Joel Anthony- MVP.

[floppymoose]

You've lost me. I don't know what you are correlating to what. SPM doesn't seem to be relevant, so I don't get that part either.

[DSMok1]

I certainly see how it could be overfitting. That's why I was suggesting trying different seasons and seeing how stable the answer was. If it was pretty stable, that's pretty suggestive.

No, Mystic is right. That would be overfitted, basically by definition. There has to be some sort of framework to "group" the players--like MPG, or a SPM rating.... something.

[floppymoose]

It could be overfitted but still more correct than assuming all the low minute players are better than league average. Or, it could be an improvement. And a very easy one to obtain.

[mysticbb]

You've lost me. I don't know what you are correlating to what. SPM doesn't seem to be relevant, so I don't get that part either.

Well, I wanted to say that the results for each year can be very different. The way you are approaching this, is basically the way APM is doing it already. Small sample players can get very huge numbers in both direction. That's due to overfitting. In that case we don't improve the ability to predict.

The part about the correlation was meant to show that small sample players most times are bad also in boxscore metrics, and while RAPM assumes they are average, the correlation is weak between RAPM and SPM. The small correlation coefficient is something we can expect. Thus it seems like assuming they are average is not the best way, maybe SPM offers a better solution here.

The rest of the post about the correlation coefficients with higher minutes players made a lot of sense when I wrote it. Right now I can't figure out what I wanted to say with that. :lol:

It could be overfitted but still more correct than assuming all the low minute players are better than league average. Or, it could be an improvement. And a very easy one to obtain.

RAPM is assuming they are average, which is a good first guess. It needs to be improved, no doubt about that. But that still doesn't change the fact that RAPM is better than APM, and for me it is more useful than raw +/- numbers anyway.

[floppymoose]

I meant to say "league average" instead of "better than league average". No idea why I typed that. Also, I typed: "ie, it could be an improvement" and my iphone spell corrected it to "Or, it could be an improvement".

[floppymoose]

Well, I wanted to say that the results for each year can be very different. The way you are approaching this, is basically the way APM is doing it already. Small sample players can get very huge numbers in both direction. That's due to overfitting. In that case we don't improve the ability to predict.

That's not correct. The RAPM values show that the low minute guys move toward the middle, because the ridge regression possessions dominate the real possessions for them. What I am suggesting would move them towards something lower than the middle, but they would not have extreme values and would not be scattered over a huge range.

[DSMok1]

Well, I wanted to say that the results for each year can be very different. The way you are approaching this, is basically the way APM is doing it already. Small sample players can get very huge numbers in both direction. That's due to overfitting. In that case we don't improve the ability to predict.

That's not correct. The RAPM values show that the low minute guys move toward the middle, because the ridge regression possessions dominate the real possessions for them. What I am suggesting would move them towards something lower than the middle, but they would not have extreme values and would not be scattered over a huge range.

I think you are getting at using a minutes-based prior: for lower minutes, move towards a lower number; higher minutes, a higher number. That's what I've been saying.

[mysticbb]

That's not correct. The RAPM values show that the low minute guys move toward the middle, because the ridge regression possessions dominate the real possessions for them.

Actually ridge regression moves everyone towards the middle.

What I am suggesting would move them towards something lower than the middle, but they would not have extreme values and would not be scattered over a huge range.

I think we have a small communication problem. I understand what you want to do, I just said that the way you want to obtain the necessary informations via the experiment will not give you a better solution. You are expecting stable results, while I said that you would most likely not get stable results. To achieve an improvement, which you want, we need to give the informations before, like DSMok1 is saying, just a prior obtained via different methods.

Assuming the low minutes players are average is wrong, we agree on this. We just don't have better informations right now. And the way you want to obtain those informations is running into the overfitting problem. That's my point.

[floppymoose]

That's not correct. The RAPM values show that the low minute guys move toward the middle, because the ridge regression possessions dominate the real possessions for them.

Actually ridge regression moves everyone towards the middle.

Right. That's what I'm saying. And the fewer the real minutes played, the stronger the move to the middle.

What I am suggesting would move them towards something lower than the middle, but they would not have extreme values and would not be scattered over a huge range.

I think we have a small communication problem. I understand what you want to do, I just said that the way you want to obtain the necessary informations via the experiment will not give you a better solution. You are expecting stable results, while I said that you would most likely not get stable results. To achieve an improvement, which you want, we need to give the informations before, like DSMok1 is saying, just a prior obtained via different methods.

Assuming the low minutes players are average is wrong, we agree on this. We just don't have better informations right now. And the way you want to obtain those informations is running into the overfitting problem. That's my point.

