**Contributors to this thread:**

For Colorado, in particular, the failure to draw seems to always generate a smattering of frustrated comments about the workings of the draw. This includes complaints such as “a guy drew with only 3+0” and “weighted points mean nothing” and “after you attain 3PP everybody has exactly the same chance”. And I’ve heard the same comments many times in personal discussions with fellow hunters. But is that really true? The notion of “meaningless weighted points” contrasts with the assertion made by CPW in their publications. Refer to the following quote contained in the Sheep & Goat brochure, page 6:

*“WEIGHTED PREFERENCE increases your probability of drawing. It is calculated by converting your application number into a different, random application number, then dividing that new application number by the amount of weighted points you have, plus one. This generates another new application number. Applications are sorted by this new number from lowest to highest and low numbers for each hunt code are awarded licenses.”*

This is a very simplified version of how they actually do it. The random number generating process is explained in much more detail in the fine write-up done by John Legnard many years ago, which can be found on the RMBS website. But for this particular discussion, we really don’t care HOW they assign random numbers. All we want to know is that it’s done fairly, meaning that the process is truly random for all applicants. So when they say “weighted preference increases your probability of drawing”, how can we know if this is true? No doubt there are various reasons for guys “not buying it”. For those who’ve applied and amassed points for decades, naturally there’s an expectation to draw which builds up over time, making the stark reality of another rejection hard to accept. We all try to stay optimistic and hopeful about drawing success, even though the stats will show us that such success is quite rare. The arrival of bad news each year is a tough pill to swallow and I think we instinctively attack the process in response. Adding to the frustration, some of us may have a friend or relative who has drawn, and we want to mentally correlate that to a future success for ourselves. But the reality doesn’t change, which is the severely over-subscribed nature of these hunts. Just knowing someone who drew, won’t help us draw.

But still, since we’re gamblers, we plod forward and continue applying again and again, hoping to beat the odds. The smart gambler however, needs to fully understand the odds and the process in order to make the best decision on which games to play and how to play them. So one key question about the Colorado draw is....does weighted preference do anything for us?

In general, my own personal preference would be for a fully random draw for all species. But most state game agencies see this much differently. Most of these game departments would like to have us “addicted” to their systems, by means of a promise for better odds over time. That way we keep playing and contributing to their coffers. Since we can’t change the way they do their draws, the very least we can do, if we want to consider gambling in their system, is to fully comprehend how it works.

When someone asserts that points are meaningless, that opinion is useful only if backed up with facts. Fortunately we now have the data needed to get an answer. Prior to 2015, we had no way to test these anecdotes.....there was not enough detail provided in the CDPW draw data. Since 2015 however, CDPW has been kind enough to provide an additional level of detail in their draw reports. Now the number of applicants in each point class is reported by hunt code, including the points held by each successful applicant. So we can analyze how point status affects draw results for individuals.

To keep this analysis simple, I’ll first look at one species. I happened to pick resident Mountain Goat. It happens to be a species that I got lucky and drew in 2014. Of course we could also do the same calculation for NR’s, and for any other species. But since it takes a lot of time to extract all that data, I’ll stick to just one species for now. For this exercise, I want to answer two basic questions:

1. How do the actual draw results compare to expected draw results that we’d calculate based on the weighted point status of the applicants? In other words, do WP’s improve draw success?

2. Did applicants in the lower weighted point classes (say those holding 0 thru 5 WP) draw an unexpectedly large share of tags, compared to the applicants in the higher weighted point classes (6-16 WP)?

To answer these questions, I’ll first calculate the expected draw success of applicants based on the following assumption. In this assumption, every additional weighted point provides a linearly proportional increase in draw odds for the individual applicant. Stated more simply, the assumption is that for each additional weighted point possessed by an applicant, an increase in odds equal to “one more ticket in the barrel” is provided to the applicant. The mathematics for this assumption are actually crystal clear, but explaining it here would take up more space than I care to use at this time. In any case, the results will tell us whether or not the assumption is correct. Because after making those calculations, we can then compare the predicted results to the actual draw success results for the various WP pools. It should be reasonable to do so at this time, now that we’ve amassed 3 years worth of draw results. If the assumption turns out to be false, then the CDPW’s draw algorithm could be flawed. If we could prove there’s a flaw in the CPW’s draw algorithm which favors one class of applicant over another, or one individual over another, then someone could sue, I suppose. Any such flaw seems extremely unlikely though, since the CDOW would have vetted their process very carefully before implementation many years ago, to avoid that very pitfall.

