Lottery probabilites

http://img.photobucket.com/albums/v2...babilities.jpg

This data comes from creating a draft where the worst team has a 25% chance of getting first pick and running it one billion times. The teams are across the top, and the picks are down the side. So if you look at column 3, row 2, then you'll see that the third worst team has a 14.36% chance of getting the 2nd pick.

Hopefully with data to go on we can have a more productive discussion. In fact looking at it has made me reconsider certain things -- for instance, the worst team has a 23.34% chance of getting 5th pick, which means it would happen about once every 4 or 5 seasons. It might be better to have some sort of requirement that no team may drop more than 2 or 3 places in the draft. Just a thought.

perhaps increasing the percentage chance they have of winning the draft or even just increasing the gap over the second and third worst teams would fix that problem

You cant have a lottery and say the best you can do is move up or down 3 spots it would be like trading, and saying you cabt trade a 15th pick for an 8th.

As a lottery you have to accept the results of it

Thanks TC - those numbers really help in picturing what the outcome would be.

I think the Horseman is right, increasing the % chance of getting the top pick should make it look better. Ideally you wouldn't want anyone to have a significant chance of dropping more than, say, 4 places?

EDIT: Apologies TC, your numbers are correct [img]redface.gif[/img]
<font color="#000002"><font size="1">[ January 20, 2005 08:06 PM: Message edited by: Leonidas ]</font></font>

<font color="#000002" size="1">[ January 20, 2005 09:11 PM: Message edited by: Leonidas ]</font>

I think it looks great. But maybe only a 25% chance for the worst team is a bit low. What it is in the NBA lottery?
dicky

If only 4 or 5 teams have a chance at the lottery picks, then yes, 25% is way too low.

The NBA uses 25%,

http://www.nba.com/history/draft_evolution.html
Scroll to the bottom for the recent rules...

You would think the worst team having less then a 50% chance of "wining" the lottery woudl be a bit too extreme. and droping more then a place or two really is a bit of a climb.

The worst team will get robbed eventualy - that is what the Lottery is designed to do, so why not make it as painless as possible when you push this through?


-- BTW, thanks for the research TC.

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Originally posted by King Z-ster:
If only 4 or 5 teams have a chance at the lottery picks, then yes, 25% is way too low.

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<font size="2" face="Sylfaen, Verdana, Helvetica">16 teams have a chance at the lottery picks.

This table really helps to understand what you are talking about.
I think it should be more than 25% chance. Can you run it with 33%?
Since the NBA has 13 teams in lottery and we seem to be heading for 16 teams, how are you adjusting the tables for that?
Is the level of complexity added justified for the possible result? While there is an occassional standout, usually the first 4 or 5 picks are reasonably strong. I was picking no 4 in my first draft and got what I believe was the best player in the draft (and Leo sure did not hesitate to buy him from the newbie with a decent player in return).
While putting in something like the NBA is nice, I am of the opinion that the amount of complexity added will not add much to the game and will increase the chance of someone feeling like that got screwed.

I think with 16 teams in the lottery, 25% is still a very high probability for the worst team to get the first pick. That means a 46% chance that they will pick either first or second. A 63% chance that they will pick in the top three, going up to 77% for top four.

In my opinion, that's a good balance between making it pretty certain that the team with the worst record will get a very high pick, and still providing enough of an opportunity for the other non-playoff teams to at least have a little bit of a chance.

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Originally posted by Tall Tex:
This table really helps to understand what you are talking about.
I think it should be more than 25% chance. Can you run it with 33%?

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<font size="2" face="Sylfaen, Verdana, Helvetica">Yes. See Below.

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Since the NBA has 13 teams in lottery and we seem to be heading for 16 teams, how are you adjusting the tables for that?

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<font size="2" face="Sylfaen, Verdana, Helvetica">They've already been adjusted. There are 16 columns for the 16 teams we'd have and the numbers are correct for 16 teams.

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Is the level of complexity added justified for the possible result? While there is an occassional standout, usually the first 4 or 5 picks are reasonably strong. I was picking no 4 in my first draft and got what I believe was the best player in the draft (and Leo sure did not hesitate to buy him from the newbie with a decent player in return).

