Math is hard... Montana Drawing Odds

[MHMT]

I have a question for people who are good at math and are familiar with the Montana detailed drawing statistics spreadsheets.

Please correct me if I am wrong at any point. Going into the special permit draw, bonus points are squared, so (looking at the detailed drawing odd spreadsheet) if I square each level of bonus points and multiply them by the number of people that applied with that amount of points and add them all together I get the total number of chances in the theoretical hat for that particular district. If I take the number of tags given out in that district and divide it by the total number of chances, I get the probability of one chance drawing that tag.

Here is my question: If I have 10 bonus points (100 chances) and I multiply the above probability by my 100 chances, will I have a percent that is close to the true odds of me drawing that tag?

I realize this number would not be exact, as there is a different number of people at each level of bonus points, but I am wondering if the number I would come up with is meaningless, or if it predicts a more accurate percentage than what FWP comes up with?

If what I just said is complete nonsense (quite possible) does anyone know how to get a more accurate percentage of drawing a tag?

 

[----]

Your math looks right to me, yeah. I think this is how the hunters trailhead site breaks it down.

I'm pretty sure FWPs odds ignore bonus points and use just amount of applicants an total tags.

 

[jerrym]

Lets say you have 10 points for 100 chances. 3 other people put in Bill has 7 points so 49, Larry has 5 points so 25, Sue has 3 points so 9 chances. Probability is favorable outcomes / all outcomes. so you are 100/183 probability, Bill has 49/183 probability, Larry has 25/183 and Sue has 9/183 probability. So if you are like me Sue will get drawn. lol

 

[MHMT]

Your math looks right to me, yeah. I think this is how the hunters trailhead site breaks it down.

I'm pretty sure FWPs odds ignore bonus points and use just amount of applicants an total tags.

Thanks.

Lets say you have 10 points for 100 chances. 3 other people put in Bill has 7 points so 49, Larry has 5 points so 25, Sue has 3 points so 9 chances. Probability is favorable outcomes / all outcomes. so you are 100/183 probability, Bill has 49/183 probability, Larry has 25/183 and Sue has 9/183 probability. So if you are like me Sue will get drawn. lol

Much simpler way of explaining it. Thanks.

But, if there are 20 people with 10 points and 500 people with 2 points isn't that going to change the probability that I came up with to some extent, or am I over thinking this?

 

[mtmiller]

Your math looks right to me, yeah. I think this is how the hunters trailhead site breaks it down.

I'm pretty sure FWPs odds ignore bonus points and use just amount of applicants an total tags.

Randy, I don't think Hunterstrailhead has updated the MT odds since the squaring process was initiated. I contacted them and it might happen in the next couple of weeks. We shall see.

 

[Sioux33]

This is good to know as I'm doing the same thing right now. One thing I'm curious about though, why do they have a blank category? When I look under the '# of points' column, I see 0, 1, 2, etc, but also a row before 0 that is blank? Are those people not requesting points if they're unsuccessful?

 

[jerrym]

Thanks.



Much simpler way of explaining it. Thanks.

But, if there are 20 people with 10 points and 500 people with 2 points isn't that going to change the probability that I came up with to some extent, or am I over thinking this?

I see what you are saying if they draw 20 people you are guaranteed in first scenerio not in the second scenario but the bonus points are the same 20X100= 2000 and 500X4=2000. Hummm Good luck lol

 

[----]

This is good to know as I'm doing the same thing right now. One thing I'm curious about though, why do they have a blank category? When I look under the '# of points' column, I see 0, 1, 2, etc, but also a row before 0 that is blank? Are those people not requesting points if they're unsuccessful?

That's what I've always assumed, people that elected to not participate in bonus points.

You're right Miller, I was thinking 2012 was squared but it wasnt.

 

[The Hedgehog]

Are the deer and elk permit points squared or just the MSG points?

 

[MHMT]

It's kind of funny I spend the time to calculate the odds out in various districts when what I find out has absolutely nothing to do with my decision on where to apply.

 

[pointingdogsrule]

Thanks.



Much simpler way of explaining it. Thanks.

But, if there are 20 people with 10 points and 500 people with 2 points isn't that going to change the probability that I came up with to some extent, or am I over thinking this?

Yes and Yes. In a "random event" your odds of being drawn are the same no matter what because there are still a set amount of "chances" (on the first try, draw).

Example #1: ((10 x 10 = 100) x 20 = 2000 chances) + ((2 x 2 = 4) x 500 = 2000)) = 4000 chances overall. "20 people at 10 points and 500 people at 2 points".

Example #2: as opposed to (10 x 10 = 100) x 40 = 4000 chances overall. "40 people at 10 points".

