Avoiding Bad Advice on Winning the Enchantment's Lottery (Part II)

Introduction

This article is a continuation of Avoiding Bad Advice on Winning the Enchantment's Lottery. In the first look at the Enchantment's Lottery data for 2021, I explored the probabilities of being awarded a permit entry based on the zone the applicant applied for.

No zone was awarded more permits than the Core Zone. However, the majority of people apply for the Core Zone, which has led to some advice online saying applicants should avoid applying for the Core Zone if they want to win.

In the first article, I hinted to the reader—that in my opinion—this advice was wrong and they should apply for the Core Enchantment Zone in at least one of their three lottery application options because:

A total of 1,039 out of 2,445 applicants were awarded a permit for a zone other than the Core Zone despite submitting at least one option for the Core Zone. A total of 673 people applied for the Core Zone and were awarded a Core Zone permit. Putting those numbers together we see that 1,712 people out of the 2,445 (70%) who were awarded permits, in 2021, applied for the Core Zone.

Similarly, I pointed out that the percentages often stated online for the odds of winning a permit (or Core Zone permit) are hard to reason about because writers don't state how they're getting their percentage. For example, in the first article, I explained the USFS statistics summary page:

[...] breaks down the zones based on the applicant's "Preferred Division 1" column. Consequently, the number (27,061) of applications submitted in the Core Enchantment Zone for 2021 is actually, applications submitted with the Core Enchantment Zone as their first option.

In practice, someone could have been awarded a Core Zone permit having applied for a different zone as their first option, which is precisely what happened for 12 applicants in 2021.

In my next analysis, I wanted to break down the results by looking at the group size, day of the week for entry, and month for entry to see if the advice online holds when we look at the data that determines whether an application is accepted or unsuccessful.

"Applying with an entry date of Monday, Tuesday, or Wednesday is better than Thursday, Friday, or Saturday"

Advice for determining which day of the week to apply as your entry date starts on the USFS website:

Bear in mind that the most popular time to go is August, and the most popular days to start a trip are Fridays, Thursdays, and Saturdays. If you really want to do a Friday-Sunday trip in mid-August, by all means apply for that trip, but remember that you’re odds of getting a permit will be less than if you tried for a Monday-Wednesday trip in July.

USFS, Enchantment Area Wilderness Permits

And that advice pops up in different variations elsewhere online (picking on the same articles from part 1).

Applying for a Monday, Tuesday, or Wednesday is your best bet at winning the permit lottery for the Core Enchantments Zone

Chris, The Enchantments Lottery: Best Ways to Win a Permit (2023)

As you can assume, more people apply for dates overlapping with the weekend to decrease the number of vacation days they have to take. [...] But if you want to increase your odds, choosing a starting date on a Tuesday or Wednesday may help you out…slightly.

Alec, Ultimate Enchantments Lottery Guide: What to know for your 2024 trip

This advice is intuitive. People have to work—obviously—so apply for a day when other people are starting their work week. But, au contraire, there seems to be a bit more going on here.

Monday, Monday

Monday, Monday, can't trust that day

The Mamas & The Papas, "Monday, Monday"

Monday was not a good day to apply for an entry date in 2021. It was the third most popular day to apply behind Friday and Thursday. More applicants applied for a Monday entry date than Saturday or Sunday.

Preferred Entry Date Day

Friday - 21,918

Thursday - 20,072

Monday - 15,372

Wednesday - 15,112

Saturday - 13,766

Tuesday - 13,734

Sunday - 8,668

Interesting probabilities were found in the data due to the fact Mondays were so popular in 2021. For example, an applicant had the same probability of their application entry being awarded a permit for a Tuesday in August (1.67%) as a Monday in September (1.53%), holding group size constant (2).

More surprising, is when you compare a busy day like Monday to Sunday, the least applied for day. Applicants applying for a Sunday entry date in August (3.88%) more than doubled their odds of getting a permit compared to a Monday in September (1.53%), again holding group size constant (2).

Sunday Funday

Sunday saw the fewest number of applications than any other day, and looking at the results above for total application entries by day, it wasn't that close.

Additionally, Sunday was awarded the most permits by day by a large margin.

