# Probability of Winning A Grand Canyon Permit



## buckmanriver (Apr 2, 2008)

I was curious if anyone, had an updated rendition of the graph linked below?


https://rrfw.org/RaftingGrandCanyon/File:Gc_stats_2011_Delagarza.png

A better under standing of month to month permit probability would be helpful. I understand that it is easer to get a permit in the winter compared to the fall and spring months. But graphed data built from lottery stats from 2010-2016 would be helpful.


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## Paul7 (Aug 14, 2012)

Looking at that graph makes it like a sure bet for winter trips? 

Sent from my SM-G900V using Mountain Buzz mobile app


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## climbdenali (Apr 2, 2006)

Paul7 said:


> Looking at that graph makes it like a sure bet for winter trips?
> 
> Sent from my SM-G900V using Mountain Buzz mobile app


Keep in mind that that graph is plotted on a logarithmic scale, so, all those lines that look like they're way up by 100% are really somewhere between 10 and 100. The 50% line should probably be between 2/3 and 3/4 of the way from 10 to 100, so the bulk of those lines are probably around 50%.

Nonetheless, much better odds in winter. . .

I'll call the creator of that- not sure how much he's on the buzz, and see if he'll post up another one.
Cheers


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## Fumble (May 23, 2013)

I've decided not to open my emails because until I do there is still a chance that I won the lottery.


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## InflatableSteve (Jun 12, 2013)

Fumble said:


> I've decided not to open my emails because until I do there is still a chance that I won the lottery.



Lol. Wouldn't matter if you did at this point. You would have had to have your $200-$400 deposit in by today at noon. None of my family got a follow up, maybe next time.


Sent from my iPhone using Mountain Buzz


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## buckmanriver (Apr 2, 2008)

As it stands the statical data provided by the park is not as usable as it could be. 

Are there any database engineer's out there that would like to work on a project improving that data? 

In theory once configured appropriately in a data base queries could be designed which would show stats for winning a permit on a given date in the future based on data from the past. 

That data could then be used to create a better graph. Thoughts?


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## climbdenali (Apr 2, 2006)

buckmanriver said:


> . . .show stats for winning a permit on a given date in the future based on data from the past.


The tricky part about that is that Sept. 4, for example, is a Tuesday some years, and a Saturday other years. The dates don't always follow through year after year. With shorter trips (high use season) it's more pronounced to see launches on Saturday, Sunday, and Monday more difficult to get because many people want to have only 2 weeks away from work, rather than parts of 3.


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## Andy H. (Oct 13, 2003)

climbdenali said:


> The tricky part about that is that Sept. 4, for example, is a Tuesday some years, and a Saturday other years. The dates don't always follow through year after year. With shorter trips (high use season) it's more pronounced to see launches on Saturday, Sunday, and Monday more difficult to get because many people want to have only 2 weeks away from work, rather than parts of 3.


Yeah, but it would still be better than what they've got now. And they manage to do it for the 4 Rivers permits. Should be possible for the GC, however with the government shrinkage that's going on, the person to do it probably retired and their position is vacant (like Logan suggests Kara Lamb's position may be on this thread).

Note: the data in the graph are from '07 - '11 lotteries, I'd be interested in knowing if it's changed any now that the legacy waitlist trip leaders have all worked out of the system, or seeing what the stats are since they're not influencing permit distributions.

-AH


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## Pickle-D (May 6, 2009)

That log scale graph is very course information. 
I have used the numbers from the NPS site:
http://www.nps.gov/grca/planyourvisit/noncommercial-riv-docs.htm

Looking at the time of year that I want to launch I then adjust for day of the week in the historical data to smooth things out. There is a noticeable bias in which day of the week people bid for though that is seasonal too as mentioned earlier and not totally consistent year to year.
There doesn't seem to be any magic technique as a lot of people are doing the same analysis. My group got lucky this year for a fall launch... I take credit for my amazing statistical prowess but reality is that it is probably just luck.


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## buckmanriver (Apr 2, 2008)

@ climbdenali - I agree with your thought of days of the week being a factor in your chances of winning. 

Even without a computer program you could review the lottery stats from every Monday the first week of June from 2010-2015 and run those numbers. 

You could then compare them with every Saturday within the first week of June in the same time range. That is actual, data. 

A SQL application would make it possible run queries based on fields for a range of dates or days or months or years. The hard part is uploading the data and writing and testing the algorithms.


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## Tom Martin (Dec 5, 2004)

Good point that the data needs updating. I have asked Dave if he will do that. Andy, I can find nowhere that the waiting list folks are all gone. It appears the NPS expects to finish the list in another ten years. Meanwhile, I can book an entire commercial trip for next year and for 2017 at this time. Yes, day of the week matters, slightly, but I have lost every year since 2007 for a mid week mid January date. You may be lucky, but at least in a waiting list system, you were guaranteed a launch if you lived long enough. Now? No guarantees, except that you can charter an entire commercial trip. Will report back what Dave says. Yours as ever, Tom


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## buckmanriver (Apr 2, 2008)

*guarantees depends on points*

@ Tom,

You could guarantee your self access to a trip if you apply to a set of dates with a group of folks with enough points to increases your chances at winning one of those dates:

Check out this attached image which shows the difference in probability of winning a permit based on a group of folks with 25 point vs a person with 1 point applying to 4 January dates and one March date from the last follow up lottery stats held 10.15.2015. 

