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Lotteries, the NBA draft, and probability

 
 
Reply Tue 19 May, 2009 07:32 pm
A question of how numbers and randomness work.

The NBA draft lottery is weighted so that teams with worse records have a greater chance of getting an early draft pick.

Right now, they do this by drawing first for the first pick, then the second pick, and so on, with worse teams having a greater of being drawn.

But this has no drama. The top pick is determined first, and everything after that is anticlimatic. (For this reason, the selection process is done behind closed doors, then the picks announced in reverse order for the benefit of television.)

But what if you gave the event a real-time dramatic arc? What if you chose the lottery picks in order from last to first, with the worst teams having the lowest likelihood of being drawn each time?

How would the results of this process differ from the way it's done now? You can rig the numbers so that, say, the very worst team still has a 1 in 4 chance of landing the top spot (as is now the case), but would the likelihood of a team that just missed the playoffs landing, say, the number 5 pick be any different?

Any of you folks got a good enough feel for statistics and probability to suss it out?

(It could be done through brute force of computation, of course, but who's got the time?)
 
Shapeless
 
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Reply Tue 19 May, 2009 08:13 pm
@patiodog,
Quote:
What if you chose the lottery picks in order from last to first, with the worst teams having the lowest likelihood of being drawn each time?


Does that mean that the team with the best record, which under the current system would be among the last teams to choose from the available prospects, will now choose first? Wouldn't that mean that the best teams will have first choice at the best prospects? I thought that the point of the current system was to help bad teams improve their lot by giving them first choice of the prospects. Wouldn't your system increase the likelihood that bad teams will stay bad and good teams stay good?
panzade
 
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Reply Tue 19 May, 2009 08:15 pm
@Shapeless,
Rolling Eyes ...you really got to read more carefully shapeless Laughing
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Shapeless
 
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Reply Tue 19 May, 2009 08:18 pm
I read the post many times, trying to make sense of it, and freely accept the possibility that I misread it. That is why I asked the question. I invite anyone to explain it to me. How would Patiodog's proposal work in practice?
Shapeless
 
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Reply Tue 19 May, 2009 08:25 pm
I think what's hanging me up is that I thought the order of picks was revealed simultaneously on the night of the draft rather than in order from top to bottom. That's how I remember it working several years ago, which was the last time I actually watched the draft rather than just read about it the next day. If they've since changed it, then that might make more sense.
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patiodog
 
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Reply Tue 19 May, 2009 09:29 pm
@patiodog,
Well, to be more simple.

The way it is now, they draw for the first pick first. 1 in 4 ping pong balls belongs to the team with the worst record. 1 in 100 (or so) belongs to the team in the lottery with the best record. So the worst team in the lottery has a 25% chance of getting the first pick, whereas the best team in the lotter has a 1% chance. The rest of the teams are stratified in between, according to their relative successes.

My proposal is that you draw for the last pick first, with the system similarly rigged in favor of the bad team. So, give the best team a 25% chance of being stuck with the worst pick and the worst team a 1% chance of being stuck with the worst pick.



I tried to work out the numbers to see what the odds would have to be for the worst team to still have about a 1 in 4 chance of ending up with the first pick, but I couldn't suss out the statistics.

The main question is whether the draft order would end up looking pretty much the same over time using the two different methods, or whether there'd be some inherent difference in the results. Because they really would be different processes -- in the present system, the worst team has just a crap shoot with pretty good odds of landing the top pick straight off, whereas in my proposal the worst team would have to not have their number drawn (albeit at very long odds) 14 or 15 consecutive times, with the likelihood of being drawn increasing each time as other teams are removed from the pool.
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panzade
 
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Reply Tue 19 May, 2009 10:49 pm
@Shapeless,
sorry about my reply shapeless...it was tacky...i'm glad you came back and got patiodog to clarify his request
patiodog
 
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Reply Wed 20 May, 2009 05:40 am
@panzade,
But no Good Will Hunting types to clue me in on the mathematics of it? Alas, alack, and ajax...
patiodog
 
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Reply Wed 20 May, 2009 06:21 am
@patiodog,
Remembering now that they only draw for the top 3 picks.


Damn it.
Setanta
 
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Reply Wed 20 May, 2009 06:29 am
Time and again, top draft picks (in all sports) have failed to lived up to their promise, while walk-ons have become superstars. In this particular scenario, the differences between the "worst" pick and the "best" pick are so small (except in those rare cases of a Larry Bird or a Shaquille O'Neal) that this appears to me to be much ado about nothing. In football, teams maintain large squads, and draft lots of players. In basketball, so few people are drafted, from such a large pool of talent, that i don't think there's any point in worrying about how the players are drafted.
joefromchicago
 
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Reply Wed 20 May, 2009 08:44 am
@patiodog,
Well, first of all, the NBA lottery only determines the top three draft positions. All of the rest are determined by the previous season's won-lost record.

