For the Statisticians Among Us

[e_blazer]

From OLive:

The New Jersey pick: The Nets remain in a tie with Toronto for the sixth-worst record at 22-42. Because teams that finish with the same record add, then divide, their combinations, if the season ended today, the Nets and Raptors would each have 53 combinations. So the Nets' odds of getting a top-three pick right now would be:
No. 1 pick: 5.3 percent
No. 2 pick: 6.0 percent
No. 3 pick: 7.3 percent

So, what are the odds that the Nets pick ends up being 1st, 2nd, or 3rd? In other words, what are the odds that they get to keep their pick this year? It's been way too many years since my probability and statistics class, so help me out here.

 

[Mediocre Man]

I still say it's 100%. Absolutely no way the NBA is going to allow them to move into a new arena, new city in that market withought a top pick

 

[e_blazer]

I still say it's 100%. Absolutely no way the NBA is going to allow them to move into a new arena, new city in that market withought a top pick

Interesting thought, MM, but I'm more looking for a pure math answer, absent cynicism and conspiracy theories.

 

[Mediocre Man]

Interesting thought, MM, but I'm more looking for a pure math answer, absent cynicism and conspiracy theories.

I was told there would be no math

 

[BLAZINGGIANTS]

From OLive:



So, what are the odds that the Nets pick ends up being 1st, 2nd, or 3rd? In other words, what are the odds that they get to keep their pick this year? It's been way too many years since my probability and statistics class, so help me out here.

Wouldn't you just add up those 3 figures right there (which is 18.6%)?

If they have those odds at each single pick, the odds should be the sum of the 3 figures.

But, like MM, I've been saying all along that I expect NJ to "magically" end up with a Top-3.

 

[Kamper]

From the data you supplied I tallied an 18.6% (just add up the numbers and subtract that by 1) chance that NJ will receive a 1-3 lottery protected pick which leaves portland with an 83.4% chance of Portland receiving the pick. However, the pick can range from 1-3 and 5-8 or 9 (depending on the outcome of a potential Toronto and NJ coin flip due to them being tied in the standings) and based on the current standings of today.

Concrete numbers will be available once the season ends. The pick most likely to occur based on this wiki page is 5th or 6th.

http://en.wikipedia.org/wiki/NBA_Draft_Lottery

Additionally, the Portland pick has roughly a 3% chance of being in the top 3.a Not as good of odds as when Portland won the lottery the last time, but anything could happen.

 

[Ed O]

From the data you supplied I tallied an 18.6% (just add up the numbers and subtract that by 1) chance that NJ will receive a 1-3 lottery protected pick which leaves portland with an 83.4% chance of Portland receiving the pick. However, the pick can range from 1-3 and 5-8 or 9 (depending on the outcome of a potential Toronto and NJ coin flip due to them being tied in the standings) and based on the current standings of today.

So an 83.4% chance that we will be between 5 and 9 with the NJ pick, huh? I think that's pretty good.

Ed O.

 

[jlprk]

The numbers in the opening post come from averaging spot numbers 6 and 7 in the chart below. Except that I calculate 6.95%, not 7.3%

http://en.wikipedia.org/wiki/NBA_Draft_Lottery
Go to "Process" section

 

[Kamper]

Although I don't really like the "behind closed doors" treatment that the NBA lottery undertakes, it is administered in front of auditors and in front of team representatives- which should completely eliminate the fallacy that the NBA lottery is still rigged (I've seen the Ewing conspiracy, and wouldn't put it past Stern). However, with this new method of ping pong balls it is very hard to believe that it is still rigged. I don't believe I or any common fan would fully understand the process of drawing 4 balls from 14 ping pong balls to determine the lottery picks 1-3, and wouldn't make for very good TV. I don't even fully understand the explanation given on the wiki page, but I'm sure the oversight committee does.

