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View Full Version : So, What does a Draft Pick Get Ya? (Sidebar # 2 - Ping Pong Balls)



count55
05-19-2009, 12:24 PM
A few factoids on the lottery:

This, you pretty much already know, but here are the odds by team and draft position for tonight's lottery:

Exhibit: Odds by Draft Position
http://img134.imageshack.us/img134/7994/09odds.png (http://img134.imageshack.us/my.php?image=09odds.png)

The History - The first lottery was held in 1985 among the 7 teams that did not make the playoffs. Each team had one chance in 7 of being the #1 pick, and the winner of that first lottery was, famously, the New York Knicks, who selected Patrick Ewing. All 7 positions were drawn for ranking.

The same procedure was followed in 1986, but some complaints arose about inequities. In 1985, Indiana and Golden State had finished tied for the worst record in the league. The Pacers picked 2nd, but Golden State picked 7th. In 1986, the Knicks posted the league's worst record but did not pick until 5th.

In 1987, the league changed to picking only the top three, thus guaranteeing for the first time that the team with the worst record would pick no worse than 4th. However, each team still had an equal chance at the top three. The team with the worst record still finished out of the money in two of the three years under this system.

In 1990, the league began weighting the chances of teams (while still picking only the top three), with the worst record of the then-11 lottery teams getting 11 lottery balls and the best record getting just one. Therefore, the team with the worst record had a one in six chance, while the team with the best record had a 1 in 66 chance.

This lasted until 1993, when Orlando scored their second straight #1 pick despite having only one ping pong ball in the hopper. Eyebrows were raised as the league's newest superstar, Shaquille O'Neal, was the beneficiary of a lottery day miracle. The following year, the league moved to the current system using 1000 combinations. The worst record now has a 1 in 4 chance of picking #1, while the best record's chances have dropped to 1 in 200.

The Results - There have been 15 lotteries conducted under more or less the current system (with expansion increasing the number of teams in 1995 and 2005).

The number one pick has gone to the worst record only twice during that time: 2003 (James to Cleveland) and 2004 (Howard to Orlando). Including those two teams, it has gone to "bottom three" teams eight times, or about 53% of the time. The team with the longest odds to win it was Chicago last year, who had a 1 in 59 shot (still better odds than the Orlando win in 1993). Prior to that, New Jersey's 2000 win was the longest shot at about 1 in 23.

The "bottom three" have ended up with the top three picks (in any order) only once, in 1996. The 2007 draft was the only draft in which none of the "bottom three" were drawn for the top three picks.

The Pacers have been in the lottery three times under this system: 1997, 2007, and 2008. There name was not drawn on any of those occasions. They used the 12th pick in 1997 to select Austin Croshere. The 11th pick in 2007 was used by Atlanta, who selected Acie Law, to complete the Al Harrington trade. The 11th pick in 2008 was used to select Jerryd Bayless, who was then traded along with Ike Diogu to Portland for Brandon Rush (the #13 pick), Jarrett Jack, and Josh McRoberts.

The Odds (and Ends)

If your team has the worst record, they are most likely to pick 4th. (While the team with the worst record has the best odds at getting #1, it is only a 25% chance, while the chances of them picking 4th (worst case scenario) is actually 36%.

It does not become more likely than not that your record rank will be the same as your draft position until 7th, when it is a 60% chance that the 7th worst record will pick 7th. This is also the rank where it becomes your most likely draft position.

It is more likely that you will draft worse than your position than better up until the 12th pick. Good news for the Pacers because it is more likely that they will pick in the top three (1 in 45) than 14th (1 in 55). (However, they still have a 24 in 25 chance of picking 13th.)

The odds of the bottom three records getting the top three picks, in any order, are about 1 in 6, while the odds of none of them getting the top three are about 1 in 570.

Edit - The section between the quotes has bad math


The odds of the draft order going in exactly the order listed in the Exhibit above are about 1 in 51,000. In a generic year, with no ties, it gets a little higher at about 1 in 49,000.

