Probability for lottery draft help

C

Commissioner_rumY

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Feb 29, 2012
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Hi,

I'm looking for some help figuring out draft pick probability for my fantasy hockey league draft (math of this level is not my thing).

It's a ping-pong ball draft (4 of 14 lotto style), like in real life, where each team is assigned a certain number of chances to weight their odds of getting a better pick. What I need to know is each team's odds of getting each of the nine draft picks. There are no duplicates, as in once a team is pulled their balls are removed from the equation. The weighting is as such:

Out of 1001 balls:

Team 1: 400 balls
Team 2: 300 balls
Team 3: 150 balls
Team 4: 75 balls
Team 5: 40 balls
Team 6: 20 balls
Team 7: 10 balls
Team 8: 5 balls
Team 9: 1 ball

I'd love to know how to figure this out myself (or how to get Excel to do it) but if that's too much of an ordeal just knowing the percentages for this scenario would be greatly appreciated.

Thank you for your time.
 
In the event that I have come to the wrong place, if someone could direct me to a more suitable forum to inquire about this that would also be appreciated.
 
Commissioner_rumY said:
In the event that I have come to the wrong place, if someone could direct me to a more suitable forum to inquire about this that would also be appreciated.
Click to expand...
It is not the wrong place, it is that I for one have absolutely no idea what you are asking.
Can you break that process down into understandable steps.
How do the selections work? How is it done?
 
Ok. So we started by generating a list of all the possible combinations (order does not matter) of 4 numbers from one to 14, producing 1001 possible "lotto ticket" combinations.

Then, each team is given a set amount of these "tickets" for when we pull random ping pong balls (numbered 1-14) in order to determine our draft order. The first team to have one of their tickets pulled gets the first first, second pulled picks second, and so on until we all have one of the nine picks.

What I need to know is what the odds are for each team to have their ticket pulled first, second, third, etc. The weighting (number of "tickets" each team has in the draw) is as stated above. I know each team's odds of getting the first overall pick (easy, just the number of tickets divided by the total number of tickets, 1001) but for subsequent picks I don't know how to map it out.

Does this make more sense?


If not, basically I need to fill this out....
Odds
Tickets1st Pick2nd Pick3rd Pick4th Pick5th Pick6th Pick7th Pick8th Pick9th Pick
10th40040.0%
9th30030.0%
8th15015.0%
7th757.5%
6th404.0%
5th202.0%
4th101.0%
3rd50.5%
2nd10.1%
1st0Champion picks last automatically
Total Tickets:1001
 
Commissioner_rumY said:
Ok. So we started by generating a list of all the possible combinations (order does not matter) of 4 numbers from one to 14, producing 1001 possible "lotto ticket" combinations.

Then, each team is given a set amount of these "tickets" for when we pull random ping pong balls (numbered 1-14) in order to determine our draft order. The first team to have one of their tickets pulled gets the first first, second pulled picks second, and so on until we all have one of the nine picks.

What I need to know is what the odds are for each team to have their ticket pulled first, second, third, etc. The weighting (number of "tickets" each team has in the draw) is as stated above. I know each team's odds of getting the first overall pick (easy, just the number of tickets divided by the total number of tickets, 1001) but for subsequent picks I don't know how to map it out.

Does this make more sense?


If not, basically I need to fill this out....
Odds
Tickets1st Pick2nd Pick3rd Pick4th Pick5th Pick6th Pick7th Pick8th Pick9th Pick
10th40040.0%
9th30030.0%
8th15015.0%
7th757.5%
6th404.0%
5th202.0%
4th101.0%
3rd50.5%
2nd10.1%
1st0Champion picks last automatically
Total Tickets:1001
Click to expand...
I have absolutely no clue what any of that means.
In the OP you say that team 1 has ten has 400 balls. (whatever that means).
In this post you change that to tickets.

WHAT IS GOING ON HERE?
 
Okay, my apologies, the "balls" instead of "tickets" in the OP is an error on my part. I was tired from trying to figure this out on my own, and mistyped. As far as "that team 1 has ten has 400 balls," goes, you are right, that is confusing, but you are wrong in saying I wrote that anywhere.

Trying to take out the sports/draft element (which it seems is part of the hang up here) I'll try to explain it again, as clearly as I can. For anyone who has made it this far, I thank you for your patience.

I'm going to post this the way I'd imagine an exam question would be written (the language of math, I presume, from perusing these and other forums).


Question: There is a lottery held with 9 prizes to be won. 1001 tickets are sold for the lottery (there are no duplicate tickets), and 9 people buy all of these tickets. If no one person may win more than one prize (i.e. their remaining tickets become ineligible once they've won something), what are the percentage chances of EACH PERSON WINNING EACH OF THE NINE PRIZEs. Below are the number of tickets purchased by each person.

1: 400 tickets
2: 300 tickets
3: 150 tickets
4: 75 tickets
5: 40 tickets
6: 20 tickets
7: 10 tickets
8: 5 tickets
9: 1 ticket



Is that clearer? Only the information required for the math is there, the rest of the frivolous stuff (sports, drafts, how our tickets are determined, how we generate our ticket list/numbers) is left out so hopefully that is a simpler way of explaining the same question.
 
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