Possession cost scheme (Charles, 2007)
Posted: Fri Apr 22, 2011 2:25 pm
Charles
Joined: 16 May 2005
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PostPosted: Sun Dec 09, 2007 9:10 am Post subject: Can some one explain the “possession cost†scheme? Reply with quote
I don’t understand this.
If I take two players and give each an "average" record based on playing 10% of their team's minutes, except one with all his points from two-pointers and the other with all his points from three-pointers the player shooting three-pointers gets 55 less PER credits.
Each player took the same number of shots. Each scored the same number of points. Yet, the two point shooter gets more PER credits (based on less FGx)
Am I missing something, or does a pound of stone actually weigh more than a pound of feathers?
Last edited by Charles on Sun Dec 09, 2007 10:41 am; edited 1 time in total
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deepak_e
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PostPosted: Sun Dec 09, 2007 10:05 am Post subject: Reply with quote
I'm looking at the PER formula right now, and here are the relevant terms:
3P + (2 - factor*(TmAst%))*FG - VOP*DRB%*(FGA_miss)
So, I think you're assuming that TmAst% is 0, DRB% is 1, and VOP is 1. Then, it reduces to:
3P + 2*FG - FGA_miss
Per possession, we expect 1 points to be scored (VOP = 1). If you have a player who scores 60% of the time on 2-pointers, then we expect:
.6*2 - .4 = 0.8 credits earned per shot attempt
And if you have a player who scores 40% of the time on 3-pointers, we expect:
.4*3 - .6 - 0.6 credits earned per shot attempt
So, according to PER, if all misses are rebounded by the defensive team, then it's better to score your X points at a higher percentage inside the arc then at a lower percentage outside the arc. This can easily be rationalized. I imagine that teams tend to be more efficient in their possessions when it follows a miss by the other team, versus a make since defense has less time to get set. So, a miss doesn't only represent lost opportunity on the offensive end, it also impacts the ensuing defensive possession. Not sure if it was intended, by Hollinger's scheme does seem to take this into account in a clever way.
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Charles
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PostPosted: Sun Dec 09, 2007 10:44 am Post subject: Reply with quote
You are correct deepak, I grossly over-simplified, since you can't determine the exact values without league averages. Could you comment on the modified first post.
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Charles
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PostPosted: Sun Dec 09, 2007 10:50 am Post subject: Reply with quote
deepak_e wrote:
So, according to PER, if all misses are rebounded by the defensive team, then it's better to score your X points at a higher percentage inside the arc then at a lower percentage outside the arc. This can easily be rationalized. I imagine that teams tend to be more efficient in their possessions when it follows a miss by the other team, versus a make since defense has less time to get set. So, a miss doesn't only represent lost opportunity on the offensive end, it also impacts the ensuing defensive possession.
Fair enough, although it is rather speculative. However, do you think this possibility makes up for about 8% less PER credits -- despite allowing 50% more offensive rebounding opportunities? This seems way out of balance to me.
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Flint
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PostPosted: Sun Dec 09, 2007 11:41 am Post subject: Reply with quote
Here is Berri on PER...
"Hollinger argues that each two point field goal made is worth about 1.65 points. A three point field goal made is worth 2.65 points. A missed field goal, though, costs a team 0.72 points.
Given these values, with a bit of math we can show that a player will break even on his two point field goal attempts if he hits on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA played does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots.
But again, our model of wins suggests that inefficient shooting does not help a team win more games. Hence the conflict between PERs and Wins Produced. Hollinger has set his weights so that inefficient scorers still look pretty good. We argue that inefficient scoring reduces a team’s ability to win games, and therefore these players are not nearly as effective as people might believe."
Hollinger also has GameScore, a simplified version of PER. Although PER is extremely complicated, it has a 99% correlation with Game Score, or at least so I have read over at the WOWJ. The formula is....
(Points x 1.0) + (FGM x 0.4) + (FGA x -0.7) + ((FTA-FTM) x -0.4) + (OREB x 0.7) + (DREB x 0.3) + (STL x 1.0) + (AST x 0.7) + (BLK x 0.7) + (PF x -0.4) + (TO x -1.0)
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Charles
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PostPosted: Sun Dec 09, 2007 11:51 am Post subject: Reply with quote
Do you agree with Berri on this point, Flint?
I do. I see the PER approach as a compensation for the minimal weight given to shot creation. I realize shot creation is difficult to determine using nothing but official stats, but that's the challenge, because shot creation is essential to understanding the reality of basketball.
When you combine PER's implementation of "lost opportunities" with the error caused by assuming everyone has the same percentage of their shots assisted (Amare actually has about 65% of his baskets assisted compared to 20% for Nash) and a very loose rationalization for the weighting of assists versus points scored) it becomes easy to understand why Nash’s plus/minus has averaged about 7.3 points per 48 minutes higher than Amare’s since they began playing together. Plus minus is noisy, but a seven point difference over 6,000 minutes played is a lot.
Incidentally, I would be reluctant to criticize these weights if they were produced through regression or some other verifiable analysis rather than logic.
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Flint
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PostPosted: Sun Dec 09, 2007 12:26 pm Post subject: Reply with quote
Yes. I definitely agree with Berri. And I don't think there is any objective basis for Hollinger's weights.
You were discussing Joe Johnson in the other thread. Here is a comp of 03-04 and last season.
http://www.basketball-reference.com/fc/ ... 02&y2=2007
To me, it seems very odd that went from a 15 PER to a 19.5 PER. What changed? His ts% was the same, 55.6% and 55.8%.
In y2, 1.4 less rebounds, .8 more assists, 1.6 more tumovers, and of course, 5.4 shots more per 48 and 8.3 points more per 48. To me, that is valuing shot creation a great deal more than necessary.
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Harold Almonte
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PostPosted: Sun Dec 09, 2007 12:27 pm Post subject: Reply with quote
Flint, the WOW logic about the team possession lost after a FGMade could be acceptable, but his approach is wrong and he created a big mess. He penalizes scorers (FGMade) by attempts and rewards the inbounds (oppFGMade) in the opp. team, by minutes. He should have done this also by attempts (if he considers FGMade a matter of individual attempts rather than team), and then scorers just recuperate the most of this team possession lost/gain-with the ball and the clock out of play (just a rule). There's no any straight relationship between FGA and player minutes for him to attempt to cancel one thing with the other, and he's just rewarding low FGA-high minutes players.
PER could be overrating a bit, but WP is overpunishing there. They did the opposite with Rebounds.
Last edited by Harold Almonte on Sun Dec 09, 2007 2:38 pm; edited 2 times in total
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Guy
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PostPosted: Sun Dec 09, 2007 12:35 pm Post subject: Reply with quote
Quote:
Do you agree with Berri on this point, Flint?
LOL.
Quote:
But again, our model of wins suggests that inefficient shooting does not help a team win more games. Hence the conflict between PERs and Wins Produced.
If the distinguishing feature of WP is it's treatment of shooting efficiency, I wonder, "Flint," if you could explain to us why WP has a lower correlation with TS% than does PER? And lower than NBA Efficiency? The truth is that because WP penalizes all shots, not just missed shots, it rewards efficient shooting less than PER.
What really distinguishes WP is that it gives zero credit to shot-taking, not its treatment of efficiency. This means that high-usage/low-efficiency players will indeed be rated very low compared to other metrics, but it also means that high-usage/high-efficiency players will be rated lower than in other metrics.
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Flint
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PostPosted: Sun Dec 09, 2007 12:51 pm Post subject: Reply with quote
Guy - What do you think of PER?
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Charles
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PostPosted: Sun Dec 09, 2007 1:08 pm Post subject: Reply with quote
Guy wrote:
What really distinguishes WP is that it gives zero credit to shot-taking, not its treatment of efficiency. This means that high-usage/low-efficiency players will indeed be rated very low compared to other metrics, but it also means that high-usage/high-efficiency players will be rated lower than in other metrics.
Guy, have you seen evidence that low percentage shot taking deserves credit? I am not talking about shot creation - which is the "unassisted" portion of an unassisted field goal - but, simply shot taking itself?
The analysis I have done says an assisted two-point field goal attempt has no value beyond the actual points scored (in fact it has a small negative value.) Assisted three point attempts do have value, even when they miss, but they are easily separated out.
