If the Season Ended Today

[KGs Knee]

Well, the debate on who understands statistics better has been fun....

I think both Nick and LarBrd33 are both partially right, and partially wrong.  But, it's not important to me.  Ultimately, the odds of getting a top pick are slim, even if you have the absolute worst record (best odds).

I stand by my original point, however, making the playoffs is always good.  The point of sports is to win the game, not to lose.  Herm Edwards was right.

Disagree if you will, it just means you're wrong.

[slamtheking]

Let's do a quick review of the draft lottery system so people understand how the odds are calculated. 14 balls are put into a bowl and mixed up and drawn in combinations of 4. That means there are 14!/4!X10! permutations or 1001 different combinations. The combo 11-12-13-14 is given to nobody so if that combo comes out the experiment is just done over.

The combinations are given out to the teams and in the case of the 10th which is what we were talking about the team is given 11 combinations.

So four numbers are drawn and a winner is found for the first drawing. let's say the 1st seeded team with 250 combinations won.

The balls are but back in the bowl and THE DRAWING IS DONE AGAIN.

There are still 1001 combinations in the bowl that could be drawn so the odds of the 10th seed getting the 2nd seed are still 1,1%, 11 out of 1000. It doesn't matter that 250 combinations are what LB calls "invalid" the combos still exist within the experiment.

This is not like the 24 cases pick one and one is removed now you have 23 cases

Its more like rolling a 10 sided die. You roll that die and you have a 10% chance of getting a 3. But after the first roll in which the number 5 won, you roll the die again. The number 5 has not been taken off the die. You aren't now rolling a 9 sided die. You are still rolling a 10 sided die so the odds of getting a 3 on the next roll remain at 10%

That is how the draft lottery works and why if you are a 10th seed your chances of getting any of the top three picks is just 1.1%

you and LB both have valid points here Nick but LB's on the right track.

Technically, you are absolutely right regarding how the lottery works with how the balls are mixed and drawn.  no argurment there. 

The concern is that the odds do shift as teams' combos are picked.  While the balls are not removed from the drawing so that technically the odds of drawing one of 11 combos out of 1000 is the same, the first team's combos are essentially removed from the selection process because they are invalid after that team has won their spot.

Sticking with the example of the team with 11 chances out of 1000: if the first team picked is the team with the best odds, 250 combos, then there are still 1000 combinations that can be drawn for pick #2 but only 750 of would matter.  Any of the 250 belonging to the first team will be rejected and the drawing conducted again.  Essentially, the team with the 11 picks has the same odds based on the volume of possible combos (11 out of 1000) but since only 750 combos are valid for selection for the second pick, that team now has odds of 11/750 = 1.5% of remaining valid combinations.  yes, that team still has a 1% chance one of their combinations is selected but they have a 1.5 % chance if the combination that comes up is one that's still in play,

Based on the lengthy back and forth between you both, you're approaching it (IMO) from the viewpoint of the odds based on no picks having been conducted yet.  LB is approaching it (IMO) from the viewpoint of each pick selection as a new lottery essentially with recalculated odds.  you're right in your analogy that a side of dice isn't removed but from LB's side, his analogy of the suitcases is very good.  the suitcase taken out of play is very much like the combos of the first-selected team being taken out of play.  it doesn't change the initial odds of winning but it does change in the frame of reference of each specific lottery slot.

[LarBrd33]

Let's do a quick review of the draft lottery system so people understand how the odds are calculated. 14 balls are put into a bowl and mixed up and drawn in combinations of 4. That means there are 14!/4!X10! permutations or 1001 different combinations. The combo 11-12-13-14 is given to nobody so if that combo comes out the experiment is just done over.

The combinations are given out to the teams and in the case of the 10th which is what we were talking about the team is given 11 combinations.

So four numbers are drawn and a winner is found for the first drawing. let's say the 1st seeded team with 250 combinations won.

The balls are but back in the bowl and THE DRAWING IS DONE AGAIN.

There are still 1001 combinations in the bowl that could be drawn so the odds of the 10th seed getting the 2nd seed are still 1,1%, 11 out of 1000. It doesn't matter that 250 combinations are what LB calls "invalid" the combos still exist within the experiment.