Preferred Entry Date Day Awarded

Sunday - 433

Saturday - 351

Tuesday - 338

Thursday - 335

Monday - 330

Wednesday - 330

Friday - 328

This is a suspiciously large margin. Why were so many more permits given out on Sunday than any other day?

By happenstance, I was readying the changes to the 2024 "Daily Walk-up Permit Lottery" because the USFS will start using an application and geofence. What I read next pointed me in the direction of discovering why Sundays are the best day to apply.

These [walk-up permits] are available Monday through Friday only for the purposes of Tuesday through Saturday hike starts (no permits will be issured or available on Sundays or Mondays)

USFS, Enchantment Area Wilderness Permits

That's our answer. Because fewer permits are held for the walk-up lottery on Sunday they are issued in the lottery!

To prove this, take a look at the total awarded group size numbers by day for Saturday, Sunday, and Monday in August for the Core Enchantment Zone.

• Total number of people awarded entrance in the Core Zone on Saturdays(4) in August: 63
• Total number of people awarded entrance in the Core Zone on Sundays(5) in August: 119
• Total number of people awarded entrance in the Core Zone on Mondays(5) in August: 80

Typically, 16 people are awarded entrance into the Core Zone per day in the lottery with 8 spots held for the daily walk-up lottery.

There were four Saturdays in August: 16 people x 4 Saturdays = 64-person quota. The total number was 63.

There were five Sundays in August: 16 people x 5 Sundays = 80-person quota. The total number was 119.

There were five Mondays in August: 16 people x 5 Mondays = 80-person quota. The total number was 80.

Nearly 120 people were awarded entrance into the Core Zone on Sundays in August: 24 people x 5 Sundays = 120-person quota.

There was more permit availability on Sundays in the 2021 lottery.

I haven't read this anywhere. Did it change? Is this still the case? Who knew about this? If there was ever advice for the Enchantments lottery to improve your odds it'd be:

Apply for days when the Daily Walk-up Lottery is closed because there are more permits available.

Sunday was, without a doubt, the best day to apply for a permit in 2021. There were more permits available and the least amount of competition from other applicants. What was the second-best day to apply for a permit in 2021?

"And then there's Saturday"

Saturday was the dark horse. It received the second most awarded permits (351) while receiving fewer application entries (13,766) than Wednesday (15,112). It almost received fewer application entries than Tuesday (13,734)! I repeat, Saturday received fewer application entries than Monday or Tuesday.

Saturday saw the second most permits awarded overall (351) putting a little daylight between the third-place finisher, Tuesday (338). In the Core Zone, Saturday was awarded one less permit (97) than Tuesday (98), putting it in third place for permits awarded by day in the Core Zone.

Based on my analysis of the 2021 Enchantments lottery data, the advice should be as follows:

The three best days to improve your odds:

1. Sunday
2. Saturday
3. Tuesday

The three worst days to improve your odds:

1. Friday
2. Monday
3. Thursday

The daily breakdown for permits, and subsequent probabilities, was the most significant finding in the analysis. It disproves an intuition-based behavior that plays into many peoples' lottery application selection process. It also points out a little-known advantage in the availability of permits by day. Maybe you'll be able to save some of those vacation days after all.

Month

I didn't find anything unusual about the monthly data. The advice for which month to apply is pretty straightforward. August is the busiest, so you're decreasing your odds if you apply for that month.

Preferred Entry Date Month

August - 40,877

July - 30,188

September - 23,842

June - 8,579

October - 3,518

May - 1,638

The weather and snowpack affect the difficulties, danger, and availability of experiences overnight permit holders have in the Enchantments. It's not surprising that there is a huge split between "snowy" months (May, June, and October) and "summer" months (July, August, September).

Despite the applications being split between these two categories, some of the "snowy" months are awarded the same number of total permits as "summer" months.

Preferred Entry Date Month Awarded

August - 486

July - 479

June - 463

September - 458

October - 316

May - 243

Just looking at the total numbers, the probabilities are below.

September (1.92%) does provide a small improvement over August (1.19%). The same is true for July. However, it's hard to say any of the summer months have an edge over the other. Conversely, June (5.40%) and October (8.98%) have much less competition than the summer months. May (14.84%) is in a class of its own.

