Assuming that these two simplified formulas are a good approximation of their more famous coutnerparts, I have some questions that I you you good people can help me with.
1. What is a posession worth in terms of a 'score' like the above formulas?
1a. Does giving a player full credit for a defensive rebound essentially credit that individual with the entirety of the defense that was played on that posession?
1b. If you don't give the rebounding player full credit, should a portion of the rebounding credit be spread out among the defending players on the court at the time as a way of representing a successful defensive posession?
1c. Is losing posession (i.e. TO , missed FGA) worth the same as a rebound?
1d. Is making a 2pt basket worth the same as rejecting
1e. Is a steal (taking posession from them, giving it to you) worth twice as much as a simple gain or loss of posession?
2. What should converting posession into a score be worth?
2a. How should assists be scored? It seems like a dunk gives the same value to the team regardless of whether it was assisted or not. I mean, the benefit to the team as a whole is the same whether the shot was assisted or not. Giving additional credit to a player for the assist makes teams with high assists look better than teams without, even if every other aspect of the teams are identical. If it's not leading to greater team success
2b. If the basket was assisted, should the assisting player be credited with 'creating' the basket, and the assisted player have their score correspondingly reduced?
Thanks in advance for any insight people might be able to shed.
Last edited by magicmerl on Mon Jan 07, 2008 3:23 pm; edited 1 time in total
Joined: 26 Mar 2007 Posts: 54 Location: Orlando, FL
Posted: Mon Jan 07, 2008 12:39 pm Post subject:
Quote:
1. What is a posession worth in terms of a 'score' like the above formulas?
One of the difficulties with linear metrics is trying to ascertain the value of the possession, since that value has to be described "in terms of" something else. Nearly every metric that I've seen states the value in terms of Points, or some point equivalent.
Generally, the value of a possession in terms of points is 1.
I'd ask you to consider an alternative view in which the value of a possession is 2. Except that instead of expressing that value in terms of points, express it in terms of stuff that gets recorded in the boxscore.
For instance, a made shot results in 2 points. A missed shot followed by a defensive rebound are recorded in the boxscore as 2 events. A turnover committed is also a turnover forced. In other words, every possession will result in a net change 2. Not 2 points, but two entries in the boxscore.
By doing so, you'll then have to re-consider the commonly accepted belief (to everyone except Berri, that is) that a OReb + DReb = 1.0.
On the other hand, you'll see the error in Berri's treatment of made vs missed field goals.
Quote:
2. What should converting posession into a score be worth?
Converting a 2-point field goal attempt should be worth [drumroll] 2 points [/drumroll].
What various possession actions are worth "at face value" can be different than their apparent impact on winning as found by regression analysis. There are several key accounting choices to make including whether to shift some of the positive or negative value of the next action in the sequence onto the one that set off the chain such as steals perhaps leading to a fastbreak and a higher percentage shot. Rating systems sort out credit differently and the lack of shot defense in the formulas contributes to the missed shot / rebounding debates. Plenty of previous threads that grapple with these issues.
Any welcome to the freshman? No commentaries. All your questions implicitally have theirselves the answers.
Um, thanks?
I'm not sure if you understood my post or not, because I definitely didn't intend for all of my questions to contain their answers. And if they did, wouldn't that imply that one or both of GS and WS are wrong in their weighting of box score variables? I mean, they use different weights. They can't both be right, if either of them are.
Rasta987 wrote:
One of the difficulties with linear metrics is trying to ascertain the value of the possession, since that value has to be described "in terms of" something else. Nearly every metric that I've seen states the value in terms of Points, or some point equivalent.
Generally, the value of a possession in terms of points is 1.
I'd ask you to consider an alternative view in which the value of a possession is 2. Except that instead of expressing that value in terms of points, express it in terms of stuff that gets recorded in the boxscore.
For instance, a made shot results in 2 points. A missed shot followed by a defensive rebound are recorded in the boxscore as 2 events. A turnover committed is also a turnover forced. In other words, every possession will result in a net change 2. Not 2 points, but two entries in the boxscore.
By doing so, you'll then have to re-consider the commonly accepted belief (to everyone except Berri, that is) that a OReb + DReb = 1.0.
