Montana Drawing Statistics Data Question

[Stone_Ice_1]

Out of intellectual curiosity, would someone with more experience in running quantitative data analysis pick a popular unit for the 2020 MT results and determine what the percentage of chance would hypothetically be per individual point based on the number of applicants, tags available, and point squaring? All assuming a perfect statistical distribution.

I tried to run this last night but my college level quant 101 class was a loooooong time ago. For a sheep unit I was coming up with each resident point being something like a 0.0054% chance.

And yeah, I know the actual odds are pretty random, but this stuff is kind of fun to mess with.

Wow this thread really took off in the time I was away.

I have done this. I'm a bit of a nerd with numbers. I do it most years with some of the tags that I specifically apply for. there are assumptions you have to make though. For example this year I know that with my points and how the draw shaped up last year, I have roughly a 15% of drawing my goat tag in the district I apply in.

Not to complicate things but something I don't think anybody mentioned is that if you have say 3 bonus points you actually get your name in the hat 10 times. You get the 3 squared = 9 plus 1 more. the reason for this one more is because if you had 0 points the first year you apply and buy a bonus point then if you square 0 you still have 0. So to make sure that person has at least a chance in the drawing every person gets the +1 at the end.

 

[Wildabeest]

Wow this thread really took off in the time I was away.

I have done this. I'm a bit of a nerd with numbers. I do it most years with some of the tags that I specifically apply for. there are assumptions you have to make though. For example this year I know that with my points and how the draw shaped up last year, I have roughly a 15% of drawing my goat tag in the district I apply in.

Not to complicate things but something I don't think anybody mentioned is that if you have say 3 bonus points you actually get your name in the hat 10 times. You get the 3 squared = 9 plus 1 more. the reason for this one more is because if you had 0 points the first year you apply and buy a bonus point then if you square 0 you still have 0. So to make sure that person has at least a chance in the drawing every person gets the +1 at the end.

Correct. So the formula for determining your probability (or the probability for any point level) would be:

(1- (((Total#Tickets - Your#ofTickets) / Total#ofTickets)) ^^#OfPrizes

Essentially what you are doing here is calculating the probability you won’t win (the underlined part), then subtracting that from 1 to get the probability you will win, and then raising that probability to the power of the number of prizes (tags) in the contest. Technically you should adjust the pool after each prize, since each winner is removed from the next prize chance, but when Total#Tickets is sufficiently large it doesn’t change the result and is far easier than trying to show a factorial formula.

And here’s how each parameter above is determined:
Your#ofTickets = (1 + YourPointLevel)^^2
Total#ofTickets = Sum (((1+PointLevel)^^2) * #ApplicantsAtPointLevel) for all point levels.
#ofPrizes is simply the number of tags issued or the sum of the #Successful at each point level the previous year.

Note that for probability at any point level, how many were successful in the previous year at that point level is nowhere to be found in the calculation. It’s irrelevant from mathematical standpoint. All it does it provide an emotional trigger to make you irrationally believe your odds are better than they are. The “so you say there’s a chance!” syndrome.

 

[BuzzH]

Absolutely. Next year everyone could stop applying altogether.

But there's a human element that these points affect, and its predictable. If everything was a completely random draw, I might not get so attached to applying in a certain unit. I might just apply wherever. A buddy might say, "hey, let's apply here this year"....I have nothing to lose because I have no points invested and next year I'll be in the same position I am this year. I won't do that in the MT draw. I target a unit and keep my points with the intention of drawing that unit, and I know that historical data tells me X points should get me that tag. I'm not going to go rogue and apply for a different unit with a buddy just because....If I draw it I could lose all my points and then have to start over on the unit I originally wanted to hunt.

The human element makes almost all the historical data a contributing factor into the next years draw. I've noticed units where it seems like after X amount of points applicants will switch units. They'll give up 80% odds for one unit for 60% for what they think is a better unit. That whole decision is based on the previous years draw stats.

People go "rogue" all the time, even in preference point pools and even in hard to draw tags. They also have different strategies.

When I was in the "acquire points" mode in Wyoming for sheep I applied for the longer odds in an area I wanted to hunt most. If my odds of a random tag are over 1:100...I don't really care if the area I want the most is 1:250. So, I applied for unit 19. Once I had the points to draw the area I ended up getting, I cut the line and drew, surely screwing up the data from the year before and I pushed at least one guy back from the lower point pool. Also, a lot of people in front of me could have jumped in the year I drew...and I would have been out my tag as well. Just don't know what people are going to to do from year to year.

Same with moose, the year I drew I was the top point holder that applied that year, I didn't apply for that area for a variety of reasons in the past, mainly because of conflicting hunts. But, I definitely skewed odds and the tag I took impacted the lower point pools and draw odds.

So, IMO, the human element is not predictable at all, and really does make it difficult to predict the next years draw odds.

 

[SAJ-99]

Wow this thread really took off in the time I was away.

I have done this. I'm a bit of a nerd with numbers. I do it most years with some of the tags that I specifically apply for. there are assumptions you have to make though. For example this year I know that with my points and how the draw shaped up last year, I have roughly a 15% of drawing my goat tag in the district I apply in.

Not to complicate things but something I don't think anybody mentioned is that if you have say 3 bonus points you actually get your name in the hat 10 times. You get the 3 squared = 9 plus 1 more. the reason for this one more is because if you had 0 points the first year you apply and buy a bonus point then if you square 0 you still have 0. So to make sure that person has at least a chance in the drawing every person gets the +1 at the end.

