Lotto odds

[ishmael]

Following wins by the Celtics and Lakers last night, there is a bit of separation between the three worst teams (Milwaukee, Philly and Orlando) and the next four teams (Boston, Utah, Sacramento, LAL) who are all within one loss of each other.
 
 
Here is the NBA draft lottery process:
http://en.wikipedia.org/wiki/NBA_draft_lottery#Process
 
It is worth noting that in 83% of all possible scenarios the 4th seed will get a pick in the top 5. Meanwhile 82% of the time the 7th seed will pick 7th or 8th.
 
Looking at this year's draft, that looks like a serious drop off in talent.
 

 

[Brickowski]

After the last regular season game has been played, someone should recompute these numbers based on the assumption that the Lakers will get the #1 overall pick.

 

[reggiecleveland]

I will bet the Lakers end up with one of the first three picks. Fix is in.

 

[oumbi]

I will bet the Lakers end up with one of the first three picks. Fix is in.

And the proof being...?

 

[wutang112878]

The Patrick Ewing draft

 

[Brickowski]

Not just Ewing.   The fact that Dan Gilbert was compensated twice for losing LeBron.  The 2011 #! pick was a 19.9% chance; the 2013 pick was a 15.6% chance and the compound probability of getting two #1 picks in those years was a little over 3%.  Then in 2012 Tom Benson is rewarded for taking the Hornets (now Pelicans) off the league's hands.  That was a 13% chance.
 
Does anyone know if Stern had his thumb on the scales?  No.  But the circumstantial evidence is there.  Meanwhile, the league needs a strong Laker franchise for marketing purposes, and the Kobe farewell tour will be pretty pathetic if the team only wins 20-25 games in his final year.

 

[moondog80]

Not just Ewing.   The fact that Dan Gilbert was compensated twice for losing LeBron.  The 2011 #! pick was a 19.9% chance; the 2013 pick was a 15.6% chance and the compound probability of getting two #1 picks in those years was a little over 3%.  Then in 2012 Tom Benson is rewarded for taking the Hornets (now Pelicans) off the league's hands.  That was a 13% chance.
 
Does anyone know if Stern had his thumb on the scales?  No.  But the circumstantial evidence is there.  Meanwhile, the league needs a strong Laker franchise for marketing purposes, and the Kobe farewell tour will be pretty pathetic if the team only wins 20-25 games in his final year.

 
Being awarded the first pick in the 2013 draft was punishment, not compensation.

 

[RG33]

Not just Ewing.   The fact that Dan Gilbert was compensated twice for losing LeBron.  The 2011 #! pick was a 19.9% chance; the 2013 pick was a 15.6% chance and the compound probability of getting two #1 picks in those years was a little over 3%.  Then in 2012 Tom Benson is rewarded for taking the Hornets (now Pelicans) off the league's hands.  That was a 13% chance.
 
Does anyone know if Stern had his thumb on the scales?  No.  But the circumstantial evidence is there.  Meanwhile, the league needs a strong Laker franchise for marketing purposes, and the Kobe farewell tour will be pretty pathetic if the team only wins 20-25 games in his final year.

The Cavs had the 2nd best and 3rd best odds of landing the top pick in the draft in 2011 and 2013 respectively. The BEST odds are only 25%, or looked at another way, a 75% chance of NOT getting the top pick. Let's keep the conspiracy theories in the Malaysian Air 370 thread.

 

[Brickowski]

 
Being awarded the first pick in the 2013 draft was punishment, not compensation.

Not if they had taken Oladipo.

 

[Stitch01]

I love lottery conspiracy theories, but anyone have an answer as to how and why Ernst and Young would put their whole business at risk to audit a rigged lottery?
 
Like that 3% compound probability number sounds suspicious until you realize the best possible compound number (both worst teams hitting the first pick) is just over 6%

 

[Brickowski]

Ernst and Young?  Pay them enough and they'll do all kinds of interesting things.  Just ask the SEC.  In fact, the elaborate, publicized audit procedures remind me of all of those rigged quiz shows in the 1960's, where they did exactly the same thing.
 
Hey, maybe the officials are all honest and competent and the draft lottery isn't rigged.  But maybe they're not.  As for the compound probability figure, what is the compound probability of ANY team getting two number ones in three years, with another suspicious result (the Pelicans) sandwiched in-between?

