gourimoko
Fighting the good fight!
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The "first order" approximation suggests that the Cavs are a .500 team without Bynum. If you want to dispute that by making a "second order" approximation that takes into account the nonuniform distribution of Bynum's minutes, go right ahead. But until you do so, there's no reason to believe that the Cavs without Bynum are worse than my approximation would suggest, let alone so much worse that they would contend for a top-5 pick.
Nate, you aren't paying attention to what's being said.. This was already addressed in my last post by declaring the system as nonuniform and therefore having the properties of a nonlinear stochastic system. Your retort that you have demonstrated a first order approximation either shows an ignorance that no such approximation can be made without defining a linear abstraction first, which you have not done, or negligence by not proving a linear composite model to preface your argument, which you have not done. Therefore, by definition, your projection model is invalid, as again you cannot project with exact confidence levels against a nonlinear model with interdependent variables.
I know very well what my argument is and what your argument is, and I know very well that the best we can hope to do is approximate how the Cavs will perform without Bynum. That said, I hold that the best approximation we have right now for how the Cavs would fare without Bynum is the one I gave in my previous post. The onus is on you to do a more precise approximation if you want to argue that your argument is more plausible than mine.
No it isn't as I have not argued that I have a predictive model to calculate wins and losses. Quite honestly, I think it's odd that you think you have by measuring an individual players production. It's just not that simple. So to answer your point, if you know exactly what my argument is, how can you then declare that the onus is on me to provide a predictive model better than yours when I clearly state no such model has been offered by either of us?
Come on gour, you're better than this. Don't tell me how many reasons you have; tell me what the reasons are!
To be clear, what I said was this: "While I do think we play better without him, for a multitude of reasons that I think are out of his control, I don't see us as a .500 team prior to the Deng trade."
I'm referring to why the team could be better without Bynum, and a lot of that includes the locker room and his attitude. Those factors are not quantitative, and I don't see any reason to detail them in this conversation. It's nothing to do with my argument at all, so why should I break down Bynum's game? Makes no sense.
With wins and losses you're looking at one binary piece of data per game. Looking at margin of victory (and other related stats) inherently gives more data, and accordingly makes it possible to make more confident claims.
This doesn't describe what you are doing. You are hoping to extrapolate play-by-play events at the granular level to fit a model that has no basis. Your "data" is insufficient to make your prediction.
Rather than going over this again.. Perhaps it's just easier to demonstrate: what's the confidence of your prediction? Once you go down that rabbit hole, you'll realize why you don't have a valid model..
Of course, I have done nothing to prove just how confident my claims are, bt it should be obvious from a mathematical standpoint that they are more precise than anything one could glean from the win/loss records you cite.
This is the only reason I'm bothering to post. It's not obvious from a mathematical standpoint. We can end all the dialogue and you can just show your proof and demonstrate the confidence level and we can be done with it. But since that's not possible, I don't know why you are claiming it is.. You realize you're trying to predict an 82 game season using one player's +/-, right? A player who played in a minority of minutes played...
You acknowledge the model is nonlinear, and you acknowledge parameter interdependence, and surely you acknowledge the system is stochastic -- so how can you claim a first order approximation using linear methods??
Perhaps "correct" was the wrong word. I can predict that I'll get 5 heads in 10 tosses of a coin and be "incorrect" when there are only 3 heads, but my initial prediction of 5 heads was certainly the best I could have done with the information I had. Similarly, I can only claim that based on the information that has been presented thus far, the most likely outcome if the Cavs had continued without acquiring Deng would have been roughly a .500 record for the remainder of the season.
From a "mathematical standpoint," it is "obvious" that you cannot make this prediction with the data you've provided.. Not at all. It's asinine to say you can, given only the data you have provided.
Agreed. If the Cavs had made the decision to lose games and get a top-5 pick, they certainly could have done it.
Then WHAT THE FUCK ARE WE ARGUING ABOUT?!? That was my whole point!!!
Again, is there a statistical basis to claiming that if you toss 10 coins you will (most likely) get 5 heads? Yes, of course there is.
Now you are describing a discrete binomial distribution, this is not comparable to a basketball game which is stochastic, nonlinear, and having multiple interdependent parameters. It's a different form of mathematics altogether.
It is impossible to find a certain answer to many problems, but that doesn't mean it becomes a matter of opinion. You can argue about how strong the statistical basis I presented is, but the statistical basis is certainly there nonetheless.
That's my point Nathan.. In this instance, it is not. I keep seeing this on the board, repeated, over and over. Lot's of times people making statistical or "mathematical" claims that are simply unfounded. I'm not trying to rain on anyone's parade here, but you asked and I'm telling you, this does not fly. You cannot use the data you provided to create any form approximation let alone a meaningful prediction.
alluded :licker:
Damn you..
Anyway, I don't think most of the posters appreciate this conversation, or want to see it.. I thought your reply had merit and thus warranted a response, but where this has to do with Chris Grant it appears we are in agreement. As you aid "if Grant wanted to tank, we could have had a top 5 pick." That's my point. I also agree with the larger point that we are better without Bynum, but not solely mathematical reasons; but because we simply don't know how to use him, and he was an intolerable cancer on the team from my understanding. From what I know, it was simply impossible to continue moving on with him, so turning him into Deng is a good haul; If and only if the team continues to progress sans the lottery. And that is a big if.
But if you want to discuss the mathematics of your prediction further, you know you can PM me..