# 2004 Draft Lottery: A Dose of Reality



## Nater (Jul 10, 2002)

With so much speculation going on regarding the Bulls draft position this year, and its impact on trade possibilities... I decided to discover the likelihood of each of the possible draft slots for the Bulls. (To my knowlege, this information has not been posted this year.) So the table below shows the probability that the Bulls will receive a given draft slot. Probabilities for Orlando are also included, as they directly impact the Bulls'.

<table border=1><tr><td> </td><td><b>Pick 1</b></td><td><b>Pick 2</b></td><td><b>Pick 3</b></td><td><b>Pick 5</b></td><td><b>Pick 6</b></td></tr><tr><td><b>Orlando</td></b><td>25.00%</td><td>21.55%</td><td>17.85%</td><td>35.60%</td>
<td>0.00%</td></tr><tr><td><b>Chicago</td></b><td>20.00%</td><td>18.91%</td><td>17.22%</td><td>28.25%</td><td>15.62%</td></tr></table>
(Note: The 4th pick automatically goes to the expansion Charlotte Bobcats.)

So there you have it: the most likely scenario is that the Bulls will 'win' the 5th overall pick. The second most likely is that the Bulls will win the 1st pick. The least likely is the worst-case scenario -- getting the 6th overall pick.

If math tickles your fancy, you can download a spreadsheet and inspect my calculations here.

Conclusion: keep your fingers crossed... :wiz:


----------



## Lusty RaRue (Sep 9, 2003)

Interesting. Thank you. 

I must be reading it wrong.

Can't the probabilities for say picks 1 & 2 be added so that we could say that there is a 38.91% chance that the Bull pick either 1 or 2? Isn't this % higher than that for the 5 pick?

20 + 18.91 = 38.91 > 28.25

Adding the 3rd pick %:
38.91 + 17.22 = 56.13% chance of getting a top 3 pick.

Or doesn't it work that way


----------



## Nater (Jul 10, 2002)

> Originally posted by <b>Lusty RaRue</b>!
> Interesting. Thank you.
> 
> I must be reading it wrong.
> ...


You've read it right. The math does work that way. My point was that the single most likely scenario is that the Bulls get the #5 pick.

So it's true that the Bulls are more likely to be #1 or #2 than #5. But if you want to start combining, they're more likely to be #5 or #6 (44%) than #1 or #2 (39%).


----------



## Wynn (Jun 3, 2002)

In laymen's terms, please stop taking Okafor to the bank. 80% likely he's gone by the time we get to the mic.


----------



## such sweet thunder (May 30, 2002)

> Originally posted by <b>Wynn</b>!
> In laymen's terms, please stop taking Okafor to the bank. 80% likely he's gone by the time we get to the mic.


You should take 1 of the following actions:

a) stop posting threads that tread on my kool-aid, or
b) change your avatar to something more appropriate, perhaps

Edit: I hope you know I'm kidding, Wynn--you speak truth . 










or,


----------



## MikeDC (Jul 16, 2002)

> Originally posted by <b>Wynn</b>!
> In laymen's terms, please stop taking Okafor to the bank. 80% likely he's gone by the time we get to the mic.


Not only that, please stop tanking seasons to get the 1st pick. Even if you have the worst record, there's a 75% chance you won't get the 1st pick and it's better than 50/50 that you won't even get the 1st or second pick.


----------



## Wynn (Jun 3, 2002)

> Originally posted by <b>C.C.C.P</b>!
> 
> 
> You should take 1 of the following actions:
> ...


I apologize for the urine that inadvertantly splattered in your kool-aid!

Nice choices of avatars, BTW, but I'm trying to get into a more light-hearted place.


----------



## bulls (Jan 1, 2004)

hey Nater anyway to go back the past few yrs say 5-10 and see who the worse 2 teams were then see where they picked?


----------



## bulls (Jan 1, 2004)

nm i went back to the 97-98 season.just going by wins on who was the worse in the nba

02-03 1 and 3
01-02 2 and 3
00-01 4 and 5
99-00 4 and 3
98-99 2 and 4
97-98 3 and 4

so just going by the wins the 2nd worse team never got a 1st or 2nd pick..:upset:


----------



## rlucas4257 (Jun 1, 2002)

assuming 4 of the lottery teams actually take Howard #1, how does that affect our odds of obtaining Emeka?


----------



## Lusty RaRue (Sep 9, 2003)

> Originally posted by <b>Nater</b>!
> 
> 
> You've read it right. The math does work that way. My point was that the single most likely scenario is that the Bulls get the #5 pick.
> ...


Oh man now why you go and do that?! You makin' me  .
The Steers worked hard for that 2nd pick and now you sayin' they might not get it?! sup wih dat dude dang that's some bad @#$% you passin out. Know wutta mean?

Can't you just whisper sweet nothings in my ear and tell me everything will be all right? 

Truth? I can't handle the truth! 
Ahhhhhhhhhhhh!!!!!!!!!!!

Now what was that MASH theme song called again? Oh yeah: "Suicide is Painless". I/We feel better now.
=================================
Sorry for the meltdown and thanks.