On to part 2 of the question. This draw is NOT a truly Random event. Why, because once a person is drawn.... that person is removed from the draw "pool" as are the persons draw chances. That is one less individual that may draw a tag.

So in Example #1: If "one" of those 500 gets lucky then your odds are about the same for drawing the next tag, as only 4 chances have been removed from the draw pool. It was 100/ 4000 and it's now 100/3996 odds. In example #2 if a person gets drawn then 100 chances are removed from the pool. It was 100/4000 and it's now 100/3900.

Hope that's "clear as mud". I knew that there was some reason that I took those statistical classes in grad school (for figuring hunting odds).

If I goofed up somewhere.... someone can correct me. Thanks.

good luck to all
the dog

 

[MHMT]

Are the deer and elk permit points squared or just the MSG points?

It doesn't specify on the website. So I assume it is all species.
http://fwp.mt.gov/hunting/licenses/bonuspoints.html

 

[The Hedgehog]

I could be wrong but I always thought they were squaring just MSG.

 

[----]

I could be wrong but I always thought they were squaring just MSG.

I can't find it in writing, but I'm pretty sure it's everything. Doe tags, lion permits etc.

 

[rmyoung1]

I have a question for people who are good at math and are familiar with the Montana detailed drawing statistics spreadsheets.

Please correct me if I am wrong at any point. Going into the special permit draw, bonus points are squared, so (looking at the detailed drawing odd spreadsheet) if I square each level of bonus points and multiply them by the number of people that applied with that amount of points and add them all together I get the total number of chances in the theoretical hat for that particular district. If I take the number of tags given out in that district and divide it by the total number of chances, I get the probability of one chance drawing that tag.

Here is my question: If I have 10 bonus points (100 chances) and I multiply the above probability by my 100 chances, will I have a percent that is close to the true odds of me drawing that tag?

I realize this number would not be exact, as there is a different number of people at each level of bonus points, but I am wondering if the number I would come up with is meaningless, or if it predicts a more accurate percentage than what FWP comes up with?

If what I just said is complete nonsense (quite possible) does anyone know how to get a more accurate percentage of drawing a tag?

Hey, MHMT, at the risk of sounding like a statistics geek.... calculating your draw odds this way doesn't actually give you an accurate result. I'll explain why with an example:

Let's say that you have 6 points. Let's say I have none. Let's say Ted Nugent has none. And let's say Barack Obama has none. And then let's say all four of us apply for a unit together that is giving out 3 tags. You will have 37 total chances in the draw (6^2 + 1 = 37). (the 1 is for your application and the 6^2 are your points being squared). The POTUS, the Nuge, and I all have only 1 chance in the draw, so there are a total of 40 chances in the draw.

Now... if we calculate the draw odds the way it was originally presented, we would calculate your odds of drawing as (3/40 x 37) = 277.5%. Clearly, that's not right because a maximum anyone could ever have would be a 100% chance of drawing. And, clearly, your chances aren't even 100% since it is possible (albeit unlikely for a number reasons) that Obama, Nugent, and I could all draw and go hunting together. So.... here's a much closer estimate...

 

[rmyoung1]

In order to get an accurate picture, it's best (and easiest to understand) to start off by calculating your odds of NOT drawing. Since you have 37 of the 40 total chances in our example, your odds of NOT drawing are 3/40. Now you would take that figure and raise it to a power equal to the number of tags available. So.... in this example since we are giving out 3 tags we would take (3/40) x (3/40) x (3/40) or (3/40)^3, which equals 0.042%. Remember... this is the chance that you DO NOT draw. So... your chance of drawing one of the tags would be (approximately) 99.958%.

 

[rmyoung1]

Even this isn't 100% accurate since, as pointingdogs stated, this isn't a random drawing and the winners are removed from the draw along with all of their chances. So your actual odds are going to be slightly better than the calculation above, but since we have no way of knowing who is going to be drawn in the actual drawing, much less the bonus points that the lucky winners hold, the calculation above will get you a respectable number.

Does that help? You probably now want to bang your head against the wall....

 

[Straight Arrow]

Not a good example. The guy from Chicago will always win.

 

[rmyoung1]

Not a good example. The guy from Chicago will always win.

hahaha.

 

[MHMT]

Even this isn't 100% accurate since, as pointingdogs stated, this isn't a random drawing and the winners are removed from the draw along with all of their chances. So your actual odds are going to be slightly better than the calculation above, but since we have no way of knowing who is going to be drawn in the actual drawing, much less the bonus points that the lucky winners hold, the calculation above will get you a respectable number.

Does that help? You probably now want to bang your head against the wall....

Thanks for the help.

I ran the numbers on several districts using the method you described and came up with similar (but not equal) results as the method I used. Probably dumb luck. Your example clearly shows how my method didn't work.