I included all the either sex Goat hunts, with no Nanny hunts or population-reduction type hunts, since there is very little participation in those draws from the higher point classes. This is a 3 year summary representing a combined 2015, 2016, and 2017.....the three years for which this data is available. Calculations were done for each of the 3 draw years separately, and the results were summed.

Column 1 is the weighted point status of resident applicants.Column 2 is the number of resident applicants with that number of points who applied for a hunt

Column 3 is the total number of points for that pool that are in play.

Column 4 is the calculated number of applicants who should draw. Here we assume a reasonable distribution of applicants across the various point classes by unit, which is why I left out the low-demand hunts. A more precise analysis could be done with unit-by-unit data, but that’s more time than I have!

Column 5 is the actual number of applicants who drew from that point pool.

In conclusion this analysis shows that:

1. The number of applicants is growing each year...no surprise there. And that the bulk of applicants are in the lower and mid point classes.

2. That we can predict overall draw success based on weighted point status.

3. That increased weighted points yields a linear increase in draw odds, comparable to the “one more ticket in the drum” concept.

4. That there is no apparent bias, statistically, in the draw process towards any particular weighted point pool.

Note that over the 3-year period, the model predicted that those applicants in the 6-16 WP groups would draw 259 tags, and the CPW report shows they actually drew 260 tags. And those applicants in the 0-5 WP pools were predicted to draw 154 tags and they actually drew 153 tags. Statistically dead-on, for all practical purposes.

The positive in Colorado’s weighted point system is that at least it gives every applicant somewhat of a chance. But here is the key concept to remember....for a given hunt, an individual applicant with 16 WP’s has (16+1) or 17 times better odds than an individual applicant with 0 WP’s.....but (hypothetically speaking) 17 times 1/10th of 1% is still poor odds. The WP system will never guarantee anyone to draw even with max points. This probably won’t change much over time, because the pool of applicants keeps growing by leaps and bounds.

Any chance you'd allow the Rocky Mountain Bighorn Society to post it the article on online or in the magazine? It would be a nice follow up to the "How the draw really works" from several years ago

One detail that is difficult to quantify is the bias of higher point holders applying for the better units and lowering their odds of drawing. I think the higher point holders feel they have more at stake and then then to look at the best units as the ones to draw. For example in the 2017 Colorado bighorn sheep stats SMS79W1R had 30 max point holders at 3 and 16. By far the most of any hunt code in 2017. A lucky person at the 3 and 14 level drew out of a total of 11 at that level. There are several unit hunt codes with no max point holders even applying. Overall Colorado's system of picking a specific unit hunt code and method of take is the best way to approach getting the tag the lucky person wants vs picking 5 hunts and the lucky winner gets the top choice that is left ie the Nevada model. I would like to see a comparison of draw chances squared vs weighted point and see if there is a big enough advantage to encourage Colorado to shift to that style of system.

Thanks for the great analysis.

Sandbrew

The results are very much like a traditional bonus point scheme. In a standard bonus point scheme your odds will scale as [1-(1-P0)^(BP+1)]; where P0 is probability of drawing with zero bonus points (BP). This expression starts out looking linear but then rolls over and asymptotically approaches 1 at high BP.

In Colorado's "divide random# by WP+1" method your results show that the odds also scale linearly, and looks very much like a standard bonus point method. At higher draw odds I predict the two methods will start to yield different results, but with the max odds still being less than 10% they will be indistinguishable.

Jims, the odds for NV will scale as [1-(1-P0)^(BP^2+1)], see the results on toprut.com (free), or gohunt (if you have a subscription) for examples. At small odds your odds scale as (BP^2 +1), so guy with 3 points has 3*3+1= 10 times the odds of guy with zero points.

