Monday, November 25, 2024
HomeRunningLottery and Qualifying Races – iRunFar

Lottery and Qualifying Races – iRunFar


With the 2024 Western States 100 right around the corner, I wanted to better understand who will be rounding the corners come race day. If you’re anything like me, this is a bucket list race on your calendar, but the prospect of getting in is so remote that it is more of a concept than a realistic possibility for so many of us at this point.

Just how difficult is it to get into this event? What is the best strategy for getting in? Will I be able to run this event before my body gives out from overuse? In this article, I dive into the numbers in an attempt to shed some light on these questions.

Breakdown of the 2024 Western States 100 Entrants

Western States is the oldest 100-mile race in the world and attracts ultrarunners from around the globe to take part in the historic event. (See my previous article for what this travel looks like.) Entry into this race has continued to grow in demand year over year, with only a tiny fraction of all applicants gaining entry. When the 2024 Western States kicks off in a few days, 375 individuals will toe the line. Here is a breakdown of how those 375 individuals gained entry into the event.

2024 Western States 100 Entrants Breakdown

We essentially have three main ways to get into the event:

  1. Become very involved with the event, such as by being a board member or by volunteering at an aid station for many years;
  2. Be really, really fast; or
  3. Gain entry through the race lottery.

With 72% (270) of people getting in via the lottery, this is the most common way to get in. That does not, however, mean that the odds are in your favor of getting in. Since options 1 and 2 are limited to approximately 100 people, while the lottery this year had 9,388 people, I will be focusing this article on the third group.

Western States is quite transparent with their lottery system — they do not do a great job of picking me — and provides a detailed breakdown of lottery statistics every year. Here you can see the growth of applicants over time and how many tickets they have accumulated over the years. The number of tickets an entrant has is calculated by 2^(n-1) where n is the number of years entering the lottery without gaining entry.

The Growth of Western States 100 Applicants From 200o to 2024

Western States 100 lottery applicants

Note: There were no lotteries for the 2009 and 2021 races as in each instance entrants were rolled over from the race canceled the previous year. Source: https://www.wser.org/2023/11/30/2024-lottery-statistics/

Because of this logarithmically scaled ticket system that rewards entrants who have been trying for many years, the 9,388 people actually translates to 53,966 total tickets. Western States runs Monte Carlo simulations — a statistics technique used to predict outcomes of an uncertain event — to show the expected likelihood of an entrant getting into the event given a certain ticket amount.

The chart below details your odds of getting in for 2024. With 1 ticket, your chances are less than 1% and those chances only increase to above 50% with 128 tickets, which means 8 years of entering the lottery and not being selected.

Based on Ticket Numbers, the Odds of Getting Into the 2024 Western States 100

Provided these dismal chances, I wanted to understand how long it would take an average runner such as myself to get into Western States. For the sake of this calculation, I assumed an applicant completed a qualification race every year. Given the above odds and taking into consideration being selected in a previous year, the expected number of years to get into Western States is 6.79 years.

Note that the above does not account for more people entering the lottery over time, which decreases one’s odds further. If we look at recent trends and apply a decay factor of 0.75 to reflect the change from the 2023 to the 2024 lottery, the expected number of years becomes 8.3 years.

Perseverance is the key to being selected for this race. Eight years is a long time, but if you continue to stack up those qualifiers, you will eventually get in. By this point, if your body is still cooperating, you will be quite experienced in ultra-distance events and in a good position to make the most of the 100 miles.

A key part to this multi-year plan is to continue to complete Western States qualifiers. In the next section, I break down the qualifying races and explore the landscape of these events.

Western States 100 Qualifying Races and Their Attributes

Western States qualifiers are “based solely on the size of the race” with large and established races getting priority, and the only restriction being that races shorter than 100 miles must have at least 8,202 feet (2,500 meters) of elevation gain. The race organization reiterates its approach is “based solely on the number of runners and not course difficulty.” This approach differs from that of other races, such as the Hardrock 100, where many factors are taken into consideration for qualifying races.

With Hardrock’s cumulative vertical gain of 33,000 feet and an average elevation of 11,000 feet, its board has set stricter criteria for its qualifying races. They look at data about race characteristics such as high elevation, long steep climbs, severe weather, and exposure to falls to ensure entrants are prepared to safely complete the Hardrock 100.

Thinking about this difficulty criteria got me interested in the diversity of races included in the Western States qualifiers. Because there is no difficulty criteria, some races are inherently easier qualifiers. At the end of the day, each race is as difficult as you choose to make it and you see runners push themselves to the brink from 100 meters to 100 miles. What I want to focus on in this section are the factors that contribute to an athlete completing a race in the requisite qualifying time for a lottery ticket. Which races are most likely to secure the average runner a qualifier?

Dataset

In this section, I look at all Western States qualifier races in the U.S. and Canada. The data is pulled from each race’s gpx files.

Using a basic scatter plot view, I mapped the distance and elevation of Western States qualifiers for 2024:

Distance Versus Vertical Gain in the Western States 100 Qualifiers

2024 Western States 100 Qualfying Races - distance vs vertical gain

A few things jump out about this chart. First, we have our outliers up and to the right, with four 200-mile or longer races. These 200-mile races are out of the scope of this article — and don’t get me started on 300-mile races. Needless to say, if you complete one of these races, you’re a monster and not looking for the ‘easy’ lottery entry into Western States.

Removing these outliers, we can get a better view of the 100-kilometer and 100-mile distances that I focus on for the rest of this section.