Group 97% chance 
Individual 8% chance 

The math is not in your favor as an individual with 1 point. As is such your choices are group points or commercial for guaranteed 2016 trip.


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## buckmanriver (Apr 2, 2008)

*Tangent*

Tom,

Perhaps, one modification to the existing system that would maintain equivalent private trip participants numbers (about 1800 people) in the winter season but also increase permit access would be to: 

Allow only small trips (8 people) with 2 launches per day in the winter season and double the amount of permits available for that season. 

According to the stats in the linked document: 



http://www.nps.gov/grca/planyourvisit/upload/River_Stats_Oct_2014_Update.pdf

CMRP predicted an average non commercial per trip participants to be 15.46 people when in actuality it was 8.73 people in 2014. Thus, over the winter period most 16 person trips are a little over half full. That, is bad policy for increasing access to a static number of river runners. 


Simple math is to offer more trips at the size closest to the average while maintaining user caps of about 1800 for the winter season.


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## Tom Martin (Dec 5, 2004)

Hi Buckman, you have an interesting idea. For years we have been writing the NPS saying the NPS forecast a huge use in the winter, and the actual number of people is half that. I have suggested year after year decreasing the hurdles in the winter, like decreasing the fees and or eliminating the one trip a year rule and or returning the winter trip lenght to Diamand to 30 days. I had not thought of doubling the winter launches and halving the group size. It would mean twice the winter trip contacts. 

As to stacking the lottery, one could try that, and i know folks who do. Without going into a lot of math, when 1259 applications try for 10 trips, as happened 6 days ago, I "think" my chances are not so good...

All the best, tom


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## buckmanriver (Apr 2, 2008)

1. Twice the contact with the same number of people. This would not be different from the summer season right? I think there are two launch's per day at during that season as well.

2. We also assume that such a change would fill or help increase total winter trip numbers to the 1800 per season allotment. I think they would go up but we have no data to suggest they would under a new model. They could very well remain the same or go up slightly or go down. 

3. Such an change would increase access though. 

4. Tom I think we share the same views on most all of this information. Thanks for you advocacy.


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## dugger (Dec 2, 2008)

Pardon my ignorance, but how does one apply as a group for a GC permit?


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## richp (Feb 27, 2005)

Hi Buckman,

The concept is sound, and the only grumbling you would get could be from the folks who want to take more than eight in their party. But a small launch option every other day could be a workable compromise.

The big thing I see is that your idea would run up against the limitation on total launches that the CRMP establishes. The Park holds that in essentially immutable status. Not sure how to maneuver around that and get the additional access. I know at least one argument to be made, but this likely would not fall within their "adaptive management" parameters.

There probably also would be some environmental concerns, most surely over doubling the number of parties competing for firewood, and the (modest) lessening in trip solitude. But the CRMP launch ceiling would be a huge obstacle to overcome.

FWIW.

Rich Phillips


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## buckmanriver (Apr 2, 2008)

Dugger,

Check out the document linked below:


http://www.nps.gov/grca/planyourvisit/upload/River_and_Weighted_Lottery_FAQs.pdf

The short answer to your question is that you have a group of folks apply for the same 5 launch dates within a given lottery. This group has an agreement to allow each other on a single permit should someone within the group win one a permit.

Example: 16 people apply for June, 1-5 launch dates in a lottery. One of those people wins a perming and invites the other 15 applications on his/her permit. 

Hope that helps.


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## buckmanriver (Apr 2, 2008)

Richp,

1. I agree, with the workable compromise. 

2. I agree, the park would be slow to change this policy for a verity of reasons based on their history of slow change. 

3. That said, and increase total launch's that is proportional to a preceding population limit for a given time frame does not in it self equal higher environmental impact. 

Example: A large 16in diamater pizza does not get bigger when the more slices you cut into it. It stays the same size. 

Why then would total allowed winter launch's be immutable?


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## richp (Feb 27, 2005)

Hi Buckman,

I pretty much agree. But over the years, I sat in a lot of meetings with Park representatives back when I was on the GCPBA Board. The first and foremost perspective they have is launches, not so much user-days. They emphasize that the CRMP is a launch-based system, and that the CRMP is pretty much a closed document (aside from minor adjustments they make through what they call "adaptive management"). To the Park, lapsed ideal user-day totals are not as critical as trying to approach 100% use of all launches. 

So in that context, the "let's try to get to 1,800 participants each year in the winter" argument we would make isn't as weighty. Yes, it's important to folks like us to optimize access. But in the CRMP launch context, the Park already is getting 95+% of all the scheduled launches out, and objectively that's not bad. It seems less important to them that the user-days are not similarly optimized.