 

[Stitch01]

Wow, conspiracies everywhere! 
 
Needless to say, these are fun entertainment stories but the NBA lottery is 100% not rigged.

 

[Brickowski]

Wow, conspiracies everywhere! 
 
Needless to say, these are fun entertainment stories but the NBA lottery is 100% not rigged.

If the Celtics get the #1 overall pick this year, I too will be convinced it isn't rigged.

 

[Jed Zeppelin]

If the Celtics get the #1 overall pick this year, I too will be convinced it isn't rigged.

 
And fans of every other team will be convinced it is.

 

[RG33]

Ernst and Young?  Pay them enough and they'll do all kinds of interesting things.  Just ask the SEC.  In fact, the elaborate, publicized audit procedures remind me of all of those rigged quiz shows in the 1960's, where they did exactly the same thing.
 
Hey, maybe the officials are all honest and competent and the draft lottery isn't rigged.  But maybe they're not.  As for the compound probability figure, what is the compound probability of ANY team getting two number ones in three years, with another suspicious result (the Pelicans) sandwiched in-between?

Just stop dude. They are not "suspicious results". The highest odds any team has is 25%. A team with the 4th highest odds of 13% as you note getting the first pick is NOT suspicious in any form or fashion.

 

[Stitch01]

Hey, maybe the officials are all honest and competent and the draft lottery isn't rigged.  But maybe they're not.  As for the compound probability figure, what is the compound probability of ANY team getting two number ones in three years, with another suspicious result (the Pelicans) sandwiched in-between?

Pretty low.
 
What are the chances of the team with the worst record winning three years in a row?  1.6%.  Literally every possible outcome is a rarity.

 

[bowiac]

The odds of a team winning the lottery twice in three years obviously depend on how bad that team is. In the abstract, the odds could be pretty high however. Start the clock in 2014 for instance - lets call that team Team2014. What are the odds that Team2014 wins the lottery again in 2015 or 2016? Well, if they're the worst team in the NBA, then they're .75 not to win in 2015, and .75 to not win in 2016. What are the odds they miss both times? 56.25%, which means a 43.75% chance of it happening. 
 
Further, lets say Team2014 doesn't win in 2015, but Team2015 does. Now what are the odds that either Team2014 or Team2015 win in 2016? They could be at high as about 45% if those are the two worst teams. So now we're looking at a 58.7% chance of it actually happening.
 
Now, this is super favorable, assuming our teams are consistently the worst teams in the NBA. The actual odds drop off a lot if they're not. On the other hand, this is for a tiny 3 year set. There is of course a constant rolling 3 year sample going on here. What if Team2014 or Team2015 was actually the Cavs (the 2013 winners?) There're as high as a 43% chance of that being the case too.
 
Unless the question was "what are the odds the Cavaliers would win twice in 2011-2013", then the odds are actually probably not so terrible. A team winning twice in three years is going to happen with some real frequency.

 

[Brickowski]

I don't understand your math, Bowiac.  The odds of missing both times isn't the issue.  The odds of hitting twice in 3 years is what is at issue.  Plus the Cavs didn't have the worst record in either of those years.

 

[bowiac]

I don't understand your math, Bowiac.  The odds of missing both times isn't the issue.  The odds of hitting twice in 3 years is what is at issue.  Plus the Cavs didn't have the worst record in either of those years.

In order to calculate the odds of them hitting in either 2015 or 2016, you need to multiply the odds of them missing in each year. 
 
As I said, the math gets worse when they don't have the worst record, but there are many many three year spans at work as well. 2011-2013 isn't the only possible three year span.

 

[snowmanny]

During the Ewing lottery I remember offering to bet my brother at 3:1 odds that the Knicks would win. He wouldn't take it. Once we see where the Lakers finish we can all make Jimmy Fund bets.

 

[wilked]

Sixers have 5 losses to go to set a new record for consecutive losing streak (currently at 21).  I wouldn't bet against them...
 
They have:
Bulls
Knicks
Bulls
Spurs
Rockets
 
Bulls will win both games by 10+, West teams will destroy them, and Knicks have won 6 in a row.  

 

[reggiecleveland]

The league is in the Lakers pocket. Guys force themselves to be traded to the Lakers, etc. If it was uncovered the guys doing the job would take the fall. I expect the Lakers to get a top three pick. If nothing else it is the crap luck they always get.

