---453627-----.508--------1.92

i don't see a whole lot of difference in the overall shooting and scoring efficiency of these 81 players one way or the other...

for kobe bryant the data is similar - 75 different players on the lakers when he played, and of those 59 played on the lakers and also on other teams during the decade. here's the stats for those 59 players on the lakers and on those other teams:

team--------min------ScFG%--pts/0ptposs
lakers----142836-----.517--------1.97
others---424594-----.526--------2.03

again not alot of difference. i've looked at similar stats for about 100 other players (high scorers) over the past 30 seasons of the nba but cannot find a definitive pattern one way or the other, and when i look at data like this for those about 100 players, the total averages are within 0.5% for both ScFG% and pts per zero point team possession, i.e. there is no definitive pattern showing that overall shooting or scoring efficiency increases or decreases when players play alongside high scoring stars and then on teams not with them...

if someone has data showing definitively that the scoring efficiency of players with and without star scorers who draw defenders either increases or decreases on a consistent basis, i'd love to see it...
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Neil Paine



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PostPosted: Sat Nov 25, 2006 1:54 am    Post subject: Reply with quote

I should have known better than to get your Fred Hoiberg-sense tingling, Bob! Very Happy I was obviously exaggerating when I said Hoiberg "never dribbled"; I'm pretty sure he took at least one dribble in 2004-05... I will not argue with The Mayor's passing ability, either, especially since he posted some damn good assist rates throughout his stint in Chicago. He was a smart player who had great fundamentals and played within himself. However, in 2004-05 the vast majority (85%) of his shots were jumpers (most of them threes), and 94% of his baskets were assisted, meaning that not a whole lot of dribbling was going on (as you can see here, most assisted baskets are preceded by either zero or one dribbles). Point is, he wasn't breaking guys down off the dribble, which involves #4 and #5, and that fact alone would have capped his "peak usage"... There are only so many kick-outs to the corner that occur in a game, and beyond that, he'd have to create with ballhandling and athleticism, attributes that were not the strengths of his game.

And surely you know what I mean by "athleticism". The ability to shoot is certainly an "athletic skill", but when scouts talk about athleticism, they're not talking about how many shots a player can take in an empty gym before his arms get tired. They're talking about burst, speed, quickness, explosiveness, vertical leaping ability -- things that Freddie H. didn't exactly possess in spades. This is what I mean when I say that some players have the "potential to add usage without penalty"... You wonder why David Robinson added usage with impunity back in 93-94? He was huge, and he was an athletic freak with a scary arsenal of post moves who could get good shots off even with added defensive pressure. Hoiberg was of average stature, he was not even close to being a good athlete by NBA standards, and he did not have the ability to consistently beat a man one-on-one off the dribble. Frankly, odds are he was being guarded on most nights by a player of at least the same height, with far better athleticism than himself. He had to rely on #1, #2, and (especially) #3 to survive in the NBA, because in terms of numbers 4, 5, and 6, he clearly had liabilities. And to be a number one option, you have to have those attributes: superior athleticism, superior ballhandling skills (or, for big men, post moves), and/or superior size. Find me a #1 option on a good offense that did not possess at least one of these attributes, and then we can talk about Hoiberg's chances of adding usage with impunity and scoring 20 PPG.
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asimpkins



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PostPosted: Sat Nov 25, 2006 11:58 am    Post subject: Reply with quote

bchaikin wrote:
i can only surmise anyone truly believing this hasn't seen hoiberg play much...


Didn't they try to stick him at PG when Cassell was injured in the playoffs a couple years ago?

Quote:
but what you can also do is to look at the players who played with the high scoring, defender drawing stars, and then look at those same players when they were not playing alongside those same high scoring, defender drawing stars - as in when they were on different teams from those stars...


That's an interesting start, but there seems to be a few problems with it. First of all, we don't know what situations these players were traded into. If they go from playing with Bryant to playing with McGrady then this doesn't mean much. Most teams have someone at least in the all-star range. What percentage of the data is really meaningful from this perspective?

But I think the larger point is not whether they play with a superstar or not, but whether their role changes after the trade. Let's say Brian Cook is traded to Chicago. That team may lack a superstar scorer like Bryant, but if Cook is still asked to just take the same shots he did with the Lakers then I wouldn't be surprised if his efficiency remained constant.

What we're interested in is if his role changes -- if he tries to play Bryant's role on another team. That is, draw the best defender available. See double teams and extra help defense. Be expected to create open shots for your teammates off the dribble or in the post. And bail the team out in bad clock situations.
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Neil Paine



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PostPosted: Sat Nov 25, 2006 12:51 pm    Post subject: Reply with quote

asimpkins wrote:

Didn't they try to stick him at PG when Cassell was injured in the playoffs a couple years ago?


