400 Headless Horseman Kills, and Still No Mount

So I hit an interesting milestone last night.  Based on data previously reported on this blog and in a few spreadsheets I'd kept in various places, I was able to calculate that last night represented my 400th Headless Horseman kill across my various toons.  This number may be low by 10 or so kills, because in 2008 and 2009, prior to the introduction of the use of the dungeon finder tool for taking on the Horseman, I likely did defeat the Horseman a handful of times by actually assembling a group and traveling to the instance.  But I'm guessing it wasn't more than a handful, so we'll ignore it for purposes of this story.

So, 400 kills.  No mount.  Frustrating yes.  What are the chances?  Which of course prompted the follow up identical question, seriously, what actually are the chances?  And now it starts to involve some math.

I'm going to start with the assumption that the reported drop rate on wowhead is correct, or at least close to it.  They're reporting it as 0.5%.  To calculating the odds of "not" having something happen a certain number of times in a row is actually pretty straightforward.  You take 1 - (chances of it happening), which in this case is 99.5%, to get the probability of it "not" happening.  You then raise that number to the power of n, where n= the number of attempts.  So in my example, this would be 99.5% to the 400th power, which is 13.5%.

So if the drop rate is accurate, there's a 13.5% probability that I would kill the Horseman 400 times and have no mount to show for it.  Which is not as low as I thought it might be.

In any given year, if I'm running the Horseman every day on 11 characters, that works out to a 46.2% chance of not getting it that year (99.5% to the 154th power, with 154 being 11 characters times 14 days), or inversely stated, it's a 53.8% chance of getting it in any given year, so a slightly better than 50/50 shot every year.

Now let's say that wowhead has it completely wrong, and do a little sensitivity analysis.  What if the drop rate is only 0.2% instead of 0.5%.  (Based on personal experience so far, I'm going to assume the drop rate isn't higher than they've reported).  In that case, the probability of me not getting it at all after 400 attempts actually rises quite a bit to 44.9%.  The odds of getting it in any one year (again, running it every day on 11 different characters) drops to 26.5%.

So, back to our old scenario of a 0.5% drop rate.  If I want to be 99% sure I'm going to get the mount, how many times do I need to kill the Headless Horseman to have a 99% chance of actually getting it.  The answer to that, is around 900, or slightly more than 3 more years worth of runs.   I'll actually get to the point where I have about a 95% chance of getting it sometime during the 2015 event.  Maybe I'll just go buy myself a sky golem instead.