Northclyde speaks onthe lottery and "the variable"

[CBAreject]

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Your simple mind doesn't allow you to see how the lottery actually works. Nothing is equal or set in this lottery. The variable constantly changes as you go through the lottery process. The variable doesn't change, when flipping a coin.

You have a 50% probability of a guy making or missing a free throw. Those are the only outcomes . . make or miss.

But when you talk about Lorenzen Wright, the actual outcome is fare less than 50% most of the time. Conversely, when you talk about Steve Nash, the outcome is far greater than 50%.

The variable between Lorenzen and Steve, is that Lo's FT mechanics and concentration levels are so bad, that it causes him to miss far more than he makes.

Steve's FT shooting mechanics and concentration levels are so good, that he hardly ever misses.

Yet . . the bare bones probability of making and missing a FT, is 50/50. But you have to take in accout of how the variables can change the outcome. That's how you have to look at the NBA draft lottery, plain and simple.

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-northclyde's musings on probability and the NBA draft lottery

Thought I'd post this in a separate thread since it's so insightful. Now we all understand how the NBA lottery works. It has something to do with "the variable" which is "constantly changing".

[bumpyphish1]

I am not posting to bash Northcyde...I think he is a good fan and usually makes a lot of sense...and, I sort of see what he is saying in the quote above, but 'Cyde, if you are out there, I don't think you are right on with your opinion on tanking or your reasoning on the probabilities...

I am not mathmatecian but I know this (and I remember you disputing a similar claim).

With the 4th most pong balls, we have like a 48% chance of getting either pick 1, 2, or 3 (ie. keeping our pick). With 5th, we would have closer to something like a 40% chance of keeping our pick. If we had the 3rd worst record, we would have something like a 57% chance of keeping the pick. Therefore, tanking improves your chances.

[AtLaS]

... I think northcyde is wrong on this matter also, but he always gives accurate and intellectual posts, and calling him "dumb" is just more reflection on your egotistical based character..

[CBAreject]

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nbasuperstar gets dumber everytime he posts.

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Did you not say the above about nbasuperstar just moments ago? Please get off your self-righteous high horse and remember that you are the most guilty of offenders in this matter.

[exodus]

Since i have been on this site i have found myself agreeing with you the vast majority of the time, the tank issue being the notable exception.

But at times you do remind me a little of KB with some of your condescending posts. Of course with nbasuperstar it is understandable but with some others..... not so much.

Of course i can be as much of a hothead as anyone so i am not trying to claim any high ground.

[CBAreject]

Yeah, I can be a jerk...and I actually don't want to be. Will never deny that I'm not condescending, but man do people ask for it sometimes. It's all the "LOL @ u" and "simple-minded" barbs. I'm not just trying to make a mockery of northclyde here. Trust me, if he phrased his post like "The way I see it...etc," I would patiently explain why I disagree.

[Guest Walter]

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With the 4th most pong balls, we have like a 48% chance of getting either pick 1, 2, or 3 (ie. keeping our pick). With 5th, we would have closer to something like a 40% chance of keeping our pick. If we had the 3rd worst record, we would have something like a 57% chance of keeping the pick. Therefore, tanking improves your chances.

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I believe you are one tier off here. I believe the 3rd worst team has a 48% chance, the 4th worst (us) approximately 38%-39%.

It was important for us to win or tie third worst = roughly a 45-50% chance and we failed thanks to a useless win over the Celtics. Let's hope a roughly 40% chance is enough.

W

[exodus]

The guy who can end an argument the best is AHF. He will break someones argument down and expose it, without getting personal. No matter how idiotic someone is acting he will always have a reasoned response. It isn't easy to do but so many times i have seen him leave people completely unable to respond.

[AtLaS]

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nbasuperstar gets dumber everytime he posts.

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Did you not say the above about nbasuperstar just moments ago? Please get off your self-righteous high horse and remember that you are the most guilty of offenders in this matter.

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I guess you can call me guilty on calling nbasuperstar dumb, but he slams people more than anyone. He calls this whole board "idiots" because we think Josh Smith is a starter. He thinks Smith will be out of the league when his rookie contract is up. He also claims to be an NBA scout, yet he spells every other word that he types incorrectly.