----------



## bulls (Jan 1, 2004)

> Originally posted by <b>rlucas4257</b>!
> assuming 4 of the lottery teams actually take Howard #1, how does that affect our odds of obtaining Emeka?


im just talkin out my butt here but if we dont land atleast the 2nd pick kiss Emeka goodby


----------



## rlucas4257 (Jun 1, 2002)

> Originally posted by <b>bulls</b>!
> 
> 
> im just talkin out my butt here but if we dont land atleast the 2nd pick kiss Emeka goodby


Of course. but there are a handful of teams (atlanta comes to mind) that would actually take Howard first. So the straight odds of us landing Emeka arent 100% tied to getting the number one pick.


----------



## bulls (Jan 1, 2004)

> Originally posted by <b>rlucas4257</b>!
> 
> 
> Of course. but there are a handful of teams (atlanta comes to mind) that would actually take Howard first. So the straight odds of us landing Emeka arent 100% tied to getting the number one pick.


no but if we dont get the 2nd pick then odds are Emeka will be gone by #2 and just throwin this out my head odds of where we pick are 50% for 3rd 40% for 5th and 10% for 2nd..is there anyone else that Might be takin b4 Okafor or Howard??


----------



## rlucas4257 (Jun 1, 2002)

> Originally posted by <b>bulls</b>!
> 
> 
> no but if we dont get the 2nd pick then odds are Emeka will be gone by #2 and just throwin this out my head odds of where we pick are 50% for 3rd 40% for 5th and 10% for 2nd..is there anyone else that Might be takin b4 Okafor or Howard??


yeah its a tough question as to how that increases our odds of drafting him. all these percentages are making my head spin


----------



## bulls (Jan 1, 2004)

> Originally posted by <b>rlucas4257</b>!
> 
> 
> yeah its a tough question as to how that increases our odds of drafting him. all these percentages are making my head spin


i was hopefull we would but after looking at this thread and going back looking at the draft #'s it dont look good so if im Pax i get a trade lined ASAP.

but hey i just looked and the 76ers were 2nd worse in 96 and landed the top pick so maybe..


----------



## rlucas4257 (Jun 1, 2002)

> Originally posted by <b>bulls</b>!
> 
> 
> i was hopefull we would but after looking at this thread and going back looking at the draft #'s it dont look good so if im Pax i get a trade lined ASAP.
> ...


Isnt NJ the only worst team in the NBA who actually landed the number one pick back in the Derrick Coleman draft?


----------



## bulls (Jan 1, 2004)

> Originally posted by <b>rlucas4257</b>!
> 
> 
> Isnt NJ the only worst team in the NBA who actually landed the number one pick back in the Derrick Coleman draft?


no last year the Cavs and nuggets were tied for worsed and the cavs got the top pick im going by http://www.nba.com/history/standings/20022003.html


----------



## rlucas4257 (Jun 1, 2002)

> Originally posted by <b>bulls</b>!
> 
> 
> no last year the Cavs and nuggets were tied for worsed and the cavs got the top pick im going by http://www.nba.com/history/standings/20022003.html.


ahhh ok. I thought Denver won some kind of toss up that gave them a few extra ping pong balls. But I might be wrong about that.


----------



## bulls (Jan 1, 2004)

> Originally posted by <b>rlucas4257</b>!
> 
> 
> ahhh ok. I thought Denver won some kind of toss up that gave them a few extra ping pong balls. But I might be wrong about that.


maybe but im just going by that site..


----------



## Nater (Jul 10, 2002)

> Originally posted by <b>rlucas4257</b>!
> 
> 
> Of course. but there are a handful of teams (atlanta comes to mind) that would actually take Howard first. So the straight odds of us landing Emeka arent 100% tied to getting the number one pick.


Atlanta tied for 4th-worst, so they have approximately a 10.5% chance at the top pick. If they're the only team that would choose Howard first, then that means there's a 10.5% that Okafor will last until the 2nd pick. If you know of other teams who are more intrigued by Howard, you can get their chances at the top pick by looking here.


----------



## rlucas4257 (Jun 1, 2002)

> Originally posted by <b>Nater</b>!
> 
> 
> Atlanta tied for 4th-worst, so they have approximately a 10.5% chance at the top pick. If they're the only team that would choose Howard first, then that means there's a 10.5% that Okafor will last until the 2nd pick. If you know of other teams who are more intrigued by Howard, you can get their percentages by looking here and here.


Thanks. Ill take a look at Chad Fords differing mocks. I think he had 5 or 6 teams taking Howard number one including the clips and atlanta. The other teams Ill have to look


----------



## Bulls96 (Jun 25, 2003)

IMO, Pax has a very simple task this summer:

1.Using first round pick, land a solid SF (only).
2.Trade JWD, Erob, Pippen plus second round pick or “waste” them.
3.Get a backup SG/SF (not older than 33)
4.Sign Jamal.
5.Sign Fizer.
6.Training/exercise, training/exercise, training/exercise …building a confidence.
7.Be prepar to find a new coach, close to December 2004, so start looking now.


