Multiple Balls: Disadvantage?

[Seachd]

Some weighted teams are now down to 1 last ball with much of the draft left. There is no stastical advantage to having more balls in a reverse draft order - basically it would be a 1/30 shot down the stretch.

Yeah, I know, it sounds fishy to me too. Someone here was claiming the odds would stay the same as going 1-30, but I'm not a statistician, so I have no idea.

 

[DJA]

No, they'd count the last ball, not the first one. So the more balls a team has, the more likely it is that their last one comes out later.

How do you figure? If all teams end up having one ball left, they are statistically even, thus leaving no advantage to the multiple-ball teams. For example, if the Rangers come up twice in the first 5 picks, their last ball is not more likely to be picked later than any of the other remaining one-ball teams.

 

[PecaFan]

That doesn't make any sense.

Even if you ignore the first balls of the mult-ball teams, it gives them no advantage whatsoever over the teams with one ball.

Of course it does. Think of it like Survivor. Last man standing wins (aka last ball out of the machine wins #1 pick).

Who has a better chance of surviving? Somebody with only 1 ball, or somebody who has 3 chances. Who lasts longer in baseball? The guy who's out after 1 strike, or the guy with 3 strikes?

It's the perfect system, means no unloading of the machine is needed, and thus allows them to telecast the whole thing live and sequentially.

Which they won't do of course. We'll just get some NHL paid lawyer telling us everything was legit.

 

[Captain Conservative]

isn't it going to be a disadvantage to have multiple balls

Confucious say, Baseball wrong, man with four balls cannot walk.

 

[CaptainShark]

If the drawing was 30-1 then the odds of the 3-ball-teams would not be as good as they would be in a 1-30 drawing (6.something per cent).

They still would have an advantage over one-ball-teams, because with every ball picked there is the chance that it will be a ball of the one-ball-teams, who will be "out of it" by then... Hard to explain, especially in english , sorry...

 

[mas0764]

Of course it does. Think of it like Survivor. Last man standing wins (aka last ball out of the machine wins #1 pick).

Who has a better chance of surviving? Somebody with only 1 ball, or somebody who has 3 chances.

That's not true.

The only thing it means is that you have better odds of being pulled out until you have one ball like all the one-ball teams, at which point its an equal playing field.

It gives absolutely no edge to the multi-ball teams.

 

[CaptainShark]

Of course it does. Think of it like Survivor. Last man standing wins (aka last ball out of the machine wins #1 pick).

Who has a better chance of surviving? Somebody with only 1 ball, or somebody who has 3 chances. Who lasts longer in baseball? The guy who's out after 1 strike, or the guy with 3 strikes?

It's the perfect system, means no unloading of the machine is needed, and thus allows them to telecast the whole thing live and sequentially.

Which they won't do of course. We'll just get some NHL paid lawyer telling us everything was legit.

good explanation! Problem is, that even though the 3-ball-teams would have an advantage, it would not be as big as it is when you draw it 1-30...

 

[Number 57]

Which they won't do of course. We'll just get some NHL paid lawyer telling us everything was legit.

Or the 30 team reps that will attend the lottery.

 

[CaptainShark]

That's not true.

The only thing it means is that you have better odds of being pulled out until you have one ball like all the one-ball teams, at which point its an equal playing field.

It gives absolutely no edge to the multi-ball teams.

of course it does... It´s not like the first 10 balls in this lottery will all be from 3 and 2-ball-teams... I thought the "last man standing"-explanation really would make it plauisble to everyone...

 

[DJA]

Umm... see my last post.

Umm...I was writing mine when you were writing yours. Pipe down.

 

[mas0764]

If the drawing was 30-1 then the odds of the 3-ball-teams would not be as good as they would be in a 1-30 drawing (6.something per cent).

They still would have an advantage over one-ball-teams, because with every ball picked there is the chance that it will be a ball of the one-ball-teams, who will be "out of it" by then... Hard to explain, especially in english , sorry...

But that means nothing, because if we're picking balls, the multi-ball teams have a better chance of being picked out.

Theoretically, due to the better odds of being picked thanks to the presense of multiple balls, all the teams with multiple balls could have all their multiples picked at the start.

And then its exactly even chances the rest of the way.

No; its simply not fair. If you intend for the multi-ball teams to have an increased chance, you have to start at one, otherwise there is no statistical favor in lasting.

 

[PDO]

Of course it does. Think of it like Survivor. Last man standing wins (aka last ball out of the machine wins #1 pick).

Who has a better chance of surviving? Somebody with only 1 ball, or somebody who has 3 chances. Who lasts longer in baseball? The guy who's out after 1 strike, or the guy with 3 strikes?

It's the perfect system, means no unloading of the machine is needed, and thus allows them to telecast the whole thing live and sequentially.

Which they won't do of course. We'll just get some NHL paid lawyer telling us everything was legit.

Sorry, you're wrong. The only way your theory would work is if everyone got 3 balls, but the last ball only counted for some and the second last for others, and still it wouldn't work out evenly.