I only namecall when it's already been casted, I don't initiate the action. When YOU make comments such as "what a thoughtless post," "you've wasted your time," or you "nonsense posters" and such, yeah I will say something.

I'm sure you're glad that Woodson's back, that way we can tank from day 1 next year.

[TheNorthCydeRises]

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Your simple mind doesn't allow you to see how the lottery actually works. Nothing is equal or set in this lottery. The variable constantly changes as you go through the lottery process. The variable doesn't change, when flipping a coin.

You have a 50% probability of a guy making or missing a free throw. Those are the only outcomes . . make or miss.

But when you talk about Lorenzen Wright, the actual outcome is fare less than 50% most of the time. Conversely, when you talk about Steve Nash, the outcome is far greater than 50%.

The variable between Lorenzen and Steve, is that Lo's FT mechanics and concentration levels are so bad, that it causes him to miss far more than he makes.

Steve's FT shooting mechanics and concentration levels are so good, that he hardly ever misses.

Yet . . the bare bones probability of making and missing a FT, is 50/50. But you have to take in accout of how the variables can change the outcome. That's how you have to look at the NBA draft lottery, plain and simple.

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-northclyde's musings on probability and the NBA draft lottery

Thought I'd post this in a separate thread since it's so insightful. Now we all understand how the NBA lottery works. It has something to do with "the variable" which is "constantly changing".

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CBA . . . the "varible" that changes, are the number of TOTAL PING-PONG COMBINATIONS DURING EACH PICK.

I love this. And this is why this board is rapidly becoming my favorite site on the net. You guys continue to make me laugh. Let me break it down for your remedial azz CBA, and put you on blast.

You have 1000 possible ping-pong ball combinations when the 1st position in the NBA lottery is selected. At this time, we KNOW what our chances to get the #1 pick are. If you're the worst team, you have 250 chances out of 1000. For hypothetical purposes, let's say that the 2nd worst team in the draft gets that top pick. The 2nd worst team has 199 total combinations.

Now we go to the 2nd pick:

The VARIABLE that changes . . is the TOTAL NUMBER OF COMBINATIONS LEFT IN THE LOTTERY. You subtract 199 from 1000, and you have 801 possible combinations left that the remaining teams have total, in order to determine the 2nd pick.

This is called a DEPENDENT EVENT . . OR DEPENDENT PROBABILITY. Dependent probability is defined as when "one outcome can affect the outcome of another."

http://www.learningwave.com/chapters/proba...ndependent.html

The odds of getting the #2 pick in the draft are DIRECTLY AFFECTED BY WHO GETS THE #1 PICK. This ish is not that hard to figure out.

Since the Hawks are the 4th worst team, we have 119 combinations. So our probability to get the 2nd pick would be 119 divided by 801 . . which is 14.9%.

But for bad luck's sake, let's say that we don't get the #2 pick, and the #5 team gets the selection, who has 88 combinations.

You would then SUBTRACT 88 from 801, and come up with 713 total combinations left for the teams vying for the #3 pick.

This also illustrates the property of DEPENDENT PROBABILITY. The 3rd pick in the draft is DIRECTLY AFFECTED by who gets the #1 and #2 picks.

Once again, the Hawks have 119 ping-pong combinations left in this lottery. Once the #3 pick is selected, there are 713 total combinations left. So our chance to get the #3 pick in this scenario would be 119 divided by 713 . . which is 16.7%

DING!! One of the Hawks combinations is selected, and we get the #3 pick.

CBA . . what you and your buddies have been doing, are taking the percentage chances of each selection, and simply adding the percentages, to get your "odds" for a top 3 pick. That's called MUTUAL EXCLUSIVE EVENT PROBABILITY.

http://www.richland.edu/james/lecture/m170/ch05-rul.html

That's why I've never directly disputed the actual probability numbers that some of you have given. I completely understood what you guys were doing. What I have disputed, are how valid those probabilty numbers are.

I do that because we have NO IDEA what our actual probabilty to get the #2 or #3 pick is. We can do a statistical average of our probabilites to get the #2 or #3 picks, and write down a percentage. But we truly won't know what our odds to get the #2 pick will be, UNTIL the #1 pick is determined.

