## Wednesday, December 2, 2015

### Hardrock 100, An Old Boys Club?

The 2016 Hardrock 100 race lottery is fast approaching, and lottery ticket data was recently released. So what is a runner with a statistics degree to do after a long day in the office ... write a Monte Carlo simulation in Python to determine everyone's chances of snagging one of the coveted slots, of course!

### Hardrock Lottery Explained

Detailed information about the lottery can be found here, but here's the basic idea:
• There are 3 distinct pools:
1. "Vets" with 5+ finishes
2. Folks who've never started before
3. Everyone Else
• There are 152 slots available:
• 35 reserved for the Vets
• 47 reserved for the Nevers
• 70 reserved for Everyone Else
• Only 2 people get automatic entry, the previous winners. They take slots away from whatever pool they would have been in. The 2015 winners -- Kilian Jornet and Anna Frost -- are both considered "Everyone Else", so there's actually only 68 slots available in that pool.
• Each pool has a different ticket allocation process:
• Vets get a ticket for each finish
• Nevers double their odds each successive year they don't make it in -- 1 ticket, 2 tickets, 4, 8, 16, 32, 64, 128, ...
• Everyone Else gets a ticket just for applying, another ticket for each previous finish, and a ticket for each successive year they don't make it in.
• There are also bonus tickets available for volunteering in support of the race, but I won't get into that.

### 2016 Lottery Odds

Here's the results of my simulation, broken out in a handful of ways.

First off, here's the odds based upon ticket counts:

 (2016 Hardrock 100 Lottery Odds)

The results are pretty dismal for anyone who's never raced before. 1,315 individuals are vying for 47 slots, an overall selection rate of 3.6%.  For first time applicants, the likelihood of being accepted is less than 1% -- 0.95% to be precise.  That's rough!

Veterans, on the other hand, all have a greater than 67% chance of being selected, with only 19% of those applicants -- 8 out of 43 people -- getting the short shrift.  So if you had the benefit of participating in Hardrock before ultrarunning really got popular, your odds of making it in are still better than the poor schmuck that's never gotten a chance to start and has been rejected 7 years in a row.

In the Everyone Else pool, there are 189 folks vying for 68 slots.  So 36% of entrants who've had the opportunity to start the race in the past but aren't yet "vets" will be able to toe the line again in 2016.  Digging a bit deeper you can see that a select few, 4 entrants, have only 1 ticket.  This means those 4 individuals started their first Hardrock race in 2015 but DNF'd ... and they all have an 11.7% chance of toeing the line again in 2016.  Contrast that with the Never pool, where someone has to get rejected 4 consecutive years before eclipsing those odds.  And for folks who started their first Hardrock race in 2015 and actually finished, their odds for making it in again in 2016 jumps to 22% ... a "Never" has to suffer through 5 consecutive rejections before achieving those kind of odds.

### 2016 Odds by "Years of Waiting"

We can break everything down a bit differently, utilizing the number of DNS's since last start (or in the "Never" case, simply the number of DNS's) to get an idea of how the odds stack up relative to how long you've been waiting to race.
 (2016 Hardrock Lottery Odds and Wait Time)
The lines show how odds increase as you patiently wait, year after year, to get into Hardrock.  The 2016 Western States odds are included for comparison.  I've also included entrant counts.

#### Takeaways

• Overall, 30% of "Everyone Else" will get to start 2 years in a row.
• Odds for "Nevers" suggest having to wait 7 years before getting those favorable odds.
• "Nevers" likely have to wait 7 years to exceed 50/50 coin flip odds, a full 2 years longer than the Western States lottery
• "Vets" are a small sample so their downward trend in odds is misleading, but overall, they clearly support the argument that Hardrock is becoming an Old Boys Club.
• Interest in Hardrock is somewhat correlated to interest in Western States -- entrant counts are shifted by 1 year.  Folks who have been waiting for 1 year to start WS is roughly equivalent to the number of Hardrock entrants who either finished last year, or have signed up for the lottery for the first time.  This makes since considering Hardrock bills itself as a "graduate level" race -- theoretically, someone new to the sport would want to first try their hand at qualifying for Western States, and then maybe move on to Hardrock in the following year(s).

### Expected Wait Times

Taking probabilities based upon the number of DNS's Since Last Start, we can calculate Expected Wait Times for various entrants.  My numbers are all based upon the 2016 odds, so these results will, sadly, be overly optimistic if interest in Hardrock continues to increase and/or race directors do nothing to alter the lottery system.

The table shows the number of years an entrant has currently been waiting -- Current Wait Time -- which is 0 for anyone that started the 2015 race or is a first time lottery entrant. The Additional Wait Time is the expected number of additional years to wait before getting into the race. The best way to think of it (though not most accurate statistically) is the amount of time it takes to get to at least a 50/50 coin flip chance of making the next race.  The Projected Next Start is what year to expect your next (or first) start -- Additional Wait Times under 0.5 were rounded down to 0, implying an expected 2016 start, but everything else is based on a ceiling function (if it says you'll wait 1.2 years, then go up to 2, implying you'd miss the 2016 and 2017 lottery but make 2018).

The results are pretty grim.  For a first time applicant, like myself, I shouldn't get my hopes up for Hardrock until at least 2022.  That means I'll spend more time staying fit in anticipation of this race than some people spend in medical school.  Fantastic!