It's very possible a couple teams would lose both of their "lives" in the first 3 rounds of the draw, and after that it's a 1/27 shot. The logic you're using is flawed, the odds are not the same.

 

[DJA]

Of course it does. Think of it like Survivor. Last man standing wins (aka last ball out of the machine wins #1 pick).

Who has a better chance of surviving? Somebody with only 1 ball, or somebody who has 3 chances. Who lasts longer in baseball? The guy who's out after 1 strike, or the guy with 3 strikes?

It's the perfect system, means no unloading of the machine is needed, and thus allows them to telecast the whole thing live and sequentially.

Which they won't do of course. We'll just get some NHL paid lawyer telling us everything was legit.

The only thing this would do is give the team with 3 balls a better chance at the 30th pick.

 

[CaptainShark]

Theoretically, due to the better odds of being picked thanks to the presense of multiple balls, all the teams with multiple balls could have all their multiples picked at the start.

And then its exactly even chances the rest of the way.

No; its simply not fair. If you intend for the multi-ball teams to have an increased chance, you have to start at one, otherwise there is no statistical favor in lasting.

That is just ONE possible scenario and it is very unlikely that it would go down like that... But because of that being one of the possibilities, the chances of the 3-ball-teams are not as good as they are in a 1-30 drawing. But they still would have the best shot...

 

[CaptainShark]

The only thing this would do is give the team with 3 balls a better chance at the 30th pick.

Absolutely not, as the balls 1 and 2 of the 3-ball-teams would not count...

 

[DJA]

Absolutely not, as the balls 1 and 2 of the 3-ball-teams would not count...

Right, so after the first 2 balls are discarded, the team is now on equal footing with the one ball teams. Where did the advantage go?

 

[AlienWorkShop]

I have a brilliant suggestion guys.

We simply accept that teams with 3 and 2 balls have an advantage over teams with one ball, we accept that every team has a chance at number 1, and we disregard the ridiculous theory the league will rig it this year because it is being done behind closed doors just like every other year.

We simply wait till the order is officially revealed, and then we can over analyze whose going to pick who! Anybody with me?

 

[mas0764]

of course it does... It´s not like the first 10 balls in this lottery will all be from 3 and 2-ball-teams... I thought the "last man standing"-explanation really would make it plauisble to everyone...

The last man standing theory isn't mathematically sound if you're trying to improve the odds of the bad teams.

You assume that because a team has more balls, they'll last longer. That's not accurate.

A weighted system starting up front means that certain teams start out with good odds that only get better as the draft continues and they aren't picked.

A weighted system starting in the back means there are certain teams that start out with good odds that decrease towards 1:1 over time.

By time you get to the first pick, its almost guaranteed there is no statistical advantage to being a team with lots of balls.

If you're going to have a weighted system, starting at the front is the only fair way to do it.

 

[allelsefails]

of course it does... It´s not like the first 10 balls in this lottery will all be from 3 and 2-ball-teams... I thought the "last man standing"-explanation really would make it plauisble to everyone...

Here's just a quick little sim I ran using Peca's simulator, which picks ascending.

1. Phx ( 4.2%) - 1 left
2. Ana ( 4.3%) - 1 left
3. Edm ( 4.5%) - 1 left
4. Pit ( 7.1%) - 2 left
5. Buf ( 7.7%) - 2 left
6. Min ( 5.6%) - 1 left
7. Car ( 5.9%) - 1 left
8. Cgy ( 6.3%) - 1 left
9. Chi ( 6.7%) - 1 left
10. NJD ( 3.6%)

NJD get the 30th overall pick, because all teams before them have mutiple balls. 9 Teams loose their ball before the 30th pick is even determined, and since Peca's simulator discards teams' balls once selected, who is to say another on of those team's balls couldn't have been drawn before New Jersey's?

And another run of the simulator.

1. CBJ ( 6.3%) - 1 left
2. Van ( 2.2%) - 30th
3. Min ( 4.5%) - 1 left
4. Nsh ( 4.8%) - 1 left
5. Col ( 2.5%) - 29th
6. NYR ( 7.7%) - 1 left
7. Ana ( 5.6%) - 1 left
8. Tam ( 2.9%) - 28th
9. Phx ( 6.1%) - 1 left
10. Fla ( 3.2%) - 27th

Again, once a team ball is pick the others are discarded in this simulator.

It seems like teams with more than 1 ball tend to have their additional balls picked earlier (statistically) until the majority of teams all have 1 left.

 

[mas0764]

It seems like teams with more than 1 ball tend to have their additional balls picked earlier (statistically) until the majority of teams all have 1 left.

Bingo.

It only SEEMS like you have a better chance of lasting.

If you use math, you'll see the only better chance you have is being pulled out.

 

[MaV]

Right, so after the first 2 balls are discarded, the team is now on equal footing with the one ball teams. Where did the advantage go?