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<font size="2" face="Sylfaen, Verdana, Helvetica">IMHO I think it adds fun to the game. Certainly someone will get a worse pick than they expect and someone will get a better one. Will they pick the best guy with that? Who knows? Obviously if someone anticipated being the worst team and getting the best pick for their trouble, they'd hate a lottery system, but do we really want to reward that kind of strategy?

Anyway, I ran the numbers with worst team having a 33% chance of top pick. They're not as exact since I didn't run it as many times, but they should be close enough to get a good feel for what would happen.

http://img.photobucket.com/albums/v2...bilities33.jpg

Thanks you for aniticipating the question.
should the 13 to 16 have more of a chance of improving their position? I have had a couple of times that I made a run at the no 8 playoff slot only to miss it by 1 or 2 games. I thought part of the logic of the lottery was to give the guys that are trying to make the playoffs but miss a chance to improve their position in the draft. 99.5% chance of being 16th does not seem to be much improvement

Reading through these posts again, there seems to be some confusion how the lottery works. I'll try to clear it up, but if there are any more questions, feel free to post.

First of all, all 16 non-playoff teams are entered into the lottery. Their chances of getting the first pick are those in the top row next to pick 1. As you can see, team 16 still has a chance at the first pick, but it's very small. Only 1 time in 285 seasons would the 16th team get first pick.

Second, only the top 4 picks are available in the lottery. That's why each team has numbers in those rows, and then the lower teams all have gaps after that. After the first four picks are randomly selected, then teams fill in based on their record. If team 15 gets lucky it can get a pick in the top 4, but if it doesn't then it's almost certain to get pick 15. There is one other option available to it, however, and that is when team 16 gets one of the top 4 picks. In that case team 15 is guranteed to pick 16th.

So, each team is guaranteed not to fall more than 4 picks from their starting pick. If team 1 is unlucky enough not to get a top 4 pick, then they will absolutely get pick 5.

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Originally posted by Tall Tex:
Thanks you for aniticipating the question.
should the 13 to 16 have more of a chance of improving their position? I have had a couple of times that I made a run at the no 8 playoff slot only to miss it by 1 or 2 games. I thought part of the logic of the lottery was to give the guys that are trying to make the playoffs but miss a chance to improve their position in the draft. 99.5% chance of being 16th does not seem to be much improvement

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<font size="2" face="Sylfaen, Verdana, Helvetica">It all depends on what everyone's after. We can make all sorts of alterations to the lottery. We can decrease the worst team's chances of first pick which bumps everyone else's chances up more. We can change from an exponential progression to a linear one which would keep everyone's chances closer together. We could have a lottery all the way down which would make it possible for any team (in the lottery) to pick from 1st to 16th.

These aren't difficult changes to make. It all just depends on what people want out of the draft lottery. I set this one up to be along the same lines as the NBA lottery with the only changes being 4 picks being random instead of 3 and 16 teams in the lottery instead of 13.

perhaps making it only the top three picks being available would help out too, it means that the worst team never picks less than 4th in my opinion this would be better and more fair than picking at fifth, yes i know its only one spot and the team would have to be unlucky to not get a top three pick anyway, its just my feelings [img]smile.gif[/img]

FIRST: Great job TC keep it up

SECOND: We use 4 teams in our league because instead of only 12/13 teams like the NBA uses we have increased it to 16 teams because thats how many dont make the playoffs for us.

By increasing that number we also increase the number of lottery spots that can change from 3 to 4

So it's decided?

I was under the impression this was only to be a tool to show the possible mechanics...

nothing has been decided upon yet ... i just asked TC to start making this stuff to show everyone what could or would actually happen if we brought this to our league

It's certainly a good idea to make sure that everybody is fully informed as to the consequences of a "yes" or "no" vote, and this a great way to help with that.

Has Scott actually said he'll go ahead and try to make the change if we vote in favour of a lottery?

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Originally posted by Fasttracker:
FIRST: Great job TC keep it up

SECOND: We use 4 teams in our league because instead of only 12/13 teams like the NBA uses we have increased it to 16 teams because thats how many dont make the playoffs for us.

By increasing that number we also increase the number of lottery spots that can change from 3 to 4

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<font size="2" face="Sylfaen, Verdana, Helvetica">This is what made me believe it's all ready been decided.