APBRmetrics

Chicago76 wrote: In this instance, there is nothing controversial about stating that the G's DRB contribution is equal to that of the big man and that each G DRB is worth twice as much to a team as one DRB from the interior player.

I think that conclusion is based on the wrong premise.The idea that replacement level would determine the value of the contribution entirely. But that is not true. For rebounding there is a simple rule: First man, then ball. That means that you first secure the position by boxing out your opponent and then you go for the ball. Why is that important to mention? Well, let us take a look at Jason Kidd and the difference in terms of DRB% in the year he was traded from the Nets to the Mavericks.
He had 21.7 DRB% in New Jersey and it went down to 16.8 DRB% in Dallas. When Kidd was on the court, the Nets had 73.5 DRB%, the Mavericks 73.1 DRB%. The first reaction by most would likely be that Kidd started to play with better rebounders in Dallas. But that is not the main reason for the difference in terms of Kidd's DRB%. The Nets had the strategy under Lawrence Frank to get the ball as soon as possible in Kidd's hand. They used their big men primarely to box out the opponents while Kidd was put into a position to grab the rebound and start the fast break immediately. Kidd didn't became a better rebounder under Frank, he was just in a different position while his teammates made the work to box out the opponent.
A similar story is there for Magic Johnson, who never played defensively as PG anyway. He was on a complete different position on the court than other PG.

That is just one example which shows in which kind of problems someone runs, if they assume those PG, SG, SF, PF or C have different replacement levels for different traits and thus they can be assigned different values for different boxscore entries.

When you want to talk about the position on the court independent from the rule of the player, it might be something useful. But that again depends heavily on the strategies of the teams. A different offensive set will put the players into different position on the court. It is bound to fail to try to adjust for position by using replacement levels, when you don't have the exact positions on the court for each player extracted via video analysis.

Maybe I should try again, a little bit clearer this time.

WP gives out credit/blame to players by putting box score activities in terms of points. A possession is said to be worth about one point. A rebound or steal is a possession your team gains for free, so it's basically a point. A turnover is a lost possession; one lost point. A made 2PT FG is like trading one dollar for two - it costs one point (one possession) but you get two back.

If a player is 2-2 for 4 points with 4 rebounds and no other stats, that's +6 score-margin points credited to that player by WP arithmetic: +4 points, +4 possessions gained, -2 possessions used. If he does that every game in a 82-game season, that's +328 for the year. This +328 is your final number. You can put it in terms of wins and wins-per-minute to make it more presentable, but this is the heart of the model: players contribute directly and concretely towards winning and losing in one-point increments by scoring, gaining possessions and losing possessions.

Now how can you reconcile that with a position adjustment that says all positive contributions from a SG help you win twice as much as contributions from a center? The positional adjustment just takes that +328, which is just one hard-earned, win-contributing action at a time, and arbitrarily makes it worth more or less points and wins depending on what position it came from. Remember, a rebound/steal is worth the same fraction of a win every time it happens, and that value is derived directly from the effect it has on the scoreboard.

It seems to me that winning is either derived concretely from scoring, gaining possessions and losing possessions in unchanging increments or is approximated in a system that includes positional adjustments. Just one of the ways that WP is an incoherent mess.

Nothing against the idea of positional adjustments in general, which is its own interesting/thorny subject.

mystic wrote:

Chicago76 wrote: In this instance, there is nothing controversial about stating that the G's DRB contribution is equal to that of the big man and that each G DRB is worth twice as much to a team as one DRB from the interior player.

I think that conclusion is based on the wrong premise.The idea that replacement level would determine the value of the contribution entirely. But that is not true. For rebounding there is a simple rule: First man, then ball. That means that you first secure the position by boxing out your opponent and then you go for the ball. Why is that important to mention? Well, let us take a look at Jason Kidd and the difference in terms of DRB% in the year he was traded from the Nets to the Mavericks.

Nope. I understand the limitation of the premise. That's why if you read again, I referred to those limitations based upon offensive/defensive scheme. This means releasing players in transition to start the O, getting back on D and forgoing responsibilities, etc. This is the obvious limitation of any replacement level or marginal production assumption, because given certain strategies, the marginal production of average player X in role Y when you're only counting production at Z may not resemble the league avg. at Z.

