Probability and Heartbreak

[Khronys-aerie-peak]

Seeing the drop rates on stuff just makes me nope out, not worth the time.

[Humanbeak-drenden]

@Tovi-moon-guard

It’s ok for there to be a one unicorn mount out of 700. One. It’s one.

Sha of Anger, Oondosta, Nalak and Galleon would like to have a word with you out back.

[Tovi-moon-guard (Tovi)]

Those can be farmed every week or bought on the BMAH. Yes, they are rare but the Big Love Rocket is the unicorn mount in WoW.

[Jonashai-queldorei]

You’re awful worked up over some pixels on a screen

[Delro-emerald-dream]

@Anjyll-moon-guard

To be “bad-luck”, you’d need to be at least 3 standard deviations above the mean if “bad-luck” means “outlier”. Indeed, the OP seems to suggest that by the mean attempt, you’ve likely already received the mount and so this should impact only bad-luck players. This makes the drop rate sound more like a maximum than a mean.

Mount farms can be modeled using a geometric distribution.
Geometric distributions cover cases where there is an experiment (in this case opening heart-shaped boxes) with two outcomes (you get the mount or you don’t) both of which have a constant probability.

The three standard deviations from the mean rule is usually only applied when the data are normally distributed so I would be hesitant to set that as your outlier threshold in this case.

@Anjyll-moon-guard

First, let’s talk probability. The OP notes that if something has a 1% drop chance then after 100 attempts you’re “statistically” guaranteed to get it. But a drop chance is better thought of as an average. Let’s take the Heartbreaker for example. Wowhead states the drop chance is 0.03%. Therefore, on average, players obtain the mount after 3,333 attempts.

Looking at the average in this case is a bad measure of how lucky/unlucky a person is since the average number of attempts required actually gets skewed towards more attempts compared to the median (center point of the data).

The median number of attempts tells you the point at which 50% of players would have seen a drop and the other 50% have not. You can find the median with the following equation, -1/(log2(1-p)) where p is the drop rate of the mount and log2 is the log of base 2. Taking into account randomness, this equation will be accurate for large populations, say 100,000 mount farmers. Smaller populations can expect to see a difference from the theoretical value.

For a large hypothetical population of players farming a 1% drop rate mount, such as invincible, 63.4% would have seen a drop by 100 attempts. Whereas the median (50%) is at ~68 attempts.

How you define the threshold of lucky and unlucky is arbitrary. You could say anyone who gets a mount before the median number of attempts is lucky and anyone that takes more than that is unlucky. You could also set the threshold further out at the 90th percentile (the point at which 90% of your large hypothetical population would have seen a drop).

Thinking about luck in terms of percentiles instead of the average gives you more insight into how your luck compares to others.

Here’s an online calculator you can use to calculate percentiles for a geometric distribution. You just enter the drop rate and percentile as a decimal then it outputs the number of attempts required for that percentile.
https://keisan.casio.com/exec/system/1180573192

[Delro-emerald-dream]

@Halite-bonechewer

A clarification: when I wrote about the math, I mainly used the 1 of 100 runs as an example when speaking about when bad luck protection would kick in (not when you are guaranteed to get something from a loot drop) and that it would be proportional to the drop chance.

The lazy way blizzard can implement a 100 attempts cap is to increase the drop rate to 4.5%. That sets the 99th percentile (the point at which 99% of players would have seen a drop) to ~100.

[Esploratore-area-52]

Agree with this, it’s to be noted that the first post of the thread is wrong, it’s not statistically guaranteed to get a 1% drop mount in 100 runs, it’s like you said around 63%, meaning 63 out of 100 people with 100 runs will already have it, so it’s only more likely than not, but not in a dominant fashion.

Generally speaking, 500 attempts should be fine for an 1%, I believe they bring you over 99,5%, making you the only person out of 200 or so to not have it yet by then.

Obviously the problem comes with a handful of mounts with terrible drop rates and limited availability, as far as I know there used to be 12: the 4 mop world bosses, yellow infernal, rukhmar, timereaver, love rocket, sea turtle, riding turtle, pond nettle, great sea ray post nerf.

Now, great sea ray can be bought from AH, which can save you hundreds of hours of fishing, riding and sea turtle can still take a lot of casts but can be done relatively quickly, there’s no comparison between the time it takes to get 5k casts rather than 5k boss kills, so I find them (and pond nettle) generally acceptable, and the yellow infernal had its drop rate improved, so it’s now in line with the raid mounts.

This leaves 7 problematic ones: mop world bosses should be 1 in 2000 drop, except oondasta 1 in 1000, love rocket 1 in 3333, timereaver 1 in 4000, rukhmar 1 in 1000 or even 800; timereaver is more constantly farmable but can be a neverending experience, it could happen to take more than 20k kills if really unlucky, world bosses are quite farmable if you have an army of characters but their timespan can go for several years in case of extreme bad luck and the rocket is the hardest due to the only 15 days a year, if really unlucky could take something like 16k kills, which isn’t possible yet with a single account full of characters, you would need 2 accs consistently and realistically speaking, a few more years, since it wasn’t always realistic to maintain 100 max level toons.

In my experience (play on eu) when you can buy these mounts on bmah for a handful of millions, which is possible for every world boss mount I listed, it’s more efficient than farming, which says enough about the drop rate!