#this was a long post and quite fun to do, so I hope you read it but if not, you can skip down to the TLDR marker to make things much simpler
50% of all matches does not mean 50% pick rate to be on both teams but that there is a 50% likelyhood that an assassin will show up for one side or the other
when I did the math I got 173.3% which means the remaining 27% are in picks so uncommon or unusual to the mid-lane that they do not get represented
it's a bit of complicated math. You are not wrong as probability is a math that I frequently have to search due to it being uncommonly used
I think it's something like X / 100 = 2x / 200 where 2x = ? , but give me a break, this is higher level algebra using actual formulas that I haven't used in around a decade
apparently the actual formula would be probability A + probability B because it is the probability of either event happening out of the same chances, but i'm seriously having to look this up as the probability for separate instances is multiplication instead of addition
so for zed, if it were the chance to be a mirror matchup, it would be (12/100) x (12/100 ) or 144 / 10000
yet for the other matchups, it would be 12% + X% = y% chance of happening if zed were picked
then i'm still getting confused for how to accurately represent data because you can only account for 1 pick in draft out of both picks presented
the simplest answer would be the direct approach where if say zed appears in 12 / 100 matches, he has a 12% pick rate, you can then add this number to the other percent pick rates to get the probability of one side facing an assassin, but if my train of thought is still right here, the chances are cut in half if you are only factoring for one team
apparently I would think that, but it does not end up that way as I am adding an extra step by mistake. The way you are supposed to check it is by multiplying the two probabilities together, for example, if I were the mid laner, my pick is 100% accounted for or 1/1 , but my opponent's pick is still based upon the average, this means that the opponent has a 1/1 x 12/100 = 12/100 chance of being zed unless circumstances apply to forbid it
it's still very confusing, but you apparently have to take the data from both sides and treat that as the data for one side, so, feel free to chime in here
#TLDR
two picks happening at once are what throws it off
the website I found uses dice as an example. let's say it's 4-sided. With a 4-sided di, any time you rolled a number, the other person would not be allowed to roll that number, so say if you rolled 4, your opponent would only roll 1 , 2 or 3
the probability for either side stays the same based upon the raw numbers, but when you throw in an external factor (such as not being able to roll the same number again), the value changes for the other side
so, let's say zed has a 12% pick rate and I choose a champion with a 1% pick rate, since my probability is accounted for, I then apply the restriction of 12 / (100 minus 1 ) = 12/99 or roughly 12.12% chance of facing zed
#MATH IS FUN, AT LEAST WHEN GAMING IS INVOLVED
you can do the same for other weird pick rates as well
say there are 2 champions with 25% pick rate, you pick one, that leaves the opponent with a 25/75 or 33% chance of being that champion
#The simpler way to sum all this up, if assassins had a total of 100% pick rate, they would be guaranteed on one side or the other. at 50%, they have 50% chance of appearing on one side or the other. If they had 150% pick rate, they would 100% show up on one side and have a 75% chance of showing up on both sides by 150/200
confusing, right? as per where you did your math, there is a 50% chance of an assassin appearing in a match, but only 25% chance of one being your opponent 50/100 x 50/100
#it's still hard to wrap my head around it and i'm certain there's a step i'm missing somewhere. If you want to add on, go ahead because it's not easy to find everything from just an internet search
I keep trying to make this post longer because I keep trying to figure out how the system with 2 picks at once works
the only conclusion that I can come to is that for some reason the numbers are represented out of 200% instead of 100, so they forgot the step to do division? so if their numbers are out of 200, it would mean that at least 1 in 4 matches have at least one assassin?
#if this is true then basically all of the websites we use for information are incorrect