 

[ALiveH]

I thought I saw Vegas sportsbooks have lines on who will win the lottery, so you could always put your money where your mouth is if you believe in conspiracies...  I'm agnostic - as a rule I don't believe conspiracies without proof, but wouldn't be surprised at all if it comes out later it was rigged.

 

[lexrageorge]

If something has a 3% chance of occurring, and actually happens, that is hardly evidence of a fix.  The reality is that going into 2013, they had a 15.6% chance of getting the top pick; that's not an unheard of probability; what happened in 2011 has no bearing on the forward looking probability; the system has no memory.  Some team is going to win the lottery, and 3 teams will have a top 3 pick.  
 
The randomness of the lottery is what makes it work; unfortunately, it also causes some surprise outcomes, and the general public cannot comprehend mathematical explanations of probabilities, so the conspiracy theories flourish.  What's forgotten is that a conspiracy requires more than 1 person, and something like this would require a lot of people; eventually, the pig squeals, or someone gets sloppy, and the facts come out.  That hasn't happened in all the years of the draft lottery.  
 
Having said that, I would still bet on the Lakers securing a Top 3 pick; if not, whomever they select will turn into the generational player of this draft anyway, so it really doesn't matter. 

 

[caminante11]

I don't believe in a fix and even if there was I can't see the Lakers being favored. After all they were the team prevented by the league from getting Chris Paul a few years ago.

 

[Tony C]

Right, in L.A. the conspiracy theorists all believe that the league has stacked the deck against the Lakers by changing the CBA to their detriment and vetoing the Chris Paul trade. Both conspiracy theories are lame, but at least Lakers fans can point to some actual tangible action against their interests by the league.

 

[The Social Chair]

Going to echo the last two comments. The Chris Paul veto was the most ridiculous thing the league has done to a team in decades.

 

[Grin&MartyBarret]

Nobody remembers this now, but that original Lakers-Rockets-Hornets deal had Dragic going to New Orleans. Hard to argue that Martin, Scola, and Dragic isn't way better than Eric Gordon and Aminu.

 

[wutang112878]

I love lottery conspiracy theories, but anyone have an answer as to how and why Ernst and Young would put their whole business at risk to audit a rigged lottery?

 
Missed this earlier, but do you think the running of the NBA lottery would really affect EY's core business?  If something happened they could pretty easily dump the blame on the NBA and exit the lottery business considering it generates miniscule revenue for them.  Thats why I always considered it a joke that 'EY running the lottery' somehow gave it more credibility, they truly dont care and they know they are just being paid to create a facade of legitimacy for the NBA.

 

[Stitch01]

Its a super profile assignment that's pretty damn easy to audit.  As you rightly point out, they're doing it for advertising, not for revenue.  Would be pretty stupid to take the assignment if the lottery was rigged. 
 
"Putting their whole business at risk" was overstating for effect, but the NBA lottery they audited being rigged would cost them a lot of money and get highly paid people fired.  Seems pretty likely they are doing the somewhat trivial task of making sure the lottery isnt rigged.

 

[scottyno]

Nobody remembers this now, but that original Lakers-Rockets-Hornets deal had Dragic going to New Orleans. Hard to argue that Martin, Scola, and Dragic isn't way better than Eric Gordon and Aminu.

in that scenario though they're probably too good to get Davis and Noel and are worse off today

 

[Carmine Hose]

Has anyone else played the ESPN lotto machine?  My first two attempts had Celtics picking 2nd and then 1st.  Stopped right there.

 

[riboflav]

Has anyone else played the ESPN lotto machine?  My first two attempts had Celtics picking 2nd and then 1st.  Stopped right there.

 
I just played an even dozen. Celts never picked better than fifth.

 

[bsj]

5 times..celts picked 3rd a couple times, which I would be fine with...5th twice and then 6th.

 

[Morgan's Magic Snowplow]

As we approach the last 10 games of the season, it seems like the bottom three are basically set at Milwaukee, Philly, Orlando.  The Celts are currently tied with the Jazz with 23 wins, the Lakers have 24, Kings have 25, and Pistons have 26, so spots 4-8 in the lotto order are still TBD.
 