That said, the position played can (and typically does) have a greater impact on rebounding production than the different roles do for a given position in the league.

"First man, then ball" is the reason. Who I'm guarding (man) anchors me to a given position on the floor, and this largely determines the # of boards I can even consider getting. If my team wants me to go after DRBs, all else equal, or I'm more athletic or instinctive, all else equal, then I'll get more. If the opposite is true, I'll get less. The biggest driver of production is still going to be if I stand 8 feet from the basket when guarding my man or if I stand 20 feet from the basket.

In the context of looking at a given position's rebounding productivity within the constraints of a particular scheme, there is no doubt that scheme plays a major role, however, there are other areas of productivity that offset this when looking at aggregate player values. This particular tradeoff contains cost (fewer DRBs) and benefits (transition baskets). For example, Jason Kidd's DRB rate declines, but his ability to get in transition and accrue points and assists in an efficient manner are probably higher than they would be if DAL adopted a different strategy. Note: I'm aware his actual ast rate and pt/min rate's dropped from NJ to DAL, but this has to do with different teammate casts, usage decline that extends far beyond the strategic tradeoff.

In other words: Kidd's rebounding value declines, but his pt production through scoring or passing should be greater. It's not always this neat and tidy, because the benefit Kidd provides in forgoing DRBs may not be attributable to his box scor line. If he passes to the man who passes to the man who scores, then he has nothing to show for it. In general though, he's going to have something show up elsewhere when he forgoes those DRB opportunities.

Implementing a well-constructed replacement level, ie, not Berri's aggregate positional repl levels, will likely remove more noise than it introduces.

Chicago76 wrote: ... I don't think it's a stretch to say that five assists from a Sabonis or a Bill Walton in 32 minutes is worth more than 5 assists from Kevin Ollie over the same minutes. ..

Worth more to whom?
It doesn't count more on the scoreboard when the center is doing the assisting.
Seems like rather a stretch, to me.

Chicago76 wrote: Nope. I understand the limitation of the premise. That's why if you read again, I referred to those limitations based upon offensive/defensive scheme.

Sorry, I see that I lost my point a bit in the previous post. It wasn't so much that the value changes depending on the different schemes, but that in Kidd's case the work underneath the basket was still made by the bigs, while Kidd got the credit alone in the boxscore with that defensive rebound.

Kidd sacrified his perimeter defense by that, something he picked up in Dallas again more often. It is pretty interesting, because in the end his defensive value improved in Dallas in comparison to his offense, while during the Frank-era in New Jersey his offensive value improved in comparison to his defensive value. Well, even though Kidd got credit for a defensive rebound, the real benefit comes on the offensive end with more transistion opportunities, something which ends up being more efficient as scoring method. Well, on the other end he traded part of his usually steals for that too, while in Dallas, within the defensive scheme in which the bigs are also allowed to catch the ball, he has more opportunities for a steal again.

I think that is an interesting case to study, especially in the lights of a positional adjustment. When we look at the Nets under Frank, we see that they became worse defensively in comparison to the league average than under Scott in the 3 years before, while offensively overall they didn't do better. Overall they got worse.

Here a couple of numbers for Kidd:

Year: NetPM (WP48) (SPM) (TRB%) (TS% over lg avg) (TOV%)
2002: +5.6 (0.242) (+3.67) (10.9) (-3.6) (18.7)
2003: +8.5 (0.260) (+4.92) (9.6) (+0.7) (17.2)
2004: +7.5 (0.212) (+3.57) (10.3) (-3.1) (16.7)
2005: +4.9 (0.274) (+3.14) (12.1) (-2.3) (15.1)
2006: +4.4 (0.299) (+3.22) (11.4) (-1.0) (15.9)
2007: +1.3 (0.297) (+2.86) (13.2) (-2.5) (17.4)

As we can see WP48 has not much to do with the OnCourt NetPM per 100 possessions. WP48 actually goes up when the Nets with Kidd are getting worse. And the big change was the rebounding part. In 2007 the rebounding increase is big enough to make Kidd the leader in total WP that season despite being worse in terms of scoring efficiency and turnovers. His 5.5 ORB% was only surpassed by his rookie and sophomore season, his 20.8 DRB% was the highest of his career.

