Wednesday, December 12, 2012

Hardrock 2013 Odds

I wasn't going to bother this year with the new lottery system, but Blake gave us the data so I couldn't resist.  Besides, it seemed to bring me luck last year when I only had a 23% chance of getting in.

The math is provided in last year's post here.  This year I will conservatively assume that only 5 get in the race off from the first-timers' and veterans' wait lists, and only 10 off the "everyone else" wait list.

1801 tickets, 619 applicants, 35 spots (plus 5 off wait list)

1 ticket = 2.3% chance of getting into Hardrock
2 tickets = 4.5%
4 tickets = 8.8%
8 tickets = 16.8%
16 tickets = 30.8%
32 tickets = 52.3%
64 tickets = 77.6%

Veterans (5-time finishers):
356 tickets, 44 applicants, 35 spots (plus 5)

5 tickets = 76.7% (fewest tickets held by a vet)
18 tickets = 99.7% (18-time finisher Kirk Apt should be in)

Everyone else (started a Hardrock, but less than 5 finishes):
638 tickets, 191 applicants, 70 spots (plus 10)

1 ticket = 15.0%
2 tickets = 27.7%
3 tickets = 38.6%
4 tickets = 47.8%
5 tickets = 55.7%
6 tickets = 62.4%

Good luck!


  1. Thank you for this.

    It's interesting to see how lucky I really was to get in last year with only two tickets. Not only did I get to run the race, but now I'm in the much smaller "everyone else" lottery and my odds of getting in a second time have shot from single digits to 38.6%. On top of that, the "everyone else" pool will grow much more slowly than the first-timers in the coming years.

    When it was first announced, I don't think many people realized how big of an effect the new lottery procedure would really have.

  2. You're right Adam, a big advantage to get into that "everyone else" group. At least those that have been shut out for many years will have a better shot this time. Hope we both get back to Silverton in 2013.

    When are you gonna do the 100-mile wilderness again? My backup plan may be to go out there and take down your FKT:)

  3. It's been long enough that I'm just starting to considering going back to the HMW. Lots of time could be cut off, but it's just such a logistical nightmare that I'd have a hard time convincing my wife to crew again. Let me know if you do decide to try it.

  4. Good work here -- Your assumptions came very close to Blake's simulation (noted on FB).
    Stats is a good place for people to say some very crazy things!
    Last year they were saying it was a disadvantage to have more than one WS ticket because your odds go "down" for each extra ticket (merely because they don't increase linearly).
    One guy this year is saying that, because the (very slight) majority of new entrants has one ticket, this gives one-ticket holders a reasonable shot.

    I wish we could set up an "insurance" pool where we could make money off of people that think like this.

    I agree with the strange observation that a one-time DNS/DNF has a better shot than a never-before. That's more a function of the number of entrants in that pool, of course.

  5. One thing you missed last year (and possibly this year) is that when someone with 64 tickets is picked, their other 63 tickets are removed increasing the remaining entrants odds a small amount. So the next round's odds are a little better. To accurately estimate this, we'd need to decease the pool each round by the average number of tickets selectees had.

    So keep watching till the end, there's always a chance ;)

    1. I do account for that (this year and last) by removing the mean number of tickets held by each applicant after each draw. The actual number of tickets removed after each draw obviously won't be the mean, but statistically this should get us close. It's certainly a skewed distribution, especially in the first-timers pool.

    2. You're right, Dominic, that the "real-time" odds increase slightly each time a "big ticket" person is drawn...and decrease slightly each time a low-ticket person is drawn. The chance of getting drawn in a specific round is very small, but has the fluctuations noted above. Rob's numbers capture all of that for an overall probability. Even with the small fluctuations per round, the overall chance is likely to converge near those odds when added up for all rounds.

      I think I'm just going to go for a run and see what happens when it's all done.
      Cheers and good luck to both of you!

  6. you're in! Redemption tour, 2013! Congratulations. I know you will get it done this year.

  7. Rematch! Try not to screw it up this time...

  8. Congrats! You're already ready and only going to get readier!
    Wanna pacer?

  9. Thanks guys! Yes Brownie, the rematch is on. Pacers Mike? Never heard of them.