Sandbrew's Link

Sandbrew

I am not a math guy and appreciate the comfort in knowing the system actually works as designed overall. I got into the sheep application game in 2002 in basically all states that offer a sheep tag. So I am a high point holder in all states, but a max point holder in none.

Lightning struck and I drew a NR AZ desert sheep tag in 2014 with 13 points. I also drew the only random NR moose tag in WY Area 1 in 2005. So I consider myself indeed fortunate and playing with "house money" at this point.

The WY draw will always be a slight source of frustration every year, as those with 2+ more points than me are drawing their tags at will, while I may never draw one. Oh well.....

It would be interesting to show side by side comparison of squaring vs weighting pts draw odds for a super tough and an easier draw unit. I know NV shows draw stats similar to Colo so this ought to be possible...and fairly easy to calculate. Even if you had 1 or 2 examples of Colo vs NV's (squaring with 1st choice) it would be a very interesting comparison!

Notice that the upper point pools could see as much as a doubling or more in their draw odds, but at a high cost to the newbies in terms of draw odds. The mid-tier applicants draw odds aren't changed much. Actual odds from draw to draw will vary of course. Note that some point tiers have the same odds....this is because of rounding in the "expected tags drawn" column (can't issue a fraction of a tag). Once again, this could be run in many different ways using other species, years, and in much more detail by drilling down to unit-by-unit results. But this should give you a general sense of the impact of point squaring.

While I appreciate all the work and figuring that went into your post, It doesn't answer your own question of "are weighted points meaningless" or put another way, "do they provide you with an advantage." The only true way to determine that is to compare within each hunt code to determine if the weighted points benefited the guys that drew. Did the guy that drew with 3+15 points start with a higher number and when the weighted point divisor was applied beat out a guy with fewer weighted points or would he have drawn regardless because his random number was much lower to begin with? How many drew a tag because of their weighted points and not their low random number?

JDM you have a point about the only way to really know how the draw played out in exact detail, but I believe the overall results in the OP answer the question. Albeit coming at it from a different (and simpler) way.

Are there better systems that would work? Maybe. But no matter what system is used, some (many) would still complain. As it is now, some complain that it should be totally random and some that it's not random enough. It's impossible to please everybody, or anybody that wasn't successful.

But wrongly maligning an entire system as not doing what it says it does/is designed to do serves no purpose other than to create needless ire among folks who don't take the time to understand the whole process.

What amazes me continues to be the # of applicants who apply for units in which they have zero chance to draw (for any number of reasons).

What also amazes me is the bad info many magazines/draw services put out there re: both odds and chance to draw.

Example: Eastmans' just put out their MRS info on the AZ sheep draw. At the end (after a basically correct description of the system) - they concluded by telling their NR readers that they had no chance to draw in AZ unit 43B unless they had maximum points. This is simply wrong/bad info. Because 43B allocates 5-7 tags each year (the highest in the state), it is one of the very few units where a NR with less than max points actually DOES have a chance to draw a sheep tag.

I am living proof - drew in 2014 with 13 points. I know of at least 3 other NRs who have drawn the 43B tag with less than max points.

The squared numbers in the table look pretty darn fair! Squaring pts makes a lot of sense to me...and is clear and simple to understand.

To add fuel to the fire....It seems like the current pref pt system in Colo for elk, deer, and antelope would be better off if everyone had a chance to draw tags and those with max pts had an even better chance to draw. With the current pref pt system kids just starting off applying will likely never draw unit 2 or 201 elk tags in their lifetimes! Colo actually doesn't have that many limited elk units so there is super high demand for the few units that offer limited tags. All Colo deer units are a draw so it disperses applicants over a lot more units and tags.

Actually, the CPW is supposed to take into account how many APPLICANTS there are for a specific unit by weapons choice, plus figuring average success rates for each weapon type when deciding how many tags are available. For example, if archers flood applications for a particular unit, that should result in more archery tags even if that results in fewer rifle tags. So you SHOULD apply for a unit and not just a PP.

"...kids just starting off applying will likely never draw unit 2 or 201 elk tags in their lifetimes!"

Maybe, maybe not. Many of us that have been in the process for ever, are getting older and will start to drop out in increasing numbers whether we want to or not.