Reverse order according to record is not the most likely order. In fact, the most likely order for this year's draft is:

Washington
LA Clippers
Minnesota
Sacramento
Oklahoma City
Memphis
Golden State
New York
Toronto
Milwaukee
New Jersey
Charlotte
Indiana
Phoenix

At about 1 in 26,000 chances. In a generic year (no ties), the most likely order is (records, worst to best):

2, 3, 5, 1, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14

I didn't go back very far, and these numbers are just a little (tiny bit) off, but the odds for the orders from the last four drafts:

2004 - 1 in 74,000
2005 - 1 in 139,000
2006 - 1 in 5.6 million (none of the bottom three in the top three)
2007 - 1 in 5.3 million (Chicago nabbing the #1)

So, there are two morals to this story:

1. Whatever you think will happen tonight, odds are, it won't.

2. I really shouldn't be allowed access to the internet and Excel/Access at the same time.

Cheers.

Los Angeles
05-19-2009, 12:30 PM
One little tiny nit-pick. When using the "1 in XXX" method, it's is preferred to use the term "chances".

If the chances are 1 in 10, the odds would be 1:9.

:nerd:

Trader Joe
05-19-2009, 12:33 PM
Count when I learned Access freshman year of college I always wondered when I would need to use it. Now I know.

count55
05-19-2009, 12:35 PM
One little tiny nit-pick. When using the "1 in XXX" method, it's is preferred to use the term "chances".

If the chances are 1 in 10, the odds would be 1:9.

:nerd:

Hmmm...I even switched in mid-post...

What are ****ing odds of that?

SoupIsGood
05-19-2009, 12:37 PM
Holy crap. I had no idea how crazily some of this stuff was weighted. That was awesome.

Los Angeles
05-19-2009, 12:39 PM
Hmmm...I even switched in mid-post...

What are ****ing odds of that?

Even money.

PacerScout
05-19-2009, 01:01 PM
I made this argument on RealGM. I know that Stern doesn't rig the lottery, but if he did we would be a prime candidate to give a top 3 pick to.

Right now we are in financial trouble. Well, we aren't a free agent signing team, so obviously the thing that would generate the most buzz and possible ticket sales here in Indy is to have the Pacers end up with a top 3 prospect.

That would sell a lot of tickets considering we haven't had a top 3 pick in what 20 years?...

rexnom
05-19-2009, 01:06 PM
So what you're saying is that there is a chance...:-p

2.2% - Nice

BillS
05-19-2009, 01:14 PM
Hmmm...I even switched in mid-post...

What are ****ing odds of that?

"One in a million chances crop up nine times out of ten." - Terry Pratchett

docpaul
05-19-2009, 01:18 PM
So what you're saying is that there is a chance...:-p

2.2% - Nice

http://jimmyakin.typepad.com/photos/uncategorized/child_praying_1.jpg

This town would go nuts if luck went our way tonight.

count55
05-19-2009, 01:41 PM
"One in a million chances crop up nine times out of ten." - Terry Pratchett

Well...


Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Heads.

Bet?

Heads I win.

Again...

Heads.

Heads.

Heads.

Heads.

Heads.

Whoops!

It must be indicative of something
besides the redistribution of wealth.

Heads.

A weaker man might be moved
to re-examine his faith,

for nothing else at least
in the law of probability...

Heads.

Consider.

One,

probability is a factor which
operates within natural forces.

Two, probability is not
operating as a factor.

Three, we are now held within um...

sub or supernatural forces.

Discuss!
What?

Look at it this way.
If six monkeys...

If six monkeys...

The law of averages,
if I have got this right means...

that if six monkeys were thrown
up in the air long enough...

they would land on their tails
about as often as they would
land on their...

Heads, getting a bit of
a bore, isn't it?

A bore?
Well...

What about the suspense?

What suspense?

It must be the law
of diminishing returns.

I still spell about to be broken.

Well, it was an even chance.

Seventy eight in a row.
A new record, I imagine.

Is that what you imagine?
A new record?

No questions?
Not a flicker of doubt?

I could be wrong.

No fear?
Fear?

Fear!

Seventy nine.

I think I have it.
Time has stopped dead.