----------



## Showtyme (Jun 24, 2002)

There's some fancy statistics going on here. Let's make the numbers jump a little bit... (I know I promised to keep my posts short, but these #'s are really interesting). All these statistics are notwithstanding trades.

1. Let's say that Washington, Phoenix, Toronto, L.A., Cleveland and Portland were basically all split 50/50 on taking Okafor instead of Howard. These teams account for 387 lottery balls.

Orlando, Golden State, Utah, Seattle and Philly would probably take Okafor over Howard, since they are needier of a real big man to contibute right away, so let's say they were about 85% sure on taking Okafor. These teams account for 309 lottery balls.

Atlanta is probably leaning towards 85% sure on taking Howard, since they want their hometown boy. They are really the only team that would draft and keep Howard over Okafor decisively. Atlanta accounts for 104 lottery balls.

When you multiply it out, it looks like this:
387*50% + 309*85% + 104 + 15% = 560 out of the 800 lottery balls would probably have Okafor's name on them.

*If the Bulls miss the #1 pick, the likelihood that Okafor is gone is 70% (560/800).*

2. Now, if the Bulls miss the #2 pick, it very much depends on who DID get the #1 pick. 
- If Atlanta takes #1, then Okafor being gone goes up to about 81.3% (the 15% chance that ATL will take him with #1 + the chance that a remaining team will take him if ATL takes Howard, which is 544/696). 
157 6
- If one of the 50/50 guys got the #1 pick, it varies from 81.3% (if Washington gets #1), to 84.8% (if Portland gets #1).
- If one of the 85% Okafor guys got the #1 pick, the Bulls would basically lose out. 90.7% chance he's gone if Orlando gets #1 and the Bulls miss on #2; a 95.5% chance he's gone if Utah gets #1.

*If the Bulls miss on #2, depending on who got #1, there will be anywhere from an 81% to a 96% chance of him being gone.*

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

This means that if the Bulls miss 1 or 2, they will most likely need to trade for Okafor. This will be very possible, if we package some talent, but at that point, the Bulls will have to consider whether taking Luol Deng and hoping on Chandler's comeback is going to be good enough for them.[/b] Taking the best player at the slot last year worked out pretty well (I'd say it's one of the only things that worked out pretty well).

There are a lot of interesting trade scenarios since the top two consensus picks are both PF's and not PF/C's, and a lot of the lottery teams are pretty set at the PF position.


----------



## RP McMurphy (Jul 17, 2003)

I don't follow your logic, Showtyme. Even if the Bulls got the #3 and both teams ahead of them would prefer Howard to Okafor, the #2 team would surely take Okafor over everyone else in the draft. I think the Bulls must get a Top 2 pick to have any chance at all of getting him.


----------



## bulls (Jan 1, 2004)

> Originally posted by <b>ArtestFan</b>!
> I don't follow your logic, Showtyme. Even if the Bulls got the #3 and both teams ahead of them would prefer Howard to Okafor, the #2 team would surely take Okafor over everyone else in the draft. I think the Bulls must get a Top 2 pick to have any chance at all of getting him.


Thank You!


----------



## Showtyme (Jun 24, 2002)

Haha, you're right. The 50/50 teams would become 100% teams for Okafor, since Howard would be gone.

I'm a dummy... I was thinking mathematical variation but I forgot to close the universe a little bit.

Well then, that's it. The only useful thing from the stats I spewed forth were that if the Bulls get #2, they probably will still not get Okafor.


----------



## fsaucedo (May 3, 2003)

> Originally posted by <b>Showtyme</b>!
> There's some fancy statistics going on here. Let's make the numbers jump a little bit... (I know I promised to keep my posts short, but these #'s are really interesting). All these statistics are notwithstanding trades.
> 
> 1. Let's say that Washington, Phoenix, Toronto, L.A., Cleveland and Portland were basically all split 50/50 on taking Okafor instead of Howard. These teams account for 387 lottery balls.
> ...


Interesting numbers. I was also puzzled by the fact that you overlooked that whoever drafts second, would probably take Okar if Howard was picked first.

I also have some numbers to throw out there. Lets say that the Hawks were to take Howard with the #1 pick, as I think they would, if they got the #1 pick. That would increase the Bulls' chances of having the opportunity to pick Okafor from 20% to 44.3%.

The Bulls already have a 20% chance of getting the #1 pick and taking Okafor. If the Hawks get the #1 pick, the Bulls have a 22.3% chance of gettin the #2 pick because the Hawks' 104 balls would be off the table and the bulls would have 200 chances out 896 of getting the #2 pick (200/896 = 22.3%). You would add this chances of 22.3% to the chances of getting the #1 pick which would be 44.3%. In this scenario, the Hawks would take Howard with the first pick and the Bulls would take Okafor with the second pick.


----------



## Philo (Feb 13, 2003)

As long as Josh Smith is on the board when the Bulls make their choice, I will be happy. We need top 3, anything else would limit our options in trading the pick. After watching garbage for the past 6 months, the only thing that excites me about this team is the possibility of receiving the #1 pick.