Good point. I forgot about that. I am also not sure the numbers contain those that just bought points. I tend to think they may not be anywhere in there because the numbers are run from the draw results.

 

[brocksw]

People go "rogue" all the time, even in preference point pools and even in hard to draw tags. They also have different strategies.

When I was in the "acquire points" mode in Wyoming for sheep I applied for the longer odds in an area I wanted to hunt most. If my odds of a random tag are over 1:100...I don't really care if the area I want the most is 1:250. So, I applied for unit 19. Once I had the points to draw the area I ended up getting, I cut the line and drew, surely screwing up the data from the year before and I pushed at least one guy back from the lower point pool. Also, a lot of people in front of me could have jumped in the year I drew...and I would have been out my tag as well. Just don't know what people are going to to do from year to year.

Same with moose, the year I drew I was the top point holder that applied that year, I didn't apply for that area for a variety of reasons in the past, mainly because of conflicting hunts. But, I definitely skewed odds and the tag I took impacted the lower point pools and draw odds.

So, IMO, the human element is not predictable at all, and really does make it difficult to predict the next years draw odds.

Sure people do. But I bet it happens in Idaho and NM more than in MT. They lose nothing by changing their mind from year to year. Some years those applicants apply for bighorn, some years they apply for a controlled elk, the next year a different unit LE elk with a different weapon. They lose nothing by going back and forth....nothing. Every single year = 1 entry and they can spend it how they wish. They don't lose points in any circumstance. They don't lose money or time that they would've invested in those points. The next year...no matter what...they're right back where they started the year before.

The human element is very predictable. Look at the draw statistics in MT, its not difficult at all to project the approximate success rate to draw a 620 archery elk tag with 4 bonus points next year. Same with 410. Same with the 900 tag. Same with a vast majority of every single bonus point unit in MT except for the extremely difficult to draw (i.e. very few tags available) units. If you can't figure out the draw odds for a Special Permit elk in the breaks, or custer, it has nothing to do with it being difficult to predict....because the numbers are there and they're incredibly consistent from year to year.

 

[BuzzH]

Sure people do. But I bet it happens in Idaho and NM more than in MT. They lose nothing by changing their mind from year to year. Some years those applicants apply for bighorn, some years they apply for a controlled elk. They lose nothing by going back and forth....nothing.

The human element is very predictable. Look at the draw statistics in MT, its not difficult at all to project the approximate success rate to draw a 620 archery elk tag with 4 bonus points next year. Same with 410. Same with the 900 tag. Same with a vast majority of every single bonus point unit in MT except for the extremely difficult to draw (i.e. very few tags available) units. If you can't figure out the draw odds for a Special Permit elk the breaks, or custer, it has nothing to do with them being difficult to predict....because the numbers are there.

Yes, I agree in the total random states, people probably jump around more. I also agree somewhat in more predictability in areas with lots of tags.

Montana NR's are forced to jump around since the moose, sheep, and goat units a NR can apply for aren't even the same every year. With no predictability in that, how can you say where people are going to have the best odds and worst odds, when the combination of units isn't even consistent from year to year?

Also, its funny how many people apply on memories...

How do you predict a guy that screws up his apps, gets too old, or whatever and draws a cow moose in WY with max points?

Happens, but ain't predictable.

 

[brocksw]

Montana NR's are forced to jump around since the moose, sheep, and goat units a NR can apply for aren't even the same every year. With no predictability in that, how can you say where people are going to have the best odds and worst odds, when the combination of units isn't even consistent from year to year?

Moose, sheep, and goat for a NR would all fall under the incredibly difficult to draw as a NR. So no matter how many points you have or don't have its difficult to predict draw stats. We've gone over this aspect already....at length.

Also, its funny how many people apply on memories...

How do you predict a guy that screws up his apps, gets too old, or whatever and draws a cow moose in WY with max points?

Happens, but ain't predictable.

Honestly Buzz...I can't comment on this. I mean this is conjecture squared by conjecture. If I had to make a bet, it's not enough to even remotely effect the draw in most cases. In the rare case that it does, I'd bet that it doesn't distort the entire applicant pool for that unit.

 

[Deleted member 28227]

People go "rogue" all the time, even in preference point pools and even in hard to draw tags. They also have different strategies.

When I was in the "acquire points" mode in Wyoming for sheep I applied for the longer odds in an area I wanted to hunt most. If my odds of a random tag are over 1:100...I don't really care if the area I want the most is 1:250. So, I applied for unit 19. Once I had the points to draw the area I ended up getting, I cut the line and drew, surely screwing up the data from the year before and I pushed at least one guy back from the lower point pool. Also, a lot of people in front of me could have jumped in the year I drew...and I would have been out my tag as well. Just don't know what people are going to to do from year to year.

Same with moose, the year I drew I was the top point holder that applied that year, I didn't apply for that area for a variety of reasons in the past, mainly because of conflicting hunts. But, I definitely skewed odds and the tag I took impacted the lower point pools and draw odds.

So, IMO, the human element is not predictable at all, and really does make it difficult to predict the next years draw odds.

Yeah when I started applying in 2014 I read this thing on a forum about "having a plan" for every tag you apply for from some, dude was some bro bra from WY.

Been doing it ever since, he's a pretty smart guy... mostly

 

[atlas]

Needed to make a full-stack web application for my resume. So I'm working on a draw odds site. It'll likely only ever be Montana, mostly because I don't think I have the mental bandwidth to dive into the rules and regs of any other state.

When I host the site, I'll share it with you all. The site will always be free.