Did everyone land?

[Anonymous]

Anonymous wrote:New poster. I believe you statistics people, really, I do! But I wish there was some way that someone could explain it to me so I would understand it. I feel dumb.

Don't feel dumb. Stats is a really complex subject, and these systems are designed by Nobel prize winners because it's really hard to make them work fairly and equitably and all that. Most people can understand basic probabilities, but when it comes to situations like these, with multiple iterations, multiple choices, and differing options for each player in the system, the complexity increases a lot.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Your explanation "using math" assumed that you had an equal chance of getting into each school (that each school has the same number of open spots and each is just as popular as each other). That is not the case. If you were truly such a math whiz you'd understand that.

It is the exact same. If you disagree, please explain it mathematically.

Sure. Let's say that there are 5,000 kids, applying for 500 places. That gives them a 1:10 chance of getting a spot somewhere under the common lottery. Let's assume that none have siblings, are IB or have proximity preference, just to make it simpler.

Now let's say that they applied to the following schools using the old system:

school 1 - 300 kids apply and there are only 30 places - odds are the same 1:10
school 2 - 100 kids apply and there are 25 places - YOUR ODDS ARE 1:4 BINGO, your odds are increased from those of the common lottery (for that school at least)
school 3 - 500 kids apply and there are only 10 places - your odds are worse than under common lottery (for that single lottery) = 1:50

etc, etc.

I'm just bumping this because all of those who claim that they are such experts in statistics have ignored it. Please take a look and tell me why you are ignoring this. Thanks.

Because there are different numbers of people applying to different schools. If under the old system, only 100 kids applied to a school with 25 spots (school 2 in the above example), then logically under the new system only 100 people would have that school in their list of 12 under the new system. Your odds for that school would still be 1:4 for that school under the new system. Everyone is confusing their odds from before the lottery is run, when the odds are the same under either system, compared to their odds after the lottery is run. Your odds after the lottery is run are different under the two systems, but that's because you have cycled through 95% of the probabilities by running it all at once. Under the old system you only got through maybe 70% of the probabilities (complete guesses!) because of all the shuffling that went on. The difference now is the final answer comes much quicker.

If I may make an analogy, it's like saying a quarterback has a 70% completion percentage of the receiver catching the ball. That's an overall percentage on every play. But if you evaluate the odds of an individual throw while the ball is in the air, you have a lot more information and the probabilities will change. You would be able to tell at that point how well covered the receiver was, if the ball looked like it was too high or too low, etc. The odds would be much closer to 0 or 100% at that point. Under the old system it was kind of like that. Under the new system it's much more binary- you have the overall odds at the beginning, and you pretty much jump to the point where the ball is caught or not. So it seems like one might have had better odds under the old system, because you were looking at the odds more along the playing out of the probabilities.

Different "dumb-feeling" PP, I appreciate you really trying to explain this! Still though, even your football analogy isn't helping me understand why overall my odds are exactly the same (according to you) in a given year of applying, whether I have only one chance at a good number vs, 12 chances. Maybe I'll never understand without taking a statistics class, but I'm still not seeing your point right now.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Your explanation "using math" assumed that you had an equal chance of getting into each school (that each school has the same number of open spots and each is just as popular as each other). That is not the case. If you were truly such a math whiz you'd understand that.

It is the exact same. If you disagree, please explain it mathematically.

Sure. Let's say that there are 5,000 kids, applying for 500 places. That gives them a 1:10 chance of getting a spot somewhere under the common lottery. Let's assume that none have siblings, are IB or have proximity preference, just to make it simpler.

Now let's say that they applied to the following schools using the old system:

school 1 - 300 kids apply and there are only 30 places - odds are the same 1:10
school 2 - 100 kids apply and there are 25 places - YOUR ODDS ARE 1:4 BINGO, your odds are increased from those of the common lottery (for that school at least)
school 3 - 500 kids apply and there are only 10 places - your odds are worse than under common lottery (for that single lottery) = 1:50

etc, etc.