 

[Kamper]

After further review of the current national standings based on current losses, NJ could very easily tie for the 4-7th lottery standings

Best case for Blazers is if NJ ends up with the #4 pick solely, and the lottery follows the odds where teams 1-3 in the standings win the lottery:

For this to happen:
NJ (currently 22-42) MUST LOSE FINAL 2 GAMES against (PHI/TOR)
Sacramento (currently 21-43) needs to beat both OKC and LAL
Toronto (currently 22-42) needs to beat NJ (prevents the tie, and NJ gets the very critical loss) doesn't matter about the outcome of the MIL game- it won't have any effect should TOR beat NJ)
Cleveland (currently 21-42) needs to win at least 1 against MEM/DC/CHI

More Likely Scenario since I don't see Sacramento beating either of OKC/LAL
and ending with the #5 pick:

NJ MUST LOSE FINAL 2 GAMES against PHI/TOR
Toronto (currently 22-42) needs to beat NJ (prevents the tie, and NJ gets the very critical loss) same as before, MIL game has no bearing.
Cleveland (currently 21-42) needs to win at least 1 against MEM/DC/CHI (this prevents a tie in the loss column)

The key game will rest upon the outcome of the Toronto/NJ game. Never before have I been so giddy to watch two horrible East Coast teams battle it out for inferiority. I can only hope that NJ has a better tanking approach to this game than TOR.

 

[Ed O]

Although I don't really like the "behind closed doors" treatment that the NBA lottery undertakes, it is administered in front of auditors and in front of team representatives- which should completely eliminate the fallacy that the NBA lottery is still rigged (I've seen the Ewing conspiracy, and wouldn't put it past Stern). However, with this new method of ping pong balls it is very hard to believe that it is still rigged. I don't believe I or any common fan would fully understand the process of drawing 4 balls from 14 ping pong balls to determine the lottery picks 1-3, and wouldn't make for very good TV. I don't even fully understand the explanation given on the wiki page, but I'm sure the oversight committee does.

I agree with you that (a) I wish we could actually see the drawing of the ping pong balls, (b) it would make for some very, very boring television, and (c) it would be almost impossible to fake it without someone, somewhere saying something based on knowledge of wrong doing.

As for the math... it's not very difficult (not bragging or anything... but I bet you're just selling yourself short in terms of understanding it). It seems like an odd way to do it, for sure, at first blush, but it makes sense to give all lottery teams SOME chance of getting into the top three without giving the best teams too good of a chance.

Ed O.

 

[Kamper]

I fully understand the odds of the numbers giving the worst team the most numerical chances, I'm just trying to remember the Derrick Rose lottery where Portland had a pretty decent shot after the first 3 balls were pulled of winning the lottery a second time in a row, if memory serves me it was between POR and CHI as to who would win the lottery that year, I think I remember Portland had fewer when it came to that final number, but this adds to the confusion I have with the process, and again supports the current format where they reveal teams in reverse order as to who won, thus making for better tv.

 

[crowTrobot]

From the data you supplied I tallied an 18.6% (just add up the numbers and subtract that by 1) chance that NJ will receive a 1-3 lottery protected pick which leaves portland with an 83.4% chance of Portland receiving the pick.

no biggie but math slightly off. 100%-18.6% = 81.4%

The pick most likely to occur based on this wiki page is 5th or 6th.

at this point 5th is the least likely pick we would get.

 

[crowTrobot]

So an 83.4% chance that we will be between 5 and 9 with the NJ pick, huh? I think that's pretty good.

Ed O.

if they finish in a 2-way tie for 6th (where they are now) we would have an 81.4% chance at a pick between 6-9. as bunched up as things are odds are the finish will be different.

if NJ were to finish alone in 5th, the odds of us getting the pick (5-8 in this case) would drop to 66.6%

 

[crowTrobot]

Best case for Blazers is if NJ ends up with the #4 pick solely

4th worst has only 10% chance at 4th pick. no significant advantange gained from the extra risk there.

 

[Ed O]

if they finish in a 2-way tie for 6th (where they are now) we would have an 81.4% chance at a pick between 6-9. as bunched up as things are odds are the finish will be different.

if NJ were to finish alone in 5th, the odds of us getting the pick (5-8 in this case) would drop to 66.6%

Thanks for the info. So... it looks like (if there's a 50% chance of each of those outcomes) then we have a 74% chance of getting a pick between 5 and 9.

Ed O.

 

[crowTrobot]

Thanks for the info. So... it looks like (if there's a 50% chance of each of those outcomes) then we have a 74% chance of getting a pick between 5 and 9.

Ed O.

there's still several other possibilities also, but yeah overall the odds at this point are probably somewhere around 3/4 us getting the pick.