The Celtics have one of the softest schedules of any of those teams, especially the final eight, which consists of some games that will be very tough to lose (2X PHI) as well as some other games that are unfortunately very winnable (2X WAS, CHA, @DET, @ATL, @CLE).  Even if we assume losses tomorrow @TOR and in the CHI back-to-back, going 4-4 or 5-3 down the stretch seems like a real possibility, which could totally fuck us.  Detroit is probably far enough ahead and also has enough soft games that we are unlikely to catch them.  But passing Utah, the Lakers, and Sacto - all of which play  mainly tough Western Conference teams down the stretch - seems like a real possibility unless the Celtics really go into tank mode.
 
What do you guys see happening here?  Will Danny hold out a few more players due to "injuries"?  Will he just let the chips fall where they may?  It'll be pretty disappointing to have to go through this awful season and then still end up picking 7th or 8th.

 

[wilked]

Sixers have 5 losses to go to set a new record for consecutive losing streak (currently at 21).  I wouldn't bet against them...
 
They have:
Bulls
Knicks
Bulls
Spurs
Rockets
 
Bulls will win both games by 10+, West teams will destroy them, and Knicks have won 6 in a row.  

Only the Rockets to go and they tie the record
 
Milwaukee is feeling the heat and answered the call by losing the last 8.  With about 10 games to go the Sixers still need to make up two games...they are making a helluva run, but I think the Bucks hold them off
 
-----------------
I looked at schedules, and looked at opponents with <30 wins.
 
Sixers: Detroit, Celtics, @Celtics
 
Bucks: Lakers, @Detroit, Cleveland
 
If the Bucks can get through tonight without a win I think they got it.  Celtics will lose one of those two to the Sixers in a battle of wills

 

[Jed Zeppelin]

Checked the box score this morning wondering how the Lakers could lose to MIlwaukee and found out that Pau Gasol is out for the time being with vertigo. Well played, Lakers, well played. Sometimes the other guys just want it more.

 

[wilked]

Philly is just one game out now...  Big swing last night

 

[Devizier]

I hope Philly and Milwaukee get bumped from the top 3.

 

[PC Drunken Friar]

Those Phili-Celtics games might be the most entertaining games if the season.

 

[Nick Kaufman]

I think Milwaukee is legitimately as bad as their record suggests but I really hope Philly has pissed off the lottery gods. There's no excuse for losing 26 straight games in such a watered down league. They will probably be the new poster child for tanking.

 
Have you checked their roster recently?

After shipping Turner and Hawes they look putrid.

 

[Nick Kaufman]

Also, this chart is handy on the kind of probability each spot gives.
 
http://en.wikipedia.org/wiki/NBA_draft_lottery#Process
 
Right now, if the Celts finish with the forth worst record, they ve got a 52% chance of picking 5 to 7. They will have around a 37% to get a top 3 pick though and an 12% shot at no 1. They only have a 10% chance of picking no 4.

With the fifth worst record their shot at a top 3 drops to 29% while there is a 70% of picking from 5 to 7.
 
So, it's a big tanking battle with Utah right now for that fourth spot and our schedule seems far easier, i.e. worse.

 

[Devizier]

What if the NBA used actual win loss totals to determine the lottery seed, as opposed to rank order in records? Right now, the curve is too steeply favoring terrible teams. A loss for Philadelphia or Milwaukee is worth a lot more than a loss by anyone else.

 

[j-man]

LA or Utah will get the 1 my gut feeling with milwaukee 2 phily \ utah 3 LA Boston or Utah 4 if i had to plck a order 1 LA 2 milwaukee 3 phily 4 utah 5 orlando 6 boston 

 

[wilked]

LA or Utah will get the 1 my gut feeling with milwaukee 2 phily \ utah 3 LA Boston or Utah 4 if i had to plck a order 1 LA 2 milwaukee 3 phily 4 utah 5 orlando 6 boston 

please let us know if your gut feeling changes...

 

[wilked]

At this point there are 8 teams vying for the top 5 spots.  The top 2 spots are locked up by PHI and MIL, and at this point MIL has to have a 2:1 edge at least with a 2 game lead and 9 to go.  I threw those 8 teams into a table below and noted how many times each plays the other.  
 
Here's the bad news: Celts play these bottom-feeders three more times in their final 10 games, Philly twice and Detroit once.  They also have a game in hand (as do the Lakers).  Orlando, on the other hand, has no games against this collective 8 and thus is almost certain to lock up that #3 spot.
 