2024 Western States 100 Qualfying Races - distance vs vertical gain - zoomed

In this graph, we see two main clusters on the x-axis around the 100k and 100-mile distances, with considerable variation in the vertical gain (y-axis) for similar distance events. For 100-mile events, this spans from the Hennepin Hundred Mile, which gains less than 1,000 vertical feet to the Hardrock 100, which boasts over 33,000 feet of climbing.

This variation is huge. A mountainous 100-mile course at elevation is a completely different race than a flat event of the same distance at sea level. Western States falls near the middle of the vertical gain distribution for 100-mile events with around 18,000 feet of vertical gain.

Vertical gain is an important factor, but what goes up must eventually come down. (Unless you’re the Cocodona 250 Mile, then you just keep going up.) Looking at distance and net gain, we can see a slightly different story.

Distance Versus Net Gain in the Western States 100 Qualifiers

2024 Western States 100 Qualfying Races - distance vs net gain - zoomed

Most courses are close to zero net gain, being run on loops or starting and ending in similar locations. The California courses take the crown for net downhill, with Western States itself having the most net downhill, edging out the Angels Crest 100 Mile and the Canyons 100 Mile.

The distance along with vertical gain and net gain are critical factors when analyzing how difficult a qualifying race is. Another important factor to consideration when securing a qualifier is the cutoff time. Looking at distance versus cutoff time, we see a close correlation with variation due to other difficulty factors of the course.

Distance Versus Cutoff Time in the Western States 100 Qualifiers

2024 Western States 100 Qualfying Races - distance vs cutoff time - zoomed

Most 100k cutoffs fall in the 17- to 22-hour range, while most 100 milers are between 30 and 36 hours.

Distance and elevation gain are the two most widely available data points around races and give us an outline of the cutoff standard in ultra races. Thinking about the Hardrock 100’s qualifier requirements, I wanted to collect data around some additional characteristics like elevation and long, steep climbs to paint a more detailed picture of these races.

I pulled this information and compiled a dataset for all races from their gpx files. The additional variables I looked at besides distance and ascent were average elevation, maximum elevation, sustained climbs of over 2,000 feet, and sustained climbs of over 3,000 feet. Initially, I wanted an overview of which variables were most closely tied to course cutoff times. By plotting a heatmap of correlation between variables, we can see which variables are closely related to other variables.

Western States 100 qualification race - race factors correlation map

This plot is very colorful and fun, but what does it really tell us? The row I am most interested by is how certain variables are correlated with cutoff time.

Western States 100 qualification race - race factors - cutoff time correlation

Zooming in on this bottom row we see that distance is most correlated with cutoff time — no surprise there, while the variables next most closely correlated to cutoff times are vertical change and sustained climbs, which refers to the number of sustained climbs of more than 2,000 and 3,000 vertical feet, suggesting a mountainous course.

Predicted Times for Ultramarathons Compared to Their Cutoffs

Considering these variables, I was curious to see if we could determine which races are theoretically the most reasonable to complete within the cutoff time. We are, of course, limited by data and the following analysis does not capture the many nuances of an ultra race. Regardless, I hope you find the following analysis interesting in terms of thinking about the relation between race features and cutoff time.

Regression Models to Show Expected Cutoff Times

Taking the previous scatter plots looking at different features, I wanted to fit a regression model to view the expected cutoff time. Here we can see the predicted line for cutoff time based off the most closely correlated feature, distance.

Western States 100 qualification race - Distance vs cutoff time regression

Taking out the 48-hour cutoff races outliers of the Hardrock 100, Fat Dog 120 Mile, and Cruel Jewel 100 Mile, we can better compare races with similar cutoff times.

Western States 100 qualification race - Distance vs cutoff time regression - zoomed

Adding in more variables we can continue to improve the accuracy of the model as we account for more features of the race.

Western States 100 qualification race - Distance vs total ascent vs cutoff time regression - zoomed

A Residual Plot Showing How Much a Race’s Cutoff Time Deviates from Expected

After accounting for all of the variables collected we can graph a residual plot showing how much a race’s cutoff time deviates from what would be expected based on its features.

Western States 100 qualification race - deviation from expected cutoff time

This graph is interesting because it allows us to look at the data points with the largest residual. Those are the races that have a lower predicted cutoff time than the actual cutoff time, i.e., a generous relative cutoff time. If you are chasing cutoffs, a change of an hour or two could be the difference between completing the race and timing out. According to this model, the races with the largest residuals (most generous cutoffs) across 100k and 100-mile distances are the Dinosaur Valley 100k, the Lost Soul 100k, the Ultra-Trail Harricana 125k, the Quebec Mega Trail 100 Mile, the Superior 100 Mile, and the Zion 100 Mile. To reiterate, these are not the easiest races, rather those with the most generous cutoffs based on the features accounted for in this model.

I would have loved to spend more time in this area to build out a more complete model around ultramarathon course difficulty (stay tuned for this in the future), but, alas, cutoffs, this time of the editorial variety! Onto the takeaways.

Takeaways

  1. There are more than 200 qualifying races to choose from. When considering a qualifying race, it is important to note that races differ significantly in distance, elevation, and a variety of other ways.
  2. If you are looking to get a Western States qualifier, it is important to consider the cutoff time. A race may appear ‘easier’ on paper, but might have a less generous cutoff time, thereby making it difficult to complete within the time constraint.

For those of you racing Western States this year, best of luck and take a moment to appreciate what got you to this moment — especially those of you who got in with one lottery ticket!

Call for Comments

  • I love data, but acknowledge it does not tell the full story. What other factors do you think contribute the most to races being more ‘difficult?’
  • For the races I identified as having the most generous cutoffs, are there any that you disagree with based on other factors that were not included in the model?
  • Are there any races you think are ‘easier’ qualifiers?



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