As to pizzas, take that pizza and cut it in half and put each half at a separate table that requires separate linen goods, wait staff, bussing, etc. (Yeah, I know that's sort of feeble, but it's the best I can do.) In this case, the Park might argue that if you have two 8-person groups each competing for firewood, that's twice the environmental impact of one 16-person group. It's also twice the load on the beaches, since the campsite use would be doubled. This all gets evaluated in the general category, "the winter is a time when the Canyon can get a little rest."

It's not the total allowed winter launches that is immutable, it's the total number for the entire year -- 504, IIRC. They consider that number (embodied in the CRMP) just about untouchable. So absent a new CRMP, the only way they could see to add launches in the winter is to chop them in some other season. 

Now I don't see it quite that way. I would argue that (notwithstanding the fact it's a launch based system) the winter component of the 504 launches was developed from some user-day use projection in the vicinity of 16 persons per trip times some arbitrary trip length. Since we now know that actual use is far less, my view is that your idea has merit, since it still is unlikely that actual participant levels will ever get to 1,800. And in my mind, that would justify an adjustment of the winter launch allocation.

Of course that, and $0.37, will get you a cup of coffee at Greasy Johnny's Cafe. 

This has been a sort of long way of saying that in every contact I've had with the Park where this came up, they considered the current launch cap to be something we as private boaters have to live with. But that still leaves some other things to advocate for, like longer trips in winter, dropping the one trip a year rule November - February, etc. 

One final thought. The permit party approach (perfectly legal and likely never to be stopped) surely puts stand-alone lottery entrants at a significant disadvantage. I would venture that it also skews the real-world probability of getting a permit in ways that charts and graphs will never accurately represent.

FWIW.

Rich Phillips


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## buckmanriver (Apr 2, 2008)

In regards to permit party thoughts: I hear you, and agree. 

Under the current system, in all lunch seasons - individual user applicants will always be at a disadvantage to group applicants. Even more so if the individual has only 1 point in any given lottery. There odds of getting a permit are so low they might as well pick a different section like cat-canyon. 

As is such, applicants must choose weather to apply as individuals to every lottery and go once every five to thirty years depending on application points/ volume.

Or to apply as a group for winter permits and go every year. 

Furthermore, the average of nine hundred folks that go on private winter rafting trips each year are an incredibly small fraction of the 5,000,000 people that visit each year. So I can see why the park would fail to respond favorably to "us" when requesting changes to the current permit system.


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## restrac2000 (Mar 6, 2008)

I can honestly say I am against changing the 1 launch a year in the Nov-Mar timeframe as my first trip was a mid-winter. I would not have likely gone had 2nd trip folks been able to flood the lottery. 

I could see allowing an amendment to the 1 launch a year rule if a certain # of follow-up lotteries are conducted and no one picks them up. I say that as we are always limited in the #of dates we can pick but there have been dates in follow-up lotteries I have wanted to use. 

I also don't fall in line with the idea that winter dates need to be filled. The solitude I experienced on our winter trip was second-to-none. No other experience in the lower 48 came close to having 25+ days and so few people. I think we saw 2 other parties. The only outdoor adventure like that was the solitude in the Wrangell-St. Elias Range. I think we need to protect that potential experience in our shrinking landscape. In the pie metaphor, I am not sure its in our best interest to continue to divide up slices into such small portions as it completely changes the experience and is likely to leave us hungry.

Phillip


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## richp (Feb 27, 2005)

Hi Phillip,

Well put. Your post illustrates very nicely the problem the Park and interested organizations have in approaching any recalibration of the CRMP. 

Put plainly, for every person who wants an adjustment of the type Buckman and I have been batting around, there is someone out there who feels the status quo is not all that bad, and things should stay the same. Weighing varied and often competing considerations in a policy environment is not an easy task. 

FWIW.

Rich Phillips


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## dugger (Dec 2, 2008)

In the past six years I've been on four winter trips where we paid the 16 person cost and never had more than 7-8 people. That's probably typical when notice can be less than 90 days. So the additional user days are lost. Ranger Dave told us years ago that we (private groups) should be pissed about the research trips launching in the Winter. "They're taking trips away from the private groups," was his comment. Tell me that ain't so.


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## buckmanriver (Apr 2, 2008)

The policy I am advocating for would increase access within the CRMP 1855 persons per winter range. 

In the majority of each year there are up to 6 launches per day. 

Adding an extra launch for a total of 2 per day in the winter and doing so through the reduction groups size numbers which on average are not already filled is a reasonable alternative. Which is in line with the goals of the environmental impact study from the current system. Furthermore, it would be an example of Adaptive Managment which the study advocates. 

http://http://www.nps.gov/grca/learn/management/upload/Appendix%20A.pdf


In regards to fear of firewood reduction that is in the impact study to, bottom of page 7: "For example if increased winter use is found to cause a significant
decline in driftwood supplies, the NPS may institute a ban on the collection of firewood for campfires; "


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## Tom Martin (Dec 5, 2004)

The real inequity in the Grand Canyon is a huge set-aside for prime season pay-and-go commercial access while the DIY public plays a lottery your chances of winning in the summer, even with lottery parties, is in the single digit percentage points. This in a 1.2 million acre National Park managed for its wilderness character. 