mystic wrote: Year: NetPM (WP48) (SPM) (TRB%) (TS% over lg avg) (TOV%)
2002: +5.6 (0.242) (+3.67) (10.9) (-3.6) (18.7)
2003: +8.5 (0.260) (+4.92) (9.6) (+0.7) (17.2)
2004: +7.5 (0.212) (+3.57) (10.3) (-3.1) (16.7)
2005: +4.9 (0.274) (+3.14) (12.1) (-2.3) (15.1)
2006: +4.4 (0.299) (+3.22) (11.4) (-1.0) (15.9)
2007: +1.3 (0.297) (+2.86) (13.2) (-2.5) (17.4)

As we can see WP48 has not much to do with the OnCourt NetPM per 100 possessions. WP48 actually goes up when the Nets with Kidd are getting worse. And the big change was the rebounding part. In 2007 the rebounding increase is big enough to make Kidd the leader in total WP that season despite being worse in terms of scoring efficiency and turnovers. His 5.5 ORB% was only surpassed by his rookie and sophomore season, his 20.8 DRB% was the highest of his career.

An interesting claim, since you list that his WP48 went down a tiny bit if anything (as did his WS48) and he played pretty much the same number of minutes those years. So it seems like Kidd's standing in the rest of the league might be due more to what other people did (which apparently must have been get worse) as opposed to what Kidd did.

Mike G wrote:

Chicago76 wrote: ... I don't think it's a stretch to say that five assists from a Sabonis or a Bill Walton in 32 minutes is worth more than 5 assists from Kevin Ollie over the same minutes. ..

Worth more to whom?
It doesn't count more on the scoreboard when the center is doing the assisting.
Seems like rather a stretch, to me.

The issue isn't one of what shows up in a box score or the scoreboard. Value in this case is credit division between the passer and the scorer, and there is a slew of evidence to support the notion that all assists aren't equal.

A Kevin Ollie level PG generates 5-6 assists per 36 min. That's pretty much the baseline assist production a PG can generate by simply swinging the ball around the perimeter to the open perimeter shooters w/out pressure. In that case, the assistor isn't generating the bulk of the pt talley--the shooter is.

A Walton/Sabonis level interior passer getting 5 assists over the same 36 min is drawing double teams, hitting cutters, hitting guys on short curls, and generally creating the double that leads to the shooter being open in the first place.

Is a pass leading to a layup/dunk worth more than a pass to a player for an open 20 footer? You bet it is. Are all assists equal? Hardly.

mystic wrote:

Chicago76 wrote: Nope. I understand the limitation of the premise. That's why if you read again, I referred to those limitations based upon offensive/defensive scheme.

Sorry, I see that I lost my point a bit in the previous post. It wasn't so much that the value changes depending on the different schemes, but that in Kidd's case the work underneath the basket was still made by the bigs, while Kidd got the credit alone in the boxscore with that defensive rebound.

Kidd sacrified his perimeter defense by that, something he picked up in Dallas again more often.

I see your point better now. Thanks for that. I think the fact that WP48 goes up while RAPM and team D goes down is a standard hazard of box score metrics. PER would have the same issue. And this isn't a defense of WP48, because as far as box score metrics goes it leaves a lot to be desired. That said, there is some place for adj +/- and a box score metric like PER. One is more prone to errors of misattribution (box score) while the other is prone to greater standard error (adj +/-).

As this relates to positional adjustments: the problem you're pointing out still boils down to scheme. NJ tells Kidd to go for boards more on both ends of the court, and this leads to poorer defense and transition O. Kidd gets more boards, which look better in a box score stat, but his defense isn't being penalized. I get it. If this is your criticism (and I think it's a valid one), and you feel that this corrupts the metric, then don't look at any box score metric, because this isn't unique to WP48. Personally, I think we need to look at some form of a box score metric just to balance out the weaknesses of adj +/-, so we might as well refine that metric as best we can.