----------



## johnston797 (May 29, 2002)

> Originally posted by <b>Nater</b>!
> If math tickles your fancy, you can download a spreadsheet and inspect my calculations here.
> 
> Conclusion: keep your fingers crossed... :wiz:


The spreadsheet did not show how you calculated the probablility for Orlando to get the 2nd pick. How did you come up with 21.5%?

As best as I can remember, the odds are not that bad that Orlando (and us) as the worst teams fall out of the top 3.


----------



## Nater (Jul 10, 2002)

*Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>johnston797</b>!
> 
> 
> The spreadsheet did not show how you calculated the probablility for Orlando to get the 2nd pick. How did you come up with 21.5%?
> ...


Sorry for not clarifying this. I did not calculate the odds for the first three picks -- those are available on websites such as this one.


----------



## Nater (Jul 10, 2002)

> Originally posted by <b>fsaucedo</b>!
> 
> I also have some numbers to throw out there. Lets say that the Hawks were to take Howard with the #1 pick, as I think they would, if they got the #1 pick. That would increase the Bulls' chances of having the opportunity to pick Okafor from 20% to 44.3%.
> 
> The Bulls already have a 20% chance of getting the #1 pick and taking Okafor. *If the Hawks get the #1 pick, the Bulls have a 22.3% chance of gettin the #2 pick because the Hawks' 104 balls would be off the table and the bulls would have 200 chances out 896 of getting the #2 pick (200/896 = 22.3%).* You would add this chances of 22.3% to the chances of getting the #1 pick which would be 44.3%. In this scenario, the Hawks would take Howard with the first pick and the Bulls would take Okafor with the second pick.


Almost. You implicitly understand the logic involved, but it did not make its way into your calculations. In the sentence I bolded, you said, "If the Hawks get the #1 pick..." You must apply the probability of this event to the events that follow. Since the Hawks only have a 10.5% chance at the 1st pick, the Bulls' chance of getting the 2nd pick and having Okafor still available is not 22.3%, but 10.5% x 22.3% = 2.3%. This is the number you add to the Bulls' probability of getting the first pick (20%) to determine their overall probability of having a shot at Okafor, which coincidentally is 22.3%.


----------



## johnston797 (May 29, 2002)

*Re: Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>Nater</b>!
> 
> 
> Sorry for not clarifying this. I did not calculate the odds for the first three picks -- those are available on websites such as this one.


I don't think your calculations take into account that Orlando and Chicago landing spot are not independent events. 

If you know that Orlando falls out of the top 3, then our probability of being in the top 3 is higher than otherwise.

The only difference that this makes is that your percentage of us getting the 6th pick is too high and the percentage of getting the 5th pick is too low.

I think....


----------



## Nater (Jul 10, 2002)

*Re: Re: Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>johnston797</b>!
> 
> 
> I don't think your calculations take into account that Orlando and Chicago landing spot are not independent events.
> ...


I'm trusting that whoever calculated the Top-3 probabilities for the NBA knows what they're doing... so the Bulls' chances for a Top-3 are already based on the possibilities of Orlando getting a Top-3.

Beyond that, I calculated the Bulls' chance at #6 by multiplying Orlando's chance of not getting Top-3 (35.6%) by the Bulls' chance of not getting Top-3 (43.9%). These are the only 2 events that can lead to the Bulls getting #6. That leaves our chance at #5 = (100% - Summed Probabilities of #1, #2, #3, & #6).


----------



## fsaucedo (May 3, 2003)

> Originally posted by <b>Nater</b>!
> 
> 
> Almost. You implicitly understand the logic involved, but it did not make its way into your calculations. In the sentence I bolded, you said, "If the Hawks get the #1 pick..." You must apply the probability of this event to the events that follow. Since the Hawks only have a 10.5% chance at the 1st pick, the Bulls' chance of getting the 2nd pick and having Okafor still available is not 22.3%, but 10.5% x 22.3% = 2.3%. This is the number you add to the Bulls' probability of getting the first pick (20%) to determine their overall probability of having a shot at Okafor, which coincidentally is 22.3%.


Darn! I knew it did not seem right. Am suppose to be a math major. I get it. The only way the odds I did would work is after the fact. After the *Hawks get the #1 pick* (if they were to get it), at that instant the Bulls chances of getting the #2 pick with Okafor still available would change from 22.3% to 42.3%. Your calculations are right. 

Now the thing that puzzles me is how do the NBA people calculate the overall chances of a team like Orlando or Chicago of getting the #2 and #3 picks. I literally played around with the numbers for about two hours and couldn't come up with the same numbers. I tried to do Orlando's chances of landing the #2 and #3 pick, but my numbers kept coming higher than the ones given. I tried to do every scenario possible, and for all scenarios for the #2 pick, Orlando had a probability higher than 25% percent of getting the #2 pick, yet the actual number is 21.55%. Any suggestions to what I am doing wrong? Any site where they show the calculations of this things?


----------



## RP McMurphy (Jul 17, 2003)

> Originally posted by <b>fsaucedo</b>!
> Now the thing that puzzles me is how do the NBA people calculate the overall chances of a team like Orlando or Chicago of getting the #2 and #3 picks. I literally played around with the numbers for about two hours and couldn't come up with the same numbers. I tried to do Orlando's chances of landing the #2 and #3 pick, but my numbers kept coming higher than the ones given. I tried to do every scenario possible, and for all scenarios for the #2 pick, Orlando had a probability higher than 25% percent of getting the #2 pick, yet the actual number is 21.55%. Any suggestions to what I am doing wrong? Any site where they show the calculations of this things?


