So often I see people asking stuff like "What do drop rates mean?" and "When will this &@%%@&*@ Lavis Cannon drop?" that I figured I'd do a little guide to the math behind the factors...and how you can use this to tell you how much time you might want to spend on something.
First off, the drop rates listed are actually a combination of 2 rates: the drop-anything rate and the rare-drop rate. The former is the chance the critter will drop something when killed. The latter is the chance that it'll drop its pretty red box. Multiply them together, and you get the actual "drop rate" that everyone talks about. The net effect is that every time a monster is killed, the game rolls the ol' percentage dice and if it hits the right roll, out springs a box.
Now, here's the most important thing you can ever remember. DROP RATES ARE NOT A GUARANTEE. Repeat that to yourself. DROP RATES ARE NOT A GUARANTEE. They are odds. Like any odds, you'll sometimes hit them and sometimes not. Statistically speaking, YOUR results will not match up exactly to the drop rates. Basically, you haven't rolled the dice often enough, even after thousands of kills. That's called "statistical significance," boys and girls.
Now for the math part. I, for one, could use a nice Spirit Garment to make some armor out of. A glance at the drop rates reveals a 1/1050 drop for a Purplenum Del-D. That looks nice, 'cause I can hunt a Y9kM and a Kamui on the same Temple run. But what does that mean for my actual chance of finding one?
Well, the two offline maps offer a choice of either 15 or 20 Del-Ds. Since which map I get is random, I'll average that to 17.5.
The odds of NOT getting a rare drop are 1049/1050 on any kill. Since I don't care if I get 1, 3, or 12 Spirit Garments (12...yeah, right... ), all I care about is my odds of getting at least 1. My odds of getting at least 1 are equal to 1 - (the odds of not getting any). The odds of not getting any are (1049/1050)^17.5. Therefore...
On any random offline Temple run, I have a 1.65% chance of coming up with a Spirit Garment!
The formula runs like this, with X being the drop rate and Y being the number of monsters of the selected type:
1 - ((1-X)^Y)
Taking this one step further, what's the expected (not guaranteed, expected!) number of Del-Ds I'll have to kill to get that Spirit Garment? Here's a tip...it's not 1050. 1050 only gives a 63.22% chance of success, in fact.
What you need is the logarithm (which I'm probably misspelling), base = (1-drop rate) (NOT the usual 10 or e), of .01 (or whatever rate of confidence is good enough for you!) Since I don't have a programmable scientific calculator on hand, I can't do that right, now, so I'll cheat a bit (using trial and error for Y on the above equation), but it turns out that to have a 99% chance of success for a drop rate of 1/1050, you have to kill somewhere around 4800 of the little buggers...which works out to around 274 runs!
Now, remember...these are NOT guaranteed results! What these formulae can do is to tell you what your % chance of success for any given number of kills is, and how realistic it is for you to go out and hunt something. Have fun! And if you happen to be a math teacher, now you have an answer for the next smart-aleck student who asks when they'll use logarithms in real life. ^_-
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