Looking at two groups of players, the first being 1500+min, 20% ast players we'll loosely call PGs, and the second being 1500+min guys B-R calls Cs, we can compare the interquartile DRB rates over the last 4 seasons (removing partial seasons in trade scenarios):

PGs: 8.6 to 10.5
Cs: 20.2 to 24.9

Even looking at Kidd's DAL seasons, when he was staying home on players more, his DRB rates were off the charts. Someone needs to be able to handle the ball, be quick enough to defend the opponent's opposing PG, and do most of this work far from the basket. If a player can do all of these things and still get 16% of DRB opps when he's on the floor, that is really, really valuable. A player producing at these rates is probably generating extra DRBs for his team. On/off #s bear this out. DAL w/ Kidd on the court fared +3.0% to +3.6% better in DRBs from 2008/09 to 2010/11. Compare that to a player like a Marc Gasol whose DRB rate is roughly 20 over those 3 seasons. When he was on the court, MEM actually rebounded on the defensive end marginally worse 2 of 3 seasons. Net over all 3 seasons, he has statistically had zero impact on MEM's defensive board work, despite accruing a greater share of DRBs than Jason Kidd.

Where production occurs and how that production compares to others in that role does matter. Another example--

The 3 highest big man ast rates of recent history and on vs. off team assisted FG rates:
06/07 Brad Miller 4.5 ast/36 min, +9% ast FGs on vs. off
10/11 Horford 3.5 ast/36 min, +12% ast FGs on vs. off
07/08 Miller 3.8 asst/36 +9% ast FG on vs. off.

Obviously some of this could be related to feeding the post, but certainly not all of it. Those are huge changes based upon relatively small ast tallys. Compare this to a PG generating an ast% of 15 to 20% over heavy minutes. In general the on-off ast fg rates would be negative for a PG genearting assists in heavy minutes.

Chicago76 wrote: Is a pass leading to a layup/dunk worth more than a pass to a player for an open 20 footer? You bet it is. Are all assists equal? Hardly.

A pass leading to a layup is likely to become an assist, while a pass for an open 20' shot is maybe 50% likely to produce a FG, and therefore to register an assist.

So you'd have to argue that (roughly) 2 passes to outside shooters are less valuable than one to a player inside, because we aren't talking about the relative value of passes but about registered assists.

The average Ast in the boxscore may be the result of one terrific pass, or 2 good passes, or 3 decent passes, etc.
Bill Russell used to say, "Make easy passes, 'til you get an easy shot". On his team, everyone got a few assists.

Bill Walton had huge turnover rates. It may well be that for each Assist, there was also a passing turnover. Does that count against the value of his assists?
The 'passing center' fad peaked in the '70s, right about the time they started tracking TO.

I calculated adjusted assists a few weeks ago using the previous "2.5" seasons. You can see the complication of having players who create assists by being good passers (Kidd, DWill, Nash, etc) or good shooters (Korver, Boozer?, etc).



Here are the PG's:

For the Lulz:

In my Stat Geek Idol entry, I slightly misrepresented diminishing returns.
Judge Mark Cuban commented that "there are no diminishing returns on defensive rebounds"

Mike G wrote:

Chicago76 wrote: Is a pass leading to a layup/dunk worth more than a pass to a player for an open 20 footer? You bet it is. Are all assists equal? Hardly.

A pass leading to a layup is likely to become an assist, while a pass for an open 20' shot is maybe 50% likely to produce a FG, and therefore to register an assist.

So you'd have to argue that (roughly) 2 passes to outside shooters are less valuable than one to a player inside, because we aren't talking about the relative value of passes but about registered assists.

For certain types of passing scenarios, this isn't a tough assumption to make.
First, we'd actually need charting data to determine eFG% of assist scenarios vs. non-assist scenarios.
Second, we'd need to take this a step further to imagine a world where O's function without assists to set a replacement baseline. Shot creators would carry loads to the point of exhaustion and guys who are bad at getting their own shot would still need to create shots to some degree. Not crazy to assume a 35%-40% efg% "replacement" baseline. This is the part you haven't included.

Value per perimeter "potential" assist is pretty simple: 45% or 50% less 35% or 40% times 2 points. Looking at all 4 assumptions, the average point per potential assist = ~0.2 pts. Dividing by efg% gets points per actual assist or ~0.4 weighing all 4 scenarios equally.