"...Lets, see...3 days to design a draw system that is complicated to laymen and my boss, 3 days to integrate it into the system, and 6 months to play Call of Duty"

"Boss, looks like about an 8 month project but I think I can get it done a little over 6 months if I pull a few all-nighters"

"That long? I thought it would be easier but your the tech guy"

"I wrote up an overview of how it works, look it over and let me know what we could change to go faster"

"....Um...wow...looks complicated, I'll let everyone know to be looking for it in 6 months"

Maybe I am missing something.....

Squaring the points and dividing by that number would provide some additional weight to the guys that have been putting in for longer that would help.

Not sure, but I think states like NV and AZ give out additional chances for each point. That would actually seem to be a more fair system. Particularly with point squaring. Over time, it is like the application fees equate to purchasing additional chances in the lottery. It is all a computer algorithm and not that difficult to change the equation.

The correct answer is 74,769 and the one with 9 weighted points would have drawn the tag in your example.

Sticksender's analysis is correct. Weighted points do make a difference and that's a fact. It's just not enough of a difference for the people complaining to be happy about the system.

__RESULTS__of the draw. What we're talking about in this analysis is the PROBABILITY of drawing. We know the CALCULATED PROBABILITY for a particular applicant to draw based on his weighted points, before any portion of the draw is conducted and before any random numbers are assigned.Here's the playing card illustration again, to possibly help you understand PROBABILITIES versus RESULTS. Let's say we have a fair shuffled deck of cards and we want to know what is the chance of turning over the top card and have it be an Ace of Spades. Following your line of reasoning, the calculated odds to turn the Ace of Spades would depend on whether the card is an Ace. After all, the lucky guys who at least get an Ace on their first turn have the best chance of winning, since there are only 4 Aces in the deck, right? Of course that is absolutely wrong with regards to calculating odds. The calculated probability of turning over an Ace of Spades is incontrovertibly 1:52 for a fair shuffled deck. Those calculated odds are known with absolute precision, the moment the deck has been fair-shuffled, and before a card is turned. By the way, don't confuse this with an analogy. It is not an analogy to the Colorado draw in any way. It is merely an illustration of the concepts of probability.

You can slice a pie many different ways but when you have one pie and 10,000 dinner guests, creative slicing won't do much.

Yeah I understand draw odds. Your first number is assigned randomly just like it says on your rmbs link of how the draw really works. It is not the result of the draw it is predetermined before the drawing actually begins. So your weighted points play no role in your first assigned random number. Again you can not remotely predict odds in the sheep draw. Take S6 rifle for example this year. 45 applicants for 1 tag from 3 plus 16 to 3 plus 0. A guy with 3 plus 4 drew. There is no way to predict odds of drawing and that guy received the tag because he started with a low random PREDETERMINED number before the rest of the draw process took place. Changing to a bonus point style does not take away from any group everyone still has a chance.

*"Again you can not remotely predict odds in the sheep draw."*Replace the word "odds" with "results" and you're correct.Orion said:

*"there is no way to predict odds of drawing and that guy received the tag because he started with a low random PREDETERMINED number before the rest of the draw process took place"*Replace the words "odds of drawing" with "results of the draw" and you are correct.Again, where you're lost is you're thinking odds calculations are some sort of attempt to predict the results of one year's draw. They are not. They are a mathematical determination of the mean results that will occur when identically-designed random events are repeated an infinite number of times.

Desert sheep tags are a true lottery, that is unfair to the applicant who has been putting in for 50 years since anyone can jump in and have the same chance. The CO elk draw for premium units is unfair to anyone starting out (unless you get extremely lucky in the hybrid draw). And the hybrid draw is unfair to max point holders who now have their chances reduced because of it. Just a couple of examples for you.

Changing sheep to a bonus point system would indeed "take away from any group". It increases the odds for higher point holders, thus it decreases the odds for lower point holders.

Orion - You changed your example above to show a scenario where a 5 weighted point holder would lose out to a 2 wp holder after I showed you that the 9 wp holder would have drawn the tag. Of course that can happen, and it does. Your (now edited) example still shows that the 5 wp had higher odds going into the draw, which is the original point of this thread.