 

[jlprk]

The demise of coolstandings.com is very, very sad. It was invaluable to me for all these years for the purposes of this thread. I always seemed to be the only one who linked to it, both on this board and before that on ESPN.

Now we have to hand-calculate these odds at the end of each season.

 

[THE HCP]

So an 83.4% chance that we will be between 5 and 9 with the NJ pick, huh? I think that's pretty good.

Ed O.

Why not 4-9?

 

[Tince]

Why not 4-9?

If you finish with the 5th worse record, you can't get the 4th pick.

If you finish with the 6th worse record, you can't get the 4th or 5th picks.

The lottery only places the top 3 teams.

 

[THE HCP]

got it, thanks.

 

[Eastoff]

Wouldn't you just add up those 3 figures right there (which is 18.6%)?

If they have those odds at each single pick, the odds should be the sum of the 3 figures.

But, like MM, I've been saying all along that I expect NJ to "magically" end up with a Top-3.

no.

 

[Eastoff]

None of you guys took/remember statistics. If you have a 50% chance to get heads, does that mean if you flip a coin twice, you have a 100% chance of getting it once? The answer is no. What you do is you have a 50% chance of not getting heads once and a 50% chance of not getting heads again. You multiply the odds of it not happening and then subtract this number from 1. Odds = 1-((1-.5)*(1-.5))=.75 or 75%. So based on those numbers NJ odds are 1-((1-0.053)*(1-0.06)*(1-0.073))=17.48% And for us it's 82.52% of keeping their pick.

 

[e_blazer]

None of you guys took/remember statistics. If you have a 50% chance to get heads, does that mean if you flip a coin twice, you have a 100% chance of getting it once? The answer is no. What you do is you have a 50% chance of not getting heads once and a 50% chance of not getting heads again. You multiply the odds of it not happening and then subtract this number from 1. Odds = 1-((1-.5)*(1-.5))=.75 or 75%. So based on those numbers NJ odds are 1-((1-0.053)*(1-0.06)*(1-0.073))=17.48% And for us it's 82.52% of keeping their pick.

This is why I asked the question, but I'm not sure that you're correct. In this instance, there's only one "flip". Given NJ's current position, it has a 5.3% chance of being the #1 pick, a 6% chance of being the #2, and a 7.3% chance of being the #3 pick. It seems to me that addition of those 3 numbers is the correct way to proceed here, but I'm more than willing to be shown otherwise.

 

[BoBoBREWSKI]

Although I don't really like the "behind closed doors" treatment that the NBA lottery undertakes, it is administered in front of auditors and in front of team representatives- which should completely eliminate the fallacy that the NBA lottery is still rigged (I've seen the Ewing conspiracy, and wouldn't put it past Stern). However, with this new method of ping pong balls it is very hard to believe that it is still rigged. I don't believe I or any common fan would fully understand the process of drawing 4 balls from 14 ping pong balls to determine the lottery picks 1-3, and wouldn't make for very good TV. I don't even fully understand the explanation given on the wiki page, but I'm sure the oversight committee does.

Agree. No way its rigged, especially now days. Way to much at stake if they got caught. It'd be like the Saints situation in the NFL but 100 times worse.

 

[crandc]

e_blazer, I am taking a statistics refresher course April 30 if you can wait that long. My recollection (damn, college was a long time ago) is that westnob is correct. The question is whether these are 3 independent events like coin toss or 3 related events where one outcome precludes any others.

 

[THE HCP]

This shit is making me dizzy!

 

[Boise Blazer]

Or... we could just say that there is a 50/50 chance. We either will or we wont get the pick this year.

 

[THE HCP]

Or... we could just say that there is a 50/50 chance. We either will or we wont get the pick this year.

I like your style!

 

[e_blazer]

As of today, I think any discussion of probabilities is a waste of time. Looking at the standings, there are 4 teams with 43 losses. NOH has 44 losses. If everybody loses out the rest of their remaining games (yeah, tankers) then NOH goes into the lottery with the 3rd spot, Sacramento & Cleveland would flip for the 4 & 5 spots, and NJ and Toronto would flip for 6 & 7. All it would take is a win by one or two of these teams to throw everything up in the air. Washington, currently with the 2nd pick, is for some insane reason on a 4 game winning streak. Their management couldn't be so inept as to allow them to win any more could they? Crazy.