Value of assist at rim from high post should result in higher efg%. Guys who receive passes down low on cuts get hacked all the time. The defense is conceding ~75% efg% in a 2 FT scenario, so expected efg% in this case is worth more than that. Call it 80-90%. 80% or 90% less 35% or 40% times 2 pts = pts per potential assist of 0.95. Pts per actual assist ~ 1.1

Mike G wrote:The average Ast in the boxscore may be the result of one terrific pass, or 2 good passes, or 3 decent passes, etc.
Bill Russell used to say, "Make easy passes, 'til you get an easy shot". On his team, everyone got a few assists.

This actually supports the notion of position adj. Assists in the NBA are overwhelmingly the result of hitting the open man after drawing a double team. Drawing a double occurs in one of two ways (generally): dribble penetration or doubles on bigs. Two common scenarios:

A-Relatively easy entry to big (who is doubled). He passes out to perimeter player X, who then passes one spot around the perimeter for basket+assist. Who did the "work" in getting the shot. I'd argue the following order: big (who drew the double), entry passer, and then ball rotator (player X). The rotator gets the assist for doing the least amount of work. Even if the entry passer ended up also being the rotator, and hence doing more, he's still not splitting the credit with the big.

B-Dribble penetrator passes to perimeter rotator, who passes to open perimeter shooter for basket+assist. The penetrator generated the bulk of the "assisting" action, but the rotator gets the credit.

Why I purposely chose a 5-6 ast/36 min "caretaker" PG like Kevin Ollie is that the bulk of his assisting is done on simple rotation. He's not doing a lot of dribble penetration that draws doubles, and he's certainly not responsible for passing out of the post. He's not much of a shooter, so he's not even spreading the floor. His "assisting actions" are basically the baseline any PG playing strongside and making entry passes or receiving the ball back out and rotating can expect. Does he make the occasional big pass to the open cutter for the easy bucket? Sure. But if you were to occurence weight his "potential assisting" actions, both passes directly and indirectly leading to an eventual shot, they result in a very low marginal FG conversion benefit. Now if he was generating say 8 or 9 assists per 36, he's clearly doing something more. You can't produce that many assists on simple PG ball rotation. He's making more incisive high FG% entry passes. He's using dribble penetration to generate direct assists on kickouts or hitting the open weakside interior man, etc. And yes, he's probably generating more TOVs (which we'll get to in a moment), but as long as the benefit of better team shot conversion outweighs the cost of those TOVs, that's a net benefit.

When you look at actual registered (and unregistered) "assisting actions", and the distribution and relative marginal value of those actions, I don't think it's a stretch at all to say that a guy like a Walton or even a Divac, Brad Miller, Shaq in many years, etc is generating more "assisting value" per team poss. than a PG like a Kevin Ollie. Their assisting value (both registed and unregistered) is greater despite maybe having only 40 to 80% of the assist totals per min to show for their work.

Mike G wrote:Bill Walton had huge turnover rates. It may well be that for each Assist, there was also a passing turnover. Does that count against the value of his assists? The 'passing center' fad peaked in the '70s, right about the time they started tracking TO.

Walton before the wheels completely fell off during the 2 yr layoff didn't have huge turnover rates compared to lg avg (+1 or +2% above). If you want an example of someone who did, look no further than one of the best passers of all time: Magic Johnson. Those count against him, but only to the degree the cost needs to be netted against marginal production of being an awesome passer. The issue is irrelevant anyway, because of course TOVs count against a player's production in a linear weights metric. They're in a variable called TOVs.

EvanZ wrote:I calculated adjusted assists a few weeks ago using the previous "2.5" seasons. You can see the complication of having players who create assists by being good passers (Kidd, DWill, Nash, etc) or good shooters (Korver, Boozer?, etc).

Thanks for succinctly providing something that I spent way too much time blathering about. A couple of questions:

-are these numbers adj for pace and/or min, or are they raw totals?
-is there a link you can shoot over to a prior thread/blog that describes the nuts and bolts of the calculation.

One comp that I think is particularly interesting is a Horford (a better passing big) vs. a D Fisher (caretaker PG).

Chicago76 wrote:

EvanZ wrote:I calculated adjusted assists a few weeks ago using the previous "2.5" seasons. You can see the complication of having players who create assists by being good passers (Kidd, DWill, Nash, etc) or good shooters (Korver, Boozer?, etc).