I'm just bumping this because all of those who claim that they are such experts in statistics have ignored it. Please take a look and tell me why you are ignoring this. Thanks.

Because there are different numbers of people applying to different schools. If under the old system, only 100 kids applied to a school with 25 spots (school 2 in the above example), then logically under the new system only 100 people would have that school in their list of 12 under the new system. Your odds for that school would still be 1:4 for that school under the new system. Everyone is confusing their odds from before the lottery is run, when the odds are the same under either system, compared to their odds after the lottery is run. Your odds after the lottery is run are different under the two systems, but that's because you have cycled through 95% of the probabilities by running it all at once. Under the old system you only got through maybe 70% of the probabilities (complete guesses!) because of all the shuffling that went on. The difference now is the final answer comes much quicker.

If I may make an analogy, it's like saying a quarterback has a 70% completion percentage of the receiver catching the ball. That's an overall percentage on every play. But if you evaluate the odds of an individual throw while the ball is in the air, you have a lot more information and the probabilities will change. You would be able to tell at that point how well covered the receiver was, if the ball looked like it was too high or too low, etc. The odds would be much closer to 0 or 100% at that point. Under the old system it was kind of like that. Under the new system it's much more binary- you have the overall odds at the beginning, and you pretty much jump to the point where the ball is caught or not. So it seems like one might have had better odds under the old system, because you were looking at the odds more along the playing out of the probabilities.

Different "dumb-feeling" PP, I appreciate you really trying to explain this! Still though, even your football analogy isn't helping me understand why overall my odds are exactly the same (according to you) in a given year of applying, whether I have only one chance at a good number vs, 12 chances. Maybe I'll never understand without taking a statistics class, but I'm still not seeing your point right now.

Because you have one chance at a good number when there are let's say 1000 applicants and 100 spots, versus let's say 10 chances (because it makes it easier) where there are 100 applicants at each of the 10 schools and 10 places at each. In each scenario your odds are 1:10. In reality the odds vary slightly by school but because the overall number of spaces and overall number of applicants is the same in either scenario (in reality they vary by year, but let's assume that both systems were run in a single year and people made the same decisions) but the overall odds of getting in somewhere remain the same.

[Anonymous]

No need to feel bad, this is really complicated. I think pp explained it pretty well, but maybe I can make it a little more simple.

Two schools. 1 spot in each. 2 applicants for A. 10 for B. Same number of applicants for each school regardless of the type of lottery.

You can only get into one school. This is true in either lottery, as your child will end up only attending one school. In the multiple lottery system, you could have gotten into more schools at first and held them, but eventually you would have to prioritize and make a decision on one school, thus freeing up the space for others. In the new system, you prioritize beforehand, so you only get into one school at the beginning and the other spots, which are less desired by you, are instantly freed up.

Imagine a 10 sided die. For school A, you only have a 1 in 10 shot, therefore, you must roll a 1 to get into school A. For school 2, you have a 1 in 2 (or 5 in 10) chance. Therefore, you must roll a 5,6,7,8,or 9 to get into school B. (It could be any 1 number and any 5 numbers, but the five numbers of B cannot contain the 1 number of A because that would mean that you would be in more than one school).

If different lotteries, you would roll 1 time for school A, and you would have a 1 in 10 chance of getting a 1. You would then roll 1 time for school B, and you would have a 5 in 10 chance of getting school B. Thus, in total, you would have 6 in 10 chance of getting into one of the schools.

If one lottery, you would roll 1 time. If you rolled a 1, you would get school A; if you rolled a 6,7,8,9, or 10, you would get school B. You would therefore have a 6 out of 10 chance to get into 1 of the schools.

Does that make sense?

[Anonymous]

Here's another way of asking the question: you and I apply to the exact same 12 schools, rank them in exact same order, have same preferences (or lack thereof). Common lottery: you get #2 and get into your top choice. I get #652 and get into none of mine. That's it, it's over for me for all 12 schools.