Rasta987, thanks for the response. Doesn't changing the posession value from 1 to 2 just change the scale? How does that help?
It seems to me that there is the following basic progression in a game:
a. Opponent makes 2 pt basket
b. Opponent has possession
c. Noone has possession
d. You have possession
e. You make 2pt basket
Now, I think that a team successfully scoring (going b-a or d-e) should be worth the same amount. And people rebounding the ball (going from c-b or c-d) should also be worth the same amount. I don't really understand why defensive rebounds are worth less than half of what offensive rebounds are in GS. Surely turning a loose ball into posession for your team should be worth the same no matter where the ball is on the court?
I get that you are saying that a possession is worth roughly a point, which means to me that the above progression has equally spaced gaps, yes?
Rasta987 wrote:
On the other hand, you'll see the error in Berri's treatment of made vs missed field goals.
I don't actually see this error. dberri's deduction of FGA (regardless of whether they were successful baskets or not) seems to be to be somewhat analogous to a company needing a cash warchest to start business. You need to spend money to make money, just like you need to spend possessions on FGA in order to generate points. Let's not ignore that we are spending possessions in this way though.
Rasta987 wrote:
Quote:
2. What should converting posession into a score be worth?
Converting a 2-point field goal attempt should be worth [drumroll] 2 points [/drumroll].
Should it? I mean, 2 points is the reward you get for scoring, but it's not just a matter of putting the ball in the bucket. You have to actually get the ball first before you can turn it into points.
So in my above progression, going from a loose ball to a made basket is worth two points. Going from having possession to a converted basket should be worth 2 pts - the value of a rebound.
Does that make sense?
edit: Mountain, thanks for your response. I'm really not considering regression at all, just basic 'logic' to try and intuitively value box score stats. I remember reading somewhere that steals were a greatly overrated stat because they usually showed someone who cheated on D and thus exposed their team to numerous defensive breakdowns, giving their opponents open looks that they wouldn't have gotten if they had just stayed between their man and the basket. Whereas on the surface, a steal would appear to be more valuable than nearly every other box score stat.
"Surely turning a loose ball into posession for your team should be worth the same no matter where the ball is on the court?"
I think this depend on if you are discusing the individual or the team level.
Not all passes, not all shots and not all rebounds are created equal in the value they create for the team. E.g. gaining the rebound off a missed free throw is not same (in terms of difficulty and value added above expected)as gaining gaining a rebound in flow of offensive.
An extra possession is important, but which are harder to get, that is the crux of why offensive rebounds are perhaps more valuable than defensive rebounds.
Any welcome to the freshman? No commentaries. All your questions implicitally have theirselves the answers.
Um, thanks?
Hey, you got off light being referred to as "freshman" after questioning the Book of John. Actually, everything you said in your last post makes perfect sense. Win Score is right about lost possession on made field goals. Everyone, other than Berri, is right about rebounds (from an individual perspective.)
Energy in responses will vary from time to time here.
Past accounting threads may have zapped some of the enthusiasm for another round at the moment. Given your interest in the subject I'd again encourage you to browse the past threads. You will see plenty of detailed presentations of ways to score and evaluations of how the various popular formulas do it and debates on the sticking points. Most of your questions including regarding assists are discussed thoroughly. At a different time I might try to identify the most relevant threads for you but they wouldn't be hard to find if you search by keyword or browse thread titles.
Some have taken the attitude that rating systems are passe, impossible to perfect or just pick the flavor you like. I still think they are useful and can be made stronger tools for assessing performance.
"1. What is a posession worth in terms of a 'score' like the above formulas? "
The value of posession is a building block of these formulas.
As Rasta said the average value of possession is close to 1. However the value of a successfully used possession is often 2 but can be different.
"1a. Does giving a player full credit for a defensive rebound essentially credit that individual with the entirety of the defense that was played on that posession?"
Yes this is a criticism that many recognize. The fix would be to include shot defense. The data is imprecise so none of the widely used formulas include it. I have thought about hacking one together that did it (and may eventually).
How much weight shot defense should get is an interesting question I haven't fully worked thru. The difference between upper quartile best and lower quartile worst shot defense in league on average might be 40% FG allowed vs 60% or 20%. Maybe the shot defense might deserve up to .4 of the credit for the miss with the rebound action getting the rest of the credit (on the defense's side of the ledger).