No, their numbers are right.

Utah gets the #1 (5/1000) of the time, and then Orlando has 250 of the remaining 995 balls. So the chances of Utah getting the #1 and Orlando getting the #2 are (5*250)/(1000*995). Then add that number to the chances of Golden State getting the #1 and Orlando getting the #2, and then Seattle and Orlando, and so on over all the lottery teams besides Orlando. I did that and I got 21.53 %. I think the reason it's slightly different from 21.55 % is that there were some ties between lottery teams, and that changes the percentage by a little bit.

Hope that makes sense.


----------



## DaBullz (Jul 15, 2002)

> Originally posted by <b>Nater</b>!
> With so much speculation going on regarding the Bulls draft position this year, and its impact on trade possibilities... I decided to discover the likelihood of each of the possible draft slots for the Bulls. (To my knowlege, this information has not been posted this year.) So the table below shows the probability that the Bulls will receive a given draft slot. Probabilities for Orlando are also included, as they directly impact the Bulls'.
> 
> <table border=1><tr><td> </td><td><b>Pick 1</b></td><td><b>Pick 2</b></td><td><b>Pick 3</b></td><td><b>Pick 5</b></td><td><b>Pick 6</b></td></tr><tr><td><b>Orlando</td></b><td>25.00%</td><td>21.55%</td><td>17.85%</td><td>35.60%</td>
> ...


I'm pretty sure you aren't looking at the data right.

The Bulls clearly have a much better chance of getting 1st OR 2nd OR 3rd pick than they do the 5th pick.

Also, I'm not sure how if you add up your odds on getting 1st through 5th pick, you get more than a 100% chance.

Peace!


----------



## TomBoerwinkle#1 (Jul 31, 2002)

> Originally posted by <b>C.C.C.P</b>!
> 
> 
> You should take 1 of the following actions:
> ...


Wynn and others have taken enough of the images I've found for avatars. "Fries with me" is my new one!

Thanks.


----------



## johnston797 (May 29, 2002)

*Re: Re: Re: Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>Nater</b>!
> I'm trusting that whoever calculated the Top-3 probabilities for the NBA knows what they're doing... so the Bulls' chances for a Top-3 are already based on the possibilities of Orlando getting a Top-3.


Agreed.



> Originally posted by <b>Nater</b>!
> I calculated the Bulls' chance at #6 by multiplying Orlando's chance of not getting Top-3 (35.6%) by the Bulls' chance of not getting Top-3 (43.9%).


Again, these are not independent events so I don't think your math works.

Someone will post the odds soon for the Bulls. We can refer back to this.


----------



## Nater (Jul 10, 2002)

*Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>DaBullz</b>!
> 
> 
> I'm pretty sure you aren't looking at the data right.
> ...


As I said in an earlier post, my results show that the *single most likely draft slot for the Bulls is #5*. Yes, if you add other probabilites together, it's true that they have a better chance at "Top-3" than #5. But that wasn't my point.



> Originally posted by <b>DaBullz</b>!
> 
> Also, I'm not sure how if you add up your odds on getting 1st through 5th pick, you get more than a 100% chance.


Check your calculator.


----------



## Nater (Jul 10, 2002)

*Re: Re: Re: Re: Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>johnston797</b>!
> 
> Again, these are not independent events so I don't think your math works.


You're correct about the dependency of the events, but all the dependencies and probabilities work themselves out in the first three spots. After that, it's no longer random. I believe that "falling out of the top 3" can be treated as independent events for the different teams. Therefore, Orlando's "non-top-3" and Chicago's "non-top-3" probabilites can be multiplied to calculate the probability of those events both happening. I have no idea if I explained this clearly... 




> Someone will post the odds soon for the Bulls. We can refer back to this.


Indeed. I'm pretty certain about my results, but if a stats guru (such as Dan or Mike) comes in here and claims otherwise, I'll certainly defer.


----------



## DaBullz (Jul 15, 2002)

How can Orlando have a 0% chance of getting the 6th pick?


----------



## MikeDC (Jul 16, 2002)

> Originally posted by <b>DaBullz</b>!
> How can Orlando have a 0% chance of getting the 6th pick?


The worst team is typically guaranteed to have it's pick not fall below a certain level. For example, in 2000, we could have had anywhere between the #1 and #4 slot. We ended up with the #4 slot and took Marcus Fizer.


----------



## johnston797 (May 29, 2002)

*Re: Re: Re: Re: Re: Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>Nater</b>!
> I believe that "falling out of the top 3" can be treated as independent events for the different teams.


How could it be independent? If we know that Orlando misses the lottery, our chances of a top 3 pick would go up substancially.

I am pretty sure you are wrong on this. If I get time, I will try to prove it.