Thanks for succinctly providing something that I spent way too much time blathering about. A couple of questions:

-are these numbers adj for pace and/or min, or are they raw totals?
-is there a link you can shoot over to a prior thread/blog that describes the nuts and bolts of the calculation.

One comp that I think is particularly interesting is a Horford (a better passing big) vs. a D Fisher (caretaker PG).

Here's a link to the blog post.

http://thecity2.com/2012/02/19/2-12-yea ... d-assists/

Everything is per 100 possessions.

It's not easy to compare between positions like you did with Horford and Fisher, because how do you separate whether assists are being "created" by passing or making shots? I haven't figured that one out yet.

EvanZ wrote:
Here's a link to the blog post.

http://thecity2.com/2012/02/19/2-12-yea ... d-assists/

Everything is per 100 possessions.

It's not easy to compare between positions like you did with Horford and Fisher, because how do you separate whether assists are being "created" by passing or making shots? I haven't figured that one out yet.

Thanks. I misinterpreted the output without understanding the methodology...pretty easy to do when I open my mouth before figuring out what the #s represent. I think what you're trying to get at is the creation of assistable opportunities when player X is on the court, whether those are indirectly or directly the result of that player's passing of the ball to the scorer.

My personal theory and what I would do to quantify this follows:

The vast majority of assists happen because something occurs on the court that creates imbalance in the defense. This can happen in two ways: a shooter stretches the floor, giving the other 4 players more room to operate, or a double team occurs via dribble penetration, doubling in the post, and less frequently due to a second defender shadowing an elite scorer or a screen. In the majority of these cases, the shooter/penetrator/big man is the catalyst of the "assistable" opportunity.

The question now is, how do you measure this? I think you might get something of value from looking at on-off team data. I'm not sure if you can tease all of this out w/ 82games data or some other source or not, but here goes, using Chicago and Derrick Rose.

Step 1: measure the % of Rose's teammate baskets that are assisted when he is on the court. it doesn't matter if he does the assisting or someone else does. I think you can get total baskets by Rose and total Bulls baskets when he's on. I also think you can also get % of Rose's baskets that are assisted and % of total Bulls baskets that are assisted when he's on. Use this to calculate % of his teammate's baskets that are assisted.

Step 2: Compare this to the % of total Bulls assisted baskets that occur when he's off the court. I realize the comparison isn't quite the same, because you're looking at assisted baskets to 4 players when he's on vs. 5 players interacting together when he's not, but because it's a rate, things should still be fairly comparable.

The reason I wouldn't compare total Bulls assisted FG % with Rose on vs. off is that a lot of his buckets are unassisted. He's not necessarily stifling the offense. He's just creating and taking the load away. He's also drawing doubles that likely result in assists. Some of these he's getting directly from passes. Others create that defensive imbalance I talked about where he makes the pass that leads to the assist. If you went out and asked a backup PG to do what he does, then team assists likely drop, because there is no need to double the backup.

Do this for plaers over x minutes and you have indirect assist % differential for every player. From there you could either go simple or complex:

Simple = indirect assist % differential x teammate FGM = implied ast added or taken away by player X. This could be expressed in abosolute terms, per min, per poss, or as an assisted basket ratio.
Complex = take the initial implied ast added or taken away by each player and run a calc similar to APM but just for assists using various teammate lineups. This probably the most correct way of doing it, because it controls for teammate interaction.

Something like this might present the evidence/argument that:
-Derrick Rose doesn't get that many assists for a PG, but his teammates do, because he draws doubles that promote assistable opportunities.
-Al Horford doesn't get that many assists, but his teammates do, because he can pass out of doubles in the post.
-Kyle Korver doesn't get that many assists, but his teammates do, because he stretches the floor.

It would also provide evidence for how much of the "assisting" is Horford vs. Teague vs. Joe Johnson or Korver vs. Rose vs. Boozer.

After controlling for lineup, you may find that some players are nothing more than assist "vessels" while others with lower APG or ast rates are doing the heavy lifting.

With some evidence in the long drawn out APM method to finding distributors, you might be able to get a shorthand ezPM type value out of it via regression.

Penetrator/post indirect assist may be found in a regression containing 2FGA and 2FG%.
Shooter indirect assist via spacing may be found in 3FGA and 3FG%..and so on.