In the winter, the NPS has set the DIY hurdles the same as in the summer. The hurdles are simply too high to jump. One could argue, as Buckmanriver does, that since the trips are not filling, let's add more launches. Rich P is right in that this is a launch based system. If the trips don't fill, the NPS does not care. One could argue as Phillip does that if the trips are only half full, that is a good thing. But the NPS made some assumptions in the huge changes to the DIY structure they made in 2006. Those assumptions are proving incorrect in the winter and the NPS is so far unwilling to make any changes, even simple ones, that might move toward fullfilling the NPS's own assumptions. I won't go into the painful historical details of the NPS being wiling to make some simple winter changes but some groups blocked the changes. 

Now, the NPS is going to roll the 2006 river management plan forward another 10 years, and the concessions contracts will be renewed for another ten years as well.

What do you predict will happen in the next 10 years? Another economic downturn where DIY demand stays strong and concessions subsidized launches go unfilled and unused? It could happen like it did in 2008. The river plan has no way to deal with real demand. The number of GC lottery players has gone up every year since 2006. Do we assume it levels off at some number? Or does it keep climbing? 

When will the DIY public get so fed up with this system who's foundations were made in the 1950's and 1960's voice enough complaints to their congressional folks that we see real change in the way river trips are distributed between concession and DIY use?

You have heard of deadbeat dams? Ones that are subsidized to help the few while the many suffer? Well, this is a deadbeat river management plan. It serves ready access to folks who can pay up to $5,790 per person for a Lee's to the Lake trip (GC Dories 2016 price on their website), not counting lodging and travel on either end. It propetuates a concessions trade association to protect the river concessions, not the resource or equitable access. Is this the way you wan to see your National Parks managed? 

My sweeite and I just did two back to back Cat trips, second half September and first half October. NO PROBLEM getting a permit. I was amazed and refreshed to run a river where I simply went on-line, placed my request, got the approval, paid my fees ($30 for the permit and $20 per person for up to 14 nights) and went boating. How refreshing!

To those that say the plan is a 50-50 plan and everything really is ok, the pizza analogy comes to mind. We'll split the pizza in half. I get the top half with the crusty ring around the edges, all the toppings, cheese and sauce, while you get... the crusty bottom. Hey, it's 50-50! Enjoy...

Until a critical mass of DIY boaters is willing to go to the mat for a true wilderness river management plan that allows concessions services to compete for commercial clients without set-aside guaranteed launches, do you really think DIY access is going to get better?

It is just possible, and mostly probable, that a Common Pool river plan would still not solve this issue of supply being nowhere near true demand, but we would have a truly fair and equitable river plan, ensuring the protecting the resource and not perpetuating a truly broken system. 

Have a Good evening, yours, Ton


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## climbdenali (Apr 2, 2006)

Here we go. . .


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## BrianK (Feb 3, 2005)

Tom - just out of curiosity, how many years in a row have you been on the grand?


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## buckmanriver (Apr 2, 2008)

One way to increase the chance of getting the park service on board with a change through the “Adaptive Management” avenue is to demonstrate the value of the change to the multiple stakeholders. 

The benefits to the various stakeholders are as follows:

Folks for protecting the canyon's biome as a whole through maintaining a sustainable biophysical carrying-capacity should know that:

The Park acknowledges through research that current winter trip participant numbers are “consistent with the wilderness and wildlife protection.”

They also acknowledge that when winter user allocation was increased it was during a time when ”vegetation was the least sensitive.”

*“Vegetation is dormant in the winter and trampling impacts have less of an effect.”

There is also a fiscal benefit to the various stakeholders: 

Potential NPS yearly funds increase:

User fees of $100 per person per trip: 900*$100= $90,000

Potential yearly outfitter revenue increases from bussing like Pro River, Ceiba and REO, that offer “Painless Private Trips” at about $1200 per person: 

900* $1200 =$1,080,000

Potential yearly Diamond Creek revenue increase to the Tribal owners: 

900*$65 =$58,500

Lastly, we have the individuals that are simply trying to increase their chance of access in allowing 2, 8 person trips to launch per day during the winter season instead of current 1 launch of 16 person trips per day in the winter season that on average only have 8 participants anyway. As is such, this change would be a beneficial step forward for the majority of all stakeholders.


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## davedlg (May 22, 2007)

I'm the original creator of the demand graphs referenced earlier in this thread. By popular demand, I've updated them with the last few years' stats. 

First off, here is the updated demand graph:








It's remarkable how consistent the demand is by date on a year-over-year basis. 

The odds have gotten a bit better in recent years however.

Speaking of dates, here is the demand by weekday:








Your best bet is a Sunday or Monday launch. 

Here's what's happened on a year-over-year basis:








The number of applications has been somewhat steadily increasing, however additional launches being made available combined with the reduction of high points applications coming off the waiting list has contributed to a decreasing number of points competing per launch. This effect bottomed out in 2014, when there was a average of 187 points per launch. The increasing number of applications in the lottery has contributed to tougher odds in the two years since, with the average launch date seeing 245 points competing for each launch. The record high was in the first 2007 lottery, with 411 points competing per launch.