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Guy
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PostPosted: Sun Dec 09, 2007 6:57 pm Post subject: Reply with quote
Flintberri: My point is not to argue for (or against) PER. My point is simply that WP does not value efficiency more highly, as claimed, as demonstrated by its lower correlation with shooting efficiency. The metric is so dominated by rebounds that it can't give proper credit even to many of the efficient shooters that Berri celebrates.
Charles: I wasn't trying to draw a distinction btwn shot-taking and usage, and wouldn't claim to know the right way to value usage. (My intuition would be to try to establish a reasonable replacement level, which certainly would be lower than league average.) But I feel pretty confident that these equations from the WP perspective are wrong:
* 0-0 = 2-4 = 12-24
* 2-4 > 11-23
* Net value of all shooting by NBA players = zero.
WP says that all below-average shooters hurt their teams, so logically I assume that means these players should stop taking shots. But here's the problem: in this new WOW version of the game, half of those still permitted to shoot will be below the new, higher ts%. So WP will then tell us again that they too should stop hurting their team by shooting, having committed the sin of being below average. Eventually, I suppose each team will have one player who takes all of its shots. Personally, I don't find this terribly plausible. Perhaps Flintberri can make sense of it?
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asimpkins
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PostPosted: Sun Dec 09, 2007 9:33 pm Post subject: Reply with quote
Charles wrote:
Fair enough, although it is rather speculative. However, do you think this possibility makes up for about 8% less PER credits -- despite allowing 50% more offensive rebounding opportunities? This seems way out of balance to me.
I think you've made a good point. The damage of a missed shot may go beyond the opportunity cost (and the chance of an offensive rebound) because the defense has less time to setup, but this should be established and measured first. Until then it seems like just an excuse.
And it seems to me the only way to avoid this discrepancy between 2p and 3p shooting is to subtract the same opportunity cost from all attempts -- makes and misses -- like you were suggesting in the other thread.
(I'm pretty sure the opportunity cost should not be '1' though.)
Quote:
Incidentally, I would be reluctant to criticize these weights if they were produced through regression or some other verifiable analysis rather than logic.
After seeing what a disaster WoW is, I don't think you should be reluctant to criticize weights just because they were produced through regression. These things don't run themselves. You always need to bring in some logic.
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gabefarkas
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PostPosted: Sun Dec 09, 2007 9:37 pm Post subject: Reply with quote
Flint wrote:
But again, our model of wins suggests that inefficient shooting does not help a team win more games.
Oh really? Who is the "our" in your sentence referring to? You and Mr Berri? Because I wholeheartedly disagree with this contention. Take a look at Iverson's 6ers teams, for one.
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94by50
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PostPosted: Sun Dec 09, 2007 10:06 pm Post subject: Reply with quote
Is it just me, or are the following possible?
* The break-even marks for 2pt and 3pt shooting in PER are too low.
* The break-even marks for 2pt and 3pt shooting in WP are too high.
* The ideal mark is somewhere in the middle.
Just eyeballing it, for example, if I take the 30% break even mark for 2pt shooting in PER, and split the difference with league average 2pt shooting (the break even mark in WP), which is, what, about 49%... the average of the two is in the high 30s. I suspect the ideal break even mark is somewhere in that neighborhood. Just a hunch.
Also, regarding the idea that "inefficient shooting does not help a team win more games"... well, of course it doesn't. The question is, how poorly does a player have to shoot before they shouldn't be shooting at all? The Sixers were more than willing to live with Allen Iverson's 40% field goal percentage for quite a while. Why is that? (And I don't think the correct answer is, "Because Iverson is a scorer and teams overvalue scorers.")
Mike G
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PostPosted: Mon Dec 10, 2007 7:27 am Post subject: Reply with quote
Doesn't the usefulness of the shot depend on a few things besides the % of time you make the shot? Like:
FT likelihood and %
the shot clock
one's teammates
In another thread we went into depth about how good/bad Willie Green is. His TS% is .470, so he should probably shoot less. How much less?
Updated, here's a chart like one I posted earlier. eTS% is estimated TS%, in which I've added (TS%-eFG%) to 82games.com's eFG% for each time interval. These shooting% are thus adjusted upward for each player; moreso for those who make more FT/FG. Assuming FT accompany FG equally at all stages of the shot clock.
Philly players, ranked by total shot attempt frequency:
Code:
eTS%% at seconds:
FG/40 FT/40 Sixers 0-10 11-15 16-20 21+
14.8 5.6 Iguodala .62 .53 .47 .39
15.0 5.4 Williams .64 .55 .56 .36
15.7 3.6 Miller .55 .54 .49 .38
16.2 2.2 Green .53 .46 .48 .43
15.0 2.2 Korver .51 .53 .49 .35
9.8 5.5 Dalembert .64 .61 .53 .52
10.9 3.9 Smith .60 .42 .48 .48
6.4 4.0 Evans .59 .24 .66 .19
Sixers .59 .50 .51 .39
The bottom line shows the team's eTS% in each time interval; estimated, again, by assuming FTA/FGA are evenly distributed in each interval.
Willie Green was criticized for taking low-% shots in the 11-15 second interval (when he had hit only 39%), thus depriving better shooters. Passing on a 46% shot to get a 50% shot is less a big deal.
But taking a 49% shot at 18 sec. is a lot better than a 39% shot at 22 sec. When you pass the ball, a few seconds have ticked away. And shooting specialists Williams and Korver seem to be worst at buzzer-beaters. Green is apparently the best (among those who actually get shots).
'Who your teammates are' should also include offensive rebounding. If 30% of missed FG are offensively rebounded, then even on a 30% FGA the odds of 'something good' happening are .30 + (.30*.70) = .51
When FT add .044 to a player's efficiency (league TS%-eFG%), then a 30% shot is 55% 'good'.
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Harold Almonte
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PostPosted: Mon Dec 10, 2007 3:09 pm Post subject: Reply with quote
If for a fairly scoring rating we need to rate: the assisted factor, the dificulty factor (how was guarded the scoring attempt, and by whom-s), and this kind of decission making factor. Why everybody say that defense is more dificult to rate than offense?
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Jacob
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PostPosted: Mon Dec 10, 2007 3:22 pm Post subject: Reply with quote
People worrying about the break-even marks in PER completely miss the point, and this includes our friend Berri. The talent level in the NBA dictates the break-even mark, not John Hollinger. A player with a 31% 2P% will never play significant minutes, let alone attempt significant shots. This is why it drives me crazy when people claim that "PER unfairly rewards 35% shooters who take 30 shots a game". Like these players actually exist in the NBA, the environment PER was designed for.
I guess there's also a continued misunderstanding what PER measures. It doesn't quantify a player's contribution to team wins, but it pragmatically identifies player quality. It recognizes the burden some players are made to carry by their coaches; it never mistook Allen Iverson for a bad offensive player, even in 03-04, and doesn't love him all of a sudden now that he shares the floor with Carmelo Anthony.
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John Hollinger
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PostPosted: Mon Dec 10, 2007 3:34 pm Post subject: Reply with quote
Part of the problem with setting a higher break-even mark for FG% and 3P% is that we only get half the story in the stats. What I mean by that is there is a stat for assists -- good passes that lead to a made basket -- but not for anti-assists -- bad passes or passes not made that lead to a missed shot. The consequence is that the shooter splits the credit for a made basket, but takes all the blame for a miss. If we can work out that quandary, we can reset the break-even threshold. Otherwise, if you set it any higher, you unfairly punish the shooter for misses that may have been the fault of others (such as the dreaded "flaming bag" pass, when a guy get thrown the ball when he's covered 20 feet from the hoop with two on the shot-clock.)
As an aside, somebody with league-average stats in every other category and the "break-even"FG% will end up with a PER around 8 or 9 -- you'd have to take a LOT of shots at that low efficiency mark to end up anywhere close to normal, and that would presumably only happen on on a horrendously bad team.
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Flint
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PostPosted: Mon Dec 10, 2007 8:07 pm Post subject: Reply with quote
Mike G - They are discussing your post over at the Wages of Wins in the Kevin Garnett thread.
http://dberri.wordpress.com/2007/12/10/ ... -nba-team/
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Harold Almonte
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PostPosted: Mon Dec 10, 2007 8:51 pm Post subject: Reply with quote
If it were prohibited to take Off. Rebs., then every FGMissed would be the same than a turnover, and will be straight canceled by DRebs.