The single experience of one coin
being spun once has been repeated.

A hundred and fifty six times.

On the whole, doubtful.

Or, a spectacular vindication
of the principle.

That each individual
coin spun individually is...

as likely to come down
heads as tails

and therefore should cause no
surprise each individual time it does.

Heads...
I've never known anything like it.

He has never known
anything like it.

But he has never known
anything to write home about.

Jonathan
05-19-2009, 01:47 PM
I would love if I turned on the tube tonight and saw Buster Douglas representing the Pacers.

naptownmenace
05-19-2009, 03:32 PM
Wait, so the draft lottery is tonight? Man, I'm really slipping. I thought it was the 24th or something.

Checks online.... Yep it's tonight. Cool. Here's hoping the Pacers finally get the number one pick.

binarysolo
05-19-2009, 04:24 PM
At about 1 in 26,000 chances. In a generic year (no ties), the most likely order is (records, worst to best):

2, 3, 5, 1, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14



How does that work out? I'm no statistics expert, but the way I see it:

%chance of 1, 2, 3:

250 / 1000 * 178 / (1000 - 250) * 177 / (1000-250-178) * 100 = 1.836%

%chance of 2, 3, 5:

178 / 1000 * 177 / (1000 - 178) * 76 / (1000 - 178 - 177) * 100 = 0.452%

Shade
05-19-2009, 04:34 PM
I think a lot of you are going to be horribly disappointed this evening.

Trophy
05-19-2009, 04:39 PM
I'm not having my hopes high on Adam Silver announcing us picking lower than 13.

Los Angeles
05-19-2009, 04:51 PM
I'm not having my hopes high on Adam Silver announcing us picking lower than 13.

We can only go down one spot and in a draft this flat in talent, there little to no difference between the 13th and 14th pick. Let the Suns rain on our day, it will only be a drizzle and we'll live.

Trophy
05-19-2009, 04:55 PM
We can only go down one spot and in a draft this flat in talent, there little to no difference between the 13th and 14th pick. Let the Suns rain on our day, it will only be a drizzle and we'll live.

I meant to say a higher pick in the draft.

count55
05-19-2009, 05:04 PM
How does that work out? I'm no statistics expert, but the way I see it:

%chance of 1, 2, 3:

250 / 1000 * 178 / (1000 - 250) * 177 / (1000-250-178) * 100 = 1.836%

%chance of 2, 3, 5:

178 / 1000 * 177 / (1000 - 178) * 76 / (1000 - 178 - 177) * 100 = 0.452%

Yeah...now that you mention it, this is probably wrong.

Basically, I was operating under the premise that the most likely outcome for the worst record was 4th, then I chained based on the most likely available outcome for all of the other picks, ignoring the fact that there would reach a point in time where the outcome for the remaining picks would become 100%.

In other words, I mistakenly started with where it was most likely for the worst record to pick, rather than who was most likely to get the first pick.

This means that the draft order odds from 2004 through 2007 are probably incorrect. I probably didn't appropriately factor in the fact that one result precludes other results, altering the odds.

But, then, I only took one statistics class in college, it was in summer session, and the teacher was a student teacher whose *** I kicked in flag football a couple of years earlier. And when I say I kicked his ***, I mean he clotheslined a friend of mine, and I knocked three of his teeth out.

It was not a productive class.

DrFife
05-19-2009, 05:12 PM
Nice review, Count; thanks!

If we don't land the #1 pick, I'm sort of hoping Minnesota (where I used to live) or the Clippers get it. Why? Because they're two teams who already are pretty well set at PF ... so if they do pick first, we'll be seeing an interesting trade by draft night. Chris Kaman, anyone?

(I'm not sure what the TWolves would do with the #1. I suppose they'd take Griffin and keep everyone long enough to try things out -- at least to make sure Al Jefferson is healthy again -- but Thabeet would fit their roster really well. They could trade down to #3 ... plus, they've got #18 and #28 as well.... Whooo-wee! Glen Taylor's new GM could be ready for some wheelin' & dealin'!)

ABADays
05-19-2009, 09:58 PM
What time is it supposed to be?