Why were Kobe's RAPM numbers better in 08-10 than 02-04?

[rrravenred]

Don't see this at all. Prime Shaq's offensive RAPM numbers (using xRAPM instead since classic RAPM is incomplete) completely demolish Pau+Odom+Bynum's even when combined.

Well... xRAPM is "complete" only in that it factors in boxscore production AS WELL AS raw impact on team offensive and defensive efficiency.

Quite a few people on here think that this is trying to create an frankenstein-like orangeapple rather than the classic single-genome varieties...

[Shot Clock]

Maybe, just maybe our ability to massage meaningful numbers using currently available defensive data isn't that reliable.

[mysticbb]

rapm is measuring the same thing apm measures, but is just doing a better job of it right?

APM and RAPM are both based on a regression on the different game snippets, in that sense, they are trying to "measure" the same thing; at that: how much does a player change the outcome of a possession.

APM is using OLS (ordinary least square), while RAPM is using ridge regression. Because we deal with a ill-posed problem (there are a lot of more game snippets than players in the dataset; more equations than variables), ridge regression will per se give a better prediction (mathematical proven theorem!). But the ridge factor also introduces a bias, which will act like an anchor, drawing everyone to the mean.
The better prediction comes partly from resolving issues with multicollinearites as well as from regression to the mean.

When calculating APM and RAPM it all comes down to matrix algebra, making it pretty simply to handle the thousands of equations going in for one season (each game snippet, 5 man vs. 5 man, is one equation).

if you look at the lakers point differential as a team in the years 2008-2010, it is much higher then their point differential in 2002-2004, so there is a bigger pie to calculate kobe's slice from in 2008-2010.

Due to the use of a regression, the coefficients derived are per se adjusted for the strength of teammates, opponents and home court advantage. It is also misunderstanding the method, if you believe, having an overall lower point differential would per se lead to a smaller RAPM value, because that is not the case. The player itself can just have played with weaker teammates against better opponents in average, which would lead to a lower scoring margin, but not per se to a lower RAPM/APM figure. In essence, there isn't really a "pie" which grows bigger or smaller.

this could easily not be the reason.. i'm just taking a shot at it... i had never looked up rapm before.. from what i can tell, there is a ton of error without proper sample sizes, which can take years to accumulate (since there is often not big sample sizes of minutes for specific 5-man units vs. other specific 5-man units).

For RAPM a full season is rather sufficient to get a good picture, but that goes more for the overall value, not for the offensive and defensive value. The issue comes with the interpretation of the numbers, a player must not be a good defender to achieve a positive value for the defensive part, he simply can be sufficient enough defensively while enabling the coach to play better defensive players with him on the court due to his great offense in order to achieve a better defensive value. Also, there is a connection between offense and defense; for example, if a player helps his team to avoid turnovers, he ultimately reduces the fast- and secondary break opportunities for the opponents, opportunities which usually are more efficient than normal halfcourt sets. A similar effect may happen with a better defensive player, who is able to disrupt the offensive sets and forces turnovers which are ending up steals, which then are leading to more efficient offensive opportunrities as well.

What we can take from those numbers is: How much changed the presence of a player the outcome of a possession, on offense, on defense and overall. We can't say how that was achieved, for that we would need the "eye test" and the boxscore to come to a meaningful conclusion. But we still can say, with reasonable certainty, by how much the outcome was/is changed (APM more for was, RAPM more for is).

Also, such numbers may not be comparable between seasons (due to various reasons including sample size). In order to normalize them, I suggest using the standard deviation before staring a comparison. In essence, a player making 1 sigma difference in one season is as valuable as the player making that 1 sigma difference in another season.

[trainwreckog]

rapm is measuring the same thing apm measures, but is just doing a better job of it right?

APM and RAPM are both based on a regression on the different game snippets, in that sense, they are trying to "measure" the same thing; at that: how much does a player change the outcome of a possession.