This is not like the 24 cases pick one and one is removed now you have 23 cases

Its more like rolling a 10 sided die. You roll that die and you have a 10% chance of getting a 3. But after the first roll in which the number 5 won, you roll the die again. The number 5 has not been taken off the die. You aren't now rolling a 9 sided die. You are still rolling a 10 sided die so the odds of getting a 3 on the next roll remain at 10%

That is how the draft lottery works and why if you are a 10th seed your chances of getting any of the top three picks is just 1.1%

Nick, I still insist that you are wrong on this and I think I finally have a way that I can explain it that will make sense.

1000 possible combinations.   The team with the worst record owns 250 of the 1000 possible combinations.

As you (and every site) explain, the odds the team with the worst record gets the #1 pick is 25%.  The odds they get the 2nd pick is 22%.  The odds they get the third pick is 18%.

That might be true prior the lottery, but my point is that as the lotto progresses, those odds change.  If the team with the worst record does NOT get the #1 pick or the #2 pick... they do not still have just 18% chance at the #3 pick.  Depending on which teams end up with the first two picks, they might now have a 39% chance at the #3 pick.  You are disagreeing with me on this.  You keep saying that the odds don't change.  You claim they still have just 18% chance at the #3 pick.

So let me make this really simple.

Let's say the Bucks are the team with the worst record.  They have 250 of the 1000 possible combinations.

First combination that comes up belongs to the Bucks.  The Bucks have the #1 pick. 

According to you... the Bucks now STILL have a 22% chance at the #2 pick and STILL have an 18% chance at the #3 pick.  Are you seeing why this is absurd?   The odds have changed.  If the Bucks have the #1 pick, they now have a 0% chance at the #2 and a 0% chance at the #3.   I'm right on this.  The only possible way I'm wrong is if the NBA changed the rules and it's possible for a team to win all 3 picks.  Again... if the first set of numbers belongs to the Bucks, they lock in the #1 pick and the rest of their combinations become "invalid".  When they do the second drawing, it's still possible that the combination belongs to the Bucks, but they would just toss it out as "invalid" and re-draw.   Since the Bucks now have a 0% chance the #2 pick and 0% chance at the #3 pick, it would adjust the odds for the rest of the teams who still have valid combinations. 

Edit:  I do kind of see your point though.  You're saying that regardless of which teams lock in the first 2 picks, there are still only 1000 possible combinations and the chance that the combination drawn belongs to you doesn't change.  If you have 11 out of 1000... it's still 11 out of 1000 even if 449 of those combinations are invalid.   Still, as you say, just 1.1% chance that you'll win the drawing.  But doesn't factor in the possibility that it might take 10 attempts for a winner to be determined.  If the Bucks (250 combos) and Jazz (199) combos are off the board... they could do a drawing for Pick #3 where the winner is Bucks (tossed out), Bucks (tossed out), Jazz (tossed out), Bucks (tossed out), Jazz (tossed out), Bucks (tossed out)... until finally Chicago wins it.  So I relent, simply saying "11 out of 551 combinations" is probably inaccurate.  But the odds aren't still "1.1%".  The odds change.

[Celtics18]

I'm not sure who is right here, Nick or LB33.  I'll admit that my math skills aren't good enough to even want to bother to pipe in on this debate.  Either way, it doesn't change the fact that all teams in the lottery have a shot at a top three pick, but at the same time, the further away you get from the worst record, those odds start to become awfully small. 

I wouldn't expect a top three pick from a seventh worst record or below.  The odds (whatever number they actually are) are very small. 

[LarBrd33]

I'm not sure who is right here, Nick or LB33.  I'll admit that my math skills aren't good enough to even want to bother to pipe in on this debate.  Either way, it doesn't change the fact that all teams in the lottery have a shot at a top three pick, but at the same time, the further away you get from the worst record, those odds start to become awfully small. 

I wouldn't expect a top three pick from a seventh worst record or below.  The odds (whatever number they actually are) are very small.

The debate is kind of off topic anyways.  I'm just saying that at the moment, I'd prefer to be in Chicago's shoes.  Same record, but the 9th best odds in the lotto.  As opposed to Boston's shoes:  8th seed and 15th pick.

We can revisit this again as the season progresses. 

