#25 Highest Peak of All Time (McGrady '03 wins)

[ElGee]

vote: 1998 Karl Malone

I don't think the discussion of "is this his peak" is bad. As I've said, 95 and even 92 have really good arguments -- it's almost splitting hairs (within a half SRS point IMO).

As for the other guys (w/T-Mac going next for me)...

Howard -- probably next because of the universal portability of "I can play 2 spots" big-man defense coupled with "I don't need the ball on offense but I'm a consistently good offensive player." But that leads me to...

Pippen -- uber uber portability for me. Along with Reggie Miller, a guy *I* and everyone under the son always puts on AT teams, for good reason. The GOAT perimeter defender, he gives you nasty upgrades on basically every defense AND seamlessly fits on offense precisely because he's not a first option of a great offensive team.

I think people have a bit of a disconnect in general when it comes to Pippen. He did REALLY good work with a Grant-led defensively-oriented supporting cast in 94-95 (like ~3 SRS -- this is really quite good), and then was part of a GOAT-level team that in long stretches without Dennis Rodman played 10 SRS ball and when healthy in 1997 15 SRS ball, confirming Pip's absolute value as well as his ridiculous scaling that we would expect. The disconnect comes because very thoughtful people think "Well, Jordan was past his prime -- an MVP level player, but not a historical outlier anymore..." but then they don't equate Pippen the appropriate amount of credit.

Barry -- underrated defensively, an AMAZING passer, slick shooter. He gunned too much but his work in unipolar settings was phenomenal, and then balanced out as a distributor more in 76 before the early PS exit.

Penny -- Penny v Pip is an interesting philosophical debate, since they met at around the height of their respective powers in 1996 and Penny was destructive offensively against Pippen. But don't let the head-to-head matter so much...Penny in general might be the best offensive player left on the board (I'm pretty sure he is).

*gap*

Then we have Durant 2012 (Getting close. Uber portable with his shooting, a better passer and decent defender.) Reed, McHale, Gilmore, Thurmond, Hill.

Besides Pippen, the two other guys I have strong (probably outlying) feelings here on are Thurmond and King. Thurmond because he demonstrates tremendous value statistically and is just a monster defensively...and King because I question his portability onto better teams. It's not clear to me that Paul Pierce isn't a better peak player than King (in my notes he is). King may be a better in-deep scorer or even iso-scorer, (I can say the same thing about Ice Man too) but the rest of Pierce's game is more complete, balanced, and fits on so many more teams. I've said before Bernard may be the best unipolar scorer EVER, but I see a fairly large mountain of evidence that one-dimensionalish volume scorers have some slick diminishing returns on really good teams...especially when they don't have great outside shots or aren't great passers (King).

To use a really crude example -- what if Andrew Toney had his own team? And for a short spring period averaged 28 ppg on good TS% and lifted his team to like -1 SRS? Toney was a dazzling and explosive scorer, and probably capable of this, but I don't see the evidence that he was all-nba level impact on the very good early 80's 76er teams, and similarly I have a hard time valuing King over some of the aforementioned players, with the Pierce comparison being the most interesting IMO.

[therealbig3]

Updated voting:

03 T-Mac - 5 (therealbig3, C-izMe, Dr Positivity, fatal9, ardee)

98 Malone - 4 (JordansBulls, Lightning25, Doctor MJ, ElGee)

11 Dwight - 1 (DavidStern)

62 Baylor - 1 (PTB Fan)

88 McHale - 1 (bastillon)

[colts18]

Elgee, Do you have the SRS in/out for Pippen 98? How does it breakdown for offense/Defense

As far as bernard King, in 85, he only played 55 games and his team went 5-22 without him (any in/out on him?) I wouldn't make that Toney comparison for King. They had a +4.6 MOV when King played in 84. They had the #3 SRS in the NBA that season would be #2 if you only counted the games King played.

King was awesome in the playoffs. They played the #4 and #1 SRS teams. He averaged 35 PPG on .620 TS% and more amazingly did it with low TO numbers (2.3 TOV/36). The Celtics were the best team in the league by far that year and had a +2.38 SRS gap over #2 team. The Knicks took them to 7 games.