I agree with the thinking behind your point 1b that the credit for an opponent miss (or penalty for a make) could / perhaps should be split by the primary defender and rest of team. A crude starting point would be to give 50% of penalty to primary defender and 12.5% to each of the rest of the guys on opponent makes and on opponent misses maybe 30% to primary defender and 7.5% to other 4 guys
and 60% left for rebounding credit. And maybe the rebound credit gets split half or 30% to the actual defensive rebounder and the other half equally in 7.5% shares to rest of team for boxing out? That would allow match with PER assigned defensive rebound credit but allow the sum of all the defensive credits to total to 1. Or adjust the splits.
(You could go strictly egalitarian and split shot defense credit /blame equally among all 5 every time but I wouldnt go that far.)
"1c. Is losing posession (i.e. TO , missed FGA) worth the same as a rebound?"
It is in some systems faithful to scoreboard and aimed at explaining wins. It might not be in a ratings system primarily aimed at ranking players against each other like PER.
The high weight for steals in some systems is due to the expectation of easy buckets and may also come from being a proxy for other defensive impact, mostly importantly shot defense (not in most ratings formulas or in some regressions used to build ratings). But players vary in their mix of ability to make steals and defend the shot so using a weight for steals than carries some of the average value of unscored shot defense for the league but not the specific player will distort valuations from true. All the more reason to include shot defense in its own right even as an approximation someday.
The freshman quote was because is the first time I ever read you here. No offense.
Quote:
Now, I think that a team successfully scoring (going b-a or d-e) should be worth the same amount. And people rebounding the ball (going from c-b or c-d) should also be worth the same amount. I don't really understand why defensive rebounds are worth less than half of what offensive rebounds are in GS.
Very good approach. Forgetting the shot defense for a while, DR and OR have the same possesion value at the team level. The 0.7 and 0.3 is not weighting the possession value of rebound, is an adjust because it doesn't exist anything like "missed rebounds" in the boxscore, and aplying sampling and shortage to the stats, is a statistical way to adjust for that. Is it fair? I'm not a statician to answer that. Neither WS nor WP did the adjust. WP should have included it in the team defense adjust. Then it's not weighting the possession value of the stats, it's trying to do a player rebounding rating.
Joined: 26 Mar 2007 Posts: 54 Location: Orlando, FL
Posted: Tue Jan 08, 2008 12:07 pm Post subject:
Quote:
Rasta987, thanks for the response. Doesn't changing the posession value from 1 to 2 just change the scale? How does that help?
It's not a question of scale. It's a matter of perspective, and how that perspective carries over into the metric.
For instance, Game Score's value for off. and def. rebounds. Why are off rebounds valued higher? Are they really more valuable? No, they simply occur less often. Yet we all agree that the value of an off rebound is equal to the value of a missed shot, right? And we see data that tells us that around 30% of missed shots are rebounded by the offensive team. Put it all together and we get these commonly accepted values: 0.3*Def Reb and 0.7*Off Reb.
I disagree with this logic, and blame it (for the most part) on the belief that "possession = 1", which results in forcing square pegs into round holes.
Quote:
I don't really understand why defensive rebounds are worth less than half of what offensive rebounds are in GS.
Join the club. Berri agrees, for what its worth.
Speaking of Berri, I should elaborate on what I believe is his main error. Actually, "error" is the wrong word. At the team level, his accounting system is fine. I'd encourage you to read NickS' analysis on this point.
OFF DEF
3PM +2.0 -2
FGM +1.0 -1
FGX -1.0 +0
OR +1.0 -0
DR -0 +1.0
TO -1.0 +1
At the team level, a made FG results in +1.0 for the offense, and -1 for the defense. Conversely, a missed FG followed by a def rebound results in -1.0 for the offense, and +1.0 for the defense. Very symmetrical. In both cases, the net effect is 2. (Again, Berri and I are on the same page: the value of the possession is 2)
(Edit to add: NickS used the decimal place to indicate stats that were attributed to individuals, and no decimal for stats attributed to the defensive team.)