Other scenario: you and I apply to same 12 schools who all hold different lotteries. School 1 you get #2 and I get #652 (let's say it's 2 Rivers). You're in, I'm out. But that's just for school 1; there are still 11 more schools for me to have a chance at abetted number than you. I understand we both might strike out at school 2, or I could still strike out at all 12 in the end. But I could also get into one of them.

How are my odds exactly the same as yours re: getting into one of these schools when the first chance isn't my only chance in scenario 2?
I believe you that it's true, but no one's explained how/why it's true.

[Anonymous]

Oops, I posted the last question without seeing the previous reply. Didn't get to read it, maybe I'll finally get it!

[Anonymous]

This thread emphasizes to me why I am going to make my daughter take a basic stats class when she is older.

[Anonymous]

Anonymous wrote:No need to feel bad, this is really complicated. I think pp explained it pretty well, but maybe I can make it a little more simple.

Two schools. 1 spot in each. 2 applicants for B. 10 for A. Same number of applicants for each school regardless of the type of lottery.

You can only get into one school. This is true in either lottery, as your child will end up only attending one school. In the multiple lottery system, you could have gotten into more schools at first and held them, but eventually you would have to prioritize and make a decision on one school, thus freeing up the space for others. In the new system, you prioritize beforehand, so you only get into one school at the beginning and the other spots, which are less desired by you, are instantly freed up.

Imagine a 10 sided die. For school A, you only have a 1 in 10 shot, therefore, you must roll a 1 to get into school A. For school 2, you have a 1 in 2 (or 5 in 10) chance. Therefore, you must roll a 5,6,7,8,or 9 to get into school B. (It could be any 1 number and any 5 numbers, but the five numbers of B cannot contain the 1 number of A because that would mean that you would be in more than one school).

If different lotteries, you would roll 1 time for school A, and you would have a 1 in 10 chance of getting a 1. You would then roll 1 time for school B, and you would have a 5 in 10 chance of getting school B. Thus, in total, you would have 6 in 10 chance of getting into one of the schools.

If one lottery, you would roll 1 time. If you rolled a 1, you would get school A; if you rolled a 6,7,8,9, or 10, you would get school B. You would therefore have a 6 out of 10 chance to get into 1 of the schools.

Does that make sense?

This is VERY helpful, thanks! I think the A and B were flipped in your original premise; I changed them above in bold.

[Anonymous]

Anonymous wrote:No need to feel bad, this is really complicated. I think pp explained it pretty well, but maybe I can make it a little more simple.

Two schools. 1 spot in each. 2 applicants for A. 10 for B. Same number of applicants for each school regardless of the type of lottery.

You can only get into one school. This is true in either lottery, as your child will end up only attending one school. In the multiple lottery system, you could have gotten into more schools at first and held them, but eventually you would have to prioritize and make a decision on one school, thus freeing up the space for others. In the new system, you prioritize beforehand, so you only get into one school at the beginning and the other spots, which are less desired by you, are instantly freed up.

Imagine a 10 sided die. For school A, you only have a 1 in 10 shot, therefore, you must roll a 1 to get into school A. For school 2, you have a 1 in 2 (or 5 in 10) chance. Therefore, you must roll a 5,6,7,8,or 9 to get into school B. (It could be any 1 number and any 5 numbers, but the five numbers of B cannot contain the 1 number of A because that would mean that you would be in more than one school).

If different lotteries, you would roll 1 time for school A, and you would have a 1 in 10 chance of getting a 1. You would then roll 1 time for school B, and you would have a 5 in 10 chance of getting school B. Thus, in total, you would have 6 in 10 chance of getting into one of the schools.

If one lottery, you would roll 1 time. If you rolled a 1, you would get school A; if you rolled a 6,7,8,9, or 10, you would get school B. You would therefore have a 6 out of 10 chance to get into 1 of the schools.

Does that make sense?

I think maybe I'm starting to get it. There's still a disconnect that maybe is more about experience than it is statistics, where I prefer to get 10 or 12 different random numbers than 1, because it feels fairer. But I'm starting to see (I think!) why maybe my actual chances are the same either way. Still pondering it

[Anonymous]

Here's a nice, simple way to visualize some basic statistics:

Imagine you have a bag that contains 99 white marbles and 1 black marble. You get one chance to (blindly) pull a marble out of the bag. What are your odds of pulling the black marble on your one try? 1 in 100.