No matter if you think or not an OReb. starts a new possession for a teammate (and he is not loosing any credit), a simple TEAM regression (used by WP to weight stats) would weight the cost of a FGMissed as a 70% of a turnover, because that is how much the opponent can steal (rebound) it. Then, I don't know why some stats are supposed to be weighted by team win regressions, and other ones by personal logic, and how some possessions are responsibility of the usager, and other ones (opp.FGMade-inbounds, opp. not stolen TOs, etc.) are for the team.
I don't understand how you can be stolen by a teammate. Or is he stealing from the opponent? Did the opponent have a possession with the ball in the air? It's not a pass, but It's not a double steal situation. It's not transfering credits from the off. rebounder to the shooter, is transfering the lost credits from the shooter to the off. rebounder of course, but not a full possession lost. The possession never was lost at all.
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Guy
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PostPosted: Mon Dec 10, 2007 11:10 pm Post subject: Reply with quote
Flint: Conceptually, there's nothing inherently wrong with basing a valuation system on average efficiency, as Berri does, rather than replacement level. However, you then have to find a separate way to value usage, so that you don't end up saying that 0-for-0 shooting is as valuable as 15-for-30 shooting, which clearly isn't true. Setting a lower break-even level provides a mechanism for valuing usage and efficiency together. You may want to quibble with the precise break-even points in PER, but until/unless Berri amends WP to penalize players for not shooting as well as for inefficient shooting, I don't see how WP is an improvement.
In the thread you link to, Berri objects to any linear weight model (like PER) that sets the "break-even" rate below 50% on the basis "that it allows an inefficient shooter to increase his value just by taking more shots." He has made this point dozens of times, and seems to feel it's a debate-ending observation -- that any metric with this feature must be wrong. But the idea that below-average players must lose value the more scoring opportunities they consume is hardly self-evident. For example, the best value metrics in baseball, based on replacement-level production, would all say that a 10%-below-average hitter is worth more when consuming 600 plate appearances than 300 plate appearances.
This determination to penalize usage among below-average shooters seems rooted in WP's radical claim that the average level of efficiency has zero value. If 1-for-2, 5-for-10, and 15-for-30 shooting all have equal value, then clearly that value is zero. I'm not aware that Berri has ever offered an explicit argument for why 50% shooting has no value -- if he has, can you explain it? It seems to me that case requires demonstrating that the skill required to maintain league-average efficiency over 48 minutues is ubiquitous -- that any team should always be able to get the ball in the hands of an average shooter. (Of course, one has to overcome a number of uncomfortable facts, such as that about half the teams in the NBA fail to achieve this standard every season, and that teams with "zero-value" shooting tend to win about 41 of 82 games.)
And, I'm still interested in your thoughts as to why Wins Produced has a weaker correlation to shooting efficiency than PER, if Berri is right that a greater emphasis on efficiency -- rather than overvaluing rebounds vis-a-vis scoring -- is what makes WP different.
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asimpkins
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PostPosted: Tue Dec 11, 2007 12:10 am Post subject: Reply with quote
And if average shooters are worthless, shouldn't the same thing go for average rebounders? But a player who never shoots and just rebounds at an average rate will do well with WoW. I think that was part of the point NickS was making in this post. Whatever criteria you enforce on shooting, you have to also enforce on rebounding.
And this got me thinking about the original point Charles made about PER here. I think he's right that PER is flawed in not counting an opportunity cost for a made basket, but at the same time it didn't seem like PER would be improved if you made only this change. I began to think that PER ended up working out kind of right, but for the wrong reasons. PER was inflating the value of made baskets, but only as a response to the inflated value of rebounds.
I did some research, and I again rediscovered another excellent post by NickS where I think he gets the right answer later in the thread:
NickS wrote:
If you deducted the full value of a possession from made baskets in PER all of a sudden you would find that the people it would rate very highly would be rebounders. Finding some balance between scoring and rebounding is necessary for the reason I laid out in the "two meanings of zero" post. Again, PER accomplishes that by setting a value for Rebounding, and then deflating it by adding extra value for made baskets.
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Flint
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PostPosted: Tue Dec 11, 2007 12:16 am Post subject: Reply with quote
Guy - How much you score matters in WP. The way I think about it is that there is a points scored benchmark and an efficiency benchmark, via fga, fta, ftm's, etc. A player is penalized if he doesn't match the benchmark for his position. So, if you have two players who both shoot a ts% of 55%, and one scores twice as many points as the other, he will produce more wins. What happens when you have two below average efficiency scorers is unclear to me, but I think you get penalized the more opportunities you use.
I think a lot of people get confused by WS, and the fact that you can shoot 20-40 on 2 pt fg's and not accumulate any WS. But people always forget to add in the effect of 3pters and fts. When you do that there is much more variation. I watch games calculating WS, and most player don't shoot over 50% from the field. But when you throw in fts and three pointers, that changes. And when you throw in position adjustments it changes again.
To me, usage is baked into WP, or at least as much as it needs to be. If you are a player who doesn't score points, its going to be harder to meet your overall target. If you don't notch assists ditto. You have to make it up in other parts of your boxscore. Yes, Steve Nash commits a lot of turnovers. But that's because he is accumulating assists at an even higher rate.
People maintain that WP has a problem evaluating high usage players. I don't really see that. Most of the top players in WP are scorers and high usage players. To me, it has always been much more clear that PER has a huge problem with evaluating low usage players. The fact that Dennis Rodman had a below average career PER and Eddy Curry is above average has always been my touchstone in that regard for me.
I don't know if PER correlates more closely with shooting efficiency. If you have done a study which shows that, post it and I will comment.
I can't say I really understand your replacement level player argument. I am not a sabermetrician, or a statistician for that matter. But I don't think its true that average efficiency has zero value, as you say above. A team of average players will win 41 games, which is a damn sight better than 0, and much better than what the Knicks will put up this year.
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Mike G
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PostPosted: Tue Dec 11, 2007 9:56 am Post subject: Reply with quote
The benchmark for shooting% that has >0 value cannot be static. In an 84-80 (avg score) playoff series, it may be that a 43% FGA is a 'good' shot.
In the '98 Finals, the Bulls forced the Jazz to shoot just 45% FG (down from 49% in the season). More aptly, Utah's TS% was off, from .567 to .506 .
Despite running 3 fewer possessions per game, Utah was forced into 1 extra turnover from their season rate.
Together, these resulted in an offensive efficiency drop of 17%, from their norm of 1.13, to .93 Pts/possession. Any shot better than about .390 eFG% was a 'better than average' possession.
That's assuming their offensive rebounding (26%) led to just their average (.506) scoring rate, with no TO and no 2nd OReb.
There were some playoff series ('80s-90s) between Phx and Den, in which a 50% FG try was almost a waste.
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Guy
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PostPosted: Tue Dec 11, 2007 10:54 am Post subject: Reply with quote
Flint wrote:
Quote:
To me, usage is baked into WP, or at least as much as it needs to be. If you are a player who doesn't score points, its going to be harder to meet your overall target.
A usage value is indeed baked into WP, and that value is zero. Usage is rewarded only for above-avg-efficiency shooters, and has negative value for below-avg-efficiency. Overall, usage has no net value, and WP has virtually no correlation with usage at the player level. And for half of the players your second sentence is demonstrably false: if you are a below-avg-efficiency shooter, the fewer points you score the easier it is to reach the overall target. A 48% TS% player is more valuable taking zero shots per game than taking 20.
Quote:
I don't think its true that average efficiency has zero value
Then you need to study WP more closely. An average efficiency player receives identical WP when taking 2, 10, or 20 shots per game. If 2*X = 10*X = 20*X, and I solve for "X," I get X=zero; don't you? This shouldn't surprise us: Berri says "efficient shooting" (by which he means above-average) creates wins and has positive value, while "inefficient shooting" causes losses and has negative value. So it follows logically that average shooting will have zero value.
Quote:
I don't know if PER correlates more closely with shooting efficiency. If you have done a study which shows that, post it and I will comment.