[C-izMe]

http://www.basketball-reference.com/pla ... 01&y6=1987

My top 6 if TMac gets in. Looking at these numbers I can't see the argument for Dwight yet (coming up real soon). Malone and McHale are just better IMO and the others are super close. Do you guys think his defense is that good?

[therealbig3]

My top 6 as of right now:

1. 03 T-Mac
2. 98 Karl Malone
3. 94 Scottie Pippen (could switch to 95)
4. 96 Penny Hardaway
5. 87 Kevin McHale
6. 11 Dwight Howard

4-6 can go in any order, but I'm pretty comfortable with T-Mac/K. Malone/Pippen as my next 3.

Pippen is probably getting very underrated...he's probably the only wing to actually have the impact of a traditional defensive anchor, and he was a pretty good offensive player. Not a super-star scorer (though not a slouch at all), but a very good passer and ball handler. As ElGee described, super portable and can fit on any team.

In comparison to Dwight...who is better defensively, since they're both primarily defensive impact players? Pippen is a poor man's KG to me...does everything KG can do, just smaller with less length, and thus, not quite as good defensively. Dwight...he does different things than KG, but again, a lot of +/- evidence says that he's not on KG's level as a defensive player. So these are both lesser versions of KG defensively...so comparable defensively.

Offensively? I think this is Pippen. A point forward that doesn't actually need the ball that much, but can facilitate very well, and can score in a variety of ways and can thus fit into an offense in a variety of ways, is a very solid offensive player to have. Howard is a good offensive player too, but he also has severe limitations (TOs, passing, FT shooting). Pippen doesn't really have any drawbacks, he's just not that great of a volume scorer. But he does so many things really well that it's hard to really knock him too much for that.

[therealbig3]

BTW, I'm not saying KG>Howard defensively solely based off +/-, it's just one of the reasons why.

[mysticbb]

Here's the full dialogue. Note the context of what you originally quoted me on was me explaining RAPM to Ardee and co.

Elgee, sorry, but you are making no sense. The evolution of the discussion was: You are explaining RAPM somewhat (in fact, you explained APM! You haven't said a single word about the ridge factor at all!), and then you wanted errors for the RAPM results Jerry presented. I then explained that the introduced bias by the ridge factor (lambda) would make standard errors not useful to interpret! That is a FACT!
After that I said that we can calculate some sort of error via bootstrap and Jerry presented the values on ABPR while the values were in the ballpark I described, I COMPARED those values to the SE by bbv and Iliardi from their APM studies. That was A COMPARISON between APM (what you explained) and RAPM in regards to the error.
The next part was me saying that this error comparison isn't the important part, but the increased predictive power, what makes RAPM better than APM in that case.

If that isn't something you wanted to discuss, so be it, but that's what I discussed and it should be easily to see.

If OLS APM never existed, I'd STILL want to know how much 10g can impact a player's score...independent of the average prediction of the overall model.

That's what the bootstraping determined!

Here's what I see ITO of variance:

What is the minute or possession weighted standard deviation? That would be the information you are looking for. But then again, you are not determining the variance of the ridge model, because the values Jerry presents are a based on ridge regression combined with a machine learn algorithm. They are expected to change more due to the increased confidence of the model. The excercise you are doing is really not that useful, because the main goal for Jerry was to find the best model for predictions, and that is actually a prior informed version of his RAPM model. And for that he gave the "errors" calculated via bootstrap based on multiple years.

So in a discussion about the variance of RAPM, you interject a point about another method (APM). And in a discussion about the variance of one method (RAPM), you point to a completely different method (machine learning) and discuss the variance of that? What are you doing here that I'm missing?

You interjected the point about APM by describing APM and NOT RAPM. And YOU brought in the 2yr APM by bbv and the respective SE. I just picked that up.
And then again, the machine learn algorithm is incorporated in Jerry's model!
I guess those are the things you are missing.

[C-izMe]

Actually I forgot about Scottie. He might be over Gilmore.