Don't get hung up on the random number. Everyone has the same odds of drawing a low random number so you can ignore that. The odds are increased for higher point holders since you use weighted points to divide that random number, thus creating more random numbers that you could draw a tag with.

It sure looked to me that Sticksender showed that the weird CO system in fact behaved exactly like a bonus point system.

But that is an incorrect statement. Everyone has the same odds of drawing a low random number, but not everyone has the same odds of drawing a tag.

Answer this question. Two applicants, one with 3+0 and the other with 3+15. 3+0 gets a random number (after reversing by the tiles) of 062501 and 3+15 gets a random number of 999999. Who gets the tag? Who had more random numbers that would allow them to get a tag? (FYI: the process they use is to divide by 1 and 16 in this situation, not 0 and 15)

samman - I'm not 100% on this, but I don't believe the DPW releases the random numbers.

All I know is it makes me happy that I'm competing for tags with some people that refuse to understand the system and blindly throw darts at a board. That in itself increases my odds.

If it were a "true bonus" point system, where your name was entered once for each point, it still might not be enough to draw the tag. The guy with fewer points might still get it. And that's the whole point of any bonus point system.

Nobody is saying that the random number is meaningless and weighted points dictate everything. It certainly helps to get lucky and draw a low random number, but it's not everything. Weighted points help by lowering your final number. Both luck and the number of weighted points play a role in drawing a tag.

Looking at Colo from an nonres perspective....Many states are charging $50 to $100/species for nonres applications. When I apply for out of state licenses at least I know I'm getting a little closer to drawing tags with a bonus pt or pref pt system that actually benefits those that consistently apply for years and years...especially when investing so much cash and years applying for tags. The draw systems that don't make sense (Wyo sheep as a great example) I have dropped out of years ago.

But I agree. The Colorado system is much more convoluted than it needs to be.

Also, those of you that want a "true bonus point" system, how different do you think the actual mechanics of that drawing are from the CO weighted system?

In theory, you just "put more tickets in the hat" for each point and have the computer pick a ticket at random. The problem is that computers can only do "pseudo-random" not true random processes, and so you end up with something like CO does. I assume any bonus point state does something similar.

Otherwise if someone has time on their hands and a really big hat, I'm sure the state would gladly let you take on all the costs and critcism of running the draw.

For this example a person with 3 -16 has the worst possible converted draw # of 999,999 that number is divided by weighted points (16) + 1 so 999,999/17 = 58,823. Anyone with one of the 941,175 higher numbers doesn't draw when the 3-16 person does. The dividing power of the weighted points just put the 3 -16 person ahead of 941,000 number combinations higher than 58,823. Sure there are still 58,823 combos of converted draw #s and and weighted pints that will beat the 3-16 persons worst case but the odds are far better than with no weighted points in play.

I do like squared chances idea but in Sticksender's model you are only dropping 7 people per year out of the top pool and there will be 32 people who think this system still doesn't work either.

Love the B&C goat. He's a monster!

Sandbrew

My life experience has shown me that hunters aren't the sharpest knives in the drawer, so the ones that are savvy about calculating draw odds are in the minority.

Sheep is a little better as some units have higher odds, and goat is actually a very draw-able tag if you play your cards right.

I'm young, and I absolutely will not apply in states that operate on preference vs bonus points. It's a lost cause for anyone who didn't start applying while I was still playing little league baseball.

sticksender, thank you for doing a fine job of evaluating and presenting this. I think that your work clearly shows that the odds did balance out in even a very small sampling. Of course those who drew with 0 or 1 points beat the odds but with so many of them applying the odds were that some would draw.

I once did a similar comparison for Nevada because a guy called BS on points helping. Turns out his claim was wrong by over one hundred fold. When forced to see it he simply said "well maybe but it still sucks for the guy with a lot of points who did not draw"! Ignorance is bliss and a sucker is born every minute.

1) has rudimentary mathematical skills 2) can read and comprehend a simple data table 3) has at least grade school reading comprehension

Then yes I confess to being a BSG.