----------



## johnston797 (May 29, 2002)

Pick 1	Pick 2	Pick 3	Below Fourth Pick
Orlando	25%	22%	18%	36%
Chicago	20%	19%	17%	44%


1.) Let’s agree that the above was available from published sources. (Granted, the last column was only implied.) Let’s agree that neither of us has determined how to calculate these numbers.

2.) Let’s agree that some serious math is used. I found a thesis paper on this as I was Googling around.

3.) Now the calculation in question is 

Given that we are 44% likely to pick fifth or sixth, how likely is it that we pick fifth and how likely to pick sixth?

I argue that you can’t just multiply 36% x 44% because the two numbers are not independent.

Here is the logic:

While we only have a 20% chance of getting the first pick, we have a (20/75) or 27% of getting the first pick *if we know that Orlando does not get the top pick*. Therefore, one row of data is not independent of the other. This increase in chance of getting the first pick alone drops the odds that we get the fifth or sixth pick.

But just as the odds of getting the first pick are greater, our odds of getting the second pick and the third pick are getter *if we know that Orlando does not have a top 3 pick*. 

Without doing the math, I guess-estimate our odds at 25% and 22% at pick 2 and pick 3* if we know that Orlando does not have a top 3 pick*. . This would drop our chances of a fifth or sixth pick to roughly 26%. This would be the percentage to multiple with the 36% chance of Orlando falling out of the lottery.

So by this estimate, our chances are closer to 9% of getting the sixth pick


----------



## RP McMurphy (Jul 17, 2003)

*Re: Re: Re: Re: Re: Re: Re: Re: 2004 Draft Lottery: A Dose of Reality*



> Originally posted by <b>johnston797</b>!
> 
> 
> How could it be independent? If we know that Orlando misses the lottery, our chances of a top 3 pick would go up substancially.
> ...


Agreed. I can't think of an obvious way to prove that they are dependent, so I don't know what to say other than what you (Nater) said seems wrong to me.


----------



## Nater (Jul 10, 2002)

> Originally posted by <b>johnston797</b>!
> Pick 1	Pick 2	Pick 3	Below Fourth Pick
> Orlando	25%	22%	18%	36%
> Chicago	20%	19%	17%	44%
> ...


I understand your logic. But the result of your line of thinking is to increase the Bulls' percentages for the first three picks -- and this violates your Assumption #1. The Top-3 percentages will not change because they already include all possible scenarios. This, combined with the fact that percentages in a row must add up to 100%, means that the only adjustment that can be made to my table is to redistribute the 44% between the 5th and 6th picks. 

I calculated the odds for the 5th and 6th picks by looking at the odds of both teams falling out of the Top-3. I could just as easily have combined the probability of the Magic getting Top-3, and the Bulls not getting Top-3, which would yield the probability of the Bulls getting #5... 64.4% x 43.9% = 28.3%.


----------



## johnston797 (May 29, 2002)

> Originally posted by <b>Nater</b>!
> I understand your logic. But the result of your line of thinking is to increase the Bulls' percentages for the first three picks -- and this violates your Assumption #1. The Top-3 percentages will not change because they already include all possible scenarios.


The Top 3 percentages don't change until the change the premise. You change the premise when you try to calculate the Bulls odds of falling out of the top 3 *at the same time* that the Magic fall out of the top 3.



> Originally posted by <b>Nater</b>!
> I calculated the odds for the 5th and 6th picks by looking at the odds of both teams falling out of the Top-3. I could just as easily have combined the probability of the Magic getting Top-3, and the Bulls not getting Top-3, which would yield the probability of the Bulls getting #5... 64.4% x 43.9% = 28.3%.


And this would be wrong, too.


----------



## Nater (Jul 10, 2002)

> Originally posted by <b>johnston797</b>!
> 
> The Top 3 percentages don't change until the change the premise. You change the premise when you try to calculate the Bulls odds of falling out of the top 3 *at the same time* that the Magic fall out of the top 3.


It seems like you want 2 different probability tables -- one for the Magic getting top-3, and one not. Neither of those tables can singularly give an accurate prediction for all possible scenarios. 

The proper table will have the "official" percentages for the top-3 picks, and will have rows that add up to 100%. One (or both) of these premises will be violated by a table based on the line of reasoning you explained earlier.


----------



## Nater (Jul 10, 2002)

edit: whoops, double-post


----------



## DaBullz (Jul 15, 2002)

Here's something to consider.

If Orlando gets the 1st pick, then the Bulls get 200 ping pong balls out of a remaining 750, for a 27% chance at #2. If the 14th team (I believe that's how many are in the lotto) gets #1 with their 1 ping pong ball, the Bulls' chances at #2 would only be .1% (1 in 1000) more than their chance for #1.

But I don't think they actually remove Orlando's ping pong balls after they get the 1st pick; they just pick again if Orlando comes up again.

Let's just say this is pretty confusing.