On the other hand, the 43 Veterans and 189 members of "Everyone Else" all have expected wait times of less than 2 years.  Just another bit of evidence that Hardrock is an exclusive club that wants to reward existing members instead of sharing in the fun.

### Service Ticket Value

The Hardrock lottery contains one very unique component: service tickets.  Individuals can increase their chances of making the lottery by volunteering.  The qualifications for these additional tickets are a bit intense -- serve as an aid station captain, 2 days of Hardrock trail work in the previous year, 5 years of "general" volunteering for the race -- but they're a great way to reward individuals who are dedicated to the race.  The service tickets are particularly of value to the "Never" pool because they have the potential to drastically increase the odds of making the lottery.

Here is a summary of the added value of one service ticket for the "Nevers" -- which acts as an additional DNS.

 (2016 Hardrock Lottery Service Ticket Value for "Nevers")

The table shows the percentage increase in your selection odds as well as the odds multiplier when factoring in the added value of a service ticket.  For a first-time applicant, a service ticket will double your odds but it's only increasing your probability from 0.95% to 1.89%.  However, someone who is applying for the 7th time could have increased their odds from 45.87% to 70.41%.  So it appears that the service ticket option is only going to be helpful for "Nevers" who have already been rejected 5 or more years (29 individuals in 2016).  Anyone with fewer DNS's than that (the remaining 1,286 "Nevers") isn't really helping their odds all that much.  Which is a bit of a shame because the whole idea of the service ticket is that it is intended on rewarding a runner that shows a commitment to Hardrock, but that commitment is effectively worthless for all but a handful.

All told, it appears that only 24 of the 1,315 "Nevers" accumulated service tickets. Only 4 runners accumulated multiple service tickets: one person with 0 DNS's who raised their odds from 0.9% to 3.7%, someone with 2 DNS's who raised their odds from 3.7% to 14.2%, someone with 3 DNS's who raised their odds from 7.3% to 26.4%, and one lucky individual with 4 DNS's who raised their odds from 14.2% to 45.9%.  All that hard work and none of their odds even reaches a 50/50 coin flip!

What's worse, is that according to the Hardrock website, some of those service tickets are use it or lose it because they're earned for service "in the previous year's event".  Odds are that those service tickets are only going to benefit 1 or 2 runners, the rest would have been better off waiting another year (or two, or three, or four, ... ) before volunteering.

This isn't to say that volunteering for races isn't a great thing to do, it's just that in this instance the added value of increasing your lottery odds is mostly a myth.

### Expected Starters

Based upon the lottery odds, we can estimate the overall level of experience that will toe the line in 2016.

 (2016 Hardrock Expected Experience)

Vets in the lottery account for 401 past starts and 371 finishes. "Everyone Else" accounts for 418 past starts and 301 finishes.  The "Nevers", naturally, are 0 and 0.  When factoring in lottery odds, the expected experience at the start of the 2016 Hardrock 100 will be a total of 515 past attempts and 446 finishes (including Kilian Jornet and Anna Frost).

These numbers are, quite frankly, absurd.  The Hardrock race directors say they want a mix of experienced and new participants in their race, but the lottery as it is currently designed will place 47 individuals at the start who have never been in the race before, and the remaining 105 runners will average nearly 5 starts apiece and 4.5 finishes.

### The Lucky Ones

With over 550 first time applicants and single-ticket odds of 0.95%, we can expect that 5 lucky runners will quite literally win the lottery and make it in on their first try -- it may be a couple more or a couple less, but there's going to be somebody that defied the odds.  Hats off to you lucky few!

While a great many of us hopeful entrants have less than a snowball's chance in Hell of making the 2016 Hardrock 100, I think we can all agree that pity needs to be taken upon two poor souls, Tom Masterson and Andy Kumeda. I have no idea who these two guys are but these two "Nevers" have missed the lottery 8 and 7 times, respectively.  What's worse, while Tom now has a 91% chance of making it, Andy has only a 70% chance -- a slim 3% better odds than Vets who have finished 5 times already (and worse odds than anyone that's finished at least 6 times).

I wish this were one of those rare circumstances that reflects simple bad luck.  But with the increasing interest in the race, it's all the more likely that Tom and Andy's situation will become the norm unless radical changes are made to the lottery process.

### Time For a Change?

It's clear that the current formulation for the Hardrock lottery is unsustainable.  Despite being revised only a few years ago to make things more fair, and recently adding 12 slots to the "Never" pool, wait times to get into the race are absurd.  And it's only looking to get worse as the ultrarunning craze continues to go mainstream.  As it stands, the Hardrock Lottery is, by its very design, meant to maintain an Old Boys Club that keeps past participants in and leaves everyone else stuck on the sidelines.  Now, I don't think anyone wants to see Hardrock turn into the debacle that Leadville has become in recent years, but something needs to happen to ensure enough new and highly motivated runners have the opportunity to run, if only just once, before they start fearing the Grim Reaper will come knocking on their door.

In a future post I'll take a look at simulation results with a modest change to the slots allocation that would increase the odds for the "Nevers" without sacrificing the "veteran" and "experience" aspect the race directors prize so much.