I think "try" is the operative word...
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Brian M



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PostPosted: Sat Nov 25, 2006 3:21 pm    Post subject: Reply with quote

As a foundational point, I'm not sure it's best to frame this in terms of usage vs. efficiency per se. The debate seems to be about how efficiency changes as a function of one's role in an offense, and so the thing being related to efficiency seems more qualitative-- what are you doing in the offense-- than quantitative-- how much are you doing in the offense. For instance, Scott Padgett might get a lot more shots than usual against a team that decides to double Yao every time he touches the ball in the post, but the nature of the shots he'd be taking-- open 3s off of kick outs from the post-- would be the same as usual. The crux of the issue, I think, wouldn't turn on how Padgett's efficiency changes as a function of how many open 3s he takes, but rather how it changes as a function of the type of shots he takes-- e.g., if he's asked to create the shot himself.

Assuming that is indeed the spirit of the argument, it would seem to me that assisted FG% is indeed a pretty good proxy for what is at issue. It seems a pretty safe bet that on average, assisted and unassisted FGs are of a qualitatively different nature, differing primarily in terms of who gets credit for creating the shot.

One way of assessing the issue, then, would be to look at how offensive effiency varies as a function of assisted FG% on the level of individual players. Intuitively, it seems likely that higher assisted FG% would always yield higher efficiency. The hypothesis, though, would just be that efficiency drops more precipitously as unassisted FG% rises for low-usage players than it does for high-usage players, i.e. there should be a usage x efficiency x assited FG% interaction. Such an analysis would involve looking at efficiency and assisted FG% on a game-by-game basis, though, making it tough to actually do the analysis (looks like a job for 82games.com?)

One complicating issue is that the semi-qualitative information given by the assist stat only applies for field goal makes. It would really be helpful if we could have access to counterfactual assist information (eg that pass would have counted as an assist, had the basket been made).
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bchaikin



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PostPosted: Sat Nov 25, 2006 4:34 pm    Post subject: Reply with quote

That's an interesting start, but there seems to be a few problems with it.

ok...

First of all, we don't know what situations these players were traded into.

not sure what you mean by situations, but yes we do know which teams each player came from and went to (before and after iverson/bryant), and who their teammates were...

If they go from playing with Bryant to playing with McGrady then this doesn't mean much.

of the 453,627 minutes players who played alongside iverson played on other teams, 8,145 minutes were played on teams mcgrady played on (tor 97-98 to 99-00, orl 00-01 to 03-04, hou 04-05 to 05-06). of the 424,594 minutes players who played alongside bryant played on other teams, 7,938 minutes were played on teams mcgrady played on. in the 1st case that's just 1.8% of the total minutes not with iverson, in the 2nd case that's just 1.9% of the total minutes not with bryant...

over the past 10 years iverson has averaged 27.9 scoring opportunities per game ((FGA + FTA/2)/G), no one else is even close on a per game basis. vince carter's at 22.9 ScOpp/g, shaq's at 22.9, webber and bryant are at 22.0 ScOpp/g. if you look at just the past 6 seasons, iverson's at 30.0 ScOpp/g, bryant's at 26.4, mcgrady 26.2, v.carter 23.2, webber 23.0, and p.pierce 22.7. so again no one is even close to iverson, and (at least for the past 6 seasons) bryant and mcgrady are also well above the others...

Most teams have someone at least in the all-star range.

over the past 6 years there have been 176 team-seasons (i.e. the celtics have had 6 team-seasons in the past 6 years). of those 176 the average ScOpp/g for the player with the most on a team has been 21 ScOpp/g. take away the 22 times a player lead his team in ScOpp/g with 25 or more, and in the other 154 team seasons the player with the most ScOpp/g averaged less than 20 per game. there is a big difference between a player like iverson averaging 30 ScOpp/g over the past 6 seasons, and 154/176 = 87% of the rest of the teams having a player with the most ScOpp/g being just around 20 per game...

What percentage of the data is really meaningful from this perspective?

if you are looking for meaningful data i would think looking at the largest pertinent data set you can find would give you the most meaningful result. you can micromanage this by looking at each and every one of the 81 players in the iverson case separately and the 59 players in the bryant case separately (and other players if you look at carter, pierce, webber, etc. in particular), but to say its an assumption that players scoring or shooting efficiency remains the same with or without playing alongside a high scoring player who draws multiple defenders is incorrect. the data shows in fact that overall it stays right about the same...