Now imagine that you get to pull a marble out of the bag 12 times, but each time the bag is reset to 100 marbles. At first glance it may seem like it makes sense that you have a better chance of pulling the black marble if you get 12 tries. However, during each of those 12 tries, there are still 100 marbles, so each draw is still a 1 in 100 chance of pulling the black marble. Get it?

Another simplified scenario is coin flips. You flip a coin 1 time and there is a 50/50 chance of heads or tails. Let's say you flip the coin 11 times and get heads each time. What is the chance of you getting tails on the 12th flip? It's still 50% despite the 11 previous heads. The outcome doesn't change based on the earlier coin flips.

[Anonymous]

Glad I could help! Sorry about the typo. PP is right, it should be 10 applicants for and 2 for B.

I know it must feel like being whacked in the head to be shut out all at once, but it really is better than being strung along for several months until after school starts and then being shut out. Moreover, it is so helpful for those who eventually did get a spot to find out right after the lottery instead of in October, after school starts. For those who hadn't been through it under the old system, it might be worth a quick gander at this forum from June to early October anytime in the past few years. So much stress about the unknown. Now there is actually very little unknown; unfortunately, there are still not enough desirable spots (and that problem may have grown as demand is outpacing supply), but let's work on fixing that, not on fixing the lottery.

[Anonymous]

awww, what a nice turn this thread has taken - people open to understanding and people open to explaining.

[Anonymous]

Ok, hoping everyone know gets why (or at least that) your chances in a combined lottery and your chances in an individual lottery are the same.

But there is also a real benefit of the common lottery algorithm that means that people are more likely to get into the schools they desire. When it was individual lotteries, you might have luck in one lottery, and not in another, and therefore get into, say, Hearst, and have a terrible number at Eaton, when really Eaton was your preferred choice. Someone else might have had the opposite happen. It was frustrating because you might have had some luck, but not necessarily with the right schools. This resulted in, say, people going to language immersion schools because they had luck of the draw there when really they would have preferred expeditionary learning or someone else, but they had no luck in their preferred schools. It was frustrating for families, but also for the schools themselves, which is why you see Yu Ying letting people line up to get a good spot on the waitlist.

In the new lottery, with a single number, the effect is that when your number is drawn, they go through your schools from #1 to #12 and see if there is room. If there isn't, you're waitlisted; if there is, then you get in and you are dropped from consideration for schools that you ranked as less desirable. (In truth, the algorithm is much more complicated than this, but this is how it plays out in the end.)

So in the common lottery example--which, again, your odds of getting in are the same as individual lotteries--if you rank Eaton #1 and Hearst #2, with an early draw then you get into Eaton and not Hearst, so you get your preference. If someone else has an early draw and has ranked them the opposite way, then they get into Hearst and not Eaton. You are also placed on waitlists of better-ranked schools in the order of your lottery # (assuming no preferences). That means that you can "trade up"--so say Eaton is actually #2, and miracle of all miracles you get into #1 Janney over the summer, then you trade up but let someone else who wants to go to Eaton trade up. It then cascades all the way through the system.

It really is the best way of helping match people with their preferred schools, all with the benefit of giving people the same odds as they would have with individual lotteries. Now, don't get me wrong, it sucks to get a bad draw. It also sucked when that happened with lots of individual lotteries. I wouldn't have gotten in anywhere this year given my awful lottery draw if I hadn't had an IB preference at an unpopular school.

This is why people say the problem is not the lottery algorithm--to the contrary, that's great at matching people with preferred schools--the problem is that there are not enough good seats to meet the demand. No algorithm can change that.

[Anonymous]

Anonymous wrote:Ok, hoping everyone know gets why (or at least that) your chances in a combined lottery and your chances in an individual lottery are the same.

