SABRES WIN LOTTERY!!!! Will pick #1 overall in the 2018 Draft

[Reddawg]

This isn't correct. The odds of any particular outcome having occurred changed as more information became available.

As the most obvious example of this, the winning odds of each team that was announced at 7:30 fell immediately to 0% as those teams were announced.

Maybe in perception, but not in reality. In reality, three sets of numbers were drawn and two of them came up Buffalo. We can talk theoretical odds all day long (or rather, you guys can) but they don't change reality.

If there were fifteen GM's lined up against a wall to get shot, and Botterill had an 18.5% chance of being killed...the two hours of artificially not knowing whether he was killed or not don't change his odds of whether it happens or not, it only changes our perception. What happened happened when it happened, it doesn't make any difference to the math of the event how it all plays out on TV for us.

 

[GellMann]

At the time of the argument, there were 310 combinations that we did not know the results of, 690 we knew for sure were not the combination drawn for Dahlin, and the Sabres still had 185 combinations, none if which had been ruled out.

It doesn't reflect exactly how the drawing was made, or anything like that. But given the information available at the time, there was still a 185/310 chance that we would see a Sabres logo, based on the information available.

That will continue to be the case every day, and long after Dahlin's number goes to the rafters.

 

[Reddawg]

It is worth doing as a math exercise, because by understanding it in real life, depending how scrupulous you are, you can win money from others who don't understand how the probabilities change with the benefit of additional knowledge. Or alternatively you can protect yourself from losing money in such circumstances.

It's a variant or analogy to the Monte Hall problem.

It's not though. In the Monte Hall problem, taking away one of the options and then giving you the opportunity to make a different choice wildly changes everything. If you're talking about making a bet with someone based on the knowledge available (ie - Buffalo, Carolina and Montreal are the last teams left) then yes, I agree there's merit to doing the math. If you're talking about us having a better or lesser real-life chance of winning first overall based on being one of the teams that won a lottery pick, well...that's silly. We only found out we won a lottery pick at all after it was already long-decided the pick we won was 1st overall. That's the whole purpose of sequestering everyone in the room until the results are revealed.

 

[brian_griffin]

^^But that's exactly what I'm talking about, making a bet with someone based on the knowledge available, i.e., that 2 teams who did not have 2 of the highest initial odds nonetheless remain 2 of the 3 remaining teams.

Another situation (to use Botterill's favorite phrase) was that after 3 balls were drawn, Chicago, and not Buffalo, had the highest odds to match the 4th ball. That one is likely easier for people to understand. But again, in real life, unscrupulous people can make money off people who don't.

In the Monte Hall problem, people generally don't understand both the magnitude of the shift in odds in their favor by switching their choice away from their initial one, as well as the change in difference in odds between the remaining choices (3 choices initially, 2 choices eventually).

In the 2018 draft scenario, once the "new knowledge" was available regarding which teams weren't in the final 3 teams, the magnitude of the odds of the remaining teams, and the differences in odds between the remaining teams change significantly relative to the magnitude and differences between the 15 original teams.

Same with card draws in poker. (I don't play poker.) Odds of drawing card / suit "X" change relative to how many cards have already been dealt, what cards / suit matching "X" are already known, etc.

Same with blackjack. (I like blackjack, but have a hard time finding $5 tables anymore on the Vegas strip.) Odds of drawing card "X" or card "<Y" change depending on how many decks are in a shoe, how many cards have been dealt, what of those have been revealed, etc.

Not arguing. Just saying the original odds are the original odds, based on original information. The new odds are equally true and valid, based on the subsequent / new knowledge.

I agree with the real-life silly comment, but, e.g., that changes in poker / blackjack once a hand / shoe has progressed.

 

[Sabresfansince1980]

If 3 through 15 were known, and it was also known that Buffalo and Carolina were the top 2 picks (but not the order), then 1 of the following 2 scenarios happened:

Buffalo won the 1st lottery, and Carolina the 2nd.
or
Carolina won the 1st lottery, and Buffalo the 2nd.

If you want to look at it that way, it's 185/215 vs 30/215, which is 86% vs 14%. But again, as Reddawg has stated, the actual odds never changed for Buffalo. It was always 18.5%.

 

[Reddawg]

Another situation (to use Botterill's favorite phrase) was that after 3 balls were drawn, Chicago, and not Buffalo, had the highest odds to match the 4th ball.

This part is totally fine and functional, as it refers to the actual mechanics of the draft lottery as it happened. The rest is just whimsical theory, as trying to calculate the odds of Buffalo, Carolina or Montreal winning 1st overall isn't an exercise in reality (when reality is that Montreal only won a lottery pick after Buffalo's win of 3rd overall was invalidated forcing a redraw).