Right now, the lottery is, in effect, picking one number out of a pool of one thousand (it's actually a lot more complicated than that, but I'm not sure why). The worst team has a 250/1000 chance to get the first pick, the second-worst team has a 199/1000 chance, and so on. Once a number is drawn, it is not replaced. If a team that has already been drawn is drawn again, that result is ignored and a new number is drawn. That means that a team's chances of being picked improve as the drawing progresses. For instance, if the second-worst team gets the first pick, then the worst team has a 250/801 chance of being picked second, since the second-worst team's 199 numbers are all withdrawn from the pool.

The problem with picking from third to first rather than first to third is that the league would have to recalculate the odds after every draw. If the league wanted to make it easier for the third-worst team to get the third pick, the second-worst team to get the second pick, and the worst team to get the first pick -- in that order -- it would have to perform some serious recalculations at each step. Frankly, I'm not entirely sure it could be done, given the nature of the lottery and the league's objectives.

The way that the league does it now is far, far easier and probably fairer than doing a reverse-order draw.
Shapeless
 
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Reply Wed 20 May, 2009 09:36 am
@panzade,
No harm done. It occurs to me that the draft I was thinking of--the last one I watched in its entirety on TV--was the 1993 draft. That was the one in which the Orlando Magic, having gone 41-41 the previous season and missing the postseason on the most miniscule of technicalities, had the least chance of landing the top pick with only one ping-pong ball in the machine. Improbably, they landed the top pick.
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Region Philbis
 
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Reply Wed 20 May, 2009 10:21 am
@Setanta,
Quote:
(except in those rare cases of a Larry Bird or a Shaquille O'Neal)
this is one of those years where the top pick (blake griffin) is highly sought after...
Setanta
 
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Reply Wed 20 May, 2009 11:43 am
@Region Philbis,
Sure, Boss . . . i was just pointing out that in regard to PPD's general principle, it doesn't really matter, because there are so few drafted (hundreds at least, perhaps thousands of schools out there with basketball teams, but only 30 teams with such small rosters) in comparison to football or baseball, sports in which the teams maintain large rosters. Many small schools can't afford a football program, or a baseball program, but most schools can afford and do have a basketball program.

Anyway, Patiodog is a bad man and we shouldn't encourage him to think for himself . . .
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Thomas
 
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Reply Wed 20 May, 2009 12:19 pm
@patiodog,
How are the balls weighed in the lotteries for the second and the third picks? The same as in the lottery for the first pick?
patiodog
 
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Reply Wed 20 May, 2009 06:13 pm
@Thomas,
Thomas -- I'll refer you to joe-from-chi's response above.

My curiosity was more about the statistical implications of the exercise rather than the basketball implications.

(Though, if you look at the list at -- http://www.nba.com/history/top_picks.html -- I'd say about half of the number one picks were or look like they are going to be first-rate players. That number would be better except for the continuing insistence on trying to draft centers or multi-tool power forwards first, even though NBA basketball isn't really a big man's game any more. I mean, Michael Olowakandi? I saw him play in person when he was at UOP, and I was profoundly underwhelmed. Not sure what they Clips' scouts saw in him, except that he was 7 feet and could walk and chew gum at the same time (on a good day). Even so, I doubt that, historically, you'll consistently find that level of talent at, say, the 20th pick. I think a quick glance here -- http://www.nba.com/history/draft_top13.html -- bears that out somewhat, though that time period does encompass the recent obsession with 7-footers with no demonstrated savvy for the game.

(Go Derrick Rose, by the way, and go Bulls for drafting a PG with the no. 1.)

)


Was more curious if you could run it in reverse order and still maintain more or less the same odds for the team in each lottery position to land the position that it's "suppose" to land according to the NBA's goals -- without rejiggering the odds after each draw.

But I'd stupidly forgotten how the lottery actually works, largely because, as set has noted, it's not all that important, and I don't usually pay attention to it...
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joefromchicago
 
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Reply Wed 20 May, 2009 06:37 pm
If the league wanted to put all fourteen teams in the lottery, then reversing the order of the draw would be no problem at all: it would simply reverse the odds for the teams. Thus the fourteenth-worst team would have a 250/1000 chance to get the first pick, the thirteenth-worst team would have a 199/1000 chance, and so on, down to the worst team, which would have a 5/1000 chance (a table of odds can be found here). The problem arises in the current system because reversing the order would mean starting in the middle rather than starting at one end or the other.
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Robert Gentel
 
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Reply Thu 21 May, 2009 01:04 am
@joefromchicago,
joefromchicago wrote:
The way that the league does it now is far, far easier and probably fairer than doing a reverse-order draw.


To add to this point, the objective of the lottery is to discourage teams from throwing games to get a franchise player in the draft.

The draft is never deep enough where this should matter beyond the first few picks. It may be worth throwing games for a Tim Duncan, but it's rarely worth it beyond the first few picks (usually just the first one) and even if there's a gem lower in the draft the team that figured that out usually doesn't need to throw games to get them and even if they did there are too many previous picks to make it a sure thing.

If I were tweaking this, I'd make it even less likely that the worst team gets the top pick. I do think San Antonio threw games (by benching David Robinson more than needed) to get Duncan.
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