APM is using OLS (ordinary least square), while RAPM is using ridge regression. Because we deal with a ill-posed problem (there are a lot of more game snippets than players in the dataset; more equations than variables), ridge regression will per se give a better prediction (mathematical proven theorem!). But the ridge factor also introduces a bias, which will act like an anchor, drawing everyone to the mean.
The better prediction comes partly from resolving issues with multicollinearites as well as from regression to the mean.

When calculating APM and RAPM it all comes down to matrix algebra, making it pretty simply to handle the thousands of equations going in for one season (each game snippet, 5 man vs. 5 man, is one equation).

if you look at the lakers point differential as a team in the years 2008-2010, it is much higher then their point differential in 2002-2004, so there is a bigger pie to calculate kobe's slice from in 2008-2010.

Due to the use of a regression, the coefficients derived are per se adjusted for the strength of teammates, opponents and home court advantage. It is also misunderstanding the method, if you believe, having an overall lower point differential would per se lead to a smaller RAPM value, because that is not the case. The player itself can just have played with weaker teammates against better opponents in average, which would lead to a lower scoring margin, but not per se to a lower RAPM/APM figure. In essence, there isn't really a "pie" which grows bigger or smaller.

this could easily not be the reason.. i'm just taking a shot at it... i had never looked up rapm before.. from what i can tell, there is a ton of error without proper sample sizes, which can take years to accumulate (since there is often not big sample sizes of minutes for specific 5-man units vs. other specific 5-man units).

For RAPM a full season is rather sufficient to get a good picture, but that goes more for the overall value, not for the offensive and defensive value. The issue comes with the interpretation of the numbers, a player must not be a good defender to achieve a positive value for the defensive part, he simply can be sufficient enough defensively while enabling the coach to play better defensive players with him on the court due to his great offense in order to achieve a better defensive value. Also, there is a connection between offense and defense; for example, if a player helps his team to avoid turnovers, he ultimately reduces the fast- and secondary break opportunities for the opponents, opportunities which usually are more efficient than normal halfcourt sets. A similar effect may happen with a better defensive player, who is able to disrupt the offensive sets and forces turnovers which are ending up steals, which then are leading to more efficient offensive opportunrities as well.

What we can take from those numbers is: How much changed the presence of a player the outcome of a possession, on offense, on defense and overall. We can't say how that was achieved, for that we would need the "eye test" and the boxscore to come to a meaningful conclusion. But we still can say, with reasonable certainty, by how much the outcome was/is changed (APM more for was, RAPM more for is).

Also, such numbers may not be comparable between seasons (due to various reasons including sample size). In order to normalize them, I suggest using the standard deviation before staring a comparison. In essence, a player making 1 sigma difference in one season is as valuable as the player making that 1 sigma difference in another season.

thank you for the post and shedding light on rapm for the thread..

it is an intriguing stat and concept that definitely has use, particularly the more reliable it becomes.

im not sure you convinced me that the point differentials did not affect the rapm scores (with the bolded underlined part of your post above), but i'll take your word for it, as you have a better knowledge of the concepts then i do.

i must say the guys that get to do this type of work are lucky.

[mysticbb]

im not sure you convinced me that the point differentials did not affect the rapm scores (with the bolded underlined part of your post above), but i'll take your word for it, as you have a better knowledge of the concepts then i do.

Just imagine you have a +5 player. Now you give him 4 average teammates, which means the overall lineup should play +5 as well (each average player contributes 0). Well, and now you give him 4 below average players as teammates, like everyone with -1. The overall expected margin would be +1. Despite the fact that +1 is smaller than +5, the player would still be identified with +5 in each case, given there is enough data to correctly assign the teammates with the respective values. Obviously, if we have just that one equation, each player would get the same value assigned to, but we have thousands of equations here.
There are more than enough players on worse teams ending with higher RAPM values than some players from better teams. Overall we still should expect that in average a better team consists of better players, thus there will always be a correlation between a better team and higher individual RAPM ratings, but that has nothing to do with a bigger pie.

Also, a major difference between RAPM and APM is how it would differentiate between the players. APM would use the smallest amount of data to conclude big differences between players (overfitting), while RAPM would rather string them more together. If two players share a lot of minutes, they are more likely to end up being rather equal when using ridge regression than when using OLS.