June is when summer starts and snowpack/weather varies from year to year. October can see some really cold and snowy nights, but it's also the time the larches are turning. There are benefits and risks to both months. Therefore, I think if someone was going to look to improve their odds, and wanted to do it by month, June and October would give them an edge.

If you plan to go in the summer, it's hard for me to convince myself that the less than 1% increase in odds is worth selecting a trip for a month other than August. As we saw, there is much more to exploit by selecting the right day of the week. And, as we'll see in the next section, if you're applying for the Core Zone, you can combine your day of the week with the right group size to increase your odds well above what a "less busy" month provide

Group Size

The lottery selection rules for the Core Zone are different compared to all the other zones.

The CORE Zone entry is by PEOPLE not GROUP. For example each day up to 16 people are allowed entry in the advanced lottery and up to 8 people are allowed in the new geofence application lottery. This can be any combination as long as the total number does not exceed 24 people in one day entering the CORE ZONE.

USFS, Enchantment Area Wilderness Permits

In zones like Stuart and Colchuck, the group size indicated for the application doesn't play an active role in determining whether your application succeeds. But, in the Core Zone, the group size could be the deciding factor in determining whether or not your application entry is awarded.

Separating the Core Zone entries from the rest of the zones I found a group size of 4 is the most popular number to apply for:

Minimum Acceptable Group Size - Core Zone

4 - 19,677

8 - 16,341

6 - 12,720

2 - 11,306

5 - 4,973

3 - 3,887

7 - 885

1 - 644

As you might expect, that also makes a group size of 4 the most awarded size.

Awarded Group Size - Core Zone

4 - 190

2 - 165

6 - 101

8 - 98

1 - 43

3 - 36

5 - 34

7 - 6

Dividing the awarded group size for the Core Zone, by the total application entries for group size in the Core Zone, we can see how each group size was awarded as a percentage of the amount of other people that applied for the group size.

Total Awarded to Total Applied - Core Zone

1 - 6.68%

2 - 1.46%

3 - 0.93%

4 - 0.97%

5 - 0.68%

6 - 0.79%

7 - 0.68%

8 - 0.60%

In the Core Zone, where group size can play a role in lottery application selection, smaller group sizes win the day. But, I want to point out a very interesting observation in this data. Notice, in the above percentage breakdown, that a group size of 3 is slightly less than a group size of 4. Similarly, a group size of 5 is less than a group size of 7.

I think what's going on here is due to the bias toward an even number selection. Consequently, the higher odd numbers do worse as a percentage.

The implication might be to avoid high odd numbers if applying for the Core Zone.

August Sunday in the Core Zone

With the discovery of more permit availability on Sundays, I found that the most awarded group size for a Sunday in August for the Core Zone was a group size of 8.

With the extra availability on Sundays, it seems the larger group size numbers did quite well. Therefore, we might want to say, that small group sizes are better when applying for the Core Zone, but, if you want to apply with a larger group size, you have a better chance on days of the week when there isn't a walk-up lottery.

View the repository on Github.

Conclusion

In this part of the analysis, I looked at group size, day of the week for entry, and month for entry. We made a few interesting discoveries:

• Mondays were more popular than people thought
• Saturdays were a dark horse
• Sundays were awarded more permits (and saw the least applicants)
• Low group size is good for the Core Zone, but more importantly, avoid high odd numbers for group size in the Core Zone
• High group sizes (like 8) did well on Sundays in the Core Zone when permit availability was higher
• There is a large divide between the "summer" months and the "snowy" months. Apply at your peril. In my opinion, there are better ways to improve your odds through zone, day of the week, and group size than by month.

At the end of the first article in this analysis, I discussed the problem of not knowing which applications were skipped. In other words, the applications that were selected but failed to secure a permit because their options weren't available. Knowing which applications were skipped might tell us what options did poorly in the lottery.

Well, despite not being able to know exactly how many applications were skipped I was able to discover a handful of application entries that were skipped. With the skipped application entries data I developed the Awarded-to-Skipped ratio. This ratio gives us an idea of how often an entry was awarded compared to how often it was skipped.

In the next part of this article series, I'll further explain the new ratio and talk about some of the findings.