----------



## Darius Miles Davis (Aug 2, 2002)

> Originally posted by <b>Nater</b>!
> With so much speculation going on regarding the Bulls draft position this year, and its impact on trade possibilities... I decided to discover the likelihood of each of the possible draft slots for the Bulls. (To my knowlege, this information has not been posted this year.) So the table below shows the probability that the Bulls will receive a given draft slot. Probabilities for Orlando are also included, as they directly impact the Bulls'.
> 
> <table border=1><tr><td> </td><td><b>Pick 1</b></td><td><b>Pick 2</b></td><td><b>Pick 3</b></td><td><b>Pick 5</b></td><td><b>Pick 6</b></td></tr><tr><td><b>Orlando</td></b><td>25.00%</td><td>21.55%</td><td>17.85%</td><td>35.60%</td>
> ...



Let's do a little extrapolating now that we've heard some insider info that Deng will be in the draft. For those of us who think a college player (Okafor or Deng) would be best for our team as of now, it looks like the odds are slightly in our favor that this will happen if it is Paxson's will.

If we get the #1 pick, the debate is not about who we can get but instead who we will choose. If we get #2, we clearly get one of the two if that's what we want. If we get #3, we'll most likely be able to grab Mr. Deng there. As things stand right now, Okafor and Howard are going to go 1 and 2 in some order. The only teams in the lottery I could see picking Deng over one of the two big men are the Bulls, the Clippers in they jump up to pick 3 (actually I think they would trade down or take a pg), Washington (they drafted Hayes last year, but they really need a center, not a PF - I get the idea they'd take Okafor but I don't know if they would want Howard), or maybe Portland, who's set at the 4. Really, I can't see anyone in the lottery taking Deng before pick 3 unless it's us, who needs a SF more than anyone.

As indicated above, the odds that we will wind up with one of the first two picks are at 56.13%. If the Bulls are at pick 5, I think the odds that Charlotte and whoever is picking at the 3 spot fall in love with Josh Smith and Shaun Livingston at spot 3 and 4 are actually greater than the odds of Deng getting picked before us if we get the 3 pick. 

*So based on some math and some speculation, let's leave the odds that we get Deng or Okafor at 56.13%. *

If we get pick #6, we'll probably be looking at Iguodala or a high schooler, or maybe even more likely a trade.


----------



## johnston797 (May 29, 2002)

> Originally posted by <b>Nater</b>!
> It seems like you want 2 different probability tables -- one for the Magic getting top-3, and one not. Neither of those tables can singularly give an accurate prediction for all possible scenarios.44


There is one probability table when we have no additional information about any one team's results. If we have additional information about one team's results (i.e. Orlando does not land in the top 3), then a different probability table exists.


----------



## Mongoose (Jun 24, 2003)

I did a quick Java brute force program for the probability, and came out with a 12.12% chance of picking 6th. The program is pretty simple, a double nested for loop that sums the probabilities for the 990 possible outcomes where neither we nor Orlando are in the top 3 (the only way we can get #6). 

So, this means our chances are: 20% for #1, 18.91% for #2, 17.22% for #3, 31.75% for #5, and 12.12% for #6. Which says, our chances of getting a top three pick are a little over 50%, but otherwise expect a #5 pick unless we get _really_ unlucky.


----------



## johnston797 (May 29, 2002)

Nater, 

Here is the clincher that shows that your logic doen't work. 

We both agree that Orlando has a 25% chance of the top pick and a 36% chance of a falling outside of the top 3.

We both agree that Bulls has a 20% chance of the top pick and a 44% chance of a falling outside of the top 3.

You think that you can calculate the odds of both teams falling out of the top 3 by multiplying 35% x 44% = 15%.

If this is true, could you calculate the probability of both teams getting the top pick? Using your method, one could just multiply 25% x 20% = 5%. 

Clearly, there is a 0% chance that both teams get the top pick.

If the logic doesn't hold for the top pick, why would it work for a non-top 3 pick?

Again, the Bulls chance of dropping all the way to the sixth pick is less than ten percent.



p.s. Nater, good thread.


----------



## Mongoose (Jun 24, 2003)

For any given lottery permutation, the chances are n1/1000 * n2/(1000-n1) * n3/(1000-n1-n2), where n# is the number of ping-pong balls the team in question has at the #th position drawn. For us to drop to #6, we and Orlando both can't be in the top 3. So, you just consider the remaining 11 teams and how they can be in the top 3, which is 11!/8! = 990 permutations. 

Sum up all the permutations, using a computer to add up each possibility, and you get 12.12% as the chance that the top three picks will not be Orlando or Chicago, which is equal to the chance we drop to #6. Not quite single digits, but not high.


----------



## chifaninca (May 28, 2002)

> Originally posted by <b>Mongoose</b>!
> For any given lottery permutation, the chances are n1/1000 * n2/(1000-n1) * n3/(1000-n1-n2), where n# is the number of ping-pong balls the team in question has at the #th position drawn. For us to drop to #6, we and Orlando both can't be in the top 3. So, you just consider the remaining 11 teams and how they can be in the top 3, which is 11!/8! = 990 permutations.
> 
> Sum up all the permutations, using a computer to add up each possibility, and you get 12.12% as the chance that the top three picks will not be Orlando or Chicago, which is equal to the chance we drop to #6. Not quite single digits, but not high.


    

After a horrible season of basketball you now throw "permutations" at us. You are sick one Mongoose! My head was about to explode from the poor basketball I endured all season......I was just rehabbing, then this!