As far as small trips go, your odds are definitely better there. As seen in the first graph, the odds are generally about 10x better on a per date basis. The odds got much better in 2012, when the number of available small trip launches increased from around 45 to about 75.









As of the most recent lottery, the average small trip only has an average of 71 points competing for each launch - much better odds than the standard trips.

I have all the data pulled out into a number of excel tables and databases, so if there is some other stat that sounds interesting, let me know and I'll run it.

Cheers,

~David Delagarza


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## buckmanriver (Apr 2, 2008)

Thanks for the updates davedlg!


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## Charlie17 (Oct 26, 2015)

What some call probability of winning sounds so simple, but it is not. It is very complicated and many parameters need to be identified and defined. It is so complicated that the Park chooses not to get into that area and suggests one simply looks at the lottery histories and data it puts out and make ones own conclusions as to which choices offer you the best opportunities.
The numbers put out by some are misleading because they are not meaningful ...ie the parameters are not identified and defined.


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## Jhit (May 31, 2005)

I didn't read most of this because so many "words" but uh, if you can get signed up for the cancelled trip list, i get emails all the time for open dates. If you can fly by the seat of your pants thats a good way. One kayak solo trip sounds good to me.


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## buckmanriver (Apr 2, 2008)

There have been 3 follow-up lotteries this year for grand canyon permits.

There as been only 1 I believe with 2016 launch dates. 

But yes applying for them does increase your probability.

And if many users only want a single trip in a lifetime all the better for the folks that want more.


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## climbdenali (Apr 2, 2006)

Charlie17,
Could you elaborate on what you're saying? What parameters need to be identified and defined?

I guess I think that the NPS data gives us a pretty good idea of our odds of winning on a specific date: I know how many points I have, I know how many points I'm up against (historically) and I know how many launches are available that day.

Probability of Winning a given date = (My points / Total points for that date) * Number of launches on that date.

What am I missing here?

I guess if you want to be specific about it, some of those total points could be removed from the pool if their owner wins a different date prior to that date being drawn. Likewise, you'd have to remove the points of the winning application before calculating the second permit drawn for a given date, but these are pretty minimal differences I think.

I feel like the NPS gives us a pretty good amount of data, that is fairly useful if you do a little legwork with it. I sure wish I could get data like this for other permitted rivers- anybody know if anything like it is available for MFS, Westwater, San Juan, etc?? I know WW is call in (lame, unfair system if you ask me), but is there another quantifiable way to gage demand for WW, other than anecdotal evidence ("It's always sold out by the time I get through. . .")


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## landslide (Dec 20, 2014)

Like everyone else in love with the Grand, I have studied the stats and regs trying to think of ways to improve my odds of getting a permit or an invite, but there's only so much you can do. As someone already pointed out, the best way to do it is to round up 15 newbies, all with 5 points each, and carpet bomb five chosen dates. Not a trip I'd like to be on, but heh!

Personally, I like the idea of increasing the number of launches in the off season because if you think your odds of winning a permit are bad now, watch what happens as the Baby Boomers retire en mass. This is only the beginning! 

The Boomers are the 500 pound pig in the python. As their age cohort passes certain milestones in life everything gets blown out of proportion from the housing market to the job market to recreational opportunities. I was talking to a raft guide with 30 years in the business who said that her business was now booming again... with Boomers, not younger people. 

The Boomers are a health conscious, nature-loving generation and many of them are itching to hit retirement at full speed. They have money, and now they have time... time to spend in the wilderness after years slogging away at work. They know that their health is a fleeting thing and that if they're ever going to do this "trip of a lifetime", they'd better get on it. Many of them will go on commercial trips, but a significant chunk will want to DIY the GC. Mark my words, your chances of winning a permit are going to get much, much worse over the next 10-15 years.

Look, I'm not bashing Boomers here and I'm not trying to be a Debbie Downer, either. At age 51, I am at the rump end of this generation (born between 1946 and 1964) and I know how this will play out because I've been dealing with it all of my life. Boomers are JUST STARTING to hit retirement in numbers and it WILL have a significant impact on your recreational opportunities. Like it or not, this is reality.


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## trevko (Jul 7, 2008)

Tom Martin said:


> When will the DIY public get so fed up with this system who's foundations were made in the 1950's and 1960's voice enough complaints to their congressional folks that we see real change in the way river trips are distributed between concession and DIY use?


Well now that is the key, along with lots of $. As it was found out in the 70's with the RMP's move to get rid of motors - the outfitters are a very powerful political force. Look what has happened elsewhere when some curtailment of wilderness outfitters was brought up (mostly horse guided operations) - and they didn't even have a cousin who is one of the most powerful Senators in Congress. 

We can stamp our feet and bitch and moan that it is not fair all we want. Until we attain the same political capital as the outfitters I doubt there will be any great change in the allotment.