The lottery is presented on TV, like it is one event determined by one element. In truth, the lottery is one event determined by three elements. The first element is independent, because we know our percentages right off the bat. The 2nd and 3rd elements are dependent, because we won't know what our percentages are, until the first element is determined.

NOW . . disprove anything I've said about the lottery CBA. You try to make me look like an idiot, when you're the one who doesn't understand a thing about probability, and the different conditions that can go along with it.

Even Walter didn't dispute what I was saying. He just said that I was making the issue too complex and trying to twist the numbers in a negative light. And he couldn't dispute what I was saying, because he knew that I was right.

But for you CBA, you're throwing up stuff like coin flips, which aren't affected by anything. And because of that, it's called an INDEPENDENT EVENT . . OR INDEPENDENT PROBABILITY. That ish has nothing to do with the NBA draft lottery.

The draft lottery is much more like Texas Hold-em, where you know your percentage chances just from the 2 cards you receive off the bat. Then, your percentage chance changes as the flop, turn, and river determines the winner.

Disprove anything that I've said as being FALSE. That's all I want you to do. But if you do, you better make sure that you're right.

(( tossing the keyboard to your dumb azz . . CBA ))

[TheNorthCydeRises]

. . not c-l-y-d-e.

LOL . . you can't even spell the name right.

[AHF]

I think you have this one wrong, Northcyde.

If you want to measure the chances of a coin coming up as heads in three flips you can measure that by going:

(1) Before flipping any of them, there is an 87.5% chance that one of the flips will result in heads.

or

(2) Before the first flip there is a 50% chance of it being heads.

Before the second flip there is a 50% chance of that being heads.

Before the third flip there is a 50% chance of that being heads.

The only difference between the 87.5% in example (1) above and in the discussions of odds we have had on lottery picks is that the odds don't change depending on the outcome. However, if you did have something where the odds changed in a predictable manner as in the NBA draft, you can calculate the conditional probability of getting on of the top three picks as a single number - 38.11%. In the coin flipping hypo, you don't need to weigh the probability of given outcomes because the odds remain the same regardless of what happens on the first flip, etc.

[TheNorthCydeRises]

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... I think northcyde is wrong on this matter also, but he always gives accurate and intellectual posts, and calling him "dumb" is just more reflection on your egotistical based character..

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Atlas, the only reason I disagree with some of you on this issue, is because I don't view the chances of getting the #3 pick as a total percentage. I view it position by position, and look at our percentage chances in that light.

Like I'll continue to say, I would love for the ENTIRE process to be shown live, where we could see how the 1st selection directly affected the selection of the next pick pick . . and how that pick affected the chances of someone getting that 3rd pick. But because we're presented with the results of the lottery, and not seeing how the process works, I think people tend to view the lottery as one event that is determined by one element.

Guys like Walter think that's the wrong way to look at it, and complicates the matter. He's entitled to his opinion. If you look at it in the same light, then you're entitled to yours as well.

This article may help some people truly understand the lottery process.

http://www.nba.com/features/inside_lottery_050524.html

LOL . . I'm just waiting on CBA's reply. Hope it comes before my lunch break is over, so I can laugh again.

[AHF]

This is the part I have a problem with:

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We can do a statistical average of our probabilites to get the #2 or #3 picks, and write down a percentage. But we truly won't know what our odds to get the #2 pick will be, UNTIL the #1 pick is determined

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We know exactly what our odds of getting one of the top 3 picks are coming into the draft.

However, in any scenario where there are conditions that affect future probabilities, the odds of getting a top 3 pick will change with each draft pick. However, that doesn't mean that the 38.1% chance that we have before any balls are drawn is not totally valid. (Likewise, it doesn't mean that the numbers in your hypo for each independent pick aren't totally valid for that given scenario.)

[Guest Walter]

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This is the part I have a problem with:

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We can do a statistical average of our probabilites to get the #2 or #3 picks, and write down a percentage. But we truly won't know what our odds to get the #2 pick will be, UNTIL the #1 pick is determined

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We know exactly what our odds of getting one of the top 3 picks are coming into the draft.

However, in any scenario where there are conditions that affect future probabilities, the odds of getting a top 3 pick will change with each draft pick. However, that doesn't mean that the 38.1% chance that we have before any balls are drawn is not totally valid. (Likewise, it doesn't mean that the numbers in your hypo for each independent pick aren't totally valid for that given scenario.)