[5.9.20.34.43]

I just read the entire topic and I think I became a bit smarter. You both seem to make sense. I just wish these other teams would get it together.  I mean I just can't pray for defeat. I enjoy winning. So I can't enjoy watching this team lose for a better pick even though I know it makes the pick better. In a perfect world we can develop this group and still end up with a good pick. By losing to the teams that get it together.

[BigAlTheFuture]

We could possibly rack up 7 or 8 straight losses when we go on our West Coast road trip.

[Celtics18]

I'm not sure who is right here, Nick or LB33.  I'll admit that my math skills aren't good enough to even want to bother to pipe in on this debate.  Either way, it doesn't change the fact that all teams in the lottery have a shot at a top three pick, but at the same time, the further away you get from the worst record, those odds start to become awfully small. 

I wouldn't expect a top three pick from a seventh worst record or below.  The odds (whatever number they actually are) are very small.

The debate is kind of off topic anyways.  I'm just saying that at the moment, I'd prefer to be in Chicago's shoes.  Same record, but the 9th best odds in the lotto.  As opposed to Boston's shoes:  8th seed and 15th pick.

We can revisit this again as the season progresses.

I'd rather be the 8th seed with a 15th pick.  I just think that after the top five, who you pick is way more important than where you pick.  If you look closely at the history of the draft, you'll see that there's nowhere near a direct correlation between where guys were picked in the draft and how good they become as pros (after the top five, of course). 

I wouldn't go so far as to say that the draft is a crap shoot, but it is far, far from being an exact science.  It's far enough away from being an exact science that I am not going to root for my team to lose themselves into barely missing the playoffs to raise our chances at a superstar in the draft by a minuscule percentage. 

I'd rather take my chances in the playoffs as a scrappy underdog.  Personally, I think it would be fun. 

[LarBrd33]

I'm not sure who is right here, Nick or LB33.  I'll admit that my math skills aren't good enough to even want to bother to pipe in on this debate.  Either way, it doesn't change the fact that all teams in the lottery have a shot at a top three pick, but at the same time, the further away you get from the worst record, those odds start to become awfully small. 

I wouldn't expect a top three pick from a seventh worst record or below.  The odds (whatever number they actually are) are very small.

The debate is kind of off topic anyways.  I'm just saying that at the moment, I'd prefer to be in Chicago's shoes.  Same record, but the 9th best odds in the lotto.  As opposed to Boston's shoes:  8th seed and 15th pick.

We can revisit this again as the season progresses.

I'd rather be the 8th seed with a 15th pick.  I just think that after the top five, who you pick is way more important than where you pick.  If you look closely at the history of the draft, you'll see that there's nowhere near a direct correlation between where guys were picked in the draft and how good they become as pros (after the top five, of course). 

I wouldn't go so far as to say that the draft is a crap shoot, but it is far, far from being an exact science.  It's far enough away from being an exact science that I am not going to root for my team to lose themselves into barely missing the playoffs to raise our chances at a superstar in the draft by a minuscule percentage. 

I'd rather take my chances in the playoffs as a scrappy underdog.  Personally, I think it would be fun.

Kinda like in 2004??  Were you around back then?  I was.  We won 36 games, made the playoffs with the 8th seed.  Lost game 1 by 16 points.  Lost game 2 by 13 points.  Lost game 3 by 23 points.  Lost game 4 by 15 points.   Coincidentally, the sweep was by Indiana.  We were nowhere near in Indiana's class. They won 61 games that year... just ripped us to shreads.  Not fun at all, imo.   

Granted, we ended up with the #15 pick and lucked into Al Jefferson.  A massive steal.  For the record, the 9th pick went to Philly that year and they took Andre Iguodala.  So yes, I see your point... theoretically there isn't going to be a major difference between picks #9 and #15 in this draft... MAYBE.  This draft is already 7 stars deep... by March we might see a consensus Top 10.  That's probably mostly hype though.  This draft is unique.  NBADraft.net has Dante Exum going #7... Some scouts think he might be the best player in the entire draft.