Perception via artificial delay is that each of the three teams had a fighting mathematical chance at the 1st overall. Reality is that we were only even told which three teams were in the "running" after the race was already over and a victor had been declared. The math of the hypothetical situation where each team still had a shot can be calculated, but that doesn't make it real life.

I fully understand and agree with the Chicago point, but that's a matter of odds during the event rather than after it's already over.

 

[brian_griffin]

Again, not arguing, but you can turn the draft lottery into a Monte Hall problem, and "make money" off it.

People staking money and sticking with "Buffalo" for the final answer will not win 86% of the time when it is known MTL and CAR were the remaining two teams in the final three (given the same initial teams & odds as the 2018 draft).

Put another way, with full knowledge of the 12 eliminated teams and the remaining 3 teams, and the original odds, hypothetically offering an $0.86 payout on each dollar bet on the BUF selection is a way worse proposition for the bettor than offering $2 payout for staking $1 on CAR (or even on MTL for that matter).

 

[Reddawg]

I'm not arguing either, as it's clear we're talking about two different things. I'm talking about functional draft lottery odds and you're talking about a betting pool based on available information.

 

[Sabretooth]

At the time of the argument, there were 310 combinations that we did not know the results of, 690 we knew for sure were not the combination drawn for Dahlin, and the Sabres still had 185 combinations, none if which had been ruled out.

It doesn't reflect exactly how the drawing was made, or anything like that. But given the information available at the time, there was still a 185/310 chance that we would see a Sabres logo, based on the information available.

That will continue to be the case every day, and long after Dahlin's number goes to the rafters.

If you want to look at it that way, it's 185/215 vs 30/215, which is 86% vs 14%. But again, as Reddawg has stated, the actual odds never changed for Buffalo. It was always 18.5%.

I wish I could explain better. Having at first been convinced of the 185/310 method, and then changed to 38%, I still can't explain why the 60% method is wrong. Only that I now realize it is. I suspect the answer is that we know more information than we accounted for when we adjusted the odds. I just don't know how to account for it.

Certainly, you will agree that if we simulate the lottery, Buffalo has an 18.5% chance of winning the first draw. Given a buffalo 1st win, Carolina has a 3.7% chance of winning the 2nd lottery. So at the start of the lottery, the odds of that specific order for top 2 occurring is 18.5%*3.7%=0.68%. Call this A.
Likewise, the odds of Carolina winning the 1st pick is 3%. Given that, the sabres have a 19.1% chance of winning the 2nd pick. So at the start of the lottery, the odds of that specific order for top 2 occurring is 3%*19.1%=0.57%. Call this B.

So if the lottery for the top 3 picks was performed and all but the top 2 were revealed, and Buffalo and Carolina were left, one of A or B happened when the lottery was performed. A happens .68% of the time. B happens .57% of the time. But given that one of those 2 outcomes happened, A:B is 54:46. A is buffalo picks first. B is Carolina picks 1st. 54%. Not 86%.

I will write the simulation and see the results. If 60% is correct, I should be able to simulate the lottery thousands of times, throw away every result that does not have Buffalo, Carolina, and Montreal in the top 3 in some order, and Buffalo should have the top pick 60% of the time. and if from those I filter out when montreal picks 3rd, then buffalo should have the top pick 86% of the remaining. but that won't be the case.

 

[dotcommunism]

I wish I could explain better. Having at first been convinced of the 185/310 method, and then changed to 38%, I still can't explain why the 60% method is wrong. Only that I now realize it is. I suspect the answer is that we know more information than we accounted for when we adjusted the odds. I just don't know how to account for it.

Having similarly come around as you have (although I wasn't going to mention it unless someone else did), the issue is that the 60% method answers the wrong question. If there had been one single drawing and we knew one of Buffalo, Montreal or Carolina had won it, then 60% would have been correct. If there had been three drawings done with replacement (that is, if a team could win multiple drawings) then those odds would have held. But that wasn't the case. The later drawings depend on what happens in the first drawing, therefore knowing who won, or potentially won, those later drawings gives us information about the results of the first drawing. If you simply ignore the later drawings, you ignore information about the first drawing.

 

[Ace]

 

[Ace]

Has anyone just stopped and thought how much better our lives are that we don’t have to spend the next seven weeks debating Brady Tkachuk?

 

[1972]

Has anyone just stopped and thought how much better our lives are that we don’t have to spend the next seven weeks debating Brady Tkachuk?

I like Brady Tkachuk more then 90% of this board, but yes I’m very glad we are not picking him.

