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Edit: my pictures aren't on here, I thought you could submit a text post with pictures. Here's my pictures I meant to include showing my kc, drops, and my graph. https://imgur.com/a/wWzLht5 Also obligatory thanks for the gold, kind stranger!
TLDR: The odds of going as dry as I did is about 1/163,736,252,064 (about 1/164 billion). My guess is that the Dragon Defender drop rate is not really reduced in Trailblazer League. I'm hoping this is the only thing that was overlooked and that there aren't more items that aren't reduced despite saying they are.
So this isn't just another rng post about bad rng... what I have goes far beyond that. Here's my data, and what I did with it.
I killed 2,000 cyclopes in the basement of the Warrior's Guild, and received 16 dragon defenders.
These are claimed to be at a reduced drop rate (1/33, compared to 1/100). Normally, after killing 2,000 basement cyclopes, you would be at around 60 dragon defenders with that drop rate.
I wanted to see what the odds are of going that dry. I do a bit of programming, and ran a simulation of 10 million players who killed cyclopes at a drop rate of 1/33, and I wanted to see how many of them had 16 or fewer defenders. (This is the histogram attached - this shows the distribution of those 10 million players.) To my surprise, NONE of the 10 million simulated players had as low of a drop rate as 16. In fact, the lowest anyone had in my simulation was 24 defenders. 16 isn't even pictured on my graph.
After this, I realized I didn't want to wait several days for my computer to compute vastly more simulations (10M simulations of 2k drops took several hours), so I looked into how to calculate the odds statistically. The odds of getting a certain amount of defenders in a certain amount of kills are (this is binomial probability, if anyone wants to look into it further):
n!/(x!(n-x)!) * px * (1-p)n-x where:
n = number of kills, 2000
x = number of drops, 16
p = probability of drop, 1/33
This only gives you the odds of having exactly 16 defenders, so I had to calculate this equation for all numbers 0-16, and then add them all together, with the help of programming again.
The final result of this calculation was 6.107383358731508 * 10-12. This is the same as about 1 in 163,736,242,064, or about 1 in 164 billion. This is the odds of having 16 or fewer defenders throughout 2,000 kills. I think it's safe to say the drop rate isn't reduced.
As suggested by someone who commented, the odds of being this unlucky while on the standard drop rate is about 21.9776% - about 1 in 4.5. Is it kind of unlucky? Sure, but it definitely could happen.
Why does this matter? Realistically, this in particular doesn't matter - it should still only take you around 100 kills which doesn't take that long. Maybe I could have had some more alchs from defenders which would have been nice. My concern is that there are other, more lengthy grinds that have drops that are out there that are not really reduced despite the game saying they are.
Feel free to correct me if anything I did is wrong - I believe it is correct as I used that equation to find the odds of having 60 defenders (which would be on drop rate, if the drop rate was 1/33), and that came out to roughly 5% - matching what my simulation showed me (around 500,000/10,000,000 had exactly 60 defenders).
I'm guessing there will be a few questions on this, so here's my answers:
- Why did you take the time to kill 2,000 cyclopes?
- It's a slayer task I can pick (hill giants), and its extremely afk, seeing as there are a lot of cyclopes down there which are aggressive, and Draining Strikes restores more than enough prayer to sustain protect from melee, even without the melee relic. Last recall also helps me pick my new task/teleport to bank drops/etc. so I can get right back to the basement. Attack cape also lets me enter without spending any warrior's guild tokens.
- You have 2332 kills on your drop log but you said you killed 2000 - why is that?
- 332 of these kills were for the previous 7 defenders, that's roughly on drop rate for 7 drops that are 1/50.
- Shouldn't the drop rate be 1/33.3333 rather than 1/33? That would be equivalent to 3/100, which is 3 times as often.
- That's not how the reduced drop rates work, it says in the areas guide that these drop rates are always rounded down. So it should be 1/33 exactly.