While this is fine at the team level, things get off track at the player level. Specifically, Berri gives the individual scorer credit for 1.0 pt on a successful FG, and then divides the -1 among all 5 of the defenders. As a consequence, nearly all of the points scored are removed from the equation at the player level. What's left? Rebounds, mostly. And that's where the criticism is centered.
Quote:
a. Opponent makes 2 pt basket
b. Opponent has possession
c. Noone has possession
d. You have possession
e. You make 2pt basket
Quote:
So in my above progression, going from a loose ball to a made basket is worth two points. Going from having possession to a converted basket should be worth 2 pts - the value of a rebound.
Does that make sense?
Um, no.
I agree that going from having possession to a converted basket (steps b-a, or d-e) should be worth 2 points. However, going from a loose ball (c) to a made basket (e) looks like 3 points to me.
Code:
Possession to Made Shot b-a or d-e 2 points
Possession to Missed Shot b-c or d-c -1 point
Loose Ball to Rebound c-b or c-d 1 point
By the way, this is basically Berri's views things, except that (as I mentioned earlier) he splits the 2 point credit for the "Possession to Made Shot" between offense (+1) and defense (-1).
uhmm. There's a topic outhere wich says you can't have or create more total possessions-points than the points scored in the game. Berri's approach about penalizing the FGMade is irrelevant because is the same for both teams, but... really is a not rebounded, not stealed possesion gained he should retribute back to scorers who convert it in points scored. The "error" as you say is he didn't credit a -1 at the DEF side when an OR is grabbed at the OFF side, and the fact is that DR cancels both the FGX and the OR.
Then in the binarian sample the OFF side has a net +2 credits, but DEF is just penalized -1. All the problem with WS is that "rebounds allowed" are not penalized.
Joined: 15 Nov 2007 Posts: 8 Location: Chicago, IL
Posted: Wed Jan 09, 2008 12:34 am Post subject:
Quote:
Maybe the shot defense might deserve up to .4 of the credit for the miss with the rebound action getting the rest of the credit (on the defense's side of the ledger).
Mountain, would the fact that rebounds/48 min. remain basically constant from year to year (per Jason on Berri's site [see my other post on the rebound rate thread]) suggest that splitting the credit is not called for?
Westy I'll have to catch up on reading a bit.
And seek clarification to your question.
First some run up comments (not all strictly on your question but related and what I want to add)...
My initial take is that I still think dividing up the total defensive credit for a missed shot / recovery sequence into shot defense and rebounding shares makes sense. And I think splitting credit in each case among all 5 players might also make some sense. The proportion of the split is up for debate- as is the method. I see several people in several places all suggesting such splits, an encouraging thing to me.
On shot defense I still lean toward 50% to boxscore counterpart (as a rough starting point) 50% to rest of team but would come down to 30-40% to the presumed most of the time defender of the opponent who scored and then equally to rest of team. Completely equal 5 way split losses sense of individual responsibility to me.
Now to your rebounding question. If you meant does it make sense to split the rebounding part of the credit for recoveries among all players I guess I'd amend what I said before. Perhaps 50% / 50% for actual rebounder and rest of team was too generous a share for the rest of team. They may or may not have contributed to its capture (lots of guys stand around, not boxing out, often but not always too far way to matter). I would probably go to something more like say 76% to actual rebounder and 24% split out to rest, partly in view of your data about rebounding consistency and because it sharpens my own reflection and gets closer to how I see the action happening and what a fair split would be.
Some recognition that rebounding is a team enterprise and that boxouts matter seems worthwhile ideally but it isn't a huge deal not doing it. But if the goal is improvement some recognition might be appropriate.
You could get out of the partial credit giving business by maybe doing something similar to what Dan Rosenbaum did in his design of overall +/- :
score the meaningful individual acts (his statistical +/- formula or do it from another system base) and give them the predominant weight and then add on say a 15-20% weight share for pure adjusted +/- to try to capture the partial credits due for actions contributed in a team context (boxouts, rotation passes, spacing, ball saves, etc.).
Wins Produced has its team adjustment. You could add a small +/- based compotent to an enhanced PER formula or a new one.
I can go either way.