Dan Rosenbaum has studied this and found a WP-TS% r of .556, compared to .613 for PER-TS%. I believe his paper will be published fairly soon, so you (and Berri) will have the chance to study and rebut it. But just as a matter of algebra, it's easy to see that PER punishes inefficient shooting more than WP if you hold shot attempts constant. WP will value inefficient/high-usage players lower than PER, but will also value efficient/high-usage players lower than PER. So my guess is Rosenbaum's calculations are correct.
* *
To some extent, the two main criticisms of WP -- undervaluing scoring, overvaluing rebounds -- are just two sides of the same coin. If either claim is true, the other has to be at least somewhat true. But it is useful to consider them separately. While I believe Berri is wrong that usage has no value and there is no usage/efficiency tradeoff (basically the same claims), I don't think critics can claim to have proven that point definitively. And a weak version of Berri's argument -- that teams could improve by giving somewhat more shots to high-efficiency shooters -- is not inherently implausible.
On rebounds, however, there is no doubt that Berri's core assumption -- that all player rebounds equal a net additional rebound for his team -- is false. A player's REB total is highly influenced by that of his teammates. For example, if you run a correlation between the REB total for a team's top rebounder and the REB of his teammates, it's about -0.80. In fact, the negative correlation is so strong that the standard deviation for rebounding is actually much higher at the player level than at the team level. The difference between good and bad rebounding teams is fairly small, and that simply couldn't happen if the real differences in players' rebounding ability were as large as raw REB stats imply.
Berri's post yesterday on Garnett and the Timberwolves is a good example of how this gets Berri in trouble. WP estimates that KG was about 23 wins above average per year in his peak years (02-03 thru 05-06). About 45% of this comes from rebounding, as he averaged 330 rebounds/season more than an average F. But, while WP assumes this meant 330 extra rebounds for the T-Wolves, in fact the team was only 33 rebounds above average in these years. While KG was +330, his teammates were -297 -- what bad luck!
Interestingly, the now terrible KG-less T-Wolves are averaging more rebounds per game (42) than in Garnett's last two seasons (40). Isn't it surprising that Minn could improve its rebounding while losing KG's 330 boards? That would mean that the rest of the team has suddenly improved by 6 REB per game, an astonishing improvement. And if rebounding is so important, shouldn't we be shocked that a team can get much worse while improving its rebounding? Yet Berri doesn't even mention it.
You find the same pattern with Rodman. At his peak, 91-92 to 97-98, Rodman was +543 REB per year (vs. avg F). Yet his teams were only +162 overall. Rodman's teammates were a horrific -381 REB on average, and were well below average in every one of these seven seasons (covering 3 different franchises). Another great rebounder saddled with lame teammates. Bad luck yet again! (I haven't done the work, but I'm pretty sure you will find that virtually every great NBA rebounder has had similar misfortune.)
The final test of what matters in winning is whether an attribute is actually correlated with winning. What led Bill James to discover that stolen bases aren't very important for winning baseball games was observing that winning teams didn't have many more SBs than losing teams, and high-SB teams didn't tend to win many more games than low-SB teams. The same is true for rebounds relative to scoring in the NBA. The correlation between point differential and shooting (PPS) is about 3 times higher than the correlation between point differential and rebounding. However, WP is more highly correlated with rebounding than with scoring (and much more correlated with rebounding than PER). Berri's whole case is built on the notion of explaining team wins. But while rebounds don't explain very much of the variance in team wins in the NBA, they explain a lot of the variance in Wins Produced.
Charles: sorry to hijack your thread.
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Flint
Joined: 25 Mar 2007
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PostPosted: Tue Dec 11, 2007 4:46 pm Post subject: Reply with quote
Guy - I don't think I can give you satisfaction here. If everything that has already been written by Berri hasn't been enough to convince you, including his direct responses to you, I don't know what more I can offer. Reading your post, what I can say it that I don't think it is an accurate depiction of Wins Produced.
The way you are thinking about rebounding and the way it is treated by Wins Produced, for instance, strikes me as flawed. Specifically, your characterization of....
"Berri's core assumption -- that all player rebounds equal a net additional rebound for his team"
"Jason" had what I hope is a germane comment at 1042 today in the Garnett post. From that:
"WP" doesn’t say that a 10 rebound/48 player replacing a 15 rebound/48 player will result in a net increase in 5 rebounds 48. It says that the increase or decrease in wins will be roughly equivalent to the win probability contributed by the player-assigned stats. The model does not say that any isolated components must stay constant. It is important not to confuse the two."
I think actually reading the rest of that post by him, and the others he has written today might be a better response to what you posted above than what I can offer you.
My interest in basketball stats is a byproduct of reading the WOW and of work done in public policy, investing, and also a very serious poker hobby. I am not a basketball statistician or professional economist. While I understand most of the arguments made, I don't think I can really engage you at the appropriate level.
Re PER
I guess unfortunately I operate by sense of smell, like some on this board, and I think like most people who watch basketball. I just have a different sense of smell, for reasons which I have articulated in the past (and been ridiculed for, which was sort of hilarious). I am also a Knicks fan, which means I have been watching Eddy Curry for the past 2+ years.
Anyway, bottom line, PER tells us that Curry has been a better player than Samuel Dalembert and Tyson Chandler in his career. It tells us also that Curry has been better than Dalembert this year and as good as Chandler.
And that's kind of what it boils down to for me. Is Eddy Curry really an above average NBA center? Is he really as good as Tyson Chandler, currently anchoring the fourth best defense in the league. Is he really only slight worse (.5 PER) than Marcus Camby, currently anchoring the second best defense in the league? Is he really dramatically better than Ben Wallace, the center on the fifth best defense, as PER suggests?
PER would have us believe, it seems to me, that if you were to swap Curry for Camby, Wallace, Chandler, Dalembert, Oberto, Ilgauskas, or any other number of big men he scores more then, the Knicks wouldn't improve. That the only serious upgrade we could make at the center position would be Ming, Bynum, or Howard. And that's just, well, incredibly bizarre to me.
Wins Produced does not ask me to believe that. It tells me in fact that getting rid of Curry and adding any of those players would help the Knicks a great deal. That makes sense to me. Argument from anecdote I know, sorry not be able to give you anything else...
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asimpkins
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PostPosted: Tue Dec 11, 2007 5:32 pm Post subject: Reply with quote
Flint wrote:
Anyway, bottom line, PER tells us that Curry has been a better player than Samuel Dalembert and Tyson Chandler in his career.
Flint. If you're going to criticize PER, you should at least get the basics right. PER doesn't make statements about who's an overall better player because it only measures what happens in the box score -- which ignores most defensive contributions. PER summarizes box score contributions only and estimates how many points those contributions would make for a typical team.
So you should say that PER tells us that Curry has been a better box score producer than Dalembert or Chandler -- which is a very different argument. Maybe you think that is incorrect as well, but at least you are characterizing PER correctly.
In the same way, PER does not say that Rodman was an average player -- another of your favorite examples. It says that he was an average box score producer. His defense would certainly have him ranked much higher. Again, maybe you think that box score analysis is incorrect, but you're not helping anyone by beating up on a strawman.
Quote:
PER would have us believe, it seems to me, that if you were to swap Curry for Camby, Wallace, Chandler, Dalembert, Oberto, Ilgauskas, or any other number of big men he scores more then, the Knicks wouldn't improve.
Again, PER makes no such claim. (Hollinger is frequently critical of the Knicks' interior defensive problems.) You've seriously misunderstood the scope of these stats. You need to re-approach all of these players and numbers from the mindset of measuring box score contributions only. Ben Wallace, who does so much off the box score, shouldn't be rated to his full actual value. That would actually be a warning flag that something is wrong.
So, of course, WoW also measures only box score contributions -- and not much of defense. If you find WoW is measuring players accurately in an overall sense, then this is actually a problem. That would imply that WoW is getting the right numbers for you, but for very wrong reasons -- the method is flawed.
Last edited by asimpkins on Tue Dec 11, 2007 5:56 pm; edited 1 time in total
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Flint
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PostPosted: Tue Dec 11, 2007 5:56 pm Post subject: Reply with quote
Asimpkins - I have heard this argument before and I find it baffling.
Would it be accurate to say:
PER is designed to provide a summary statistic measuring a players production of box score stats. It is not designed to capture a player's actual contribution to winning basketball games for his team.
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asimpkins
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PostPosted: Tue Dec 11, 2007 5:58 pm Post subject: Reply with quote
It would be correct to say:
It is not designed to capture a player's full contribution to winning basketball games for his team.