1. TMac
2. Malone
3. McHale
-------------
4. Penny
5. Pip
6. Zo
7. Dwight
8. Barry
9. Baylor
10. King or Hill

[lorak]

Updated voting:

03 T-Mac - 5 (therealbig3, C-izMe, Dr Positivity, fatal9, ardee)

98 Malone - 4 (JordansBulls, Lightning25, Doctor MJ, ElGee)

11 Dwight - 1 (DavidStern)

62 Baylor - 1 (PTB Fan)

88 McHale - 1 (bastillon)

So I'm switching my vote to: TMac '03

[lorak]

Elgee, Do you have the SRS in/out for Pippen 98? How does it breakdown for offense/Defense

I don't have SRS, but I have ortg/drtg splits. And in 1998 Bulls offense was better with Pippen by 7.4 ortg and defense with him was worse by 3.9 drtg.

BTW, It's also sad nobody provided any explanation why Malone over Dwight, McHale and Hayes. DH and Kevin have bigger advantage on defense than Malone over them on offense and in Hayes case his advantage on defense is very close to Malone's advantage on offense.

[Dr Positivity]

I still have Malone as slightly better offensively than McHale. I love McHale's 1 on 1 ability but I'm not sure if I'd trust him as someone to run an offense through.

[Doctor MJ]

McGrady '03 takes it, and we are now halfway through the project.

[lorak]

I still have Malone as slightly better offensively than McHale. I love McHale's 1 on 1 ability but I'm not sure if I'd trust him as someone to run an offense through.

Slightly better offensively - I could agree with that. But what with the other half of the game? (which is more important for big man) Wasn't McHale significantly better defensive player?

[ElGee]

Here's the full dialogue. Note the context of what you originally quoted me on was me explaining RAPM to Ardee and co.

Elgee, sorry, but you are making no sense. The evolution of the discussion was: You are explaining RAPM somewhat (in fact, you explained APM! You haven't said a single word about the ridge factor at all!), and then you wanted errors for the RAPM results Jerry presented. I then explained that the introduced bias by the ridge factor (lambda) would make standard errors not useful to interpret! That is a FACT!
After that I said that we can calculate some sort of error via bootstrap and Jerry presented the values on ABPR while the values were in the ballpark I described, I COMPARED those values to the SE by bbv and Iliardi from their APM studies. That was A COMPARISON between APM (what you explained) and RAPM in regards to the error.
The next part was me saying that this error comparison isn't the important part, but the increased predictive power, what makes RAPM better than APM in that case.

If that isn't something you wanted to discuss, so be it, but that's what I discussed and it should be easily to see.

You interjected the point about APM by describing APM and NOT RAPM.

OK -- I must be confused. Explain RAPM then. Just make sure you do it without any of the background I provided to Ardee.

Here's what I see ITO of variance:

What is the minute or possession weighted standard deviation? That would be the information you are looking for. But then again, you are not determining the variance of the ridge model, because the values Jerry presents are a based on ridge regression combined with a machine learn algorithm.

(1) All I care about is the variance of the NUMBERS BEING DISCUSSED ON HIS WEBSITE. What part of this is unclear to you?

(2) How do you know that JE is using machine learning on the numbers on his website?

They are expected to change more due to the increased confidence of the model. The excercise you are doing is really not that useful, because the main goal for Jerry was to find the best model for predictions, and that is actually a prior informed version of his RAPM model. And for that he gave the "errors" calculated via bootstrap based on multiple years.

WHERE are the "errors?" I've asked this before...Instead of just saying "he gave them" post a link.

[JordansBulls]

After Malone I am thinking of Penny in 1996 and Hill 1997.

[mysticbb]

OK -- I must be confused. Explain RAPM then. Just make sure you do it without any of the background I provided to Ardee.

a_x = (M^(T)M+lambda E)^(-1)M^(T)R

a_x are the coefficents, M is the matrix in which the information who played and who not is stored via 1 and 0, E is the identity matrix, R is the response vector (scoring margin), the HCA is the intercept. lambda is the ridge factor, which is found via crossvalidation.

The introduced bias is:

bias(a_x) = lambda(M^(T)M+lambda E)^(-1)a_x

(1) All I care about is the variance of the NUMBERS BEING DISCUSSED ON HIS WEBSITE. What part of this is unclear to you?

I gave you the ballparks of the numbers.

(2) How do you know that JE is using machine learning on the numbers on his website?