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## richp (Feb 27, 2005)

Hi,

A useful additional statistic (and I'm not sure how to obtain it) would be how many people applying in a given year's lottery still end up on the river that year -- on their own permit or someone else's.

Rich Phillips


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## BrianK (Feb 3, 2005)

> A useful additional statistic (and I'm not sure how to obtain it) would be how many people applying in a given year's lottery still end up on the river that year -- on their own permit or someone else's.


This is the stat that matters. Winning the lottery is hard. Getting on a Grand trip has gotten a lot easier. So while the lottery is not perfect - it does seem like it has greatly increased the availability of spots available and the likelihood of getting on a grad trip if you are motivated. 

I would like more private launches. But I am not in favor of lifting the one trip per year limit. That seems to run against the goal of getting more private people on the river.


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## paulk (Apr 24, 2006)

Says the guy who keeps riding my coat tails...

It's hard carrying all the weight around here Brian.


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## richp (Feb 27, 2005)

Hi,

Well it turns out when I pursued a vague memory on this subject, I found an old email that had the answer to my own question, from back when I was on the GCPBA Board. 

This past summer, GCPBA posed the question to the Park about how many people who applied in the lottery eventually made it on the river. The last complete year for which the Park had this category of data was 2014. In that year there were 3,579 lottery applications. Of that total,1,187 of those applicants eventually went on trips in 2014.

So it looks like in the real world, lottery applicants that year actually had about a one in three chance of actually getting on the river. 

That gives some of these numbers a little different look. It also slides this discussion toward the subjective realm -- how important it is to have your own permit, versus going on someone else's trip. 

FWIW.

Rich Phillips

FWIW.

Rich Phillips


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## Charlie17 (Oct 26, 2015)

climbdenali said:


> Charlie17,
> Could you elaborate on what you're saying? What parameters need to be identified and defined?
> 
> I guess I think that the NPS data gives us a pretty good idea of our odds of winning on a specific date: I know how many points I have, I know how many points I'm up against (historically) and I know how many launches are available that day.
> ...


ClimbDenali...Thank you for making my point which was that the NPS gives us a pretty good amount of data......Which for me (mathematician by training) gives me more information than some number someone assigned to a series of calculations he did which may or may not reflect the situation.

Your calculation above seems quite simple but overlooks the fact that this is not a single phase lottery but two separate lotteries. The first is that your name is drawn and put on an ordered list. ie first name drawn is first last name drawn is the last on the list. Your name is drawn at random. If you have 5 chances your name is in the drawing pot 5 times. Once your name is drawn it and the 4 others are removed from the pot changing everyone after you chances' of being drawn. 

The second part of the lottery is starting at the top of the above list and matching your name with the available dates list and seeing if you have one that matches. YOu no longer have 5 chances to match the available dates The number of chances is no longer meaningful for anyone.The first match is the date you win. Once a trip is awarded it of course comes off the list for everyone else. The very first name will get his very first choice. The next name in the priority list is matched up in a similar way and the date he wins is taken of the list for all the following folks. Eventually down the list somewhere ones name comes up, but there may not longer be any of his dates available. The process continues until all the launch dates are awarded.

I hope this partially explains why simple calculations cannot come up with a probability of winning the lottery(s). 

Taking a close look at Park histories and stats is most likely the most meaningful way for most of us to figure odds that we can relate to.


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## buckmanriver (Apr 2, 2008)

richp said:


> Hi,
> 
> The last complete year for which the Park had this category of data was 2014. In that year there were 3,579 lottery applications. Of that total,1,187 of those applicants eventually went on trips in 2014.
> 
> ...


33% seems high do can you post the screen shot of the email from the park? 

The lottery application numbers you sight do not match what is posted on nps web site. See attachment:


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## buckmanriver (Apr 2, 2008)

landslide said:


> The Boomers are the 500 pound pig in the python. As their age cohort passes certain milestones in life everything gets blown out of proportion from the housing market to the job market to recreational opportunities. I was talking to a raft guide with 30 years in the business who said that her business was now booming again... with Boomers, not younger people.


2014 data is not quite as dramatic's as you present. In fact folks in the 25-30 year old range are 2ed to the boomers. But the boomers are still the largest group of applicants year over year. See attachment from the nps web site:


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## richp (Feb 27, 2005)

Hi Buckman,

The cited chart appears to show lotteries for a partial mixture of 2014 and 2015 launch dates -- not all 2014 launches. 

As I understood the email, it referred to lottery activity that determined actual 2014 launches. Actual 2014 launches would have been the cumulative result of a main lottery in February 2013, subsequent 2013 secondary lotteries for 2014 dates, and additional secondary lotteries into 2014 (which are indeed depicted in that chart) . So I'm not sure that particular data set helps with discussing lottery success probabilities. Could be wrong, but that's the way I'm reading it...

On the email itself, I was working from a forwarded copy of a message between the River Office and GCPBA, which said, "The last complete year we had was 2014. In 2014 there were 3,579 applications that also included another 737 PATLs. All in all it looks like 1,187 of these went on trips in 2014."

