Does APM have a standard formula?

[WarriorGM]

What is the reason there are different RAPM and adjusted plus-minus (APM) numbers from different sources? If there is a common standard everyone should be producing the same numbers. But reading into it further it seems the APM formula is at the discretion of the one making the calculation. Is that correct? Weights are arbitrarily assigned to various factors? It's possible for example to assign time on the court as a positive variable so that the more time a player plays the higher his APM will be? True or false?

[eminence]

Here's an article from Daniel over at Bbref on APM's and their calculations: http://godismyjudgeok.com/DStats/2011/nba-stats/a-review-of-adjusted-plusminus-and-stabilization/

[Colbinii]

This forum would be much better if we did our research before criticizing.

Thank you Eminence.

[WarriorGM]

Confirms my suspicions. Was reading Rosenbaum and he was incorporating box score statistics according to his version of APM. AuPM by Elgee seems to do something along those lines. RAPM as expected dampens outliers much like a moving average does to get a cleaner number for predictions for the entire the population but penalizes the outliers and probably underestimates them to do so. Must get numbers from the same source for consistency and they should be transparent with their methodology.

I did not see any adjustments for time on the court. Still unclear to me if playing less results in a lower APM than playing more if one is generally positively efficient in plus-minus. Did I miss something that shows that playing 30 minutes compared to 40 minutes isn't penalized? If that is the case though no wonder playing on bad teams confers an advantage in APM. When you are on a bad team you need to play more.

[eminence]

Confirms my suspicions. Was reading Rosenbaum and he was incorporating box score statistics according to his version of APM. AuPM by Elgee seems to do something along those lines. RAPM as expected dampens outliers much like a moving average does to get a cleaner number for predictions for the entire the population but penalizes the outliers and probably underestimates them to do so. Must get numbers from the same source for consistency and they should be transparent with their methodology.

I did not see any adjustments for time on the court. Still unclear to me if playing less results in a lower APM than playing more if one is generally positively efficient in plus-minus.

I haven't looked at Reosenbaum's stuff myself as far as I'm aware so no comment there.

Elgee's AuPM is an attempt to estimate RAPM from earlier incomplete data (years we don't have play by play for). A problem with naming clarity is a real thing.

The main outliers in APM calculations tend to be extremely low minutes guys, so I'm not too concerned about them being pulled to 0 (you state underestimates, but overestimations are just as possible).

I have seen Daniel use minutes as his prior for RAPM on one occasion (I believe it was used as the prior for a playoff only RAPM, but I'm not sure on that), it's not a regular practice as far as I'm aware.

[eminence]

All variants are usually reported as a /100 possession #, so playing time doesn't impact it directly in that sense. If you see two guys with a +2 or whatever and one is a starter and the other is an end of bench guy you can assume the starter is having more impact in total over the season.

[WarriorGM]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

[Colbinii]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

Wait, one players stats gives you an example of an entire umbrella of statistics into how it works?

Payton in Stockton generally look great in NPI RAPM yet played on good teams.

We cant conclude anything with a 1 player sample size.

[Mavericksfan]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

Wait, one players stats gives you an example of an entire umbrella of statistics into how it works?

Payton in Stockton generally look great in NPI RAPM yet played on good teams.

We cant conclude anything with a 1 player sample size.

Do you disagree with the notion that it’s “easier” to put up more impact on a bad team?

[trex_8063]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

Not necessarily; or at least certainly there are counters to this observation. And to some small degree, this could be a Lebron thing, too. Personally, I think he's a little better "floor raiser" [perhaps the GOAT in this] than he is a "ceiling raiser"; as such, it might be expected to see higher RAPM's when with lesser supporting casts. EDIT: Though as far as "dip when with the Heat", it must be acknowledged that '11 was sort of a weird outlier [in a bad way] within the middle of his prime; that effects things both in his actual '11 figure, but also the PI RAPM figures of immediately subsequent years.