He explained it on the old ABPR board.

WHERE are the "errors?" I've asked this before...Instead of just saying "he gave them" post a link.

Unfortunately I can't, because the old board was lost due to a hack, and Jerry had a different user name then, thus I can't easily search for it.

And then again, you have data available, you can easily calculate the minute weighted standard deviation and the minute weighted average change, in that case you would get a result you are looking for.

The minute weighted average SE for the Iliardi 6yr study was 1.3. The minute weighted standard deviation for Jerry's numbers are typically between 2.1 and 2.2, with the error being something like 0.5 standard deviations, which makes +/- 1.1 as the error. If I look through your post, I see a similar number being out there. So, what exactly is your issue?

[ElGee]

OK -- I must be confused. Explain RAPM then. Just make sure you do it without any of the background I provided to Ardee.

a_x = (M^(T)M+lambda E)^(-1)M^(T)R

a_x are the coefficents, M is the matrix in which the information who played and who not is stored via 1 and 0, E is the identity matrix, R is the response vector (scoring margin), the HCA is the intercept. lambda is the ridge factor, which is found via crossvalidation.

The introduced bias is:

bias(a_x) = lambda(M^(T)M+lambda E)^(-1)a_x

(1) How is the response vector generated?
(2) Do you think Ardee would understand what you just typed?

[mysticbb]

(1) How is the response vector generated?
(2) Do you think Ardee would understand what you just typed?

1. The scoring margin per 100 possession for each game snippet, if you want the coefficients for the players as values per 100 possessions.
2. Well, I don't know how much Ardee knows about math, but without any knowledge in matrix algebra it will be rather tough to understand it. Anyway, it was meant for you, and the matrix notation is not only easier to understand, but also much shorter.

[ElGee]

Now think about what I said to Ardee about the "game snippets" and tell me how you can calculate RAPM without it. It's been a few years since I did any matrix algebra (machine learning) but *conceptually,* I do not see how what I described doesn't apply nor do I see how to get RAPM without what I explained. Thus, my confusion for why you would respond about saying "RAPM is better" and claiming I was "describing APM, NOT RAPM" simply because I didn't delve into the details of the mathematical process behind RAPM...

[mysticbb]

Now think about what I said to Ardee about the "game snippets" and tell me how you can calculate RAPM without it. It's been a few years since I did any matrix algebra (machine learning) but *conceptually,* I do not see how what I described doesn't apply nor do I see how to get RAPM without what I explained.

Where did I say anything about RAPM being calculated without the "game snippets"? The issue is that you didn't understand why I brought up the part about RAPM being a better predictor, and I then went on trying to explain why I brought that up.
And it is really important to note that, because the main difference between APM and RAPM is the used regression. You showed how OLS is working, but that has a couple of issue when used to solve an ill-posed problem like we have. That's why we see such big errors for APM, and see that it is not a good method to predict the outcome of future games. Using ridge regression instead will solve most of the issue and gives a better predictor. Obviously, if we introduce a bias, the errors are not interpretable in the same fashion anymore, that is just a simple mathematical fact. And thus, your request to see the errors in the fashion as bbv has them, makes not much sense. But then again, the real advantage by using ridge regression instead of OLS comes with the better predictions. And that is all I wanted to say.

Thus, my confusion for why you would respond about saying "RAPM is better" and claiming I was "describing APM, NOT RAPM" simply because I didn't delve into the details of the mathematical process behind RAPM...

You described APM and not RAPM, sorry, but that is a fact. No idea how you can not understand that part here. It makes a difference whether I use OLS or ridge regression, that should be clear. And again, I pointed out that whether the errors are bigger or smaller is not that important, but that the predictive power increases when using ridge regression for an illposed-problem. And the latter is also a proven mathematical fact.
That the matrix M and the response vector R are the same as in APM, and that the result would be again a coefficient vector a_x was never in question at all. And in fact, you can use the same equation here as I described, just with lambda being 0 for APM. And yet, lambda!=0 is the important part for the ridge regression, and thus without it you are not describing RAPM.
I really don't understand where your confusion comes from, because if you really understand the math and how those different regressions work, you shouldn't be confused at all.