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Statistics!! Like for rivers and permits and stuff

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Dang. For all those who wondered. Just got this from Rec.gov in an email

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Complete bullshit. They manage this site likes its private forgetting completely that they're managing public lands. The point isn't to get them their $6 per applicant, its to fill the permits. I think land managers should make a Trip Leader certification or other limiting factor to a. control the total amount of applicants, and b. ensure that the person holding the permit knows what they're doing. Of course res.gov has no interest in that concept cuz they want their $6.
 

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There was some interesting, but now way outdated analysis, on this: Estimating Monetary Values For Use Permits on Western Rivers by Bo Shelby, Journal of Forestry 1984.

The number of available permits listed in the email isn't actually the number available during the lottery season. Take the MFS for example. There are a little under 400 private permits during the lottery season, not the 681 listed. Average odds are about 1 in 65. The odds are much better or worse depending on the dates you pick. The Main Salmon is closer to 300 lottery permits per season.

Does anyone else think about a 1 in 65 chance with a $6 entry basically means the value of the permit is $400? How much would you pay for a guaranteed permit?
 

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Ah, duh. Thank you. I weirdly like the summer crowds. I wouldn’t want to recreate this permit system across the board, but it lends itself to a unique river culture that I don’t mind.
The Rogue permit allocation system is unique and I also don't mind. Getting a camp with a larger group in the summer can be a PITA . Rabbit boats are common, even with private groups. Just know what to expect. The current permit system on the Rogue benefits me. I never apply for a Rogue permit. I live close enough to the river and there are enough last minute cancellations that I can go just about any time I want.
 

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I think Booz is mixing apples and oranges for the Rogue: there are 9,100 INDIVIDUAL non-commercial slots for the year, but the lottery applications they refer to will almost always be for a whole GROUP (almost no one runs a 1-person trip) -- so multiply applications by 6 or 8 to get a truer sense.
 

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Sending one boat out very early in the morning to get to and claim a desirable camp (with the bulk of the group arriving later in the day).
And it's actually legal for both commercial and private trips to split the group as long as each part of the group has a copy of the permit. They give you two copies. The Rogue has some unique rules. Rabbit boats can be frustrating, and it's just part of the experience. You probably shouldn't go. It's truly awful. Nobody should go. They should just close up all the commercial outfits and....

Oh never mind. I love the Rogue.
 

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Sending one boat out very early in the morning to get to and claim a desirable camp (with the bulk of the group arriving later in the day).
Aha. Well, nothing stopping you from pulling in with your whole group and just camping all around whatever they’ve set up.

Bet you a dollar they leave.
 

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I couldn’t make your math work. It looks like you were taking a single persons chance to win the lottery and multiplying it by the number of people in your permit party. With a large permit party you end up with like 150% chance of winning, which we know isn’t true. I spent about two hours on this, but my college statistics is 30 years old, don’t have a clue now.
Here's the math. We'll just take the Middle Fork numbers. 681/22586 = 3.0% or 1 out of 33, i.e. between 1 out of 20 and 1 out of 40. Some are easier (Snake) and some are harder (Selway).

Now, if I apply to 10, what are my odds of winning something? 10/33. That is to say, on average I'll win 1 out of every 3 years. There's no guarantee I'll win every 3 years. I might win twice in a year. I might not win for 10 years. But on average, my odds are winning 1 out of every 3 years with that approach.

Now, take 5 other friends doing the same thing. Now our odds to win in a given year are 50/33. So I'm now likely to win at least once a year. So yes, you have a 150% chance of winning. Why would you say that isn't true? It seems true to me. On average, my group of friends gets a permit or two every year, i.e. a greater than 100% chance of winning something.
 

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Exactly. Statistics doesn't quite work like that. If you flip a coin twice, you are not guaranteed that at least one of the results will be "heads."

But, if you buy every single lottery number for a big draw, you are guaranteed to win. Some guy did that. He didn't quite get them all. He paid a bunch of people to put in as many combinations as there are possibilities for the lottery. I think he did it more than once before they changed the rules and made that verboten.
No, there is no guarantee. You might flip tails twice. But the odds of that are 25%. (i.e. 1/2 x 1/2). but you have a 75% chance of getting heads at least once.

The math of probability isn't that complicated. I don't like that it is harder to win these permits than it used to be, but it's certainly not impossible to win. And there is a lot that can be done to increase your odds of being able to do a river in a given year.

1) Go do it outside the permit season. I've only done the MFS once, and it was the week after the permit season ended. Yes, it sucks to have very slippery frost on the rubber in the morning, we had to fly into Indian Creek, and I wore a drysuit in the IK, but it beats not going at all.

2) List dates outside the peak windows. It's much easier to draw out early and late than in July for most of these rivers (see the link above).

3) Go on a trip composed entirely of adults and have every adult on the trip apply. Yea, it's expensive, but it's still way cheaper than a commercial trip. Our biggest limiting factor to putting in more permits is that so many of those going on trips with us are minors. If you put in 20 applications for the MFS every year, your group is going to get to do it every other year on average.

4) Apply to a lot of rivers. No, the San Juan isn't the Selway, but it beats the couch.

5) Be flexible enough to take cancellation permits. The truth is that you can do Deso just about every week of the summer on a cancellation permit. I think the Rogue is similar. I can't believe how many people cancel their Grand Canyon permits. Yea, a lot more people are applying every year, but my sense is many of them aren't so hard core. Plus, some groups get two permits and really only want to take one trip. Voila! Cancellation permit.