Joined: 16 May 2005
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PostPosted: Sun Dec 09, 2007 9:10 am Post subject: Can some one explain the “possession cost†scheme? Reply with quote
I don’t understand this.
If I take two players and give each an "average" record based on playing 10% of their team's minutes, except one with all his points from two-pointers and the other with all his points from three-pointers the player shooting three-pointers gets 55 less PER credits.
Each player took the same number of shots. Each scored the same number of points. Yet, the two point shooter gets more PER credits (based on less FGx)
Am I missing something, or does a pound of stone actually weigh more than a pound of feathers?
Last edited by Charles on Sun Dec 09, 2007 10:41 am; edited 1 time in total
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deepak_e
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PostPosted: Sun Dec 09, 2007 10:05 am Post subject: Reply with quote
I'm looking at the PER formula right now, and here are the relevant terms:
3P + (2 - factor*(TmAst%))*FG - VOP*DRB%*(FGA_miss)
So, I think you're assuming that TmAst% is 0, DRB% is 1, and VOP is 1. Then, it reduces to:
3P + 2*FG - FGA_miss
Per possession, we expect 1 points to be scored (VOP = 1). If you have a player who scores 60% of the time on 2-pointers, then we expect:
.6*2 - .4 = 0.8 credits earned per shot attempt
And if you have a player who scores 40% of the time on 3-pointers, we expect:
.4*3 - .6 - 0.6 credits earned per shot attempt
So, according to PER, if all misses are rebounded by the defensive team, then it's better to score your X points at a higher percentage inside the arc then at a lower percentage outside the arc. This can easily be rationalized. I imagine that teams tend to be more efficient in their possessions when it follows a miss by the other team, versus a make since defense has less time to get set. So, a miss doesn't only represent lost opportunity on the offensive end, it also impacts the ensuing defensive possession. Not sure if it was intended, by Hollinger's scheme does seem to take this into account in a clever way.
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Charles
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PostPosted: Sun Dec 09, 2007 10:44 am Post subject: Reply with quote
You are correct deepak, I grossly over-simplified, since you can't determine the exact values without league averages. Could you comment on the modified first post.
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Charles
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PostPosted: Sun Dec 09, 2007 10:50 am Post subject: Reply with quote
deepak_e wrote:
So, according to PER, if all misses are rebounded by the defensive team, then it's better to score your X points at a higher percentage inside the arc then at a lower percentage outside the arc. This can easily be rationalized. I imagine that teams tend to be more efficient in their possessions when it follows a miss by the other team, versus a make since defense has less time to get set. So, a miss doesn't only represent lost opportunity on the offensive end, it also impacts the ensuing defensive possession.
Fair enough, although it is rather speculative. However, do you think this possibility makes up for about 8% less PER credits -- despite allowing 50% more offensive rebounding opportunities? This seems way out of balance to me.
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Flint
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PostPosted: Sun Dec 09, 2007 11:41 am Post subject: Reply with quote
Here is Berri on PER...
"Hollinger argues that each two point field goal made is worth about 1.65 points. A three point field goal made is worth 2.65 points. A missed field goal, though, costs a team 0.72 points.
Given these values, with a bit of math we can show that a player will break even on his two point field goal attempts if he hits on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA played does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots.
But again, our model of wins suggests that inefficient shooting does not help a team win more games. Hence the conflict between PERs and Wins Produced. Hollinger has set his weights so that inefficient scorers still look pretty good. We argue that inefficient scoring reduces a team’s ability to win games, and therefore these players are not nearly as effective as people might believe."
Hollinger also has GameScore, a simplified version of PER. Although PER is extremely complicated, it has a 99% correlation with Game Score, or at least so I have read over at the WOWJ. The formula is....
(Points x 1.0) + (FGM x 0.4) + (FGA x -0.7) + ((FTA-FTM) x -0.4) + (OREB x 0.7) + (DREB x 0.3) + (STL x 1.0) + (AST x 0.7) + (BLK x 0.7) + (PF x -0.4) + (TO x -1.0)
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Charles
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PostPosted: Sun Dec 09, 2007 11:51 am Post subject: Reply with quote
Do you agree with Berri on this point, Flint?
I do. I see the PER approach as a compensation for the minimal weight given to shot creation. I realize shot creation is difficult to determine using nothing but official stats, but that's the challenge, because shot creation is essential to understanding the reality of basketball.
When you combine PER's implementation of "lost opportunities" with the error caused by assuming everyone has the same percentage of their shots assisted (Amare actually has about 65% of his baskets assisted compared to 20% for Nash) and a very loose rationalization for the weighting of assists versus points scored) it becomes easy to understand why Nash’s plus/minus has averaged about 7.3 points per 48 minutes higher than Amare’s since they began playing together. Plus minus is noisy, but a seven point difference over 6,000 minutes played is a lot.
Incidentally, I would be reluctant to criticize these weights if they were produced through regression or some other verifiable analysis rather than logic.
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Flint
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PostPosted: Sun Dec 09, 2007 12:26 pm Post subject: Reply with quote
Yes. I definitely agree with Berri. And I don't think there is any objective basis for Hollinger's weights.
You were discussing Joe Johnson in the other thread. Here is a comp of 03-04 and last season.
http://www.basketball-reference.com/fc/ ... 02&y2=2007
To me, it seems very odd that went from a 15 PER to a 19.5 PER. What changed? His ts% was the same, 55.6% and 55.8%.
In y2, 1.4 less rebounds, .8 more assists, 1.6 more tumovers, and of course, 5.4 shots more per 48 and 8.3 points more per 48. To me, that is valuing shot creation a great deal more than necessary.
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Harold Almonte
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PostPosted: Sun Dec 09, 2007 12:27 pm Post subject: Reply with quote
Flint, the WOW logic about the team possession lost after a FGMade could be acceptable, but his approach is wrong and he created a big mess. He penalizes scorers (FGMade) by attempts and rewards the inbounds (oppFGMade) in the opp. team, by minutes. He should have done this also by attempts (if he considers FGMade a matter of individual attempts rather than team), and then scorers just recuperate the most of this team possession lost/gain-with the ball and the clock out of play (just a rule). There's no any straight relationship between FGA and player minutes for him to attempt to cancel one thing with the other, and he's just rewarding low FGA-high minutes players.
PER could be overrating a bit, but WP is overpunishing there. They did the opposite with Rebounds.
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Guy
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PostPosted: Sun Dec 09, 2007 12:35 pm Post subject: Reply with quote
Quote:
Do you agree with Berri on this point, Flint?
LOL.
Quote:
But again, our model of wins suggests that inefficient shooting does not help a team win more games. Hence the conflict between PERs and Wins Produced.
If the distinguishing feature of WP is it's treatment of shooting efficiency, I wonder, "Flint," if you could explain to us why WP has a lower correlation with TS% than does PER? And lower than NBA Efficiency? The truth is that because WP penalizes all shots, not just missed shots, it rewards efficient shooting less than PER.
What really distinguishes WP is that it gives zero credit to shot-taking, not its treatment of efficiency. This means that high-usage/low-efficiency players will indeed be rated very low compared to other metrics, but it also means that high-usage/high-efficiency players will be rated lower than in other metrics.
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Flint
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PostPosted: Sun Dec 09, 2007 12:51 pm Post subject: Reply with quote
Guy - What do you think of PER?
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Charles
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PostPosted: Sun Dec 09, 2007 1:08 pm Post subject: Reply with quote
Guy wrote:
What really distinguishes WP is that it gives zero credit to shot-taking, not its treatment of efficiency. This means that high-usage/low-efficiency players will indeed be rated very low compared to other metrics, but it also means that high-usage/high-efficiency players will be rated lower than in other metrics.
Guy, have you seen evidence that low percentage shot taking deserves credit? I am not talking about shot creation - which is the "unassisted" portion of an unassisted field goal - but, simply shot taking itself?
The analysis I have done says an assisted two-point field goal attempt has no value beyond the actual points scored (in fact it has a small negative value.) Assisted three point attempts do have value, even when they miss, but they are easily separated out.