Very Cold..... 


Just say our odds of getting a top six pick are 100%....much easier for me after this hellish season....

Thank you and I am now putting down my theasurus - Permutations, mutations, deliniations, united nations....nite all


----------



## johnston797 (May 29, 2002)

> Originally posted by <b>Mongoose</b>!
> For any given lottery permutation, the chances are n1/1000 * n2/(1000-n1) * n3/(1000-n1-n2), where n# is the number of ping-pong balls the team in question has at the #th position drawn. For us to drop to #6, we and Orlando both can't be in the top 3. So, you just consider the remaining 11 teams and how they can be in the top 3, which is 11!/8! = 990 permutations.
> 
> Sum up all the permutations, using a computer to add up each possibility, and you get *12.12%* as the chance that the top three picks will not be Orlando or Chicago, which is equal to the chance we drop to #6. Not quite single digits, but not high.


Ding, Ding, Ding!!!

Looks like we have a right answer.

http://www.nbadraft.net/lottery.asp


----------



## DaBullz (Jul 15, 2002)

Just to show how bad we are at losing, we'll probably get the 7th pick.


----------



## LaurenLuvsDaBulls (Apr 20, 2004)

I'm confused.

Let's say Orlando gets the first pick. That would increase our chances for the second pick, no? (would eliminate all the combinations having Orlando getting 2nd-5th)


----------



## DaBullz (Jul 15, 2002)

> Originally posted by <b>LaurenLuvsDaBulls</b>!
> I'm confused.
> 
> Let's say Orlando gets the first pick. That would increase our chances for the second pick, no? (would eliminate all the combinations having Orlando getting 2nd-5th)


You have to figure out the .5% chance Utah gets the 1st pick, too. What are the Bulls' odds of getting 2nd pick then?


----------



## Mongoose (Jun 24, 2003)

> Originally posted by <b>LaurenLuvsDaBulls</b>!
> I'm confused.
> 
> Let's say Orlando gets the first pick. That would increase our chances for the second pick, no? (would eliminate all the combinations having Orlando getting 2nd-5th)


It does seem a little strange that our overall chances of getting the 2nd pick are smaller. You're right, anybody else that gets picked first improves our chances of getting the 2nd pick. However, those are assuming that another team gets the top pick, so you have to also multiply by the chance that happens at all. So, for instance, assuming Orlando gets the top pick, we have a 200/750 = 26.67% chance of getting the top pick in that case. However, the chances that situation happens at all are equal to the chances Orlando gets the top pick, times the chances we get the 2nd pick assuming Orlando gets the top pick, or 25% * 26.67% = 6.67%. (There's some mathematical rule for that, but the name escapes me.) Add up all those scenarios and you end up with the 18.89% chance we have at the 2nd pick.

Another way to think about it is that we have a decent chance at the top pick, and our odds are good enough such that the chance we get the top pick is better than the chance we don't get the top pick _and_ we get the second pick instead.

Or, the more practical way to think of it is, we have a 20% chance at the top pick, a 39% chance at a top 2 pick, and a 56% chance at a top 3 pick. The bigger numbers make people feel better.


----------



## spongyfungy (Oct 22, 2003)

> Originally posted by <b>LaurenLuvsDaBulls</b>!
> I'm confused.
> 
> Let's say Orlando gets the first pick. That would increase our chances for the second pick, no? (would eliminate all the combinations having Orlando getting 2nd-5th)


How about, all the combinations are set and once a team gets the first pick, everything doesn't get reset. Let's say Orlando gets the first pick. 250 balls aren't removed and odds don't improve.


----------



## Mongoose (Jun 24, 2003)

That would make no sense. Why keep Orlando in the drawing when they already have their pick? The NBA may not actually remove Orlando's picks, but they'll redraw if Orlando comes up for the second pick, which essentially removes them from consideration and increases everyone else's odds.


----------



## DaBullz (Jul 15, 2002)

> Originally posted by <b>Mongoose</b>!
> That would make no sense. Why keep Orlando in the drawing when they already have their pick? The NBA may not actually remove Orlando's picks, but they'll redraw if Orlando comes up for the second pick, which essentially removes them from consideration and increases everyone else's odds.


I think you have it right - they redraw if Orlando comes up again. However, I don't think this changes the odds the same as if they removed the ping pong balls for Orlando entirely.


----------



## Mongoose (Jun 24, 2003)

> Originally posted by <b>DaBullz</b>!
> 
> 
> I think you have it right - they redraw if Orlando comes up again. However, I don't think this changes the odds the same as if they removed the ping pong balls for Orlando entirely.


Sure it does. If you have three balls, and one of them is a redraw, then essentially you only have two real choices, so your chances are 50/50. Sure, each ball itself can only come up 33% of the time, but since one of them is a dud, when you're talking about the actual odds that count, it doesn't get taken into consideration. Essentially the odds are 50/50, but you have to redo the draw 33% of the time.

So the same thing applies here. 250 of the balls are invalidated if Orlando gets the 1st pick, so the odds effectively are reduced to out of 750 rather than 1000 for the 2nd pick.


----------