The team is on equal footing with those one ball teams who didn't already lose their balls. That's the advantage. If we are talking strictly about the number one pick, it really makes no difference what the odds are for them to beat the other teams at that point. The odds leading to that particular case have to be considered too!

Or can someone somehow prove me that if the last ball wins the #1 pick, the chances for one particular ball to be drawn last is still 1/48 and thus teams with 3 balls have 1/16 chances, two balls 1/24 and one ball 1/48?

 

[crossxcheck]

They are going 30-1

If you have 3 balls and you get picked 1st time, then you have 2 balls, they go down to whoever has the last one.

If the lottery were to be performed from 1-30, then statistically speaking a team that has 3 balls (such as columbus) has a 6.25% of being the #1 pick. conversely, a team such as detroit would have roughly a 2.1% chance of being picked first.

If they pick from 30-1 and the way you describe then columbus would have a 6.25% chance of one of their balls being elimiated first. While detroit would have a 2.1% chance of being the 30th pick.

It's hard to do much of the math outside of that simply because you cant predict who exactly will be picked.

I'm by no means a statistitian (nore can I spell it), but if I'm detroit I like my chances in the reverse lottery a lor better than than the 1-30 lottery.

 

[bcrt2000]

the probabilities are exactly the same in the 1-30 lottery as the 30-1 lottery... each ball has a 1/48 chance of being picked at the start-- so... the possible orders of the 48 balls being picked out from 1-30 is the same as the possible orders of the 48 balls being picked out from 30-1.. now just take the 30-1 order, and reverse it to make it 1-30.. so you have a 30-1 order, and a 1-30 order, and in the 30-1 order ignore 2nd/3rd balls, and in the 1-30 order ignore all but the last ball for each team... you get the same result.. and the probability of getting the 30-1 order is the same as getting the 1-30 order

might be a bit confusing to people who havent done stats/finite, but it really is that simple



edit: when i say 1-30 order i really mean the 1-48 ball order, and same thing with 30-1 order (48-1)

 

[MaV]

It only SEEMS like you have a better chance of lasting.

If you use math, you'll see the only better chance you have is being pulled out.

Ok, let's see the math. What are you comparing here? I'm claiming that teams with more balls obviously have better chance to last longer. It's true that there is a bigger chance for ONE of their balls being picked in one particular time a ball is picked, because there are more balls they own, that's true. But you should look it that way. Think every ball is independent one. Every ball has as good chances, right? And when you have more of them your chances are better, as you get to "choose" the ball that gives you the best position. Easy, isn't it?

 

[mas0764]

the probabilities are exactly the same in the 1-30 lottery as the 30-1 lottery... each ball has a 1/48 chance of being picked at the start-- so... the possible orders of the 48 balls being picked out from 1-30 is the same as the possible orders of the 48 balls being picked out from 30-1.. now just take the 30-1 order, and reverse it to make it 1-30.. so you have a 30-1 order, and a 1-30 order, and in the 30-1 order ignore 2nd/3rd balls, and in the 1-30 order ignore all but the last ball for each team... you get the same result.. and the probability of getting the 30-1 order is the same as getting the 1-30 order

might be a bit confusing to people who havent done stats/finite, but it really is that simple



edit: when i say 1-30 order i really mean the 1-48 ball order, and same thing with 30-1 order (48-1)

I find it hard to take your word because no statistician looks at it that way.

The statistical probability of any one ball being pulled out is all that matters and it changes after every pull.


If you start at 30, and for ease's sake, lets say the Rangers and Blackhawks have three balls each, and every other team only has one.... meaning there are 34 balls....

Each team has a 1/34 chance of being picked, except the Rangers and Blackhawks, who have a 3/34 chance of being pulled out.

If the Rangers and Blackhawks aren't picked, they now have a 3/33 chance of being picked out, while the other teams still only have a 1/33 chance of being pulled.

On the next pick, the Rangers first ball comes out.

Now its:

Blackhawks 3/32
Rangers 2/32
Everyone else 1/32

Next its someone else.

Blk 3/31
Rangers 2/31
Everyone 1/31

Eventually, you will reach a point, and given the odds of lasting, probably well before the tenth overall pick, where the Rangers and Blackhawks catch up with all the remaining teams right about 1/16. It is inevitable that they catch up because of their better chance of being pulled out every time.

So instead of the Rangers and Hawks having a 6% chance to get the first pick and everyone else having a 2% chance, they are now on equal footing to get any particular draft pick from here on out, thus offering the Ranger and Hawks no statistical advantage.

The problem with doing it like this is that the Rangers and Hawks now have pretty good odds at being pulled out at 16 or 15.

This isn't fair, because if you do it the other way, it is very difficult for the Rangers or Hawks to not have been pulled by 16, since the odds get BETTER when you work the other way.

Given that we are in the business of helping the bad teams out by weighting the system, the only fair way to do it is to start at the front. It protects the interests of bad teams while maintaining reasonable odds for the good teams.