As to a prior comment about how RAPM will "stifle" or under-report outliers: I suspect that's largely only going to be the case with NPI (which treats everyone equally and curves toward the mean [0]). PI will often have more of a "it's not spurious; see? he's done this before" outlook on those outlier results.

[eminence]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

Not necessarily; or at least certainly there are counters to this observation. And to some small degree, this could be a Lebron thing, too. Personally, I think he's a little better "floor raiser" [perhaps the GOAT in this] than he is a "ceiling raiser"; as such, it might be expected to see higher RAPM's when with lesser supporting casts. EDIT: Though as far as "dip when with the Heat", it must be acknowledged that '11 was sort of a weird outlier [in a bad way] within the middle of his prime; that effects things both in his actual '11 figure, but also the PI RAPM figures of immediately subsequent years.

As to a prior comment about how RAPM will "stifle" or under-report outliers: I suspect that's largely only going to be the case with NPI (which treats everyone equally and curves toward the mean [0]). PI will often have more of a "it's not spurious; see? he's done this before" outlook on those outlier results.

Overall I think there's a little bit of truth to the sentiment on average, but it's hard to say too much. There's only 10-15 guys we really think of as great players who had their primes after '97, it's just tough with that few guys to draw strong conclusions from. Case by case is probably the way to go (and agree with Trex that LeBron himself is a bit more of a floor than a ceiling raiser).

And yes, PI or multi-year RAPM will allow the very top end guys to pull themselves further from the average.

[Colbinii]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

Wait, one players stats gives you an example of an entire umbrella of statistics into how it works?

Payton in Stockton generally look great in NPI RAPM yet played on good teams.

We cant conclude anything with a 1 player sample size.

Do you disagree with the notion that it’s “easier” to put up more impact on a bad team?

Depends on your teammates and the system in which you play.

Klay Thompson is more impactful in his role now than he would in place of LeBron on Cleveland for example.

[WarriorGM]

Thank you eminence for the explanations. Since you seem to be pretty
familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative
to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the
Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again
when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great
players. Is that unusual?

Not necessarily; or at least certainly there are counters to this observation. And to some small degree,
this could be a Lebron thing, too. Personally, I think he's a little better "floor raiser" [perhaps the GOAT
in this] than he is a "ceiling raiser"; as such, it might be expected to see higher RAPM's when with lesser
supporting casts. EDIT: Though as far as "dip when with the Heat", it must be acknowledged that '11 was
sort of a weird outlier [in a bad way] within the middle of his prime; that effects things both in his actual
'11 figure, but also the PI RAPM figures of immediately subsequent years.

I looked at the numbers again paying closer attention to other good players and this does seem to stand out.
APM seems pretty good at illustrating the concept of floor raisers and ceiling raisers. KG and LeBron had
their highest APM when they had to do it all while Curry and Paul had APMs that rose the more competent their
teammates were.

Draymond Green we know is an APM darling. He sticks out in terms of the company he is keeping using this
metric and as the most anomalous result probably deserves the most scrutiny in assessing how APM works.
Draymond is largely credited with making the Death Lineup possible and I suspect that is one of the things
that gives him a bump. The ability to unlock high plus lineups probably distinguishes ceiling raisers from
floor raisers. Draymond's strengths also coincide with KG's and LeBron's at their peak namely defense and
playmaking. Indeed his weakness in scoring seems to emphasize playmaking as a trait APM ascribes great value
to. I wonder if an analogy can be drawn to the value of quarterbacks in football.

APM excels at teasing out obscured traits and players that have an impact on winning. But even after looking
closer at APM though my concerns aren't mollified. The complicated calculation detracts from clarity of
understanding. The limited number of sources and the conflicting values they can give do not inspire
confidence. The inconsistency in level of play year-to-year with many players seems unnatural. Some of the
results are questionable, for example was 36 year old Steve Nash more valuable a player than he was in his
MVP years? It may be confounded by intangibles like opponents possibly raising their game when facing the champions.
My statistical concerns regarding interpretation of data remain. It's too imprecise even under the best
circumstances to use as a ranking the way many seem to.