Weighted points give you a slight advantage but when it comes to ram and goat tags, odds of drawing are slim no matter how many you have. As we add more and more people to the applicant pool, the worse the odds get for everyone.

There is no way to predict when or if you might draw. The odds are you won't at any weighted point level, but that beats the odds you have if you don't apply.

I do not claim to be able to predict the odds but I'm either really really lucky or very good at using draw odds to my advantage to draw tags. Likely a combo of the two.

So far in Colorado I've draw- Archery sheep tag with 3 points. Rifle ewe tag with 1 point. My son drew a rifle ewe tag with one point.

Mt goat drew a tag with 3 and 5 weighted points. Was first runner up with only 1 points on a tag last year.

How about moose tags on same weighted system. Cow tag with 3 points Then an archery bull tag with 3 and 4. Another cow tag with 1 point.

That's a pretty good run in 17 years.

Bottom line no draw/bonus point/weighted point system is ever going to make everyone happy. There are simply not enough tags to go around to everyone that is applying. Using math/odds/statics/luck and reports like the one Sticksender prepared to increase you portability of drawing is all part of the game for me.

Best of luck to all who drew and good luck next year for those who didn't.

Sandbrew

If the intent of weighted points was to give applicants who have been in the system the longest a statistical advantage then the system is failing. YES there is a mathmatical/statistical advantage with the current system but it is so slight as to be meaningless.

The system could be fixed by squaring weighted points, or using any multiplier against a weighted point to increase the statistical viability of a weighted point. Doing that wouldn't really harm any point group IMO, unless we believe someone with 3 points should have NEARLY the same statistical opportunity as someone with 16.

The answer to the burning question is, yes weighted points are (almost) meaningless

Lets say we cut off goat applications right now so that guys in the system get the best possible chances of drawing a tag. No new applications until we are done and the current guys have all finally got a tag. We could even allocate a big portion guaranteed to high point holders every year to get them out hunting sooner. It would take 39 years.

And you just did it again.

Horniac

*"your added weighted point is offset by the new applicants coming into the species drawng pool"*Yes for sure that's happening. If you look at the total draw pool for resident Mt Goat, the key number to consider is the "total draw points" (for all those who actually applied for a hunt). For 2015, all resident Goat hunts included, that number was 26763. Then in '16 it rose to 30183. And in '17 it rose to 33952. An increase of roughly 12.5% each year. There are 3 reasons for the increase......first are the new entrants who reach their 3 PP's and enter the draw; second, a net gain in people choosing to apply for a tag instead of just points; and third, everyone who didn't draw a tag the prior year and therefore gained one WP each.The key to remember though in Colorado's draw set-up, is that you can, to a degree, have some control of your chances, depending on your wants and needs in a hunt. Since the hunt you select can be low demand, moderate demand, or high demand. And of course you'll only be competing with the applicants who pick the same hunt. Some hunts have far fewer applicants, and fewer higher point holders participating. This aspect of the draw in Colorado differs from some other state's systems, in which names are 'drawn from a hat' and the hunt choices are filled from a list of multiple choices by each drawn applicant, until all the quotas are full. The system in those states provides less advantage to an applicant willing to accept a lower-demand hunt as his first choice. In Colorado, unit selection helped my draw success for Goat in '14, because I was willing to settle for a low demand hunt with very few applicants. But as time passes, people are getting wiser to this concept, as they lower their expectations after realizing they may never draw otherwise. So the easy-to-draw tags are slowly becoming tougher to draw.By the way congrats on drawing a great tag Horniac, and best of luck on the mountain!

The WP system was initiated because the sentiments on here about having some additional weight to those waiting longest, but yet designed so that the new or young people just getting in have a reasonable crack at it as well.

The system is not failing, it's the perception of those that these are true Preference Points, or Bonus points- which is not the case.

Not saying that is the perfect solution but I do know that the change has not discouraged new and young hunters from jumping in. In fact, this year they set a record for both res and non-res applications. That is the point I'm trying to make with this post.

The facts show that weighted points are exactly as advertised, a statistically better chance to draw the more you have, but with limited supply and extremely high demand there is never any guarantees. It is better than the old 3 points and then all are the same of years past, but certainly doesn't provide any guarantee.

Todd