Saturday, November 4, 2017

Western States Waitlist Odds

2017 was the first year that Western States instituted a waitlist to compliment their lottery system. At the end of the day, the most important question for anyone entering the lottery is: How does this increase my chances?!

I conducted MonteCarlo simulations to answer that question.

But first, some lottery and waitlist info:

  • In 2016, 270 individuals were selected in the lottery
    • To maintain the 369 starter average over time, the lottery was constructed to assume a number of these 270 (and other) runners would not actually start the race.
  • In 2017, only 250 individuals were selected, but a 50-deep waitlist was drawn as well.
    • By controlling this 250 individual set plus the waitlist, the race organizers vastly increase their control over 369 starter limitation.
  • Due to increasing popularity, odds for lottery tickets went down across the board from 2016 to 2017
  • The waitlist ended up going 39 deep for 2017, so 250+39=289 individuals had a chance to start from the lottery, an increase from 270 in the year prior.
MonteCarlo details:
  • I set up a simulation to replicate draws from a lottery that mimicked the actual 2017 lottery. Details of the lottery can be found on the Western States lottery webpage.
  • I expanded my simulations to create a waitlist.
  • I created a 2016 simulation from the 2016 data, as well as a 2017 simulation with no waitlist and 270 draws to replicate what would've happened if no waitlist had been instituted.
  • I ran 10,000 iterations of the Monte Carlo simulations.
    • My 2016 scenario reveals slightly different values from the Western States 2016 Monte Carlo results, but they're damn close -- our odds differed by only 0.06% on average. So you can rest assured that I know what I'm doing! (I have a Master of Statistics degree, trust me!)
  • I looked at various Waitlist options to observe a range of possible outcomes:
    • Drawing 39 deep -- what actually happened for 2017
    • Drawing 30 deep -- a reasonable estimate of how far the waitlist will go at a minimum
    • Drawing 50 deep -- fully utilizing the 50-deep waitlist


First Takeaway: Damn Popularity!


Here's a table of the odds for:
  • 2016
  • 2017 if there had been no waitlist
  • 2017 with the actual 39-deep waitlist utilized


1 2 3 4 5 6 7
2016 No Waitlist 3.66% 7.16% 13.86% 25.73% 44.89% 69.40% 90.75%
2017 No Waitlist (270 draws) 2.69% 5.30% 10.35% 19.58% 35.40% 58.18% 82.37%
2017 Pre-Waitlist (250 draws) 2.47% 4.89% 9.53% 18.18% 33.01% 55.04% 79.82%
2017 39-deep Waitlist 2.89% 5.72% 11.08% 20.98% 37.49% 60.95% 84.89%



As you can see, odds dropped across the board from 2016 to 2017 because the number of entrants increased.

Note that the 2017 No Waitlist odds represent a draw of 270 participants. The odds of being drawn before the waitlist for 2017 were actually a bit smaller all around because only 250 runners were selected.


Second Takeaway: The waitlist itself doesn't seem all that helpful


This table indicates your conditional odds of being given a chance to start in 2017 from the waitlist ... that is, you didn't get drawn in the lottery, but you were one of the first 39 in the waitlist. Pretty meager, right?!

Years Waitlist Odds
1 0.42%
2 0.83%
3 1.55%
4 2.80%
5 4.48%
6 5.91%
7 5.08%


Third Takeaway: The waitlist value reveals itself!


The value of the waitlist becomes much clearer when you contrast it with a scenario where 2017 had no waitlist at all.

This chart shows the relative gain in odds for the 3 simulated waitlist variants -- 30 deep, 39 deep, and 50 deep -- when compared against a 270-draw No Waitlist scenario for 2017.

If you were in the lottery for the first time and had just one ticket your odds without an instituted waitlist (scenario reminiscent of 2016) would have been 2.69%. But in reality for 2017, as per the 39 deep waitlist utilization, your odds of having a chance to start increased to 2.89%. While that 0.2% gain looks rather meager, it represents a 7.4% relative increase in your chances.

The longer you've been waiting to start Western States, the less the waitlist helps you. This is rather obvious because you have a higher chance of actually making it through the initial lottery draw. But for, say, folks waiting 1-4 years, in 2017 the waitlist increased the chance to start by 7-8%. For someone waiting 4 years (8 tickets), that represents a jump from what would have been 19.6% odds to 21.0% odds, a 7.1% relative increase; if the waitlist had gone 50 deep the odds would've increased further to 21.8%, representing an 11.1% relative increase ... every little bit helps!


Conclusion:


Cutting back the lottery from 270 to 250 runners obviously makes it harder to initially get into Western States.  BUUUUUUUT, it's more than made up for by the utilization of the waitlist. All in all, the waitlist implementation seems to have been an incredible success.

Here's a rundown of all the reasons to love the new Western States waitlist:
  • It increases your odds of being given the chance to start
    • For most runners in 2016, the odds were on the order of a 6-8% relative increase
    • If the waitlist gets fully utilized, those relative odds shoot up even further, to north of 10%
  • It makes it easier for the race organizers to fully utilize the 369 participant limitation each year
  • It makes for one heck of an exciting run-up to race day -- hello, John Fegyveresi!
  • Being selected from the waitlist gives you the chance to start but also leaves you the ability to decline without resetting your ticket count for next year.
  • It keeps the hope alive for 50 runners well past December!
  • It's a phase-shift in lottery strategy that helps to delay/reduce the inevitable creep of decreasing odds due to increased interest in the race.


Once the lottery entrance period closes and entrants data is released for the 2018 event, I'll provide a follow-up analysis that looks at updated odds, expected wait times, and all that jazz.


All the data:


Here's a table with all of the odds, if anyone is interested.

1 2 3 4 5 6 7
2016 No Waitlist 3.66% 7.16% 13.86% 25.73% 44.89% 69.40% 90.75%
2017 No Waitlist (270 draws) 2.69% 5.30% 10.35% 19.58% 35.40% 58.18% 82.37%
2017 Pre-Waitlist (250 draws) 2.47% 4.89% 9.53% 18.18% 33.01% 55.04% 79.82%
2017 30-deep Waitlist 2.80% 5.50% 10.72% 20.34% 36.62% 59.65% 83.43%
2017 39-deep Waitlist 2.89% 5.72% 11.08% 20.98% 37.49% 60.95% 84.89%
2017 50-deep Waitlist 3.01% 5.94% 11.56% 21.76% 38.68% 62.49% 85.73%

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