Hope this helps.

Rich Phillips


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## buckmanriver (Apr 2, 2008)

richp,

That makes sense, the "3,579 applications" matches the main lottery data for the 2013 year.


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## davedlg (May 22, 2007)

Charlie - Good points all around. 

I agree that one cannot compute exact statistics, because the internal working of the lottery do affect the statistics on any given day. I do however believe that we can extract meaningful numbers from the statistics beyond that which are provided by the park service. 

It is very difficult to state that on any particular date, you odds are exactly 4.723% or something like that. However, the bottom line is that if you are competing with 100 people for a particular date, your odds of winning a permit are around 1% - this number has some variability in it, but it is not 10%, and it is not 0.1% This is why I showed the results on a log scale, as I think the order of magnitude is more important than the specifics. The details of the lottery have less impact as the number of entries get larger for any particular date, as the points that would go to people who may have already won an entry become less of a factor in the overall odds - removing 5 chances from a date that has 500 points competing for it has much less effect than removing 5 chances from a date with 10 points competing. 

This really does matter on the winter dates. It's nearly impossible to say whether the odds are 33%, 50% or 100% without knowing who applied for what date and how the lottery is put together - and I think that is your point. However, the bottom line for those dates is that if you want to go in winter, you'll probably be able to get a permit if you apply for 5 dates. 

Good discussion, and thanks for you input. 



Charlie17 said:


> ClimbDenali...Thank you for making my point which was that the NPS gives us a pretty good amount of data......Which for me (mathematician by training) gives me more information than some number someone assigned to a series of calculations he did which may or may not reflect the situation.
> 
> Your calculation above seems quite simple but overlooks the fact that this is not a single phase lottery but two separate lotteries. The first is that your name is drawn and put on an ordered list. ie first name drawn is first last name drawn is the last on the list. Your name is drawn at random. If you have 5 chances your name is in the drawing pot 5 times. Once your name is drawn it and the 4 others are removed from the pot changing everyone after you chances' of being drawn.
> 
> ...


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## Charlie17 (Oct 26, 2015)

buckmanriver said:


> 33% seems high do can you post the screen shot of the email from the park?
> 
> The lottery application numbers you sight do not match what is posted on nps web site. See attachment:


This is a good example why its important to define your terms and parameters.
You are correct in that these numbers do not match what the NPS has on its website and what you posted. RichP's numbers are from the NPS and are correct as well.

The difference is that What the Park gave RichP is the initial lottery #of applicants and what you posted appears to be the total # of applications for the year (which includes a number of folk who applied each lottery)

You are both correct.


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## buckmanriver (Apr 2, 2008)

Charlie17,

What probability equation would you used based on the data available to better show probability? 

A simple one is linked below: 
*The numbers in this sheet and attached image are not based on actual data. 
http://https://docs.google.com/spreadsheets/d/1m5PouLJXODJ5FnJG_rUebRpuA45mPMw3J3vhC4IU67M/edit?usp=sharing

You could also add your equation to that sheet.


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## Charlie17 (Oct 26, 2015)

buckmanriver said:


> Charlie17,
> 
> What probability equation would you used based on the data available to better show probability?
> 
> ...


I can't because its way too complicated for me. Its very difficult (and maybe misleading) to boil a very complex problem down to a simple equation.

Besides it really doesn't interest me that much. My focus is my chances of getting on a river trip rather than winning the lottery for my own trip. These two concepts are often used in discussions interchangeably and they are not.


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## davedlg (May 22, 2007)

You cannot simply add independent statistics like that - you have to account for the probability of winning twice, which get double counted when you add up statistics. That sounds like a good thing, but it lowers your overall odds. 

A simple example - think of flipping a coin. Each time you flip the coin you have exactly a 50% chance of seeing heads. If flip the coin twice, and add up 50% + 50%, you would compute 100% odds of seeing heads in two flips, which is not true. 

What you actually have to do is subtract out the possibility of getting heads twice, which gets double counted by when adding the probabilities of getting heads -> 50% + 50% - (50%*50%) = 75%

This gets even more complicated when you start adding up 3 or more probabilities in series, because you start having to add combinations back in.

Now to make it more complex, if you and your friends are applying for the same dates, the data is no longer independent, but your odds are a reflection of the overall number of entries that belong to you and your friends as a fraction of the overall number of entries in the lottery. 

Yeah - it's complex. Let's not even talk about how everyone having 5 entries affects the results. 

Still, for any individual entry in the lottery, I think it is a good assumption that that that entry's odds are generally (num of points) / (number of total points) for that launch, given a sufficiently large number of points. Yeah, the complexities of the lottery system might throw those odds around a few percentage points (mostly in your favor), but it should generally be a good guess. 



buckmanriver said:


> Charlie17,
> 
> What probability equation would you used based on the data available to better show probability?
> 
> ...


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## GoRiverGo (Sep 15, 2013)

Dave D.

Thanks for updating your original chart with the current data and adding the additional analysis. A few questions -

What is the green line on the first chart?