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Guy
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PostPosted: Sun Dec 09, 2007 6:57 pm Post subject: Reply with quote
Flintberri: My point is not to argue for (or against) PER. My point is simply that WP does not value efficiency more highly, as claimed, as demonstrated by its lower correlation with shooting efficiency. The metric is so dominated by rebounds that it can't give proper credit even to many of the efficient shooters that Berri celebrates.
Charles: I wasn't trying to draw a distinction btwn shot-taking and usage, and wouldn't claim to know the right way to value usage. (My intuition would be to try to establish a reasonable replacement level, which certainly would be lower than league average.) But I feel pretty confident that these equations from the WP perspective are wrong:
* 0-0 = 2-4 = 12-24
* 2-4 > 11-23
* Net value of all shooting by NBA players = zero.
WP says that all below-average shooters hurt their teams, so logically I assume that means these players should stop taking shots. But here's the problem: in this new WOW version of the game, half of those still permitted to shoot will be below the new, higher ts%. So WP will then tell us again that they too should stop hurting their team by shooting, having committed the sin of being below average. Eventually, I suppose each team will have one player who takes all of its shots. Personally, I don't find this terribly plausible. Perhaps Flintberri can make sense of it?
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asimpkins
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PostPosted: Sun Dec 09, 2007 9:33 pm Post subject: Reply with quote
Charles wrote:
Fair enough, although it is rather speculative. However, do you think this possibility makes up for about 8% less PER credits -- despite allowing 50% more offensive rebounding opportunities? This seems way out of balance to me.
I think you've made a good point. The damage of a missed shot may go beyond the opportunity cost (and the chance of an offensive rebound) because the defense has less time to setup, but this should be established and measured first. Until then it seems like just an excuse.
And it seems to me the only way to avoid this discrepancy between 2p and 3p shooting is to subtract the same opportunity cost from all attempts -- makes and misses -- like you were suggesting in the other thread.
(I'm pretty sure the opportunity cost should not be '1' though.)
Quote:
Incidentally, I would be reluctant to criticize these weights if they were produced through regression or some other verifiable analysis rather than logic.
After seeing what a disaster WoW is, I don't think you should be reluctant to criticize weights just because they were produced through regression. These things don't run themselves. You always need to bring in some logic.
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gabefarkas
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PostPosted: Sun Dec 09, 2007 9:37 pm Post subject: Reply with quote
Flint wrote:
But again, our model of wins suggests that inefficient shooting does not help a team win more games.
Oh really? Who is the "our" in your sentence referring to? You and Mr Berri? Because I wholeheartedly disagree with this contention. Take a look at Iverson's 6ers teams, for one.
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94by50
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PostPosted: Sun Dec 09, 2007 10:06 pm Post subject: Reply with quote
Is it just me, or are the following possible?
* The break-even marks for 2pt and 3pt shooting in PER are too low.
* The break-even marks for 2pt and 3pt shooting in WP are too high.
* The ideal mark is somewhere in the middle.
Just eyeballing it, for example, if I take the 30% break even mark for 2pt shooting in PER, and split the difference with league average 2pt shooting (the break even mark in WP), which is, what, about 49%... the average of the two is in the high 30s. I suspect the ideal break even mark is somewhere in that neighborhood. Just a hunch.
Also, regarding the idea that "inefficient shooting does not help a team win more games"... well, of course it doesn't. The question is, how poorly does a player have to shoot before they shouldn't be shooting at all? The Sixers were more than willing to live with Allen Iverson's 40% field goal percentage for quite a while. Why is that? (And I don't think the correct answer is, "Because Iverson is a scorer and teams overvalue scorers.")
Mike G
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PostPosted: Mon Dec 10, 2007 7:27 am Post subject: Reply with quote
Doesn't the usefulness of the shot depend on a few things besides the % of time you make the shot? Like:
FT likelihood and %
the shot clock
one's teammates
In another thread we went into depth about how good/bad Willie Green is. His TS% is .470, so he should probably shoot less. How much less?
Updated, here's a chart like one I posted earlier. eTS% is estimated TS%, in which I've added (TS%-eFG%) to 82games.com's eFG% for each time interval. These shooting% are thus adjusted upward for each player; moreso for those who make more FT/FG. Assuming FT accompany FG equally at all stages of the shot clock.
Philly players, ranked by total shot attempt frequency:
Code:
eTS%% at seconds:
FG/40 FT/40 Sixers 0-10 11-15 16-20 21+
14.8 5.6 Iguodala .62 .53 .47 .39
15.0 5.4 Williams .64 .55 .56 .36
15.7 3.6 Miller .55 .54 .49 .38
16.2 2.2 Green .53 .46 .48 .43
15.0 2.2 Korver .51 .53 .49 .35
9.8 5.5 Dalembert .64 .61 .53 .52
10.9 3.9 Smith .60 .42 .48 .48
6.4 4.0 Evans .59 .24 .66 .19
Sixers .59 .50 .51 .39
The bottom line shows the team's eTS% in each time interval; estimated, again, by assuming FTA/FGA are evenly distributed in each interval.
Willie Green was criticized for taking low-% shots in the 11-15 second interval (when he had hit only 39%), thus depriving better shooters. Passing on a 46% shot to get a 50% shot is less a big deal.
But taking a 49% shot at 18 sec. is a lot better than a 39% shot at 22 sec. When you pass the ball, a few seconds have ticked away. And shooting specialists Williams and Korver seem to be worst at buzzer-beaters. Green is apparently the best (among those who actually get shots).
'Who your teammates are' should also include offensive rebounding. If 30% of missed FG are offensively rebounded, then even on a 30% FGA the odds of 'something good' happening are .30 + (.30*.70) = .51
When FT add .044 to a player's efficiency (league TS%-eFG%), then a 30% shot is 55% 'good'.
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Harold Almonte
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PostPosted: Mon Dec 10, 2007 3:09 pm Post subject: Reply with quote
If for a fairly scoring rating we need to rate: the assisted factor, the dificulty factor (how was guarded the scoring attempt, and by whom-s), and this kind of decission making factor. Why everybody say that defense is more dificult to rate than offense?
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Jacob
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PostPosted: Mon Dec 10, 2007 3:22 pm Post subject: Reply with quote
People worrying about the break-even marks in PER completely miss the point, and this includes our friend Berri. The talent level in the NBA dictates the break-even mark, not John Hollinger. A player with a 31% 2P% will never play significant minutes, let alone attempt significant shots. This is why it drives me crazy when people claim that "PER unfairly rewards 35% shooters who take 30 shots a game". Like these players actually exist in the NBA, the environment PER was designed for.
I guess there's also a continued misunderstanding what PER measures. It doesn't quantify a player's contribution to team wins, but it pragmatically identifies player quality. It recognizes the burden some players are made to carry by their coaches; it never mistook Allen Iverson for a bad offensive player, even in 03-04, and doesn't love him all of a sudden now that he shares the floor with Carmelo Anthony.
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John Hollinger
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PostPosted: Mon Dec 10, 2007 3:34 pm Post subject: Reply with quote
Part of the problem with setting a higher break-even mark for FG% and 3P% is that we only get half the story in the stats. What I mean by that is there is a stat for assists -- good passes that lead to a made basket -- but not for anti-assists -- bad passes or passes not made that lead to a missed shot. The consequence is that the shooter splits the credit for a made basket, but takes all the blame for a miss. If we can work out that quandary, we can reset the break-even threshold. Otherwise, if you set it any higher, you unfairly punish the shooter for misses that may have been the fault of others (such as the dreaded "flaming bag" pass, when a guy get thrown the ball when he's covered 20 feet from the hoop with two on the shot-clock.)
As an aside, somebody with league-average stats in every other category and the "break-even"FG% will end up with a PER around 8 or 9 -- you'd have to take a LOT of shots at that low efficiency mark to end up anywhere close to normal, and that would presumably only happen on on a horrendously bad team.
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Flint
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PostPosted: Mon Dec 10, 2007 8:07 pm Post subject: Reply with quote
Mike G - They are discussing your post over at the Wages of Wins in the Kevin Garnett thread.
http://dberri.wordpress.com/2007/12/10/ ... -nba-team/
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Harold Almonte
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PostPosted: Mon Dec 10, 2007 8:51 pm Post subject: Reply with quote
If it were prohibited to take Off. Rebs., then every FGMissed would be the same than a turnover, and will be straight canceled by DRebs.