So yeah... I'm with you.  Maybe we should let history repeat itself... Dropping 5 spots in the draft for a chance to get curb-stomped 4 games in a row by Indiana sounds like a real blast.    This year, Indiana is on pace to win 67 games.  We're on pace to win 34.  But hey... maybe you're right and our scrappy underdog could pull off a victory in the midst of getting blown out by 30.  I've said it before, but good lord... I admire your optimism.

[hwangjini_1]

Memory can be a terrible burden sometimes.  good post by lb.

For what it's worth, horford's  jury is good for the celtics draft, clearly. At this point I cheer for Chicago to win, win, win and bump the celtics from the dreaded eight seed position. Lb has it right about being curb stomped, no fun at all.

My fantasy is for all three of Atlanta, Brooklyn, and the celtics to miss the playoffs and all three to get lucky in the draft, placing 1,2, and 3. 

Hey, I'm allowed to be delusional on cb.

[Moranis]

Memory can be a terrible burden sometimes.  good post by lb.

For what it's worth, horford's  jury is good for the celtics draft, clearly. At this point I cheer for Chicago to win, win, win and bump the celtics from the dreaded eight seed position. Lb has it right about being curb stomped, no fun at all.

My fantasy is for all three of Atlanta, Brooklyn, and the celtics to miss the playoffs and all three to get lucky in the draft, placing 1,2, and 3. 

Hey, I'm allowed to be delusional on cb.

yeah the 1st and 3rd pick to Boston would be quite nice.  Parker/Wiggin and Embiid/Randle.  I think I'd be ok with that.

[TwinTower14]

Best case scenario is that the C's get two lottery picks but I doubt that happens.  If they fall out of the lottery and one of their picks is in the 20's I would jump all over PJ Hairston.  Hairston is going to be a rock solid NBA player...I bet he joins a D-League team here shortly.  Roy Williams has been saying all year that he was practicing better than any player he has ever had.  If he played this year I bet he would have been an All-American, he can flat out score and has limitless range...

[Celtics18]

I'm not sure who is right here, Nick or LB33.  I'll admit that my math skills aren't good enough to even want to bother to pipe in on this debate.  Either way, it doesn't change the fact that all teams in the lottery have a shot at a top three pick, but at the same time, the further away you get from the worst record, those odds start to become awfully small. 

I wouldn't expect a top three pick from a seventh worst record or below.  The odds (whatever number they actually are) are very small.

The debate is kind of off topic anyways.  I'm just saying that at the moment, I'd prefer to be in Chicago's shoes.  Same record, but the 9th best odds in the lotto.  As opposed to Boston's shoes:  8th seed and 15th pick.

We can revisit this again as the season progresses.

I'd rather be the 8th seed with a 15th pick.  I just think that after the top five, who you pick is way more important than where you pick.  If you look closely at the history of the draft, you'll see that there's nowhere near a direct correlation between where guys were picked in the draft and how good they become as pros (after the top five, of course). 

I wouldn't go so far as to say that the draft is a crap shoot, but it is far, far from being an exact science.  It's far enough away from being an exact science that I am not going to root for my team to lose themselves into barely missing the playoffs to raise our chances at a superstar in the draft by a minuscule percentage. 

I'd rather take my chances in the playoffs as a scrappy underdog.  Personally, I think it would be fun.

Kinda like in 2004??  Were you around back then?  I was.  We won 36 games, made the playoffs with the 8th seed.  Lost game 1 by 16 points.  Lost game 2 by 13 points.  Lost game 3 by 23 points.  Lost game 4 by 15 points.   Coincidentally, the sweep was by Indiana.  We were nowhere near in Indiana's class. They won 61 games that year... just ripped us to shreads.  Not fun at all, imo.   

Granted, we ended up with the #15 pick and lucked into Al Jefferson.  A massive steal.  For the record, the 9th pick went to Philly that year and they took Andre Iguodala.  So yes, I see your point... theoretically there isn't going to be a major difference between picks #9 and #15 in this draft... MAYBE.  This draft is already 7 stars deep... by March we might see a consensus Top 10.  That's probably mostly hype though.  This draft is unique.  NBADraft.net has Dante Exum going #7... Some scouts think he might be the best player in the entire draft.