For the small trips, the 10 year average line on the first chart is probably affected by the fewer number of permits available in the first six years, as described for your last chart. Can you add a line on the first chart for the average odds under current conditions, i.e. the 2013 - 2016 data?

Gary


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## davedlg (May 22, 2007)

Good questions. The green line got cutoff in the legend before - that is this year's (2016) lottery statistics. I've added the 2016 small trip line to the graph. 












GoRiverGo said:


> Dave D.
> 
> Thanks for updating your original chart with the current data and adding the additional analysis. A few questions -
> 
> ...


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## fiya79 (Feb 9, 2010)

Thank you for the analysis and the discussion. I found it all informative and look forward to winning in 2017.


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## GoRiverGo (Sep 15, 2013)

I agree, thank you again, and I'm hoping to be a winner in 2017 as well.


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## marley (Dec 19, 2013)

davedlg said:


> You cannot simply add independent statistics like that - you have to account for the probability of winning twice, which get double counted when you add up statistics. That sounds like a good thing, but it lowers your overall odds.
> 
> A simple example - think of flipping a coin. Each time you flip the coin you have exactly a 50% chance of seeing heads. If flip the coin twice, and add up 50% + 50%, you would compute 100% odds of seeing heads in two flips, which is not true.
> 
> ...


This is one of the more interesting conversations I have seen regarding the probability of winning the lottery. Dave is really onto something here regarding probability that most don't seem to consider. One way to think about a series of events with two possible outcomes for each event (e.g., win vs lose, heads vs tails, red card vs. black card, etc.) is to calculate the simple probability of each event and then multiply them together. For example, the probability of flipping heads twice in a row is .50 x .50 = .25. You can draw this on paper to prove it to yourself. This means the probability of not flipping two heads in a row is .75. This generalizes to repeated independent events. P(3 heads in a row) = .5^3 = .125 and can be applied to a group (e.g., what's the probability of 16 five pointers all losing?).

This can be extended to lotteries at the individual level so if the probability is .02 of winning a given lottery. The probability of winning multiple times is .02^X. It's likely more informative to calculate the probability of losing multiple times 1-P(winning) = .98. Then we can roughly calculate the probability of losing twice .98^2 or 3 time .98^3 and so forth. This does assume the events are independent, which they are not because the number of permits and people applying are changing and it's possible the probability of winning increases with each successive lottery, but it doesn't seem to because the numerator and denominators are maintaining a similar ratio across lotteries relative to one another across lotteries. So one could calculate the probability of winning with a sequence when an event that occurred influences the next event or the probability is changing as P(A)*P(B|A) = 

As mentioned in the thread this does not include groups applying together, time of year, etc. but it gives one a rough idea of what one is up against. Somewhere else an individual posted that around 30-35% of people who apply do go on a trip. And some may consider this a good thing. I guess it's good if you're not one of the 65-70% and their friends and family who did not get to go.


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## mattman (Jan 30, 2015)

But what about the 7 out of 5 people that are just plain bad at math? ( AND FRACTIONS)


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## landslide (Dec 20, 2014)

*Help for bad math*

I have discovered through extensive testing that my odds of winning a permit are zero percent. Until I win one, and then it's 100%. Does that help?


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## mattman (Jan 30, 2015)

ya, most definitely, I would rate that statement as "exceptionally true"!


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## marley (Dec 19, 2013)

mattman said:


> But what about the 7 out of 5 people that are just plain bad at math? ( AND FRACTIONS)


I suspect that some of that 7 out of 5 will win on occasion. The other 10 won't though.


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## mattman (Jan 30, 2015)

Well that clears it up then! 
Starting to think that it is partly a matter of manipulating the odds, a number of us coordinated our efforts and pulled a permit for 2016 in the main lottery. Admitedly we have to go in the middle of winter, but stoked for a chance to go none the less!!!
Since a lot of people put in for permits as groups, you kind of have to,
does theoretically improve your statistics though.
Who you enter with matters a lot to, if every one has all 5 points, you stand a better chance. 
How many boating connections you have is another factor, I know some one that did a trip every year for like 10 years, he has been boating for a long time, and knows lots of people, and have to admit the man deserves it!
You could also consider things that get you invited on the grand, like previous experience, being a solid boater, owning lot's of the gear needed, playing the gittar people actually wanting to hang out with you! Etc.
Damn, this could really be some complicated math, something to waste my time with while wishing I was on a river though!


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## mattman (Jan 30, 2015)

Could also find way's to enhance your odds of being able to go if you ever actually get a chance, like altering what you do for a living, having a grand canyon savings account,(so you can afford to go) only having a significant other that will let you go( or hopefully go with!)


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## marley (Dec 19, 2013)

mattman said:


> Could also find way's to enhance your odds of being able to go if you ever actually get a chance, like altering what you do for a living, having a grand canyon savings account,(so you can afford to go) only having a significant other that will let you go( or hopefully go with!)


One of the best ways to alter what one does for a living is to quit their job. I did this for a couple of Grand Trips when I was in my 20s. That's not saying much though because I could always get another restaurant job then.


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