[Colbinii]

Thank you eminence for the explanations. Since you seem to be pretty
familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative
to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the
Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again
when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great
players. Is that unusual?

Not necessarily; or at least certainly there are counters to this observation. And to some small degree,
this could be a Lebron thing, too. Personally, I think he's a little better "floor raiser" [perhaps the GOAT
in this] than he is a "ceiling raiser"; as such, it might be expected to see higher RAPM's when with lesser
supporting casts. EDIT: Though as far as "dip when with the Heat", it must be acknowledged that '11 was
sort of a weird outlier [in a bad way] within the middle of his prime; that effects things both in his actual
'11 figure, but also the PI RAPM figures of immediately subsequent years.

I looked at the numbers again paying closer attention to other good players and this does seem to stand out.
APM seems pretty good at illustrating the concept of floor raisers and ceiling raisers. KG and LeBron had
their highest APM when they had to do it all while Curry and Paul had APMs that rose the more competent their
teammates were.

Draymond Green we know is an APM darling. He sticks out in terms of the company he is keeping using this
metric and as the most anomalous result probably deserves the most scrutiny in assessing how APM works.
Draymond is largely credited with making the Death Lineup possible and I suspect that is one of the things
that gives him a bump. The ability to unlock high plus lineups probably distinguishes ceiling raisers from
floor raisers. Draymond's strengths also coincide with KG's and LeBron's at their peak namely defense and
playmaking. Indeed his weakness in scoring seems to emphasize playmaking as a trait APM ascribes great value
to. I wonder if an analogy can be drawn to the value of quarterbacks in football.

APM excels at teasing out obscured traits and players that have an impact on winning. But even after looking
closer at APM though my concerns aren't mollified. The complicated calculation detracts from clarity of
understanding. The limited number of sources and the conflicting values they can give do not inspire
confidence. The inconsistency in level of play year-to-year with many players seems unnatural. Some of the
results are questionable, for example was 36 year old Steve Nash more valuable a player than he was in his
MVP years? It may be confounded by intangibles like opponents possibly raising their game when facing the champions.
My statistical concerns regarding interpretation of data remain. It's too imprecise even under the best
circumstances to use as a ranking the way many seem to.

As a standalone statistic APM is still one of the strongest measurements we have. Ultimately, like any statistic it should never be alone but completely dismissing it or devaluing it below other measurements (especially team achievements) is disingenuous and disappointing.

FWIW LeBron had to do more in Miami than he did in his second stint in Cleveland (imo).

[giberish]

Thank you eminence for the explanations. Since you seem to be pretty familiar with it, what is your experience in looking at numbers of APM in terms of marginal increase relative to team quality? In one set of numbers I was looking at LeBron for example had high NPI RAPM with the Cavaliers in his first stint but then that number dipped while he was with the Heat then it went up again when he went back to the Cavs. Gives me the feeling bad teams are conducive to high NPI RAPM for great players. Is that unusual?

Wait, one players stats gives you an example of an entire umbrella of statistics into how it works?

Payton in Stockton generally look great in NPI RAPM yet played on good teams.

We cant conclude anything with a 1 player sample size.

Do you disagree with the notion that it’s “easier” to put up more impact on a bad team?

I'm too lazy to try and check this, but I would assume that great players will try harder during the regular season if they're on otherwise weak rosters, just to get them to the playoffs (and ideally with a decent seeding). When they're on stacked teams there's a very strong tendency for top players to coast during the regular season.

So, because they have to do more for decent team success, a great player will play better during the regular season on a weak team then when they're on a strong team. So a higher NPI RAPM in those cases is 'real'. I recall this coming up in KG vs Duncan debates.