Statistical +/- or any other linear weight system can be looked at in aggregrate- and also broken out into 4 categories in alignment with 4 factors to get a better picture of a player's style/role/impact.
Pure adjusted +/- can be broken out into adjusted 4 factors by the teams if they want or if any site wanted to push to that level available in public. But until then you can look at the raw team +/- details on the 82 games +/- page and try to "adjust" as best you can for the context you believe the player was in.
Last edited by Mountain on Wed Jan 09, 2008 6:22 pm; edited 2 times in total
So in my above progression, going from a loose ball to a made basket is worth two points. Going from having possession to a converted basket should be worth 2 pts - the value of a rebound.
Does that make sense?
Um, no.
I agree that going from having possession to a converted basket (steps b-a, or d-e) should be worth 2 points. However, going from a loose ball (c) to a made basket (e) looks like 3 points to me.
<snip>
By the way, this is basically Berri's views things, except that (as I mentioned earlier) he splits the 2 point credit for the "Possession to Made Shot" between offense (+1) and defense (-1).
I don't agree that Berri credits a made field goal with 2 pts. Yes the basket is worth two points, but my understanding of WoW is that it's accrediting one of those points with the act of getting posession (moving from c-d or c-b) and only one point with the act of dropping th eball through the basket (b-a or d-e).
Westy wrote:
Quote:
Maybe the shot defense might deserve up to .4 of the credit for the miss with the rebound action getting the rest of the credit (on the defense's side of the ledger).
Mountain, would the fact that rebounds/48 min. remain basically constant from year to year (per Jason on Berri's site [see my other post on the rebound rate thread]) suggest that splitting the credit is not called for?
I've seen Jason post that several times on Berri's site, and I think that it is misleading at best. To me, the only point to making that arguement is to then infer that players take their rebounds with them where they go, and that the players as individuals are solely responsible for the rebounds they haul down. As someone here said on another thread, Dennis Rodman rebounded quite well for the bulls while he was with them, but it's a fallacy to reach the conclusion that the WoW model does that he earned all of those rebounds for his team. This post says it better than I could.
They explicitly say that the players rebounds don't necessarily give their team that many rebounds, but they then implicitly and repeatedly contradict this point by using reboudns they way they do in their formula and then they top level summaries talk about WinScore and WinsProduced as if their rebounds did give their team that many rebounds and that they would not have got them unless that player who hauled in the reboudns was playing for that team.
Joined: 26 Mar 2007 Posts: 54 Location: Orlando, FL
Posted: Wed Jan 09, 2008 4:46 pm Post subject:
Quote:
I don't agree that Berri credits a made field goal with 2 pts. Yes the basket is worth two points, but my understanding of WoW is that it's accrediting one of those points with the act of getting posession (moving from c-d or c-b) and only one point with the act of dropping th eball through the basket (b-a or d-e).
That's not correct. The act of getting possession (ie the defensive rebound), while indeed worth 1 point, marks the end of the previous unsuccessful possession. It isn't part of the subsequent possession.
On a made field goal, Berri actually agrees with this partial formula, although only at the team level:
Code:
WS = Pts + FGM - FGA
Note: "FGM - FGA" is just another way of saying "Missed Shots"
At the player level, the variable "FGM" is missing. We only see this:
Code:
WS = Pts - FGA
That's because the credit for the made FG is allocated to the defensive team in a later step. In theory, each of the five defenders share the blame for allowing the shot to be made. To illustrate the net effect of a made FG:
Code:
Scorer = 2.0 points - 1.0 FGA = 1.0
Opposing PG = -0.2 FGM
Opposing SG = -0.2 FGM
Opposing SF = -0.2 FGM
Opposing PF = -0.2 FGM
Opposing C = -0.2 FGM
Team Total = -1.0
If you read NickS' analysis, he was questioning the fairness of this from the point of view of the defender. If I'm defending Allen Iverson, and he makes a shot, I'm penalized a fraction of a point. However, if I play great defense and force a missed shot, Iverson is penalized for the miss (-1 FGA) while my teammate gets credit for the def rebound (+1 Def Reb). What about me? As the defender, I'm getting screwed in this situation.
What a nice segue into Westy and Mountain's discussion about somehow dividing credit for that Def Rebound between the five defensive players.
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