The 4-8 positions realistically could go any which way, not easy to predict.  For the Celtics to be top 5 they cannot sweep the Sixers.  

Team	Losses	Wins	Games Rem	xPlaying Each Other
MIL	59	14	9	         1
PHI	57	16	9	         2
ORL	52	21	9	         0
UTAH	50	23	9	         2
BOS	49	23	10	         3
LAL	48	24	10	         1
SAC	48	25	9	         2
DET	47	26	9	         2

 

[j-man]

why i have the Lakers 1 btw not a lakers fan i lean toward the knicks only because their NBA blog on SB Nation is funny and anything goes their it a gut feeling like i said up top funny things happen in the lottery also brad stevens is a outstanding coach

 

[Tito's Pullover]

What if the NBA used actual win loss totals to determine the lottery seed, as opposed to rank order in records? Right now, the curve is too steeply favoring terrible teams. A loss for Philadelphia or Milwaukee is worth a lot more than a loss by anyone else.

Interesting, but if I understand you correctly, I think such a solution would even out the odds a bit too much, to the point that the lottery would almost be even money for the worst ten teams or so.

My interpretation was that you wish to weigh team losses when determining draft probabilities. Here's how that would shake out:

"Current Win %" is each current lottery team's win percentage as of this post, and "Proj. Loss Total" is the number of losses the team will have at the end of the year, at their current pace. "Current Prob." shows you the probability of that team securing the number one pick in the current system and "Loss-Weighted Prob." shows the probability based on each team's projected loss total. The "Diff." column is how the two numbers compare.

Milwaukee would lose 60% of their lottery balls, and their chance of winning the #1 pick would not be significantly higher than the Lakers or Kings.  Dallas, a team way above .500 that happens to play in a highly competitive conference, would get half the chances that Milwaukee has (as they would finish with half the number wins) and see their actual number of ping pong balls increase ninefold.

 

[Devizier]

Interesting, but if I understand you correctly, I think such a solution would even out the odds a bit too much, to the point that the lottery would almost be even money for the worst ten teams or so.

My interpretation was that you wish to weigh team losses when determining draft probabilities. Here's how that would shake out:

"Current Win %" is each current lottery team's win percentage as of this post, and "Proj. Loss Total" is the number of losses the team will have at the end of the year, at their current pace. "Current Prob." shows you the probability of that team securing the number one pick in the current system and "Loss-Weighted Prob." shows the probability based on each team's projected loss total. The "Diff." column is how the two numbers compare.

Milwaukee would lose 60% of their lottery balls, and their chance of winning the #1 pick would not be significantly higher than the Lakers or Kings.  Dallas, a team way above .500 that happens to play in a highly competitive conference, would get half the chances that Milwaukee has (as they would finish with half the number wins) and see their actual number of ping pong balls increase ninefold.

 
You can still bias the chances. For example, you could have a team's number of balls determined by the following formula:
 
Balls = Loss total - 41
 
Teams that are at or better than .500 get no balls -- they're slotted according to their record (sorry Minnesota, Dallas).
 
In this scenario, Milwaukee gets 25 balls (17.2%), Boston gets 15 balls (10.3%), New York gets 7 balls (4.8%), etc.
 
The spread still favors the bad teams noticeably but the incentives for tanking are greatly diminished.
 
There are other ways you could adjust the odds, using exponents or what not, but this is much simpler.

 

[wutang112878]

This certainly reduces the advantage of tanking but it doesnt eliminate it, the more losses you get the better your odds the relationship between losses and chances just changed slightly. 
 
One option is the Celts suggested rotating lottery system, where you get a specific pick each year with a specific schedule.
 
You could also just scare the crap out of teams and just say that everyone who doesnt make the playoffs has the same odds.  You could do a hybrid where everyone has the same odds but (after ranked by # of losses) you can only move down 5 slots.  So if you should have got the #1 pick based on losses the worst you can do is the #6  I think that might be enough because it seems the big draw to tanking is to get one of those top 3-5 picks and teams are looking for a franchise changer.  Or something real simple where top 5 is lottery based with no move down protection, and the rest is determined in order of most losses. 
 
If you make the odds really long that they could get that high pick everyone is after, then I think you see a change in behavior.  When teams look at it they really have to think 'my chances of getting a top 5 pick are not good'