But there is also a real benefit of the common lottery algorithm that means that people are more likely to get into the schools they desire. When it was individual lotteries, you might have luck in one lottery, and not in another, and therefore get into, say, Hearst, and have a terrible number at Eaton, when really Eaton was your preferred choice. Someone else might have had the opposite happen. It was frustrating because you might have had some luck, but not necessarily with the right schools. This resulted in, say, people going to language immersion schools because they had luck of the draw there when really they would have preferred expeditionary learning or someone else, but they had no luck in their preferred schools. It was frustrating for families, but also for the schools themselves, which is why you see Yu Ying letting people line up to get a good spot on the waitlist.

In the new lottery, with a single number, the effect is that when your number is drawn, they go through your schools from #1 to #12 and see if there is room. If there isn't, you're waitlisted; if there is, then you get in and you are dropped from consideration for schools that you ranked as less desirable. (In truth, the algorithm is much more complicated than this, but this is how it plays out in the end.)

So in the common lottery example--which, again, your odds of getting in are the same as individual lotteries--if you rank Eaton #1 and Hearst #2, with an early draw then you get into Eaton and not Hearst, so you get your preference. If someone else has an early draw and has ranked them the opposite way, then they get into Hearst and not Eaton. You are also placed on waitlists of better-ranked schools in the order of your lottery # (assuming no preferences). That means that you can "trade up"--so say Eaton is actually #2, and miracle of all miracles you get into #1 Janney over the summer, then you trade up but let someone else who wants to go to Eaton trade up. It then cascades all the way through the system.

It really is the best way of helping match people with their preferred schools, all with the benefit of giving people the same odds as they would have with individual lotteries. Now, don't get me wrong, it sucks to get a bad draw. It also sucked when that happened with lots of individual lotteries. I wouldn't have gotten in anywhere this year given my awful lottery draw if I hadn't had an IB preference at an unpopular school.

This is why people say the problem is not the lottery algorithm--to the contrary, that's great at matching people with preferred schools--the problem is that there are not enough good seats to meet the demand. No algorithm can change that.

AMEN. This reminds me of that line in the famed "algorithm" thread. DROPS MIKE.

Could everyone please just cut and paste this to their desk top? And MYSchoolDC - umm. Maybe try and find a way to explain this better to the 95% of people who understandably remain confused.

[Anonymous]

Anonymous wrote:Here's a nice, simple way to visualize some basic statistics:

Imagine you have a bag that contains 99 white marbles and 1 black marble. You get one chance to (blindly) pull a marble out of the bag. What are your odds of pulling the black marble on your one try? 1 in 100.

Now imagine that you get to pull a marble out of the bag 12 times, but each time the bag is reset to 100 marbles. At first glance it may seem like it makes sense that you have a better chance of pulling the black marble if you get 12 tries. However, during each of those 12 tries, there are still 100 marbles, so each draw is still a 1 in 100 chance of pulling the black marble. Get it?

Another simplified scenario is coin flips. You flip a coin 1 time and there is a 50/50 chance of heads or tails. Let's say you flip the coin 11 times and get heads each time. What is the chance of you getting tails on the 12th flip? It's still 50% despite the 11 previous heads. The outcome doesn't change based on the earlier coin flips.

Your first claim is obviously incorrect and does nothing but confuse the whole issue. You have a 1 in 100 chance of winning each of the 12 times you play, so your chances of winning at least one of the lotteries in 12 in 100. If what you appear to claim is true -- your chances of winning remain 1 in 100 no matter how many times you play -- there would be no point in playing more than once, which is absurd. Your second claim is, of course, trivially true but not really on point.

The reason all this is so confusing is that both sides have some truth on their side. Statistically, the old and new systems will result in the same overall odds of winning a desirable spot assuming that you hold all of the variables constant -- the number of "good" spots are the same, the numbers of children are the same, the number of people playing are the same, etc. However, the new system is simpler and reveals to everyone much more quickly how small their chance were from the gitgo of winning a spot they really wanted. The old system was better at keeping more people's hopes up for a longer time that they would come out a winner. And hope is a thing with wings.
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