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...and trying to obfuscate the simple reality that we KNOW what the probability is that we will win a top 3 pick, PERIOD. There is no other reason to trace through this with a blurry marker except to obfuscate. We know Northcyde didn't want to tank. We also know that he can't justify it to himself much less us without intentionally confusing the issue.

W

[TheNorthCydeRises]

AHF . . we know the formula of determining our percentage for each pick.

team combinations / total combinations left on the board = % chance.

The lottery is tricky, because they don't take ping pong balls away from the machine. What they do though, is take the combinations that a team has, away from the possibile combinations, once that team is selected for a certain position. So if one of those team's combinations comes up, they simply disregard that combination, and keep selecting until some other combination comes up.

That's exactly what happened in 2005, when we got the #2 spot. When selecting the #3 spot, the lottery machine actually spit out one of our combinations again. All they did, was disregard the result, and repeated the process again. This time, Portland came up.

http://www.nba.com/features/inside_lottery_050524.html

From the article:

The next combination brought forth: 1—5—7—14. The Atlanta Hawks claimed the second overall pick in the NBA Draft – down one spot from their regular season finish.

The process is repeated for the third pick, but one of Atlanta’s 250 combinations surface again. The balls are returned to the tumbler and redrawn, similar to what would have happened in the event the 1,001st combination, 11—12—13—14, not assigned to a team, had surfaced.

The fourth drawing produces the third and final winning combination: 4—10—12—14. The Portland Trail Blazers join Milwaukee and Atlanta in the win-place-show grouping, despite holding only a 10.64 percent chance of winning the third pick.

I think I see what is happening here though. Because ping-pong balls aren't being removed, you technically still have 1,000 combinations left in the machine. But after the 1st selection, the lottery process disregards any combination that comes up for a team, after they've already been selected in the #1 or #2 position.

What I'm doing, is determining the probability of the team's chances by removing the combinations that won't be counted after a team is selected. But I think the numbers that you guys are using, are the probability numbers if those combinations weren't discarded in the process.

Like I said, it's all in the way you look at it. I think the way I'm looking at the lottery, by discarding the combinations once a team has been selected, is the right way to look at it. I haven't seen anything you guys have posted, that can disprove what I'm seeing. If you can, I'll gladly back down on my stance.

But it's a pretty common sense issue to me.

If the worst team with 250 combinations lands the #1 pick . . and those combinations aren't even counted in selecting the #2 pick . . then the combinations that are counted, will be 750. And if that's the case, the variable changes.

Hawks have 119 ping-pong combinations.

Hawks odds if 1000 total combinations are valid for that #1 pick: 11.9%

Hawks odds if 750 total combinations are valid for that #2 pick: 15.9%

That's pretty cut and dry to me.

[CBAreject]

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I guess you can call me guilty on calling nbasuperstar dumb, but he slams people more than anyone. He calls this whole board "idiots" because we think Josh Smith is a starter. He thinks Smith will be out of the league when his rookie contract is up. He also claims to be an NBA scout, yet he spells every other word that he types incorrectly.

I only namecall when it's already been casted, I don't initiate the action. When YOU make comments such as "what a thoughtless post," "you've wasted your time," or you "nonsense posters" and such, yeah I will say something.

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Oh, now I see. Only you can decide when it is appropriate to call someone "dumb". When you do it, it is just and righteous. When I do it, it's ego-stroking. Yes, now I follow. I'm glad you write the moral code for the rest of us. Now I know where to go when I need to settle a dilemma.

I'd be glad to know how exactly you know that I am the one "initiating the action". How carefully must you keep track of every discussion to be sure of this? Also, how can you be so sure that you are never guilty of initiating?

[TheNorthCydeRises]

Walter, I'm not confusing the issue at all. All I'm doing is stating the facts. Like I told CBA, if you want to directly dispute anything I've said about the lottery, go right ahead. But come with FACTS, not with opinions.

If you want to have total confidence in that 38% chance to get a top 3 pick, go right ahead.

But let me ask you this, what is the chance that a team 5th - 14th will get a top 3 pick? Is it less than 38% or more than 38%?

We all know if one of those teams jumps ahead of us in the process, then we're most likely screwed. So is the chance of that happening greater than our chance of getting a top 3 pick?

