AZ Bighorn Draw System Broken

[AZ4life]

I was looking through the 2011 Bonus Point Reports to decide what to do with my applications going forward. I noticed that it appears the system is not actually drawing tags randomly and have come to the conclusion that during the SECOND PASS something in the draw system is not operating correctly. The very high bonus point holders are not being given their fair chance at being drawn. Again, this problem is for the Second Pass, the first pass is the 20% of tags going to highest bonus points, and that is being done just fine.
I noticed that there were WAY too many O, 1, 2 and 3 bonus point holders who drew in the Second Pass in 2011 than should be statistically possible. I added up the number of applicants and tags allocated for all of the sheep hunts for these bonus point groups and then compare the results to those in the highest bonus point pools of 19, 20, 21, and 22 bonus point holders.
I've made up the table below to show the analysis I have done. To help understand how I see it, lets look at the 22 bonus point group and 0 bonus point group. There were 430 1st and 2nd choice applicantion with 22 bonus points. Each applicant with this many points get 23 "random" numbers assigned to them(1 for applying and one for every bonus point). If you then take the 430 multiplied by the 23, you arrive at 9,890 random numbers that were assigned to these top pool hunters for the Second Pass. Only TWO of these 9,890 numbers ended up being low enough numbers to actually draw a tag in this Second Pass. Now lets compare this to the 0 bonus point holders. 938 zero bonus point holders with 1st and 2nd choices, 1 random number each = 938 random numbers to be assigned in total to the zero bonus point group to get drawn and THREE got drawn! 2tags/9890 numbers vs. 3tags/938 numbers !! I could understand this happening once in 100 years, but it is consistent with 0, 1, and 3 bonus point groups drawing clearly way too often too be at all probable. I realize I may be double counting the number of applicants since one hunter applies for both a first and second choice, but this would just cut all of the applicant numbers in half for all bonus point groups I'm looking at and still end up with the same result. It just simply appears to be that the 1, 2, 3, or 4 random numbers assigned to the 0,1, 2, and 3 bonus point applications are MUCH MUCH MUCH more likely to be drawn(such as.32% vs .02%) on an INDIVIDUAL RANDOM ASSIGNED NUMBER basis than 20, 21, 22, and 23 random numbers assigned to the 19, 20, 21, and 22 bonus point holders. Someone help me see the light.

 

[Austin]

I think your logic is valid, but possibly not sound. I too have thought the SAME thing you just did when I look at the results of who drew tags and who didn't.

Possible Explanations in my Mind:

Retention : If you dont have 0,1,2,3 bp holders draw tags, you are more likely to lose new applicants year to year. Everyone has to "feel" there is a chance at being drawn. I will not speculate on how this method is carried out, if it is true.

Selection : As you get in the upper bracket of bonus points, you tend to turn towards the trophy units, a majority would. I remember when I started applying just going for any tag I could get a hand on... 45B, 45C, 13, 12, etc. Now I am at 17 bonus points, and I say to myself "If I draw after all these years, I want it to be a "quality" unit. (subject to debate) So now the upper point holders are selecting 44, 24B, 22, etc.. Most of these quality tags are drawn in the 20% bonus pass, so when it gets to the Second pass there just aren't tags left.

Maybe?

 

[AZ4life]

Looking at the hunts individually, your "Selection" explanation appears to be a valid reason for a portion of this huge difference, but when I adjust for these and take them out of the analysis, the results stay almost identically skewed. Hunts 6014, 6016, 6017, and 6035 look like the only hunts where all available tags were allocated in the 20% Bonus Point Pass, leaving no chance for anyone in the Second Pass for those hunts to draw. So I took these hunts out and we still have this huge unexplained difference in the "Weight" of the random numbers being drawn. Updated table that excludes the four hunts mentioned above:

 

[sagebrush]

Now analyze the data for the past 22 years and you will have a trend.

 

[ElmerFudd]

LAST EDITED ON May-29-12 AT 07:11PM (MST)[p]Here is the error... an applicant really only gets one random number, the lowest of however many he/she gets. An applicant can only draw one tag. More bonus points only gives a better chance at getting a low number. More applicants at fewer points should pull more tags than fewer applicants with more points. I'm betting if you found the right formula, and applied it over the years, the results would be within the expected ranges.

One more thing... The max points applications who did not draw in first max points pass had a lowest random number not good enough to draw in that round, so it likely isn't going to make the cut in the free for all round.

There is a reason some call them "Bogus Points"

 

[AZ4life]

Elmer,

By taking the lowest of all random numbers given to a person, it is in essence as if the person was given that many raffle tickets, etc.

Also, the draw and random number assigments are "redone" in each pass, in other words, the numbers used for the 20% bonus round are thrown out new numbers are produced for every applicant for the Second Pass round.

 

[mike111]

Just a reason why we should be squaring bonus points here in Arizona. It would put an end to bogus pts and still give low bonus pt holders a chance at drawing...

 

[ElmerFudd]

If they do redraw #'s between rounds, my bad.

If there were one tag, one prize, yes, you could say that it is essentially like a raffle. But most units have multiple tags. Say for example, one guy with 10 random numbers gets lucky and gets several numbers low enough. He just gets one tag and is out. Now, say the ten applicants with one chance get several low enough numbers... They pull several tags from the pool. More applicants with fewer numbers will pull more tags.

One more thing to consider... The nonresident caps, 10% of total and 50% of unit... That also automatically diverts many high points nonresidents even if they had a low enough random draw number...