Right now we are treating low minute players as average. I see no reason to think that is more stable than some other value, even if that other value was overfitted. Indeed, if we strongly suspect that low minute players are below average as a group, than a very slightly below average performance estimation in the ridge extra possessions is very likely to be both more correct and more stable.

I understand the reluctance to pick a value without a theoretical foundation. I entirely get that. But I disagree with the reasoning on the critiques so far. They apply even more strongly to the current RAPM system, so in that sense what I am suggesting can be an improvement despite the flaws.

[DSMok1]

Right now we are treating low minute players as average. I see no reason to think that is more stable than some other value, even if that other value was overfitted. Indeed, if we strongly suspect that low minute players are below average as a group, than a very slightly below average performance estimation in the ridge extra possessions is very likely to be both more correct and more stable.

By grouping "low minute players", you are using a prior (grouping players) based on minutes! Which is what I was proposing, anyway.

[floppymoose]

Well, it's just the ratio of the extra ridge possessions to the actual possessions that is doing the grouping. From your explanation that is already in RAPM. So if I've understood everything correctly the way I'm "grouping the low minute players" is identical to the RAPM way. Just with a different value for the extra possessions.

Normally in APM, each equation looks like this:
P1 + P2 + P3 ... - P9 - P10 + HCA = Eff.Dif. (with weight = N Poss.)

Ridge regression keeps all of those equations, and adds a bunch like this:
P1 = 0 (with weight = X Poss.)

I'm thinking instead:
P1 = RPV (with weight = X Poss.)
where RPV is closer to replacement player value than league average.

[DSMok1]

Well, it's just the ratio of the extra ridge possessions to the actual possessions that is doing the grouping. From your explanation that is already in RAPM. So if I've understood everything correctly the way I'm "grouping the low minute players" is identical to the RAPM way. Just with a different value for the extra possessions.

Normally in APM, each equation looks like this:
P1 + P2 + P3 ... - P9 - P10 + HCA = Eff.Dif. (with weight = N Poss.)

Ridge regression keeps all of those equations, and adds a bunch like this:
P1 = 0 (with weight = X Poss.)

I'm thinking instead:
P1 = RPV (with weight = X Poss.)
where RPV is closer to replacement player value than league average.

So just use RPV for the regression, instead? But then the league wouldn't sum to 0...

Interesting, though. I might try that. At least it's simple!

[floppymoose]

Right, the league won't sum to zero. It's ugly in all sorts of theoretical ways. I'm absolutely not suggesting it is theoretically defensible as a stopping point for APM. But I think it would be interesting to try changing the value from zero to a range of negative values, and see if any of those led to better cross validation results.

Even if it didn't lead to better results, it would be instructive to see which high minute player values moved the most, and which the least, from this adjustment.

[Doctor MJ]

Just wanted to say you guys are getting into something I've wanted to try with the thorough analysis of replacement players. Surprised more hasn't been done on this already.

[DSMok1]

Just wanted to say you guys are getting into something I've wanted to try with the thorough analysis of replacement players. Surprised more hasn't been done on this already.

If I recursively adjust the prior and then look at the results, should I not be able to hone in on the exact quality of a 0 MPG player for a league average team (which I would define as replacement level?)

[floppymoose]

That's what I was referring to as "finding it experimentally" earlier.

[DSMok1]

That's what I was referring to as "finding it experimentally" earlier.

What I'd probably do (though I wish I had a supercomputer to do it!) would be to assign a prior based on minutes & team eff, run the regression, and then calculate the new prior based on those results as the average based on minutes & team eff, and so on.

[laika]

The final playoff +/- numbers are in. Anthony didn't quite get MVP numbers, but finished as one of the top performers in the playoffs. The bigger story is Lebron though. I can't remember a superstar ever having worse numbers.

------------------------min-------net +/-
Jones, James---- 271.93----- 13.12
Anthony, Joel---- 574.72----- 10.23
Chalmers, Mario- 510.80----- 10.15
Miller, Mike------ 214.90------- 9.28
Bosh, Chris------- 834.17------- 5.52
Haslem, Udonis-- 290.02------- 0.54
Wade, Dwyane--- 827.83----- (-2.81)
James, LeBron--- 921.62---- (-14.34)
Bibby, Mike------ 414.80----- (-15.31)
Ilgauskas, Zydr-- 103.55----- (-42.55)

Either +/- is useless since it can't give us reasonable playoff values, Lebron is wildly overrated, or both.

[DSMok1]

laika, those aren't adjusted for context/opposition, and if it were, it's way too small a sample size to mean anything without really good stabilization--and even then it'd be iffy.