No matter if you think or not an OReb. starts a new possession for a teammate (and he is not loosing any credit), a simple TEAM regression (used by WP to weight stats) would weight the cost of a FGMissed as a 70% of a turnover, because that is how much the opponent can steal (rebound) it. Then, I don't know why some stats are supposed to be weighted by team win regressions, and other ones by personal logic, and how some possessions are responsibility of the usager, and other ones (opp.FGMade-inbounds, opp. not stolen TOs, etc.) are for the team.
I don't understand how you can be stolen by a teammate. Or is he stealing from the opponent? Did the opponent have a possession with the ball in the air? It's not a pass, but It's not a double steal situation. It's not transfering credits from the off. rebounder to the shooter, is transfering the lost credits from the shooter to the off. rebounder of course, but not a full possession lost. The possession never was lost at all.
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Guy
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PostPosted: Mon Dec 10, 2007 11:10 pm Post subject: Reply with quote
Flint: Conceptually, there's nothing inherently wrong with basing a valuation system on average efficiency, as Berri does, rather than replacement level. However, you then have to find a separate way to value usage, so that you don't end up saying that 0-for-0 shooting is as valuable as 15-for-30 shooting, which clearly isn't true. Setting a lower break-even level provides a mechanism for valuing usage and efficiency together. You may want to quibble with the precise break-even points in PER, but until/unless Berri amends WP to penalize players for not shooting as well as for inefficient shooting, I don't see how WP is an improvement.
In the thread you link to, Berri objects to any linear weight model (like PER) that sets the "break-even" rate below 50% on the basis "that it allows an inefficient shooter to increase his value just by taking more shots." He has made this point dozens of times, and seems to feel it's a debate-ending observation -- that any metric with this feature must be wrong. But the idea that below-average players must lose value the more scoring opportunities they consume is hardly self-evident. For example, the best value metrics in baseball, based on replacement-level production, would all say that a 10%-below-average hitter is worth more when consuming 600 plate appearances than 300 plate appearances.
This determination to penalize usage among below-average shooters seems rooted in WP's radical claim that the average level of efficiency has zero value. If 1-for-2, 5-for-10, and 15-for-30 shooting all have equal value, then clearly that value is zero. I'm not aware that Berri has ever offered an explicit argument for why 50% shooting has no value -- if he has, can you explain it? It seems to me that case requires demonstrating that the skill required to maintain league-average efficiency over 48 minutues is ubiquitous -- that any team should always be able to get the ball in the hands of an average shooter. (Of course, one has to overcome a number of uncomfortable facts, such as that about half the teams in the NBA fail to achieve this standard every season, and that teams with "zero-value" shooting tend to win about 41 of 82 games.)
And, I'm still interested in your thoughts as to why Wins Produced has a weaker correlation to shooting efficiency than PER, if Berri is right that a greater emphasis on efficiency -- rather than overvaluing rebounds vis-a-vis scoring -- is what makes WP different.
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asimpkins
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PostPosted: Tue Dec 11, 2007 12:10 am Post subject: Reply with quote
And if average shooters are worthless, shouldn't the same thing go for average rebounders? But a player who never shoots and just rebounds at an average rate will do well with WoW. I think that was part of the point NickS was making in this post. Whatever criteria you enforce on shooting, you have to also enforce on rebounding.
And this got me thinking about the original point Charles made about PER here. I think he's right that PER is flawed in not counting an opportunity cost for a made basket, but at the same time it didn't seem like PER would be improved if you made only this change. I began to think that PER ended up working out kind of right, but for the wrong reasons. PER was inflating the value of made baskets, but only as a response to the inflated value of rebounds.
I did some research, and I again rediscovered another excellent post by NickS where I think he gets the right answer later in the thread:
NickS wrote:
If you deducted the full value of a possession from made baskets in PER all of a sudden you would find that the people it would rate very highly would be rebounders. Finding some balance between scoring and rebounding is necessary for the reason I laid out in the "two meanings of zero" post. Again, PER accomplishes that by setting a value for Rebounding, and then deflating it by adding extra value for made baskets.
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Flint
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PostPosted: Tue Dec 11, 2007 12:16 am Post subject: Reply with quote
Guy - How much you score matters in WP. The way I think about it is that there is a points scored benchmark and an efficiency benchmark, via fga, fta, ftm's, etc. A player is penalized if he doesn't match the benchmark for his position. So, if you have two players who both shoot a ts% of 55%, and one scores twice as many points as the other, he will produce more wins. What happens when you have two below average efficiency scorers is unclear to me, but I think you get penalized the more opportunities you use.
I think a lot of people get confused by WS, and the fact that you can shoot 20-40 on 2 pt fg's and not accumulate any WS. But people always forget to add in the effect of 3pters and fts. When you do that there is much more variation. I watch games calculating WS, and most player don't shoot over 50% from the field. But when you throw in fts and three pointers, that changes. And when you throw in position adjustments it changes again.
To me, usage is baked into WP, or at least as much as it needs to be. If you are a player who doesn't score points, its going to be harder to meet your overall target. If you don't notch assists ditto. You have to make it up in other parts of your boxscore. Yes, Steve Nash commits a lot of turnovers. But that's because he is accumulating assists at an even higher rate.
People maintain that WP has a problem evaluating high usage players. I don't really see that. Most of the top players in WP are scorers and high usage players. To me, it has always been much more clear that PER has a huge problem with evaluating low usage players. The fact that Dennis Rodman had a below average career PER and Eddy Curry is above average has always been my touchstone in that regard for me.
I don't know if PER correlates more closely with shooting efficiency. If you have done a study which shows that, post it and I will comment.
I can't say I really understand your replacement level player argument. I am not a sabermetrician, or a statistician for that matter. But I don't think its true that average efficiency has zero value, as you say above. A team of average players will win 41 games, which is a damn sight better than 0, and much better than what the Knicks will put up this year.
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Mike G
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PostPosted: Tue Dec 11, 2007 9:56 am Post subject: Reply with quote
The benchmark for shooting% that has >0 value cannot be static. In an 84-80 (avg score) playoff series, it may be that a 43% FGA is a 'good' shot.
In the '98 Finals, the Bulls forced the Jazz to shoot just 45% FG (down from 49% in the season). More aptly, Utah's TS% was off, from .567 to .506 .
Despite running 3 fewer possessions per game, Utah was forced into 1 extra turnover from their season rate.
Together, these resulted in an offensive efficiency drop of 17%, from their norm of 1.13, to .93 Pts/possession. Any shot better than about .390 eFG% was a 'better than average' possession.
That's assuming their offensive rebounding (26%) led to just their average (.506) scoring rate, with no TO and no 2nd OReb.
There were some playoff series ('80s-90s) between Phx and Den, in which a 50% FG try was almost a waste.
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Guy
Joined: 02 May 2007
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PostPosted: Tue Dec 11, 2007 10:54 am Post subject: Reply with quote
Flint wrote:
Quote:
To me, usage is baked into WP, or at least as much as it needs to be. If you are a player who doesn't score points, its going to be harder to meet your overall target.
A usage value is indeed baked into WP, and that value is zero. Usage is rewarded only for above-avg-efficiency shooters, and has negative value for below-avg-efficiency. Overall, usage has no net value, and WP has virtually no correlation with usage at the player level. And for half of the players your second sentence is demonstrably false: if you are a below-avg-efficiency shooter, the fewer points you score the easier it is to reach the overall target. A 48% TS% player is more valuable taking zero shots per game than taking 20.
Quote:
I don't think its true that average efficiency has zero value
Then you need to study WP more closely. An average efficiency player receives identical WP when taking 2, 10, or 20 shots per game. If 2*X = 10*X = 20*X, and I solve for "X," I get X=zero; don't you? This shouldn't surprise us: Berri says "efficient shooting" (by which he means above-average) creates wins and has positive value, while "inefficient shooting" causes losses and has negative value. So it follows logically that average shooting will have zero value.
Quote:
I don't know if PER correlates more closely with shooting efficiency. If you have done a study which shows that, post it and I will comment.
Dan Rosenbaum has studied this and found a WP-TS% r of .556, compared to .613 for PER-TS%. I believe his paper will be published fairly soon, so you (and Berri) will have the chance to study and rebut it. But just as a matter of algebra, it's easy to see that PER punishes inefficient shooting more than WP if you hold shot attempts constant. WP will value inefficient/high-usage players lower than PER, but will also value efficient/high-usage players lower than PER. So my guess is Rosenbaum's calculations are correct.