6) Go run unpermitted rivers. I have a friend who did a river in the Northwest Territories that had not been done in 20 years. They did have to cut their way through some of the portages. I was in Colombia last month and we did a river that involved hiking the raft in on the back of a mule. I don't think there are any permitted rivers in Alaska at all. There are still lots of rivers in the world that don't have permits. Sure, there aren't commercial shuttle services already set up nor a groover cleaning station nor a ranger there to give you a safety talk, but they paddle pretty similarly.

7) Do first come/first serve rivers. Westwater and Cataract permits are pretty much available anytime you want just by planning two months in advance.
 

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Here's the math. We'll just take the Middle Fork numbers. 681/22586 = 3.0% or 1 out of 33, i.e. between 1 out of 20 and 1 out of 40. Some are easier (Snake) and some are harder (Selway).

Now, if I apply to 10, what are my odds of winning something? 10/33. That is to say, on average I'll win 1 out of every 3 years. There's no guarantee I'll win every 3 years. I might win twice in a year. I might not win for 10 years. But on average, my odds are winning 1 out of every 3 years with that approach.

Now, take 5 other friends doing the same thing. Now our odds to win in a given year are 50/33. So I'm now likely to win at least once a year. So yes, you have a 150% chance of winning. Why would you say that isn't true? It seems true to me. On average, my group of friends gets a permit or two every year, i.e. a greater than 100% chance of winning something.
Unfortunately, that is not quite how probability works. If your probability of winning is 1/33, your probability of not winning is 32/33. Your probability of not winning on all 10 applications is (32/33)^10. Your probability of winning at least once on ten applications is the opposite, 1-(32/33)^10 or 8.7/33. For 5 people with 10 applications each, the odds of at least one win is 26/33. You also have decent odds of multiple wins.

I'd also point out that the numbers in the email are not the number of permits available in the lottery season for private groups. The MFS typically has 387 private lottery permits in a season or about 1/60 odds (assuming a similar number of people apply as in 2021).
 

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Unfortunately, that is not quite how probability works. If your probability of winning is 1/33, your probability of not winning is 32/33. Your probability of not winning on all 10 applications is (32/33)^10. Your probability of winning at least once on ten applications is the opposite, 1-(32/33)^10 or 8.7/33. For 5 people with 10 applications each, the odds of at least one win is 26/33. You also have decent odds of multiple wins.

I'd also point out that the numbers in the email are not the number of permits available in the lottery season for private groups. The MFS typically has 387 private lottery permits in a season or about 1/60 odds (assuming a similar number of people apply as in 2021).
I'm still not sure that you're right and I'm wrong. According to this:


When calculating the probability of either one of two events from occurring, it is as simple as adding the probability of each event and then subtracting the probability of both of the events occurring:

P(A or B) = P(A) + P(B) - P(A and B)

Which would suggest you add the probabilities. Which makes intuitive sense to me.
 

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The other part that I'm not sure the above math takes into account is your name gets drawn, and if someone(s) that was drawn in front of you already picked your dates, you get nothing. I don't know how to weight the 1st, 2nd, & 3rd choice and model that math but it is relevant and, intuitively, makes the odds worse than what we're talking above. For instance, from their data last year you never had better than .5% odds of drawing a date from June 11-end of July, regardless of if it was a 1st, 2nd or 3rd choice. You can pull it down from the FS website and throw it into excel and model it all. I believe that is what Ron did when he made all those graph sheets for DRE years ago that are still on their website, albeit dated now (2015 I think).
 

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I'm still not sure that you're right and I'm wrong. According to this:


When calculating the probability of either one of two events from occurring, it is as simple as adding the probability of each event and then subtracting the probability of both of the events occurring:

P(A or B) = P(A) + P(B) - P(A and B)

Which would suggest you add the probabilities. Which makes intuitive sense to me.
Yeah, that equation gives the same answer. You didn't subtract the last term P(A and B).
 

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Complete bullshit. They manage this site likes its private forgetting completely that they're managing public lands. The point isn't to get them their $6 per applicant, its to fill the permits. I think land managers should make a Trip Leader certification or other limiting factor to a. control the total amount of applicants, and b. ensure that the person holding the permit knows what they're doing. Of course res.gov has no interest in that concept cuz they want their $6.
Well said and totally agree. We should get some tech and business savvy buzzards together to start a non-profit version of rec.gov and convince the powers that be to let us take over the contract from Booz Allen Hamilton. The fact that a for-profit company is optimizing a public lands reservation system for maximum number of applicants in order to move the needle on their own revenue is, as you said, complete bullshit.
 

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Do you really have to subtract it since that outcome (getting two permits) would still be considered a success? I don't think you do.
Yes, all three terms in the equation are necessary. In some cases, the last term is zero but that is not the case with these lotteries.

As an example, let's say the permit lottery was performed by flipping a coin. A tails wins you a permit and a heads doesn't. You and your buddy enter. You have a 1/2 chance of winning and your buddy has a 1/2 chance of winning. There are four possible outcomes. You or your buddy get a permit in three of the outcomes and don't in one outcome (both get heads) which is a 3/4 chance.

P(A or B) = 0.5 + 0.5 - 0.5*0.5 = 0.75
 
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