But I think the larger point is not whether they play with a superstar or not, but whether their role changes after the trade.

what does their role have to do with their scoring or shooting efficiency?
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schtevie



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PostPosted: Sun Nov 26, 2006 7:41 pm    Post subject: Reply with quote

It appears there are two debates on "whether or not a player can increase his usage/touches/possessions without a corresponding decrease in offensive efficiency"? One is a theoretical debate, that shouldn't exist. The second is an empirical debate that hasn't really been joined in any substantive way.

The theoretical argument for the negative relationship between increased usage and offensive efficiency is less theoretical than axiomatic. There are two strands. First, ALL ELSE EQUAL increasing usage by a particular player increases the predictability of the team offense. Accordingly, the risks to double-teaming and defensive switching decreases, and the offensive player in question faces more difficult shots on the margin, decreasing offensive efficiency. The second strand is a fatigue argument, where it becomes increasingly difficult for an offensive player (over the relevant range, it is assumed) to maintain offensive efficiency, becoming relatively fatigued compared to his defensive counterparts.

Now, for the theoretical argument asserting a negative relationship to be overturned, one can argue that the aforementioned assumptions are incorrect and/or suggest an alternative theoretical argument for a counterveiling positive relationship. I have never seen either, never mind both, of these two conditions met.

Then there is the issue of the empirical debate. What is the size of the supposed negative relationship? It could be "large"; it could be almost zero. I have never seen persuasive evidence on the point. And there is a reason for this: it is a pretty big job to get the data to speak. The key is to get ALL ELSE EQUAL.

BobC's experiment is to..."look at the players who played with the high scoring, defender drawing stars, and then look at those same players when they were not playing alongside those same high scoring, defender drawing stars - as in when they were on different teams from those stars"...and finds that..."there is no definitive pattern showing that overall shooting or scoring efficiency increases or decreases when players play alongside high scoring stars and then on teams not with them".

This is not really surprising because this experiment is not designed to identify the relationship in question. What the data are in this case are gobs of 2nd through Nth fiddles being shuffled around, presumably by and large repeating the same roles on subsequent teams. So, what you find is a big mix, some guys on the upswing of their careers (i.e. entering their competitive prime) and they do a little better, some on the downside, doing a little worse; some guys getting larger shares of the offensive pie, others shrinking (the implications here differ).

To try to tease the relationship out of the data, it seems to me that you would need to run a regression of yearly data, controlling for some key variables, such as: player age/experience, the initial share of offensive usage, and how these shares are dispensed within the time of position (as well as a variety of dummies for position and year).
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bballfan72031



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PostPosted: Sun Nov 26, 2006 10:32 pm    Post subject: Reply with quote

bchaikin wrote:
there is no definitive pattern showing that overall shooting or scoring efficiency increases or decreases when players play alongside high scoring stars and then on teams not with them...


I'm sorry, I thought the biggest debate was over the idea that turnover rate increases as possession usage increases....I thought that there would be a strong correlation with turnover rates, stronger than with shooting percentages.

Or am I on an entirely different subject here?
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Neil Paine



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PostPosted: Sun Nov 26, 2006 10:50 pm    Post subject: Reply with quote

The debate is whether or not all sorts of "bad things" (turnovers, missed shots, etc.) increase when a player is forced to take on more possessions/touches. DeanO's ORtg sums a player's efficiency into one number, so that metric is what I'm talking about when I say that a player's efficiency is rising or falling. It would be interesting, though, to see if one or the other (turnovers or missed shots) is more correlated with increased usage.
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asimpkins



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PostPosted: Mon Nov 27, 2006 1:44 am    Post subject: Reply with quote

bballfan72031 wrote:
I'm sorry, I thought the biggest debate was over the idea that turnover rate increases as possession usage increases....


Yeah, it definitely wouldn't have to be an increase in turnover rate. One of the easiest ways to avoid a turnover is just to throw up a bad shot. So drops in shooting efficiency needs to stay in the discussion.

schtevie wrote:
This is not really surprising because this experiment is not designed to identify the relationship in question. What the data are in this case are gobs of 2nd through Nth fiddles being shuffled around, presumably by and large repeating the same roles on subsequent teams.


Nice post. That's pretty much what I was trying to get at.
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bballfan72031



Joined: 13 Feb 2005
Posts: 54

PostPosted: Mon Nov 27, 2006 11:52 pm    Post subject: Reply with quote

Oh, okay, thanks. Yeah, the individual Ortg makes the most sense. I got mixed up with the talk of efficiency and thought the discussion was focusing on simply shooting efficiency.

I was also for some reason under the impression that I had seen more evidence for the turnover rate correlation than shooting percentage....though in retrospect, I would say it's about even.

My apologies, carry on.
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