The AZ draw is so tough to figure... No point in trying.. Just figure sheep is something most will die before drawing. Appreciate your luck if you beat the odds....

 

[sagebrush]

mike

I agree. I think the NV system is the best, but some would never want to give up the 20% preference draw.

 

[BigFin]

Could it be that a huge number of Non-residents make of that high level point-holder group and they are out of luck immediately, due to the 10% limited being hit early in the Bonus Pass round?

I am one of those high point holders, as a NR, are most my NR friends who apply for sheep in AZ. Given the 10% threshold, we don't expect to have the same draw odds as Residents with the same points. Heck, once the NR limit is reached, we don't have the same draw odds of a Resident with Zero points, which is fine.

So, is your total of high point holders both resident and non-resident? I suspect it is, if you took it from the pages off the downloadable reports on the website.

If so, your analysis is going to give those results shown, as many NRs have no chance of drawing after the 10% limit, but they are included in your totals when determining what percent of high point holders drew.

"Hunt when you can - You're gonna' run out of health before you run out of money!"

 

[AZ4life]

Yes, good point BigFin. There are actually alot more residents than non Res with high points, see below. So this would explain some of this phenomenon, but not alot(and would explain almost none of the highest bonus point group since there are 200+ res and only 10 non-res.)

 

[ElmerFudd]

Roughly half of the NR 10% sheep cap normally goes in the max points round. Not many NR got in from the start of sheep points, like they did with deer points. The top few sheep pools are heavily weighted resident. The hunter services hadn't got the apply, apply, apply message out yet... But still, looking at only 5% ish of the tags can go to NR in the free for all round... The NR cap does have a huge effect on nonresidents in the next round.

AZ4Life, To add to what I was trying to say, each point helps an applicants chances less than the one before it. The chance of getting a better random draw number on your next chance decreases as you get more numbers. Your table shows that. The value per bonus point gets higher as you drop in points...

 

[Heat]

I drew in 2010. I think it works perfect!

 

[tooele]

I don't forget the tags given out to friends, family, and big donors, that will scew the numbers a bit

 

[AZ4life]

LAST EDITED ON May-31-12 AT 01:32PM (MST)[p]LAST EDITED ON May-31-12 AT 01:28?PM (MST)

Elmer, I don't think you are thinking about the probablity aspect correctly with the draw numbers. For me, it should be pretty straight forward. If we simplify the process and say there are only two hunters applying for one hunt with one tag available in the Second Pass: You with one bonus point(you will receive two random numbers) and me with no bonus points(I will receive just one random number). You therefore have two chances of pulling the lowest number, #1, and I only have one chance at pulling a lower number. Therefore, your chances are double my chances. Your odds do not decrease(or at least they are not supposed to) with each bonus point from what I have read because the draw is set up in the manner I just described, and all the random numbers are given out all at the same time. This is why i don't understand why the actual results are what they are. The higher end bonus point groups should be pulling 4 time more tags than the the lower/no bonus point groups because they have 4 times as many random numbers among them.

 

[AZBob]

AZ4Life,
Pretty interesting stuff. It would be interesting to check some of the prior years to see if it was just an anomaly last year. I'm sitting on maximum resident points and hope I get a chance to hunt some day while I can. I don't just apply for the primo tags, either. Thanks for crunching the numbers.
Bob

 

[akamissedagain]

With all the technical difficulties that they have I would not be surprised at all if they ran the drawing without regard to bonus points. At a glance looking at page 4 of the 2011 hunt az book it does not look like there was the phenomenon in the 2010 drawing.

 

[mike111]

>mike
>
>I agree. I think the NV
>system is the best, but
>some would never want to
>give up the 20% preference
>draw.

I'm not sure if your referring to the 20% pass of applicants with the most points? If we did have the multiplier system in Arizona, I think the 20% pass could still take place.

 

[Arrow1]

Part of the problem here (at least my understanding of it) is you are looking at the total number of applicants in each group of bonus points. You are assuming for this comparison people with differing numbers of bonus points are applying randomly for the hunts. This is not the case, and the best example to explain this would be deer or elk tags. For example lots of folks with 1 or 2 points can draw tags in say unit 7, or its a given they will get there tag in some of the southern units, same with elk. So in this case a large percentage of people with low bonus points draw a huge percentage of the tags when you see only a few tags in the high bonus point numbers. Biggest reason here is because the folks with high bonus numbers are biding their time for a particular hunt and may ony be applying for a certain unit. Why blow 20 points on unit 7. So their perceived draw success is lower because they in reality are competting against other folks with high draw numbers rather than the masses. This is true with most hunts. Look at the distribution of applicants among units. Some units have a low number of applicants so the chance of drawing a tag goes way up, these are also the units that likely have a higher percentage of low bonus poitns foks applying. I almost guarantee guys are not blowing 20 points on those units. They are all applying for 13b or a real trophy unit.

Finally we are looking at very small tag numbers 1-3 per bonus point number. Your success numbers change up to an order of magnitude depending on if a group gets 1 tag or 2. I think if you broke it down more by unit than totals you will see the process comes more into line.

 

[ElmerFudd]

Yep. It's not a random process. There is some selection getting in the higher pools due to applicant choices and noinresident restrictions. Small numbers of tags for each hunt lead to high variance. And most important, again, is that an applicant can remove only one tag at most from the pool no matter what. I doubt the bonus point process is dishonest. But it also cannot be expected that tag pull of each pool will be proportionate to the applicants times tags respective to the total of the same. All the other factors weight the lower pools to draw more tags in that respect.