So yeah... I'm with you.  Maybe we should let history repeat itself... Dropping 5 spots in the draft for a chance to get curb-stomped 4 games in a row by Indiana sounds like a real blast.    This year, Indiana is on pace to win 67 games.  We're on pace to win 34.  But hey... maybe you're right and our scrappy underdog could pull off a victory in the midst of getting blown out by 30.  I've said it before, but good lord... I admire your optimism.

I don't subscribe to the theory of "competition" that the best way to avoid getting completely spanked is to just not compete.  Yeah, it's competition.  You run the risk of getting embarrassed, but if my team tries to compete, I can live it. 

What's it more about for you?  Is it more about the draft pick, or is it more about avoiding embarrassment? 

Remember 2012?  It's more recent.  There was a vocal group of fans who didn't want to make the playoffs that year, because they didn't want to see the team get embarrassed.  They were too old, it was going to be a bloodbath when we faced the elite teams.

That team ended up making me proud as a fan by taking the Heat to seven in the conference finals.  I'm glad that team made the playoffs, they gave me some fantastic moments. 

You play to win and let the chips fall where they may.  That's my very basic take on sports, both playing and watching.  I've suffered some embarrassing moments as both a participant and a spectator.  But, you always give it your best shot.  In my opinion, not doing so is more embarrassing than suffering a lopsided loss.

I understand that I'm in the minority on this.  I'll take the sarcastic comments, and I'll keep rooting for my Celtics to go out and try to win basketball games. 

[nickagneta]

I don't subscribe to the theory of "competition" that the best way to avoid getting completely spanked is to just not compete.  Yeah, it's competition.  You run the risk of getting embarrassed, but if my team tries to compete, I can live it. 

What's it more about for you?  Is it more about the draft pick, or is it more about avoiding embarrassment? 

Remember 2012?  It's more recent.  There was a vocal group of fans who didn't want to make the playoffs that year, because they didn't want to see the team get embarrassed.  They were too old, it was going to be a bloodbath when we faced the elite teams.

That team ended up making me proud as a fan by taking the Heat to seven in the conference finals.  I'm glad that team made the playoffs, they gave me some fantastic moments. 

You play to win and let the chips fall where they may.  That's my very basic take on sports, both playing and watching.  I've suffered some embarrassing moments as both a participant and a spectator.  But, you always give it your best shot.  In my opinion, not doing so is more embarrassing than suffering a lopsided loss.

I understand that I'm in the minority on this.  I'll take the sarcastic comments, and I'll keep rooting for my Celtics to go out and try to win basketball games.

TP C18. I'm with you on this one and I think a lot more people here at CB are too.

You compete with every effort in your body and if you end up with the 12th seed in the East, so be it, its time to cheer for ping pong ball combinations. If you end up with the 8th or 7th seed then its time to cheer for a possible upset win against Miami or Indiana and once again give it every effort in your body and let the chips fall where they may

[Celtics18]

I don't subscribe to the theory of "competition" that the best way to avoid getting completely spanked is to just not compete.  Yeah, it's competition.  You run the risk of getting embarrassed, but if my team tries to compete, I can live it. 

What's it more about for you?  Is it more about the draft pick, or is it more about avoiding embarrassment? 

Remember 2012?  It's more recent.  There was a vocal group of fans who didn't want to make the playoffs that year, because they didn't want to see the team get embarrassed.  They were too old, it was going to be a bloodbath when we faced the elite teams.

That team ended up making me proud as a fan by taking the Heat to seven in the conference finals.  I'm glad that team made the playoffs, they gave me some fantastic moments. 

You play to win and let the chips fall where they may.  That's my very basic take on sports, both playing and watching.  I've suffered some embarrassing moments as both a participant and a spectator.  But, you always give it your best shot.  In my opinion, not doing so is more embarrassing than suffering a lopsided loss.

I understand that I'm in the minority on this.  I'll take the sarcastic comments, and I'll keep rooting for my Celtics to go out and try to win basketball games.

TP C18. I'm with you on this one and I think a lot more people here at CB are too.

You compete with every effort in your body and if you end up with the 12th seed in the East, so be it, its time to cheer for ping pong ball combinations. If you end up with the 8th or 7th seed then its time to cheer for a possible upset win against Miami or Indiana and once again give it every effort in your body and let the chips fall where they may

TP back at ya