* *
To some extent, the two main criticisms of WP -- undervaluing scoring, overvaluing rebounds -- are just two sides of the same coin. If either claim is true, the other has to be at least somewhat true. But it is useful to consider them separately. While I believe Berri is wrong that usage has no value and there is no usage/efficiency tradeoff (basically the same claims), I don't think critics can claim to have proven that point definitively. And a weak version of Berri's argument -- that teams could improve by giving somewhat more shots to high-efficiency shooters -- is not inherently implausible.
On rebounds, however, there is no doubt that Berri's core assumption -- that all player rebounds equal a net additional rebound for his team -- is false. A player's REB total is highly influenced by that of his teammates. For example, if you run a correlation between the REB total for a team's top rebounder and the REB of his teammates, it's about -0.80. In fact, the negative correlation is so strong that the standard deviation for rebounding is actually much higher at the player level than at the team level. The difference between good and bad rebounding teams is fairly small, and that simply couldn't happen if the real differences in players' rebounding ability were as large as raw REB stats imply.
Berri's post yesterday on Garnett and the Timberwolves is a good example of how this gets Berri in trouble. WP estimates that KG was about 23 wins above average per year in his peak years (02-03 thru 05-06). About 45% of this comes from rebounding, as he averaged 330 rebounds/season more than an average F. But, while WP assumes this meant 330 extra rebounds for the T-Wolves, in fact the team was only 33 rebounds above average in these years. While KG was +330, his teammates were -297 -- what bad luck!
Interestingly, the now terrible KG-less T-Wolves are averaging more rebounds per game (42) than in Garnett's last two seasons (40). Isn't it surprising that Minn could improve its rebounding while losing KG's 330 boards? That would mean that the rest of the team has suddenly improved by 6 REB per game, an astonishing improvement. And if rebounding is so important, shouldn't we be shocked that a team can get much worse while improving its rebounding? Yet Berri doesn't even mention it.
You find the same pattern with Rodman. At his peak, 91-92 to 97-98, Rodman was +543 REB per year (vs. avg F). Yet his teams were only +162 overall. Rodman's teammates were a horrific -381 REB on average, and were well below average in every one of these seven seasons (covering 3 different franchises). Another great rebounder saddled with lame teammates. Bad luck yet again! (I haven't done the work, but I'm pretty sure you will find that virtually every great NBA rebounder has had similar misfortune.)
The final test of what matters in winning is whether an attribute is actually correlated with winning. What led Bill James to discover that stolen bases aren't very important for winning baseball games was observing that winning teams didn't have many more SBs than losing teams, and high-SB teams didn't tend to win many more games than low-SB teams. The same is true for rebounds relative to scoring in the NBA. The correlation between point differential and shooting (PPS) is about 3 times higher than the correlation between point differential and rebounding. However, WP is more highly correlated with rebounding than with scoring (and much more correlated with rebounding than PER). Berri's whole case is built on the notion of explaining team wins. But while rebounds don't explain very much of the variance in team wins in the NBA, they explain a lot of the variance in Wins Produced.
Charles: sorry to hijack your thread.
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Flint
Joined: 25 Mar 2007
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PostPosted: Tue Dec 11, 2007 4:46 pm Post subject: Reply with quote
Guy - I don't think I can give you satisfaction here. If everything that has already been written by Berri hasn't been enough to convince you, including his direct responses to you, I don't know what more I can offer. Reading your post, what I can say it that I don't think it is an accurate depiction of Wins Produced.
The way you are thinking about rebounding and the way it is treated by Wins Produced, for instance, strikes me as flawed. Specifically, your characterization of....
"Berri's core assumption -- that all player rebounds equal a net additional rebound for his team"
"Jason" had what I hope is a germane comment at 1042 today in the Garnett post. From that:
"WP" doesn’t say that a 10 rebound/48 player replacing a 15 rebound/48 player will result in a net increase in 5 rebounds 48. It says that the increase or decrease in wins will be roughly equivalent to the win probability contributed by the player-assigned stats. The model does not say that any isolated components must stay constant. It is important not to confuse the two."
I think actually reading the rest of that post by him, and the others he has written today might be a better response to what you posted above than what I can offer you.
My interest in basketball stats is a byproduct of reading the WOW and of work done in public policy, investing, and also a very serious poker hobby. I am not a basketball statistician or professional economist. While I understand most of the arguments made, I don't think I can really engage you at the appropriate level.
Re PER
I guess unfortunately I operate by sense of smell, like some on this board, and I think like most people who watch basketball. I just have a different sense of smell, for reasons which I have articulated in the past (and been ridiculed for, which was sort of hilarious). I am also a Knicks fan, which means I have been watching Eddy Curry for the past 2+ years.
Anyway, bottom line, PER tells us that Curry has been a better player than Samuel Dalembert and Tyson Chandler in his career. It tells us also that Curry has been better than Dalembert this year and as good as Chandler.
And that's kind of what it boils down to for me. Is Eddy Curry really an above average NBA center? Is he really as good as Tyson Chandler, currently anchoring the fourth best defense in the league. Is he really only slight worse (.5 PER) than Marcus Camby, currently anchoring the second best defense in the league? Is he really dramatically better than Ben Wallace, the center on the fifth best defense, as PER suggests?
PER would have us believe, it seems to me, that if you were to swap Curry for Camby, Wallace, Chandler, Dalembert, Oberto, Ilgauskas, or any other number of big men he scores more then, the Knicks wouldn't improve. That the only serious upgrade we could make at the center position would be Ming, Bynum, or Howard. And that's just, well, incredibly bizarre to me.
Wins Produced does not ask me to believe that. It tells me in fact that getting rid of Curry and adding any of those players would help the Knicks a great deal. That makes sense to me. Argument from anecdote I know, sorry not be able to give you anything else...
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asimpkins
Joined: 30 Apr 2006
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PostPosted: Tue Dec 11, 2007 5:32 pm Post subject: Reply with quote
Flint wrote:
Anyway, bottom line, PER tells us that Curry has been a better player than Samuel Dalembert and Tyson Chandler in his career.
Flint. If you're going to criticize PER, you should at least get the basics right. PER doesn't make statements about who's an overall better player because it only measures what happens in the box score -- which ignores most defensive contributions. PER summarizes box score contributions only and estimates how many points those contributions would make for a typical team.
So you should say that PER tells us that Curry has been a better box score producer than Dalembert or Chandler -- which is a very different argument. Maybe you think that is incorrect as well, but at least you are characterizing PER correctly.
In the same way, PER does not say that Rodman was an average player -- another of your favorite examples. It says that he was an average box score producer. His defense would certainly have him ranked much higher. Again, maybe you think that box score analysis is incorrect, but you're not helping anyone by beating up on a strawman.
Quote:
PER would have us believe, it seems to me, that if you were to swap Curry for Camby, Wallace, Chandler, Dalembert, Oberto, Ilgauskas, or any other number of big men he scores more then, the Knicks wouldn't improve.
Again, PER makes no such claim. (Hollinger is frequently critical of the Knicks' interior defensive problems.) You've seriously misunderstood the scope of these stats. You need to re-approach all of these players and numbers from the mindset of measuring box score contributions only. Ben Wallace, who does so much off the box score, shouldn't be rated to his full actual value. That would actually be a warning flag that something is wrong.
So, of course, WoW also measures only box score contributions -- and not much of defense. If you find WoW is measuring players accurately in an overall sense, then this is actually a problem. That would imply that WoW is getting the right numbers for you, but for very wrong reasons -- the method is flawed.
Last edited by asimpkins on Tue Dec 11, 2007 5:56 pm; edited 1 time in total
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Flint
Joined: 25 Mar 2007
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PostPosted: Tue Dec 11, 2007 5:56 pm Post subject: Reply with quote
Asimpkins - I have heard this argument before and I find it baffling.
Would it be accurate to say:
PER is designed to provide a summary statistic measuring a players production of box score stats. It is not designed to capture a player's actual contribution to winning basketball games for his team.
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asimpkins
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PostPosted: Tue Dec 11, 2007 5:58 pm Post subject: Reply with quote
It would be correct to say:
It is not designed to capture a player's full contribution to winning basketball games for his team.