That's why I don't stress out over where we land in the lottery, especially if we have a good idea of the range we're going to eventually be.

Our best shot to get into the top 3 comes if Memphis and Boston can get the #1 and #2 spot. Then, when that 3rd selection is chosen, we'll have a 21.6% chance at getting that 3rd pick ( 119 Hawk combinations divided by 551 total combinations that are valid ).

Simple mathematics people.

[TheNorthCydeRises]

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I guess you can call me guilty on calling nbasuperstar dumb, but he slams people more than anyone. He calls this whole board "idiots" because we think Josh Smith is a starter. He thinks Smith will be out of the league when his rookie contract is up. He also claims to be an NBA scout, yet he spells every other word that he types incorrectly.

I only namecall when it's already been casted, I don't initiate the action. When YOU make comments such as "what a thoughtless post," "you've wasted your time," or you "nonsense posters" and such, yeah I will say something.

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Oh, now I see. Only you can decide when it is appropriate to call someone "dumb". When you do it, it is just and righteous. When I do it, it's ego-stroking. Yes, now I follow. I'm glad you write the moral code for the rest of us. Now I know where to go when I need to settle a dilemma.

I'd be glad to know how exactly you know that I am the one "initiating the action". How carefully must you keep track of every discussion to be sure of this? Also, how can you be so sure that you are never guilty of initiating?

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Don't respond to Atlas CBA . . respond to my post. Please discount my numbers, and the logic behind it. You're the one that called me out, so use some FACTS to back up what you say, and make me look dumb.

[CBAreject]

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That's pretty cut and dry to me.

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The expression is "cut and dried". See how something you thought you knew can be quite wrong?

Consider that you are wrong in the case of your understanding of probability. I ask again if you've ever taken a probability and statistics course? I have taken 3 such courses (over the span of 2 engineering degrees), so it would seem that though I am not an expert, I would know far more about this topic than the average person.

Is it possible that I understand this better than you do, given that you have little to no education in this area?

As AHF (whose intellect you obviously respect even if you don't respect mine) says, this is a problem of conditional probability. You may have heard of Bayes' Theorem if you've taken a prob/stats course.

Here's a simpler example:

You have an urn with 3 red balls and 3 white balls.

You draw balls from the urn without replacing them.

What is the probability that the 2nd ball you draw is red?

How do we approach this?

If we use your logic, we can never find an answer.

You see, in the one case, we draw red first (a probability of 3/6 or 1/2). That leaves 5 balls, 2 of which are red. The probability is 2/5 of drawing red again (call this RR).

In the second case, we draw white first (a probability of 3/6 or 1/2). That leaves 5 balls, 3 of which are red. The probability of drawing red 2nd is now 3/5 (call this WR).

How do we resolve these different numbers? Well, we apply our understanding of conditional probability. The "condition" is which ball was drawn first. The probability of drawing red 2nd is the sum of the probabilities of the two ways we can draw red 2nd.

The probability of RR is the probability we draw red 2nd TIMES the probability that we draw red 1st. Recall that the probability we draw red first is 1/2.

As such >>>> prob. of RR = 1/2 * 2/5 = 2/10

Furthermore prob. of WR = 1/2 * 3/5 = 3/10

Total probability of drawing red 2nd = WR + RR = 5/10 = 1/2

NOTE: The above answer is INTUITIVE! Yes, it makes no sense for the probability of drawing Red 2nd to be greater or less than the probability of drawing White 2nd! It must be 1/2 or "50/50" by SYMMETRY.

I say this because the answer I've reached by using conditional probability (and Bayes Theorem) is the answer we KNOW MUST BE TRUE.

NOW! See what this means? The composition in the urn CHANGES (just like your "variable"). We see that there are 2 distinct possible outcomes through which a red may come up 2nd. Each has a distinct probability associated with it. HOWEVER, we are able to calculate an overall probability by summing the probabilities of the respective outcomes.

I use this simple example because it is easy to follow and INTUITIVE. You cannot dispute the answer because it's obvious. If you'd like, we may look at more complicated problems. The NBA lottery is a more complicated but quite workable problem in conditional probability. I have calculated it all before through an excel sheet.

P.S. I stand corrected on your name and apologize for misreporting it.