 

[Ace]

I like Brady Tkachuk more then 90% of this board, but yes I’m very glad we are not picking him.

I like him fine. But boy was I afraid of nearly two months of the fighting between what I thought they would do with 4 (Tkachuk) and what most people wanted them to do (not Tkachuk)

 

[1972]

I like him fine. But boy was I afraid of nearly two months of the fighting between what I thought they would do with 4 (Tkachuk) and what most people wanted them to do (not Tkachuk)

I’m just glad we don’t need to talk about taking second rate defensive prospects at 2-4th overall...

 

[Ace]

I’m just glad we don’t need to talk about taking second rate defensive prospects at 2-4th overall...

3 was probably the spot I was most afraid of. I would have dismissed anyone saying D at 2 with Svechnikov there. I would have fought for Zadina at 3 but I bet I’d have been outnumbered.

What’s crazy is how superior a prospect Dahlin is to the next D...and I like them.

 

[1972]

3 was probably the spot I was most afraid of. I would have dismissed anyone saying D at 2 with Svechnikov there. I would have fought for Zadina at 3 but I bet I’d have been outnumbered.

What’s crazy is how superior a prospect Dahlin is to the next D...and I like them.

Boqvist and Hughes are massive question marks IMO. Bouchard and Dobson are locks to be a top 4 but I’m not sure they become more then that.

 

[Sabretooth]

I like Brady Tkachuk more then 90% of this board, but yes I’m very glad we are not picking him.

I dispute that %age on account of I'm sure you did not consider the conditional probability of the 100% knowledge of drafting #1 overall changes the probability of any individual poster claiming they dislike Tkachuk








just in case

 

[haseoke39]

Actually, the Monty Hall problem is a great example, and the debate going on here really mimics the one that confused a whole bunch of mathematicians for 30 years who got hung up on causality, too.

There's a prize behind one of 15 doors, and you know the odds of all fifteen. The prize was placed there before we walked into the studio, causality is done with, the "original odds" are obsolete, if you will. But your job is now to guess what happened.

If, e.g., we tweak the rules of the game to the effect that you can wager different sums on all the doors rather than just pick the most probable one, you'd absolutely want to change your wagering strategy after it was revealed to you that 12 doors have goats behind them. You'd absolutely reallocate the odds of all the goat doors proportionally between the remaining options. It doesn't change the "original odds," but you're not solving the original problem. You're solving a different probability problem with different information.

 

[haseoke39]

I'm not arguing either, as it's clear we're talking about two different things. I'm talking about functional draft lottery odds and you're talking about a betting pool based on available information.

Right. But between 730 and 930 PM, what you were talking about became irrelevant. Otherwise at 8 PM Chicago still had 6.5% chance of winning a pick they had been eliminated from.

 

[Sabresfansince1980]

Actually, the Monty Hall problem is a great example, and the debate going on here really mimics the one that confused a whole bunch of mathematicians for 30 years who got hung up on causality, too.

There's a prize behind one of 15 doors, and you know the odds of all fifteen. The prize was placed there before we walked into the studio, causality is done with, the "original odds" are obsolete, if you will. But your job is now to guess what happened.

If, e.g., we tweak the rules of the game to the effect that you can wager different sums on all the doors rather than just pick the most probable one, you'd absolutely want to change your wagering strategy after it was revealed to you that 12 doors have goats behind them. You'd absolutely reallocate the odds of all the goat doors proportionally between the remaining options. It doesn't change the "original odds," but you're not solving the original problem. You're solving a different probability problem with different information.

So let me get this straight...you're saying that if I picked a door with a goat behind it, that I would be unhappy? I reject your entire premise based on that alone!

 

[26CornerBlitz]

 

[Chainshot]

So let me get this straight...you're saying that if I picked a door with a goat behind it, that I would be unhappy? I reject your entire premise based on that alone!

Dahlin as GOAT?

 

[Montag DP]

I can see it now: it's 20xx, and the Sabres have just won their first Cup with Dahlin winning the Conn Smythe trophy. Rather than enjoy the victory, Sabres fans on HFBoards continue to debate the Sabres' 2018 draft lottery odds.

 

[La Cosa Nostra]

Very cool video. I think one day in about 20 years the story of the lotto draw will be just as much as Sabres lore as the wheel spin for the right to pick Gilbert Perreault in 1970.

And yes it was very scary that a vocal majority wanted to pass on the clear 2nd best prospect at #2 if we landed there just to reach on a D even though there isn't a dman besides Dahlin worthy of a top 5 pick. Thank god it's all moot, no more crying about the Sergachevs etc. our franchise LHD has been acquired.