[Wannabe MEP]

Either +/- is useless since it can't give us reasonable playoff values, Lebron is wildly overrated, or both.

OR it's more complicated than that. That's like saying, "Either laika is stupid, or he's a troll, or both." And of course we don't believe that.

Don't ask a tool to be something it's not. "Dammit, my chainsaw is TERRIBLE at hammering in nails!!" With a small sample size, +/- tells a story. That's it. As the sample size increases, it starts to hint at strengths and weaknesses on a team. Eventually, when there's enough data and enough VARIETY of data, we can run it through the APM/RAPM machine and see what kicks out. Even then, it's still just a tool; you don't just fire up the chainsaw and walk away to let it run on its own; there's still interpretation to be had by intelligent people. Ya know, like you and me.

So let's interpret, shall we?

Why are Joel Anthony's numbers so high??
According to hype, money, and common sense, this team is built around its 2-3-4, which suggests that the team's weakest point is at the 1 and/or 5. Since LeBron and Wade are both adequate facilitators, it makes sense that PG might not make a huge difference. Especially since the defensive frontcourt is so critical to a team's success, however, the 5 could make a huge difference for this Heat team. So what does the data show?

------------------------min-------net +/-
Jones, James---- 271.93----- 13.12
Anthony, Joel---- 574.72----- 10.23
Chalmers, Mario- 510.80----- 10.15
Miller, Mike------ 214.90------- 9.28
Bosh, Chris------- 834.17------- 5.52
Haslem, Udonis-- 290.02------- 0.54
Wade, Dwyane--- 827.83----- (-2.81)
James, LeBron--- 921.62---- (-14.34)
Bibby, Mike------ 414.80----- (-15.31)
Ilgauskas, Zydr-- 103.55----- (-42.55)

You started this thread while Haslem was still injured, which means that the only people playing the 5 were Joel Anthony and Zydrunas Ilgauskas. Compared to the old, hobbled, slow, worthless Ilgauskas, Anthony was pretty much Dwight Howard.

By the end of the playoffs, the sample size was better...AND UDONIS HASLEM STARTED PLAYING, so Anthony was nowhere near as crucial to the team's success. His inflated numbers came pretty much entirely from the first two rounds, and they say more about how worthless Ilgauskas was than how great Anthony was. Still, he filled a desperate need so he was very valuable.

Why are LeBron's numbers so low??
1) See above. Then realize: for every minute Ilgauskas was on the floor, so was LeBron. Also, for all but 2.55 of Bibby's 414.80 minutes, so was LeBron. Guess what happens when you play with an epically horrible center AND an epically horrible pg...

2) If we could magically put prime Bill Russell and Dwight Howard on the same team, each player's individual value wouldn't be as great because what they bring to the team isn't really additive if you double it. Same with Steve Nash and Chris Paul. Wade and LeBron? Similar. Probably not to the same extent, but you can still only have one guy with the ball at a time. But the important thing is that the Heat still have a phenomenal facilitating wing (and an excellent post player) in there whenever LeBron sits, so it's not like they suddenly become: Phoenix without Nash, Dallas without Nowitzki, Orlando without Howard...or the Cavs without LeBron...

3) If you have a great pick-and-roll, one of the best things the other players can do is chill at the 3-point line and knock down wide open shots if the defense collapses into the paint. That kind of sit-around-and-wait complementary role is not in LeBron's nature, so there are definitely times when a better shooter to complement the Wade-Bosh pick-and-roll may actually improve the offense. To say that James Jones is a better fit than LeBron James at certain times--depending on the other players on the court for both teams--is not at all equivalent to saying that James Jones is actually a better player...that doesn't mean that LeBron James is "wildly overrated." Perhaps LeBron is better 96% of the time, but theoretically that still leaves 4%.

4) The playoffs is a small sample size in the first place, but it's much, much smaller if you look at LeBron. Why? Because he was always on the court, so there's very little non-LeBron time for comparison. He was on the court for more than 90% of his team's minutes. When he played, the Heat outscored their opponents. When he didn't play, the Heat outscored their opponents as well, but by more. However, the non-LeBron time is a very small sample size, and it may have been heavily influenced by garbage minutes, or opponents might have tried to rest their stars while LeBron rested. Just a quick glance suggests there's something to that : out of the only 3 non-Lebron units that played at least 10 minutes, all of them have a MUCH lower APM than unadjusted rating (-3.34 to 13.46, -3.81 to 4.45, and 15.40 to 64.58) and opponents featuring guys like Jeff Green, Nenad Krstic, and Ian Mahinmi. Very possible that they were beating up on crap most of the time.